A Nearby Galaxy Perspective on Dust Evolution. Scaling relations and constraints on the dust build-up in galaxies with the DustPedia and DGS samples
Frédéric Galliano, Angelos Nersesian, Simone Bianchi, Ilse De Looze, Sambit Roychowdhury, Maarten Baes, Viviana Casasola, Letizia, P. Cassará, Wouter Dobbels, Jacopo Fritz, Maud Galametz, Anthony P. Jones, Suzanne C. Madden, Aleksandr Mosenkov, Emmanuel M. Xilouris, Nathalie Ysard
AAstronomy & Astrophysics manuscript no. manuscript © ESO 2021January 5, 2021
A Nearby Galaxy Perspective on Dust Evolution
Scaling relations and constraints on the dust build-up in galaxies with theDustPedia (cid:63) and DGS samples
Frédéric G alliano , Angelos N ersesian , , Simone B ianchi , Ilse D e L ooze , , Sambit R oychowdhury , , ,Maarten B aes , Viviana C asasola , Letizia, P. C assar ´ a , Wouter D obbels , Jacopo F ritz , Maud G alametz ,Anthony P. J ones , Suzanne C. M adden , Aleksandr M osenkov , , Emmanuel M. X ilouris , and Nathalie Y sard AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, Francee-mail: [email protected] National Observatory of Athens, Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, Ioannou Metaxaand Vasileos Pavlou GR-15236, Athens, Greece INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125, Florence, Italy Sterrenkundig Observatorium, Ghent University, Krijgslaan 281 - S9, 9000 Gent, Belgium Dept. of Physics & Astronomy, University College London, Gower Street, London WC1E 6BT, UK Université Paris-Saclay, CNRS, Institut d’Astrophysique Spatiale, 91405 Orsay, France International Centre for Radio Astronomy Research (ICRAR), M468, University of Western Australia, 35 Stirling Hwy, Crawley,WA 6009, Australia ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia INAF – Istituto di Radioastronomia, Via P. Gobetti 101, 40129 Bologna, Italy INAF - Istituto di Astrofisica Spaziale e Fisica Cosmica, Via Alfonso Corti 12, 20133, Milan, Italy Instituto de Radioastronomía y Astrofísica, UNAM, Antigua Carretera a Pátzcuaro Central Astronomical Observatory of RAS, Pulkovskoye Chaussee 65 /
1, 196140 St. Petersburg, Russia St. Petersburg State University, Universitetskij Pr. 28, 198504 St. Petersburg, Stary Peterhof, RussiaReceived 16 October 2020; accepted 23 December 2020
ABSTRACT
Context.
The e ffi ciency of the di ff erent processes responsible for the evolution of interstellar dust on the scale of a galaxy, are to datevery uncertain, spanning several orders of magnitude in the literature. Yet, a precise knowledge of the grain properties is the key toaddressing numerous open questions about the physics of the interstellar medium and galaxy evolution. Aims.
This article presents an empirical statistical study, aimed at quantifying the timescales of the main cosmic dust evolutionprocesses, as a function of the global properties of a galaxy.
Methods.
We have modelled a sample of (cid:39)
800 nearby galaxies, spanning a wide range of metallicity, gas fraction, specific starformation rate and Hubble stage. We have derived the dust properties of each object from its spectral energy distribution. Through anadditional level of analysis, we have inferred the timescales of dust condensation in core-collapse supernova ejecta, grain growth incold clouds and dust destruction by shock waves. Throughout this paper, we have adopted a hierarchical Bayesian approach, resultingin a single large probability distribution of all the parameters of all the galaxies, to ensure the most rigorous interpretation of our data.
Results.
We confirm the drastic evolution with metallicity of the dust-to-metal mass ratio (by two orders of magnitude), found byprevious studies. We show that dust production by core-collapse supernovae is e ffi cient only at very low-metallicity, a single supernovaproducing on average less than (cid:39) .
03 M (cid:12) / SN of dust. Our data indicate that grain growth is the dominant formation mechanism atmetallicity above (cid:39) / (cid:39)
50 Myr at solar metallicity. Shock destruction is relativelye ffi cient, a single supernova clearing dust on average in at least (cid:39) (cid:12) / SN of gas. These results are robust when assuming di ff erentstellar initial mass functions. In addition, we show that early-type galaxies are outliers in several scaling relations. This feature couldresult from grain thermal sputtering in hot X-ray emitting gas, an hypothesis supported by a negative correlation between the dust-to-stellar mass ratio and the X-ray photon rate per grain. Finally, we confirm the well-known evolution of the aromatic-feature-emittinggrain mass fraction as a function of metallicity and interstellar radiation field intensity. Our data indicate the relation with metallicityis significantly stronger. Conclusions.
Our results provide valuable constraints for simulations of galaxies. They imply that grain growth is the likely dustproduction mechanism in dusty high-redshift objects. We also emphasize the determinant role of local low-metallicity systems toaddress these questions.
Key words.
ISM: abundances, dust, evolution; galaxies: evolution; methods: statistical (cid:63)
DustPedia is a collaborative focused research project supportedby the European Union under the Seventh Framework Programme (2007–2013) call (proposal no. 606847, PI J. I. Davies). The data usedin this work is publicly available at http: // dustpedia.astro.noa.gr.Article number, page 1 of 64 a r X i v : . [ a s t r o - ph . GA ] J a n & A proofs: manuscript no. manuscript
1. INTRODUCTION
Characterizing the dust properties across di ff erent galactic envi-ronments is an important milestone towards understanding thephysics of the InterStellar Medium (ISM) and galaxy evolution(Galliano et al. 2018, for a review). Interstellar grains have a ne-farious role of obscuring our direct view of star formation ( e.g.
Bianchi et al. 2018). The subsequent unreddening of
Ultravi-olet -(UV)-visible observations relies on assumptions about theconstitution and size distribution of the grains, as well as on therelative star-dust geometry ( e.g.
Witt et al. 1992; Witt & Gordon2000; Baes & Dejonghe 2001). Dust is also involved in severalimportant physical processes, such as the photoelectric heatingof the gas in
PhotoDissociation Regions (PDR; e.g.
Draine 1978;Kimura 2016) or H formation ( e.g. Gould & Salpeter 1963;Bron et al. 2014). The uncertainties about the grain propertieshave dramatic consequences on the rate of these processes andare the main cause of discrepancy between PDR models (Röl-lig et al. 2007). Finally, state-of-the-art numerical simulations ofgalaxy evolution are now post-processed to incorporate the fulltreatment of dust radiative transfer in order to reproduce realisticobservables ( e.g.
Camps et al. 2016, 2018; Trayford et al. 2017;Rodriguez-Gomez et al. 2019; Trˇcka et al. 2020). These simula-tions rely on assumptions about the dust emissivity, absorptionand scattering properties, which changes from galaxy to galaxy( e.g.
Clark et al. 2019; Bianchi et al. 2019).We are far from being able to predict the dust composition,structure and size distribution, in a given ISM condition.
Ab ini-tio methods are currently impractical because of the great com-plexity of the problem. Empirical approaches face challenges,too. The last four decades have shown that each time we were in-vestigating a particular observable with the hope of constrainingthe grain properties, these properties were proving themselvesmore elusive because of their evolution, as illustrated in the fol-lowing. – The diversity of extinction curve shapes within the MilkyWay (Fitzpatrick 1986; Cardelli et al. 1989) and the Magel-lanic Clouds (Gordon et al. 2003) can be explained by vari-ations of the size distribution and carbon-to-silicate grain ra-tio (Pei 1992; Kim et al. 1994; Clayton et al. 2003; Cartledgeet al. 2005). – Elemental depletion patterns strongly depend on the densityof the medium, suggesting that dust is partly destroyed andreformed in the ISM (Savage & Mathis 1979; Crinklaw et al.1994; Jenkins 2009; Parvathi et al. 2012). – Variations of the
InfraRed (IR) to submillimeter (submm)emissivity as a function of the density of the medium,whether in the Milky Way (Stepnik et al. 2003; Ysardet al. 2015) or in the Magellanic clouds (Roman-Duvalet al. 2017), are interpreted as variations of the grain man-tle thickness and composition, and grain-grain coagulation( e.g.
Köhler et al. 2015; Ysard et al. 2016). – The wide variability of the relative intensity and band-to-band ratio of the mid-IR aromatic feature spectrum, wit-nessed within the Milky Way and nearby galaxies, is the evi-dence of the variation of the abundance, charge and size dis-tribution of the band carriers ( e.g.
Boulanger et al. 1998;Madden et al. 2006; Galliano et al. 2008b; Schirmer et al.2020). – The wavelength-dependent polarization fraction in extinc-tion and emission provides additional constraints on thecomposition of the grains, as well as on their shape and align-ment ( e.g.
Andersson et al. 2015; Fanciullo et al. 2017). To understand the evolution of the global dust content of agalaxy, one must be able to quantify the timescales of the pro-cesses responsible for dust formation and destruction. These pro-cesses can be categorized as follows.
Stardust production takes place primarily in the ejecta of: (i) Asymptotic Giant Branch (AGB) stars; and (ii) type II Su-perNovae (SN II; core-collapse SN). SNe II potentially dom-inate the net stardust injection rate ( e.g.
Draine 2009, for areview), but their actual yield is the subject of an intense de-bate. Most of the controversy lies in the fact that, while largeamounts could form in SN II ejecta ( e.g.
Matsuura et al.2015; Temim et al. 2017), a large fraction of freshly formedgrains could not survive the reverse shock ( e.g.
Nozawa et al.2006; Micelotta et al. 2016; Kirchschlager et al. 2019). Es-timates of the net dust yield of a single SN ranges in theliterature from (cid:39) − to 1 M (cid:12) / SN ( e.g.
Todini & Ferrara2001; Ercolano et al. 2007; Bianchi & Schneider 2007; Boc-chio et al. 2016; Marassi et al. 2019).
Grain growth in the ISM refers to the addition of gas atomsonto pre-existing dust seeds ( e.g.
Hirashita 2012). It could bethe main grain formation process, happening on timescales (cid:46) e.g.
Draine 2009). It is however challenged due tothe lack of direct constraints and because we currently lacka proven dust formation mechanism, at cold temperatures.
Grain destruction can be attributed to: (i) astration, i.e. theirincorporation into stellar interiors during star formation; (ii) sputtering and shattering by SN blast waves. The sec-ond process is the most debated, although it is less contro-versial than stardust production and grain growth e ffi cien-cies. Timescales for grain destruction in the Milky Way rangefrom (cid:39)
200 Myr to (cid:39) (i) stardust accounts for at most (cid:39)
10 %of ISM dust; (ii) most grains are therefore grown in the ISM( e.g.
Draine & Salpeter 1979; Dwek & Scalo 1980; Jones et al.1994; Tielens 1998; Draine 2009). The goal of this paper is toexplore how particular environments could a ff ect these conclu-sions, by modelling nearby extragalactic systems. By studyingnearby galaxies, we also aim to provide a di ff erent perspectiveon these questions.Several attempts have been made in the past to quantify theevolution of the dust content of galaxies via fitting their SpectralEnergy Distribution (SED; e.g.
Lisenfeld & Ferrara 1998; Mor-gan & Edmunds 2003; Draine et al. 2007; Galliano et al. 2008a;Rémy-Ruyer et al. 2014, 2015; De Vis et al. 2017b; Nersesianet al. 2019; De Looze et al. 2020; Nanni et al. 2020). Althoughthese studies provided important benchmarks, most of them werelimited by the following issues: (i) their coverage of the param-eter space was often incomplete, especially in the low-metal-licity regime, which is crucial to quantify stardust production( cf.
Sect. 5); (ii) potential systematic e ff ects, originating either inthe SED fitting or in the ancillary data, were questioning someof the conclusions; (iii) dust evolution models were most of thetime not fit to each galaxy, but simply visually compared , whichcan lead to some inconsistencies ( cf. Sect. 5.2.3).The present paper is an attempt at addressing these limita-tions. We rely on the homogeneous multi-wavelength observa-tions and ancillary data of the DustPedia project (Davies et al.2017) and of the
Dwarf Galaxy Sample (DGS; Madden et al. Among the cited studies, only Nanni et al. (2020) and De Looze et al.(2020) perform an actual fit of individual galaxies.Article number, page 2 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Hierarchical Bayesian (HB; cf. Sect. 3.1)approach when comparing models to observations, in order tolimit the impact of systematic e ff ects on our results (Galliano2018, hereafter G18). Finally, we perform a rigorous dust evo-lution modelling of individual objects in our sample, in order tounambiguously constrain the dust evolution timescales. Sect. 2presents the data we have used. Sect. 3 presents our model anddiscusses the robustness of the derived dust parameters. Sect. 4provides a qualitative discussion of the derived dust evolutiontrends. Sect. 5 describes the quantitative modelling of the maindust evolution processes. Sect. 6 summarizes our results. Severaltechnical arguments are detailed in the appendices, so that theydo not alter the flow of the discussion.
2. THE GALAXY SAMPLE
This study focuses on global properties of galaxies. Integrat-ing the whole emission of a galaxy complicates the interpre-tation of the trends, as we will discuss in Sect. 4. However, italso presents some advantages: (i) we can include galaxies un-resolved at infrared wavelengths; and (ii) we can provide bench-marks for comparisons to unresolved studies of the distant Uni-verse or to one-zone dust evolution models. Several upcomingstudies on a subsample of resolved DustPedia galaxies will dis-cuss the improvements that the spatial distribution of the dustproperties provides (Roychowdhury et al., in prep. ; Casasolaet al., in prep. ). We present here the integrated, multi-wavelength photometry ofour sample, used to constrain the global dust properties of eachgalaxy. We focus on the mid-IR-to-submm regime, as it is wheredust emits.
We use the photometry of the 875 galaxies of the DustPedia sam-ple presented by Clark et al. (2018, hereafter C18) . Since wefocus on the mid-IR-to-submm regime, we restrain the wave-length range to photometric bands centered between 3 µ m and1 mm. The list of photometric bands we have used is given inTable 1. C18 has provided a dedicated reduction of the Herschel broadband data and an homogenization of the
Spitzer , WISE and
Planck observations. Foreground stars have been masked.Aperture-matched photometry has been performed on each im-age and a local background has been subtracted from each flux.A consistent noise uncertainty was estimated for each measure-ment.
IRAS fluxes from Wheelock et al. (1994) were added tothe catalog. We refer the reader to C18 for more details aboutthe data reduction and photometric measurement.The SED model (Sect. 3.1), that we have applied to our data,performs a complex statistical treatment, allowing us to analyzeeven poorly sampled SEDs. However, the e ffi ciency of such amodel can be a ff ected by the presence of systematic e ff ects notproperly accounted for by the uncertainties. In order to be con-servative, we have therefore excluded a series of fluxes, based onthe following criteria. In principle, we should say
Bayesian-Laplacian , in place of
Bayesian , as Pierre-Simon L aplace is the true pioneer in the devel-opment of statistics using the formula found by Thomas B ayes (Hahn2005; McGrayne 2011). Available at http: // dustpedia.astro.noa.gr / Photometry.
Table 1.
Number of galaxies observed through each photometric band.During the inference process (Sect. 3.2), the observed fluxes are com-pared to the SED model integrated within the transmission of these fil-ters, with the appropriate flux convention.
Instrument Wavelength Label Number of galaxies(central) 3 σ detection TotalWISE 3 . µ m WISE1 725 7514 . µ m WISE2 663 73911 . µ m WISE3 554 72822 . µ m WISE4 438 694IRAC 3 . µ m IRAC1 277 292( Spitzer ) 4 . µ m IRAC2 359 3905 . µ m IRAC3 100 1137 . µ m IRAC4 116 130MIPS 23 . µ m MIPS1 125 178( Spitzer ) 71 µ m MIPS2 32 41156 µ m MIPS3 18 25PACS 70 µ m PACS1 108 144( Herschel ) 100 µ m PACS2 273 456160 µ m PACS3 296 493SPIRE 250 µ m SPIRE1 481 674( Herschel ) 350 µ m SPIRE2 446 658500 µ m SPIRE3 404 634IRAS 60 µ m IRAS3 282 360100 µ m IRAS4 391 501HFI 350 µ m HFI1 217 275( Planck ) 550 µ m HFI2 127 182850 µ m HFI3 93 1251. The C18 catalog flags about 22 % of its fluxes, for di ff erentreasons: artefacts, contamination by nearby sources, incom-plete extended emission, etc. We have excluded all the fluxesthat are flagged. For 89 galaxies, all IR fluxes end up flagged.These galaxies have therefore been excluded.2. Several galaxies contain a significant emission from their
Ac-tive Galactic Nucleus (AGN). This emission is characterizedby a prominent synchrotron continuum and copious amountsof hot dust ( T dust (cid:38)
300 K), resulting in a rather flat mid-IR continuum. Our dust model (Sect. 3.1.1) is optimized forregular interstellar dust. Our distribution of starlight intensi-ties (Sect. 3.1.2) is usually not flexible enough to account forthe hot emission from the torus. We have therefore excluded19 sources presenting such an emission at a significant level,following Bianchi et al. (2018), who used the criterion ofAssef et al. (2018) based on the WISE1 and WISE2 fluxes toidentify AGNs .3. We have performed a preliminary least-squares fit with ourreference SED model (Sect. 3.3), in order to identify wherethe largest residuals are.(a) A few short wavelength bands present a large deviationfrom their SED model and their adjacent fluxes . Afterinspection of the images, the discrepancies are likely dueto residual starlight contamination.(b) Several long-wavelength IRAS fluxes are significantlydeviant from their nearby MIPS and PACS fluxes . Those are: ESO 434-040, IC 0691, IC 3430, NGC 1068, NGC 1320,NGC 1377, NGC 3256, NGC 3516, NGC 4151, NGC 4194,NGC 4355, NGC 5347, NGC 5496, NGC 5506, NGC 7172,NGC 7582, UGC 05692, UGC 06728, UGC 12690. Those are: WISE2 and IRAC2 for ESO 0358-006, ESO 0116-012and ESO 0358-006; and IRAC3 for NGC 3794. Those are: IRAS4 for NGC 254, NGC 4270, NGC 4322, NGC 5569and UGC 12313; and both IRAS3 and IRAS4 for IC 1613, NGC 584,Article number, page 3 of 64 & A proofs: manuscript no. manuscript
The reason of these discrepancies is obscure. However,Sect. 3.3 will present a test comparing SED results withand without
IRAS data, showing they are not crucial toour study.(c) Three additional galaxies are not properly fitted . Theseobjects present the characteristics of an AGN and are in-deed classified as such (Liu & Zhang 2002). They werenot accounted for by the Assef et al. (2018) criterion. Itis however consistent with the fact that this criterion hasa 90 % confidence level.We have excluded all these problematic fluxes. Criterion 3is more qualitative than 1 and 2, but it allows us to identifypotential systematics that were missed.In total, we are left with 764 DustPedia galaxies.The monochromatic fluxes (in Jy) were converted tomonochromatic luminosities (in L (cid:12) / Hz), using the distancesfrom the HyperLeda database (Makarov et al. 2014).
Metallicity is a crucial parameter to study dust evolution( cf.
Sect. 5 and Rémy-Ruyer et al. 2014, 2015). In particular, thelow-metallicity regime, represented by dwarf galaxies, providesunique constraints ( e.g.
Galliano et al. 2018), yet the DustPediasample selected sources larger than 1 (cid:48) . In order to improve thesampling of the low-metallicity regime, we have thus includedadditional galaxies from the
Dwarf Galaxy Survey (DGS; Mad-den et al. 2013).Among the 48 sources of the DGS, 35 are not in the DustPe-dia sample. We have added these sources to our sample. Thesegalaxies have been observed with
Spitzer , WISE and
Herschel .We use the aperture photometry presented by Rémy-Ruyer et al.(2013, 2015). We do not expect systematic di ff erences betweenthe DustPedia and DGS aperture fluxes. Appendix B.1 comparesthe photometry of the DGS sources that are in DustPedia. Bothare indeed in very good agreement. Similarly to the DustPediasample, we apply the three exclusion criteria of Sect. 2.1.1.1. We exclude the fluxes that have been flagged.2. No significant AGN contribution is present in this sample.3. Rémy-Ruyer et al. (2015) advise to not trust the PACS pho-tometry for HS 0822 + Our combined sample contains 798 galaxies. For each of them,we consider the following two sources of photometric uncer-tainty.
The noise: it includes statistical fluctuations of the detectorsand residual background subtraction. It has been thoroughlyestimated by C18 and Rémy-Ruyer et al. (2015). We assumethat the noise of each waveband of each galaxy follows anindependent normal distribution . PGC 090942, IC 2574, UGC 06016, NGC 3454, NGC 4281,NGC 4633, NGC 5023, NGC 7715. Those are: NGC 1052, NGC 2110 and NGC 4486. We note here that the background subtraction introduces an uncer-tainty which is independent between galaxies. Indeed, we estimate the
Calibration uncertainties: they are systematics, i.e. fully cor-related between di ff erent galaxies, and partially correlatedbetween wavebands. We assume they follow a joint, multi-variate normal distribution, whose covariance matrix is givenin Appendix A.Table 1 gives the number of galaxies observed though eachwaveband, and the number of detections (flux greater than 3 σ ,where σ refers solely to the noise uncertainty). The number ofavailable filters per galaxy ranges between 1 and 19, and its me-dian is 11. There is a median number of 2 upper limits per galaxy. We present here the ancillary data gathered in order to character-ize the ISM conditions in each galaxy.
For the DustPedia sample, we adopt the stellar masses of Ners-esian et al. (2019). Theses masses were derived from UV-to-mmSED fitting, using the code
CIGALE (Boquien et al. 2019), withtwo stellar populations. For the DGS, the stellar masses are givenby Madden et al. (2014), using the Eskew et al. (2012) relation,based on the IRAC1 and IRAC2 fluxes. Eskew et al. (2012) em-phasize that the largest source of systematic uncertainties in thestellar mass is the
Initial Mass Function (IMF). Both Nersesianet al. (2019) and Eskew et al. (2012) adopt a Salpeter (1955)IMF, therefore limiting potential biases between the two sam-ples. Other potential biases, such as the form of the assumed starformation history, should not be an issue with our sample. For in-stance, both Mitchell et al. (2013) and Laigle et al. (2019) testedthe reliability of stellar mass estimates using numerical simula-tions of galaxies, and showed that they gave consistent results atlow redshift. We use M (cid:63) to denote the stellar mass.Nanni et al. (2020, hereafter N20) have reestimated the stel-lar masses of the DGS, with CIGALE . They report systematicallylower values, compared to Madden et al. (2014), sometimes byan order of magnitude. We discuss the possible reasons of thisdiscrepancy in Appendix B.2, concluding that our estimates arelikely more reliable.
For DustPedia galaxies, we use the metallicities derived by DeVis et al. (2019), using the S calibration of Pilyugin & Grebel(2016, hereafter PG16_S). For the DGS, we use the metallic-ities derived by De Vis et al. (2017b), using the same PG16_Scalibration. De Vis et al. (2017b) show that this particular cali-bration is the most reliable at low-metallicity.We adopt the solar elemental abundances of Asplund et al.(2009): the hydrogen mass fraction is X (cid:12) = . Y (cid:12) = . Z (cid:12) = . + log(O / H) (cid:12) = . ± .
05. Throughout this study, we as-sume a fixed elemental abundance pattern. It implies that the to-tal metallicity, Z , scales with the oxygen-to-hydrogen numberratio as: Z (cid:39) . × − × + log(O / H) Z (cid:12) . (1) background in each waveband for each galaxy separately. The result-ing biases are thus randomly distributed across the sample. It wouldnot have been the case, if we had considered individual pixels inside agalaxy.Article number, page 4 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution For that reason, in the rest of the paper, we refer to both Z and12 + log(O / H), as metallicity . The neutral hydrogen masses, derived from[H i ]
21 cm , have been compiled by De Vis et al. (2019), for Dust-Pedia, and Madden et al. (2013), for the DGS. Integrating the H i mass in the aperture used for the photometry is not always pos-sible for the smallest sources, as they are not resolved by singledish observations. This is particularly important for dwarf galax-ies, where the H i disk tends to be significantly larger than theoptical / IR radius ( e.g.
Begum et al. 2008), as we will discuss inSect. 4.1.3. Roychowdhury et al. ( in prep. ) recently obtained in-terferometric, spatially-resolved [H i ]
21 cm observations of 20 ofthe lowest-metallicity galaxies in our sample (12 + log(O / H) ≤ . . They integrated these H i masses in the aperture used forthe photometry in order to provide a better estimate of the gasmass associated with the dust emission. We have adopted thesemore accurate values, for these 20 objects. We have multipliedthe H i mass of each galaxy by 1 / (1 − Y (cid:12) − Z ) (cid:39) .
35 to accountfor helium (assumed independent of metallicity) and heavier el-ements. We use M H i to denote the total atomic gas mass probedby [H i ]
21 cm . Molecular gas.
Casasola et al. (2020a) compiled observationsof CO lines for 245 late-type DustPedia galaxies. They con-verted these observations in molecular masses, assuming a con-stant X CO conversion factor (Bolatto et al. 2013), and correctedthem for aperture e ff ects. The uncertainties are the quadratic sumof the CO line noise measurement and 30 %, corresponding tothe uncertainty on the X CO . We adopt these values when avail-able. For the other DustPedia and DGS galaxies, we infer the H mass, with the approximation used by De Vis et al. (2019, Eq. 7).It uses the scaling relation between M H i / M (cid:63) and M H / M H i , de-rived by Casasola et al. (2020a). The scatter of this relation ispropagated and accounted for in the uncertainties. These molec-ular gas masses are also corrected for helium and heavy ele-ments. We use M COH to denote the total molecular gas mass de-rived from actual CO line observations, and M H , to denote themethod-independent total molecular mass, either derived from CO lines or from the De Vis et al. (2019) approximation.
For DustPedia, the
Star Formation Rate (SFR), has been derivedby Nersesian et al. (2019). The SFR was a free parameter ofthe SED fit they performed with
CIGALE . For the DGS, we usedthe SFR estimated by Rémy-Ruyer et al. (2015), using a combi-nation of the H α . line and of the Total InfraRed luminos-ity (TIR). Although the two estimators are di ff erent, we do notexpect significant biases between DustPedia and the DGS. In-deed, both account for: (i) the escaping power from young ion-izing stars, with the UV SED or the H α . line; and (ii) thepower re-radiated by dust, with the IR SED or the TIR. In addi-tion, both assume a Salpeter (1955) IMF, which, similarly to thestellar mass (Sect. 2.2.1), is the main source of uncertainty. We Those are: UGC 00300, NGC 625, ESO 358-060, NGC 1569,UGC 04305, UGC 04483, UGC 05139, UGC 05373, PGC 029653,IC 3105, IC 3355, NGC 4656, PGC 044532, UGC 08333, ESO 471-006, Mrk 209, NGC 2366, VII Zw 403, I Zw 18 and SBS 1415 + use SFR to denote the numerical value of the SFR, expressed inM (cid:12) / yr and, sSFR ≡ SFR / M (cid:63) , to denote the specific SFR . The SED analysis we will present in Sect. 3.1 includes the ancil-lary data, as a prior . For that purpose, it is preferable to considerthe logarithm of quantities that can span several orders of mag-nitude. The independent ancillary data parameters we use as aconstraint are listed in the first five lines of Table 2. The total gasmass is M gas = M H i + M H and the CO-line-estimated molecu-lar fraction, f COH = M COH / M gas . We also list, in the second part ofTable 2, parameters derived from these quantities, including themethod-independent molecular fraction, f H = M H / M gas . Allthe extensive quantities (masses and SFR) have been homoge-nized to the distances adopted in Sect. 2.1. Table 2.
Number of galaxies per ancillary data constraint.
Ancillary data Parameter Number of galaxiesTotal gas mass ln M gas f COH M (cid:63) + log(O / H) 376Molecular fraction ln f H M gas / M (cid:63) ) 514Gas fraction ln f gas
3. THE SED MODELLING APPROACH
We now describe our modelling approach, as well as the con-sistency tests we have performed to assess the robustness of ourresults.
HerBIE ( HiERarchical Bayesian Inference for dust Emission ;G18) is a hierarchical Bayesian model aimed at inferring the
Probability Density Functions (hereafter PDF) of dust parame-ters (dust mass, etc. ), from their SED, rigorously accounting forthe di ff erent sources of uncertainties. As any Bayesian model, HerBIE computes a posterior
PDF as the product of a classi-cal likelihood and a prior
PDF. What makes this model hier-archical is that the prior depends on a set of hyperparameters .These hyperparameters are: (i) the average of each physical pa-rameter; and (ii) their covariance matrix. The hyperparametersare inferred, together with the parameters of each individualgalaxy. We are therefore sampling a single, large-dimension ,joint PDF. Since the shape of the prior is inferred from the data,the information of the whole sample is used, in this process, to The dimension of the parameter space is approximately the productof the number of galaxies and the number of model and ancillary param-eters (G18, Sect. 3.3). In the present case, it has (cid:39) × (7 + (cid:39)
10 000dimensions. Article number, page 5 of 64 & A proofs: manuscript no. manuscript refine our knowledge of each individual galaxy. In particular, itis relevant to keep in our sample even poorly-constrained SEDs,with upper limits or missing fluxes. Such a model is also e ffi -cient at suppressing the numerous noise-induced, false correla-tions between parameters, encountered when fitting SEDs withleast-squares or non-hierarchical Bayesian methods (Shetty et al.2009; Kelly et al. 2012; Galliano 2018; Lamperti et al. 2019). Ithas recently been used to study the anomalous microwave emis-sion in the Milky Way (Bell et al. 2019).From a technical point of view, HerBIE uses a
Markov ChainMonte-Carlo (hereafter MCMC), with Gibbs sampling (Geman& Geman 1984). As mentioned in Sect. 2.2, we include the an-cillary data in our prior. This process is fully demonstrated inSect. 5.3 of G18. These ancillary data do not enter the dustmodel, but they provide information that helps to better constrainthe hyperparameters, in a holistic way. In other words, the infor-mation provided by the gas mass or the metallicity helps to bet-ter constrain the dust SED fit. It is a Bayesian implementation of
Stein’s paradox (Stein 1956; Efron & Morris 1977).
To infer dust parameters with
HerBIE , we adopt the frameworkprovided by the grain properties of the
THEMIS model (Joneset al. 2017). THEMIS is built, as much as possible, on labora-tory data, and reproduces dust observables of the Galactic ISM.One of its originalities is that it accounts for the aromatic andaliphatic mid-IR features with a single population of small, par-tially hydrogenated, amorphous carbons, noted a-C(:H). Conse-quently, it does not include
Polycyclic Aromatic Hydrocarbons (PAH) per se . Although largely dehydrogenated, small a-C(:H)are very similar to PAHs. The other main component of
THEMIS is a population of large, a-C(:H)-coated, amorphous silicates,with Fe and FeS nano-inclusions.
THEMIS is designed to model the evolution of: (i) the sizedistribution, (ii) the a-C(:H) hydrogenation, and (iii) the man-tle thickness, with the
InterStellar Radiation Field (ISRF) andgas density. With the observational constraints of Sect. 2.1, wecan not reliably constrain the mantle thickness, as its e ff ect onthe shape of the far-IR SED is too subtle. Nor can we constrainthe a-C(:H) hydrogenation, as broadband fluxes do not provideunambiguous constraints on the 3.4 µ m feature. We can how-ever study the variations of the size distribution of small a-C(:H),from galaxy to galaxy, as it will a ff ect the strength of the brightmid-IR aromatic features.We have therefore parametrized the size distribution in thefollowing way.1. We have divided the a-C(:H) component into ( cf. Fig. 1):
Very small a-C(:H) (denoted VSAC) of radius smaller than7 Å, responsible for the mid-IR feature emission, withmore weight in the short wavelength bands;
Small a-C(:H) (denoted SAC) of radius between 7 Å and15 Å, responsible for the mid-IR feature emission, withmore weight in the long wavelength bands;
Medium and large a-C(:H) (noted MLAC) of radius largerthan 15 Å, carrying the featureless mid-IR continuumand a fraction of the far-IR peak.2. The silicate-to-MLAC ratio is kept constant.Using q X to denote the mass fraction of component X , the sizedistribution is controlled by two parameters: (i) the mass fraction / themis / Fig. 1.
Parametrization of the
THEMIS model.
Panel (a) shows the sizedistribution of the two main components of
THEMIS : amorphous car-bons and silicates. We show how we divide the a-C(:H) size distributioninto three independent components. Panel (b) shows the SED corre-sponding to each component (same color code as panel a ). The SED isshown for the ISRF of the solar neighborhood (Mathis et al. 1983). of aromatic-feature-carrying grains, q AF ≡ q VSAC + q SAC ; and (ii) the very-small-a-C(:H)-to-aromatic-feature-emitting-grainratio, f VSAC ≡ q VSAC / q AF . Comparing these parameters to dustmodels with PAHs ( e.g. Zubko et al. 2004; Draine & Li 2007;Compiègne et al. 2011), q AF is the analogue of the PAH massfraction, q PAH introduced by Draine & Li (2007, hereafterDL07). The di ff erence here is that, q AF =
17 %, while q PAH = Article number, page 6 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution . ff use Galactic ISM . This is because a-C(:H)have a smaller fraction of aromatic bonds per C atom. More massis therefore needed to produce the feature strength of a PAH.This parametrization has the great advantage of being lin-ear. A simpler version, fixing f VSAC , has been implemented in
CIGALE by Nersesian et al. (2019). A more physical way to varythe size distribution would be to vary the minimum cut-o ff sizeand the index of the power-law size distribution ( cf. Jones et al.2013, for the description of the size distribution of
THEMIS ).However, this alternate parametrization would be CPU time con-suming, and would not produce noticeable di ff erences in the re-sulting broadband SED ( cf. Appendix C).
A model, such as
THEMIS , is not directly applicable to observa-tions of galaxies. Indeed, the monochromatic flux of a wholegalaxy comes from the superposition of grains exposed to arange of physical conditions. This well-known problem can beaddressed assuming a distribution of starlight intensity insideeach galaxy. We adopt the prescription proposed by Dale et al.(2001), where the dust mass, M dust , follows a power-law distri-bution, as a function of the starlight intensity, U :d M dust ∝ U − α d U for U min < U < U min + ∆ U . (2)The parameter U is the frequency-integrated monochromaticmean intensity of the Mathis et al. (1983) di ff use ISRF. It is nor-malized so that U = e.g. Eq. 2 ofGalliano et al. 2011). This phenomenological composite SED isthe powerU model component of G18 (Sect. 2.2.5). We add tothe emission the starBB component of G18 (Sect. 2.2.6), in or-der to account for the residual di ff use stellar emission at shortwavelengths.The list of free SED model parameters, that HerBIE infers,is thus the following. Similarly to the ancillary parameters (Ta-ble 2), we use the natural logarithm of quantities varying overmore than an order of magnitude.1. ln M dust , the dust mass, scales with the whole dust SED.2. ln U min ∈ [ln 0 . , ln 10 ] is the minimum cut-o ff in Eq. (2).3. ln ∆ U ∈ [ln 1 , ln 10 ] controls the range in Eq. (2).4. α ∈ [1 , .
5] is the power-law index in Eq. (2).5. ln q AF ∈ [ln 10 − , ln 0 .
9] is defined in Sect. 3.1.1.6. f VSAC ∈ [0 ,
1] is defined in Sect. 3.1.1.7. ln L (cid:63) is the luminosity of the residual stellar emission ( cf. G18, Sect. 2.2.6).These parameters are however not the most physically relevant.In the rest of the present article, we focus our discussion on thefollowing three parameters, marginalizing over the other ones: (i) M dust ; (ii) (cid:104) U (cid:105) ; and (iii) q AF , where (cid:104) U (cid:105) (Eq. 9 of G18) isthe mean of the distribution in Eq. (2). It quantifies the mass-averaged starlight intensity illuminating the grains. It is a func-tion of the three parameters U min , ∆ U and α (Eq. 10 of G18).It can be related to an equivalent large grain equilibrium temper-ature, T eq , through: (cid:104) U (cid:105) (cid:39) ( T eq /
18 K) . ( e.g. Nersesian et al.2019). We note here that the estimated mass fraction of PAHs in the dif-fuse Galatic ISM depends on the set of mid-IR observations used toconstrain it. For instance, DL07 use
COBE / DIRBE broadbands, whileCompiègne et al. (2011) use a scaled
Spitzer / IRS spectrum. It results indi ff erent levels of mid-IR emission and PAH fraction: Compiègne et al.(2011) find q PAH = . THEMIS is calibrated with the sameobservations as Compiègne et al. (2011), it is possible to estimate thevalue of q PAH that would result in the same level of mid-IR emission as q AF : q PAH (cid:39) . × q AF (ratio of 7 . In our experience, the model of Sect. 3.1.2 is the most appropri-ate for galaxies observed with the typical spectral coverage ofTable 1. It presents however the following limitations.
Shape of the ISRF.
We assume that dust is heated by theMathis et al. (1983) ISRF, scaled by a factor U . We assume in themodel that the shape of this ISRF does not vary between galaxiesnor within regions inside galaxies. It is obvious that this assump-tion is not correct. However, its consequences are minimal on theparameters we are interested in, for the following reasons. – M dust and (cid:104) U (cid:105) depend mainly on the far-IR peak emission,which is dominated by large grains. These grains are at ther-mal equilibrium. Their emission therefore does not dependon the shape of the ISRF, only on the absorbed power. – q AF controls the fraction of small, stochastically-heatedgrains. The emission from these grains depends on the shapeof the ISRF ( e.g. Camps et al. 2015). However, since smalla-C(:H) are destroyed in H ii regions ( cf. Sect. 4.2.3 of Gal-liano et al. 2018, and Sect. 4.2), they are e ff ectively heatedby a rather narrow spectral range (4 eV (cid:46) h ν < . ff ect is demonstrated on Fig. 7 ofDraine (2011), with PAHs. We thus do not expect that ac-tual variations of the ISRF shape will significantly bias ourestimate of q AF . Evolution of small a-C(:H).
The abundance of small a-C(:H)and their properties evolve with the ISRF and the gas density.These grains are dehydrogenated and destroyed by intense IS-RFs; they are also accreted onto large grains, in dense regions( e.g.
Jones et al. 2013; Köhler et al. 2015). Our parametriza-tion (Sect. 3.1.1) allows us to explore variations of q AF betweengalaxies, but we assume that q AF is constant, for all U , withineach galaxy. However, this assumption will not bias our globalestimate of q AF , as this parameter is merely a way to give a phys-ical meaning to the observed L AF / TIR ratio ( L AF denoting thepower emitted by the aromatic features). This assumption wouldonly be problematic if we were trying to estimate the local valueof q AF in PDRs, for instance. Indeed, we would, in this case,underestimate q AF , by assuming that a fraction of the aromaticfeature emission comes from H ii regions, which are generallyhotter than PDRs, and thus more emissive. Grain opacity.
We assume that the grain opacity does notvary between galaxies, nor within regions inside galaxies. Thereare several indications that this hypothesis is not correct ( e.g.
Sect. 4.2.1 of Galliano et al. 2018). In particular, the far-IRopacity can typically vary by a factor of (cid:39) / removal of mantles and grain-grain coagulation (Köh-ler et al. 2015). Such variations will bias our estimate of thedust mass. In addition, the submm / mm silicate emissivity im-plemented in THEMIS has an unphysical power-law dependenceat long wavelengths. Accounting for a more realistic opacity,based on laboratory measurements such as those of Demyk et al.(2017b,a), will likely a ff ect our dust mass estimates. This is animportant e ff ect that we can not avoid. We discuss its conse-quences in Sect. 4.1.3, when interpreting our results. Article number, page 7 of 64 & A proofs: manuscript no. manuscript
Residual contaminations.
The following emission processes,not accounted for in our model, could be present in our observa-tions. – Several gas lines contribute to the emission in the photomet-ric bands of Table 1. The brightest are: [O i ] µ m , [O iii ] µ m ,[C ii ] µ m , [O i ] µ m and CO(J = → µ m . Without ded-icated spectroscopic observations, the subtraction of theselines is hazardous. Luckily enough, their intensities are, tofirst order, proportional to TIR ( e.g. Cormier et al. 2015).They constitute therefore a bias proportional to the flux, thatcan be taken into account together with the calibration bias,as we will show in Sect. 3.2. – The submm excess is an excess emission of debated origin,appearing longward 500 µ m ( cf. Sect. 3.5.5 of Galliano et al.2018, for a review). Since it is not accounted for in ourmodel, it could bias our submm SED. This e ff ect is howeverprobably negligible in our sample, for the following reasons.1. This submm excess is model-dependent. THEMIS has aflatter submm opacity than models based on the DL07optical properties ( e.g.
Fig. 4 of Galliano et al. 2018).It is therefore more emissive in the submm regime andminimizes the contribution of the excess.2. This excess is observed in dwarf galaxies, but is rarelydetected in higher metallicity systems ( e.g.
Gallianoet al. 2003, 2005; Galametz et al. 2009; Rémy-Ruyeret al. 2015; Dale et al. 2017). Yet, data longward 500 µ m,in our sample, are available only for large objects, due tothe large Planck / HFI beam.3. Residuals of our model run (Sect. 3.2) do not show sig-nificant excesses in the submm bands. – Residual stellar emission could contaminate the shortestwavelength bands. Improper stellar subtraction could leadto positive or negative o ff sets, independently in the di ff erentbands. The results we will present in Sect. 4 are obtained with the modeldescribed in Sect. 3.1. We call it our reference run. Fig. 2 showsthe SED fit of four representative objects, obtained with thisrun. In panels (a) , (b) and (c) , SEDs of three arbitrarily cho-sen galaxies, representative of Early-Type Galaxies (ETG),
Late-Type Galaxies (LTG) and irregulars, respectively, are displayed.The PDF of the SED is shown as a yellow density plot. We alsoshow the PDF of the synthetic photometry (violin plots of dif-ferent colors). The comparison of this synthetic photometry tothe observed flux (circles with an error bar) reflects the qualityof the fit. We discuss a more thorough and technical fit qualitytest in Appendix D. Panel (d) shows the example of a galaxywhere most of the fluxes are 3 σ -upper limits (displayed when F ν < σ noise ν ). When the evidence provided by the data is weak,which is the case when few detections are available, the poste-rior distribution becomes dominated by the prior. This is whatwe see here. The range spanned by this SED PDF is the extentof the prior. The global scaling of this SED is very uncertain,but its shape is realistic. This would not be the case with a non-hierarchical model.Fig. 3 shows the inference of the calibration biases, δ ( λ ), ofeach waveband (Sect. 2.1.3). Basically, the model fluxes are cor-rected by factors 1 + δ ( λ ). For each waveband, the dashed-line violin plots are 90 ◦ -rotated histograms. error bar represents the ± σ interval of the prior on the calibra-tion bias. This prior is a multivariate normal distribution, cen-tered on 0, with the covariance matrix of Eq. (A.2). As discussedin Sect. 3.1.3, besides accounting for the uncertainty in the cali-bration of each instrument, these coe ffi cients can account for ex-ternal contaminations and fitting residuals. We can interpret themost deviant values of Fig. 3 in this light. The posterior valuesof δ lying outside their ± σ prior are the following. µµµ m: both overlapping bands PACS3 and MIPS3 indicate anexcess emission of about 15 %. A significant fraction of thisexcess is likely due here to contamination by the brightestline of the ISM, [C ii ] µ m . The [C ii ] µ m intensity is about (cid:39) µ m) power (Malhotra et al.1997, 2001; Brauher et al. 2008; Cormier et al. 2015). Itscontribution to the PACS3 and MIPS3 is thus expected tobe a few percent, as these bands are narrower than the FIRrange. µµµ m and 22 µµµ m: the deficit could be due to a systematic dif-ference between the size distribution of medium a-C(:H)grains implemented in THEMIS and in the di ff use ISM ofthese galaxies. Although the model was di ff erent, Gallianoet al. (2011, Appendix A.2) had to decrease the abundance ofthe grains carrying the 24 µ m continuum in the Large Mag-ellanic Cloud (LMC), for a similar reason.Apart from these deviations, the two overlapping bands WISE1and IRAC1 indicate that the model, on average, underestimatesthe observations by (cid:39)
10 % around 3.5 µ m. This could be due toeither the continuum or the 3.3 / µ m features. The constraintof the size distribution of THEMIS by the SED of the Milky Way(Fig. 3 of Jones et al. 2013), has been performed with a mediumresolution IRS spectrum for all a-C(:H) features, except the twoin question here. The global emissivity of these features is themost uncertain of the model. We also notice that the SPIRE cal-ibration biases go in opposite directions, while they should bepartially correlated (Appendix A.5). The HFI1 and HFI2 cal-ibration biases agree very well with SPIRE. This is the signthat there is a systematic residual proportional to the flux in thiswavelength range. It could mean that the slope of
THEMIS is notsteep enough in the 200 − µ m range . The fact that theHFI3 is almost 0 would mean that the slope flattens again long-ward (cid:39) µ m. This is very speculative, but we note that thisbehaviour is qualitatively consistent with the optical propertiesmeasured in the laboratory by Demyk et al. (2017a).The parameters inferred with this run, for each galaxy, aregiven in Table H.1 (electronic version only). We report only theparameter values and their uncertainties (mean and standard-deviation of the posterior PDF). The skewness and correla-tion coe ffi cients can be retrieved from the DustPedia archive(http: // dustpedia.astro.noa.gr). The length of the MCMC of thisrun is 1 000 000, where we have excluded the first 100 000 steps,to account for burn-in. The maximum integrated autocorrelationtime (Eq. 43 of G18) is 65 000. In order to assess the robustness of our results, we have per-formed several additional runs, with di ff erent assumptions. Wenow discuss the comparison of these tests with our referencerun. We focus on the derived dust mass and do not display theredundant comparisons with (cid:104) U (cid:105) . Indeed, TIR is usually well We do not implement the evolution of the grain properties with ac-cretion and coagulation that could account for a steeper far-IR slope.Article number, page 8 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Fig. 2.
Select SED fits.
Each panel shows the inferred SED PDF, in yellow intensity scale, normalized by the MCMC-averaged TIR. The colorviolin plots represent the synthetic photometry PDF, for each waveband. The black error bars are the observations. Panels (a) , (b) and (c) showarbitrary chosen galaxies, representative of their classes (early-type, late-type and irregulars, respectively). Panel (d) shows the case, where mostconstraints are only upper limits. constrained and, by model construction, TIR ∝ M dust × (cid:104) U (cid:105) . Wediscuss the di ff erence in q AF , when relevant. Figs. 4 – 6 compares M dust or q AF derived by these tests to the same quantity derivedby the reference run, M refdust and q refAF , respectively. Table 3 reportssome statistics on this comparison. We color code the galaxiesaccording to their Hubble stage, T : Early-type: T ≤ Late-type: < T < Irregulars: T ≥ We have fit the full sample of Sect. 2 withthe physical model of Sect. 3.1, using a standard least-squaresmethod ( cf.
Appendix C of G18). The goal of this run is todemonstrate the importance of the fitting method. The result isshown in panel ( a ) of Fig. 4. The results for sources with highsignal-to-noise ratio ( M refdust (cid:38) M (cid:12) ; mainly LTGs) are in verygood agreement with the reference run. However, there is a sig-nificant scatter for sources with M refdust (cid:46) M (cid:12) (mainly ETGs Article number, page 9 of 64 & A proofs: manuscript no. manuscript
Table 3.
Robustness assessment.
Statistics of the comparison between the reference run and the various tests of Figs. 4 to 6. The median, 68 % and95 % intervals refer to the distribution of the quantity in the first column. See Sect. 3.3 for more details.
Quantity Run Median 68 % interval 95 % interval Number of sources M dust / M refdust Least-squares 0 .
86 0 .
128 – 1 .
50 2 . × − – 7 . M dust / M refdust Non-hierarchical Bayesian 0 .
92 0 . .
22 0 . . M dust / M refdust No Planck & IRAS data 1 .
19 1 .
00 – 1 .
60 0 .
69 – 2 .
44 783 M dust / M refdust Galliano et al. (2011) AC mixture 0 .
91 0 .
69 – 0 .
97 0 .
51 – 1 .
15 798 q PAH / q refAF Galliano et al. (2011) AC mixture 0 .
60 0 .
48 – 0 .
68 0 .
37 – 0 .
80 798 M dust / M refdust MBB with β = .
79 0 .
85 0 .
61 – 1 .
08 0 .
35 – 1 .
39 798 M dust / M refdust MBB with β free 1 .
00 0 .
43 – 2 .
75 0 .
183 – 5 . M dust / M refdust Draine & Li (2007) ISRF distribution 0 .
71 0 .
49 – 1 .
31 0 .
186 – 4 . M dust / M refdust CIGALE 0 .
70 0 .
50 – 1 .
06 0 .
227 – 3 . Fig. 3.
Inferred calibration biases.
This figure shows our inference ofthe calibration bias, δ , defined in Sect. 3.2.2 of G18, for each of thephotometric filters in Table 1. Each instrument is color-coded. The ver-tical dashed error bars represent the calibration prior, i.e. the ± σ rangegiven in Appendix A. The violin plots show the actual posterior PDFs of δ , for each broadband. The width of a single violin plot is proportionalto the PDF as a function of δ (vertical axis). and irregulars). Furthermore, there are more drastic underesti-mates than overestimates. The galaxies with M dust / M refdust (cid:39) − are indeed essentially sources with only far-IR upper limits, hav-ing a negligible weight in the chi-squared. These SEDs are thuswrongly fit a with very high (cid:104) U (cid:105) , and scaled on the mid-IRfluxes, leading to a drastic underestimate of the dust mass. Non-hierarchical Bayesian.
We have fit the full sample ofSect. 2 with the physical model of Sect. 3.1, replacing the hy-perparameter distribution by a flat prior ( cf.
Sect. 4.2.3 of G18).This flat prior is bounded, with limits well beyond the displayedparameter range. This run thus samples the likelihood of eachgalaxy, independently, but does not benefit from an informativeprior, inferred from the whole sample. The result is shown inpanel (b) of Fig. 4. Similarly to the least-squares example above, there is no bias for the well sampled sources ( M refdust (cid:38) M (cid:12) ),but there is a significant scatter for sources with M refdust (cid:46) M (cid:12) .The scattered sources are underestimates, for similar reasons asthe least-squares example. The amplitude of the scatter is how-ever smaller than for the least-squares run. In addition, even themost extremely scattered sources are 2 σ -consistent with the 1:1relation. This is because a Bayesian method samples the likeli-hood as a function of the parameters, but stays conditional onthe data, while a frequentist approach ( e.g. least-squares) sam-ples the likelihood as a function of the data, thus consideringdata that have not actually been observed, leading to biases ( e.g. Jaynes 1976; Wagenmakers et al. 2008). No Planck & IRAS data.
To understand the role of the far-IRcoverage, we have fit the sample of Sect. 2 without the
Planck and
IRAS data, using the physical model of Sect. 3.1. In thiscase, the far-IR coverage is provided by the sole
Herschel data.There is thus no data longward 500 µ m. The result is shown inpanel (c) of Fig. 4. The absence of this data does not bias the fit,it simply introduces some scatter, consistent with the 1:1 rela-tion ( cf. Sect. 5.2 of G18 for more discussion on this e ff ect). Theirregulars are marginally overestimated, due to the lack of su ffi -cient SPIRE detections. Some of these sources do not have anysubmm detections, higher dust masses are therefore allowed. We have fit thefull sample of Sect. 2 with the HB model of Sect. 3.1, replacingthe
THEMIS grain properties by those of the
Amorphous Carbon (AC) model of Galliano et al. (2011). The far-IR opacity of thetwo grain mixtures are comparable ( cf.
Fig. 4 of Galliano et al.2018). The only fundamental di ff erence is that the aromatic fea-tures are accounted for by PAHs, not by a-C(:H). Panel (a) ofFig. 5 compares M dust to our reference model. As expected, thetwo values are in good agreement. The moderate scatter is dueto the mild di ff erence between the two far-IR opacities. How-ever, most of the ratios are 1 σ -consistent with the 1:1 relation.Panel (b) of Fig. 5 compares the q PAH of this run to the q AF ofthe reference run. In Sect. 3.1.1, we noted that we should have q PAH / q AF (cid:39) .
45. In the present case, we have a ratio of (cid:39) . ff erence is the following. Theparametrization of the THEMIS ’s aromatic spectrum shape is con-trolled by f VSAC (Sect. 3.1.1), which alters the a-C(:H) mass. Onthe contrary, for the Galliano et al. (2011) AC model, the shapeof the aromatic spectrum is controlled by the fraction of ion-ized PAHs, which does not alter the PAH mass. A systematically
Article number, page 10 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Fig. 4.
Robustness assessment.
Each of the three horizontal panels of Figs. 4 to 6 display the comparison of the various tests of Sect. 3.3 to ourreference run (Sect. 3.2). The left column panels show the ratio of either M dust or q PAH , derived from the test (grey label in the top left corner),to its equivalent with the reference run, as a function of M refdust . Galaxies are color-coded according to their type. The right column plot shows thePDF (normalized) of the distribution of the ratio. The median of the ratio is displayed as an orange solid line. The 1:1 ratio is highlighted as anorange dashed line. This figure shows the influence of various fitting methods. Article number, page 11 of 64 & A proofs: manuscript no. manuscript
Fig. 5.
Same as Fig. 4. This figure shows the influence of various fitting methods.Article number, page 12 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Fig. 6.
Same as Fig. 4. The first two panels continue to show the influence of various dust model assumptions as in Fig. 4. The other panel is acomparison with results from a previous work done using the same sample but di ff erent method. Article number, page 13 of 64 & A proofs: manuscript no. manuscript lower 8-to-12 µ m ratio compared to the Galaxy’s di ff use ISMwould explain a q PAH / q AF ratio higher than expected. Modified black body with β = . . We have fit the photom-etry of Sect. 2, longward 100 µ m, with a Modified Black Body(MBB; e.g. Sect. 2.2.2 of G18). In this first test, we fix the emis-sivity index β = .
79 and the level of the opacity to mimic thefar-IR opacity of
THEMIS : κ ( λ ) = .
64 m kg − × (250 µ m /λ ) . ( e.g. Sect. 3.1.1 of Galliano et al. 2018). Panel (c) of Fig. 5 com-pares M dust to our reference run. We can see that M dust is about0.8 times lower. This value is consistent with what Galliano et al.(2011, Appendix C.2) found in the LMC. This di ff erence is dueto the fact that a MBB is an isothermal approximation. Since aSED fit is roughly luminosity weighted, the MBB does not ac-count for the coldest, less emissive, but massive regions in thegalaxy. It thus systematically underestimates the mass. Modified black body with free β . Similarly to the previous test,we have fit the photometry of Sect. 2, longward 100 µ m, witha MBB, but letting β free, this time. Such a model can poten-tially infer the grain optical properties through the value of β andthe grain physical conditions through the temperature, T d . Thispotentiality is however limited by the mixing of physical condi-tions ( e.g. Sect. 2.3.1 of Galliano et al. 2018). Panel (a) of Fig. 6compares M dust to our reference run. We can see the dust mass isnot extremelly biased, although there is some scatter. The β − T d relation of this run is presented in Appendix E. With the DL07 ISRF distribution.
We have fit the full sample ofSect. 2 with the physical model of Sect. 3.1, replacing the ISRFdistribution of Eq. (2) by the DL07 prescription:d M dust d U = M dust (1 − γ ) δ ( U − U min ) + γ ( α − U − α U − α min − ( U min + ∆ U ) − α . (3)This prescription is our Eq. (2) plus a uniformly illuminatedcomponent at U = U min , with the parameter γ controlling theweight of the two components. We follow DL07 by fixing α = U min + ∆ U = . Consequently, the far-IR / submm slope,beyond the large grain peak emission ( (cid:39) µ m), is the slopeof the large grain emission at U = U min , making this model verysimilar to a fixed- β MBB in the far-IR / submm range. In compar-ison, the ISRF distribution of our reference run allows us to ac-count for a flattening of the far-IR / submm slope, by mixing dif-ferent ISRF intensities, down to lower temperatures (Sect. 2.3.1of Galliano et al. 2018). Apart from the ISRF distribution, theother features are similar to our reference run: THEMIS grainmixture and HB method. Panel (b) of Fig. 6 compares M dust toour reference run. We notice, as expected, the same systematicshift, here by a factor (cid:39) .
7, as for the fixed- β MBB (Table 3).
CIGALE
Results
Nersesian et al. (2019) have modelled the DustPedia sample,using the code
CIGALE (Boquien et al. 2019), which fits thedust SED with: (i) the
THEMIS grain properties; (ii) the DL07ISRF distribution; and (iii) a non-hierarchical Bayesian method.Panel (c) of Fig. 6 shows its comparison to our reference run. Asexpected, it is very similar to the DL07 ISRF distribution test inpanel (b) of the same figure. In particular, the mass is shifted bythe same (cid:39) . M refdust . Concerning the fractionof small a-C(:H), the values of Nersesian et al. (2019) are in verygood agreement with our reference run.In summary, the comparisons of Sects. 3.3.1 to 3.3.3 havedemonstrated that the discrepancies induced by di ff erent fittingmethods or model assumptions can be well understood. We aretherefore confident that our reference run is the most robustamong the diversity of approaches we have tested. Lianou et al. (2019, hereafter L19) recently used our model,
HerBIE , to analyze the DustPedia photometry. There are threemain technical di ff erences between our analysis and theirs.1. They used the implementation of the 2013 version of the THEMIS model (Jones et al. 2013), while we use the revised2017 version (Jones et al. 2017).2. They did not profit from the possibility to include ancillarydata in the prior (Sect. 3.1).3. They did not include the remaining sources from the DGSsample.The comparisons of M dust and q AF are shown in Fig. 7.Panel (a) of Fig. 7 shows that their dust mass is about a fac-tor of 2 lower than ours. This can be partly understood in thelight of the di ff erence in grain mixtures. Indeed, Jones et al.(2017) revised the THEMIS model by including the more real-istic Köhler et al. (2014) optical properties. To fit the same ob-servational constraints, they compensated this update by chang-ing the mantle thickness, as well as the dust-to-gas mass ratio: M dust / M H = . × − according to Table 2 of Jones et al. (2013)and M dust / M H = . × − according to Table 1 of Jones et al.(2017). This sole modification explains why a mass derived withthe 2013 THEMIS version would be a factor of (cid:39) .
86 lower thanwith the 2017 version. However, this does not explain the wholeextent of the discrepancy. The comparison of our dust masseswith those derived with
CIGALE (Sect. 3.3.3) certainly excludessuch a large error, on our side. It can be noted that there is alsosome scatter around the median ratio of M dust / M refdust . A part ofthis discrepancy can naturally be explained by the fact that sev-eral galaxies have a very poor spectral coverage. As demon-strated in Sect. 3.2, the prior becomes dominant in this case.In our case, the prior contains the information provided by theancillary data, thus helping to reduce the dust parameter range.Panel (b) of Fig. 7 shows the comparison of q AF . The twoquantities are in good agreement. There is some scatter aroundthe median, for the same reason as mentioned for M dust . How-ever, the problem with this quantity is the way L19 discussit. They improperly report the meaning of q AF that they call“ ‘QPAH’ ” (L19, Sect. 3, 5 th item). They write it represents “themass fraction of hydrogenated amorphous carbon dust grainswith sizes between 0.7 nm and 1.5 nm” , while it actually is themass fraction of a-C(:H) with sizes between 0.4 nm and 1.5 nm.Furthermore, they claim the Galactic value of this parameteris 7 . q GalAF = . q GalAF = . . cf. Sect. 4.2).In summary, we are confident that our derived parameters areboth more precise and more accurate than L19’s.
Article number, page 14 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Fig. 7.
Comparison to Lianou et al. (2019).
Same conventions as Fig. 4.
4. THE DERIVED DUST EVOLUTION TRENDS
In this section, we present the main dust evolution trends derivedfrom the reference run (Sect. 3.2). These results are displayed ascorrelations between two inferred parameters, for each sourcein the sample. Displaying the full posterior PDF of each galaxyas density contours is visually impractical. Instead, we displayits extent as a
Skewed Uncertainty Ellipse (SUE; Appendix F).SUEs approximately represent the 1 σ contour of the PDF, re-taining the information about the correlation and the skewnessof the posterior, with a dot at the maximum a posteriori . Whendiscussing parameter values in the text, we often quote the % Credible Range (CR ), which is the parameter range exclud-ing the 2 . . – We call
Extremelly Low-Metallicity Galaxy (ELMG), a sys-tem with Z (cid:46) Z (cid:12) / – To simplify the discussion, since the heavy-element-to-gasmass ratio, Z , is usually called metallicity , we introduce theterm dustiness to exclusively denote the dust-to-gas mass ra- tio: Z dust ≡ M dust M gas . (4) – We denote by specific , quantities per unit stellar mass (simi-lar to sSFR): (i) the specific dust mass is s M dust ≡ M dust / M (cid:63) ; (ii) the specific gas mass is s M gas ≡ M gas / M (cid:63) .Note that, in all the displayed relations, the number of objectsdepends on the availability of the ancillary data (Table 2). We first focus on scaling relations involving the total dust mass, M dust , with respect to the gas and stellar contents, the metallic-ity and the star formation activity. Casasola et al. (2020a) haveexplored additional scaling relations, focussing on DustPediaLTGs. Article number, page 15 of 64 & A proofs: manuscript no. manuscript
Fig. 8.
Dust-related scaling relations.
In the four panels, the SUEs represent the posterior of each galaxy, using the reference run (Sect. 3.2). TheSUEs are color-coded according to the Hubble stage of the object (Sect. 3.3). We show the Milky Way values, as a yellow star, for comparison.We emphasize that, although we are showing di ff erent parameters of the same sample, the di ff erent panels do not exactly contain the same numberof objects (Table 2). In particular, there are fewer reliable metallicity measurements, especially for ETGs. Fig. 8 presents four important scaling relations. Panel (a) showsthe evolution of the dust-to-baryon mass ratio: f dust ≡ M dust M gas + M (cid:63) , (5)as a function of the gas fraction: f gas ≡ M gas M gas + M (cid:63) . (6) This well-known relation was previously presented by Clarket al. (2015), De Vis et al. (2017a) and Davies et al. (2019).It shows that: (i) at early stages ( f gas (cid:38) .
7; mainly irregu-lars), there is a net dust build-up; (ii) it then reaches a plateau(0 . (cid:46) f gas (cid:46) .
7; mainly LTGs) where the dust production iscounterbalanced by astration; (iii) at later stages ( f gas (cid:46) . f dust (cid:39) .
01 is PGC 166077. Itis however technically not an outlier, as CR ( f dust ) = [1 . × − , . × − ], overlapping with the rest of the sample. Article number, page 16 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
2. The two ETGs (red SUEs) with a low f dust , at f gas (cid:39) . f gas (cid:39) .
6, are NGC 5355 and NGC 4322, respectively.For NGC 4322, CR ( f dust ) = [1 . × − , . × − ],marginally overlapping with the rest of the sample. ForNGC 5355, however, CR ( f dust ) = [2 . × − , . × − ],making it a true outlier.3. The ETG (red SUE) with f gas (cid:39) (b) of Fig. 8 presents the relation between the specificgas mass, and the dustiness. Such a relation was previously pre-sented by Cortese et al. (2012), Clark et al. (2015) and De Viset al. (2017a). There is a clear negative correlation between thesetwo quantities, showing that when a galaxy evolves, its ISM getsprogressively enriched in dust and its gas content gets convertedto stars. There is one notable feature deviating from this mainsequence : a vertical branch at s M gas (cid:39) .
1, exhibiting a sys-tematically lower dustiness. This branch is mostly populated byETGs and contains most of the ETGs of the relation. We willdiscuss the likely origin of this branch in Sect. 4.1.2. Finally, thepeculiar sources of panel (a) logically stand out in this panel too.1. PGC 166077 is the blue SUE at Z dust (cid:39) .
05. It is not a clearoutlier, as CR ( Z dust ) = [0 . , . M gas (cid:39) . M gas (cid:39) .
5, respectively.3. The bottom red SUE, at s M gas (cid:39) (c) of Fig. 8 shows the relation between the specificdust mass and the specific star formation rate, sSFR. This re-lation was previously presented by Rémy-Ruyer et al. (2015)and De Vis et al. (2017a). It was also discussed in Corteseet al. (2012) with sSFR replaced by its proxy NUV-r. In thesame way, but on resolved 140-pc scales, it was shown inM 31 by Viaene et al. (2014). There is a clear positive cor-relation between the two quantities. The di ff erent galaxy typesare grouped in distinct locations: (i) ETGs are clustered around10 − (cid:46) sSFR (cid:46) .
01 Gyr − ; (ii) LTGs are clustered around0 . (cid:46) sSFR (cid:46) − ; (iii) Irregulars tend to lie around0 . (cid:46) sSFR (cid:46)
10 Gyr − , but are more scattered than the othertypes, with a systematically lower s M dust than what the extrapo-lation of the trend would suggest. This scaling relation providesan interesting approximation to derive the dust content from SFRand M (cid:63) , two quantities which usually are easy to estimate. Inparticular, the relation is quasi-linear in the low sSFR regime,with: M dust M (cid:12) (cid:39) . + . − . × × SFRM (cid:12) / yr for sSFR (cid:46) . − , (7)with CR ( M dust / SFR) = [0 . , × yr.Panel (d) of Fig. 8 shows the variation of the dustiness asa function of the metallicity (Eq. 1). Such a relation is one ofthe most common benchmarks for global dust evolution mod-els ( cf. Sect. 5), and has been presented by numerous studies( e.g.
Lisenfeld & Ferrara 1998; James et al. 2002; Draine &Li 2007; Galliano et al. 2008a; Galametz et al. 2011; Rémy-Ruyer et al. 2014; De Vis et al. 2017b). There is a clear corre-lation between the two quantities, reflecting the progressive dustenrichment of the ISM, built from heavy elements injected bystars at the end of their lifetime. Few ETGs are present, due tothe lack of reliable gas metallicity estimates for these objects.These would occupy the high-metallicity regime. Compared toRémy-Ruyer et al. (2014), who presented a similar trend for the DGS sources, we notice that a few sources are missing and somemetallicities have been updated. This comes from the fact thatwe have adopted the more robust DGS metallicity reestimates byDe Vis et al. (2017b), with published nebular lines and using thePG16_S calibration (Sect. 2.2.2). The lowest metallicity source,at 12 + log(O / H) (cid:39) .
15, is I Zw 18. The most dust-deficientsource of the panel, at Z dust (cid:39) . × − , is UGCA 20. It is a clearoutlier to the trend with CR ( Z dust ) = [1 . × − , . × − ]. The ETG outliers, visible in panel (b) of Fig. 8 and discussed inSect. 4.1.1, are likely due to enhanced dust destruction by ther-mal sputtering in their hot, X-ray emitting gas ( e.g.
Bocchioet al. 2012; Smith et al. 2012), as suggested by De Vis et al.(2017a). We could conceive a reverse causality where it is thelow dust abundance that allows a higher fraction of escapingX-ray photons. However, this is unrealistic, as X-ray observa-tions clearly indicate that ETGs are permeated by a coronal gasthat is usually not found in later types of galaxies (Mathews &Brighenti 2003, for a review). In order to support the likelinessof the thermal sputtering scenario, we have compiled X-ray lu-minosities from the literature (Table 4). Fig. 9 displays the dust-to-stellar mass ratio as a function of the X-ray photon rate perdust grain, L X / M dust , for the 256 galaxies in our sample withpublished X-ray luminosities. This figure shows a mild negativecorrelation between the two quantities, consistent with the en-hanced dust destruction in X-ray-bright galaxies. ETGs clearlylie in the bottom right quadrant of this figure. It is reminiscent ofFigure 10 in Smith et al. (2012), displaying L FIR / L B as a functionof L X / L B .We note there is however a significant intrinsic scatter in thisrelation. This could be due to the fact that most of the studieslisted in Table 4 quote a total X-ray luminosity, including both: (i) point sources (AGNs, binary systems); and (ii) the di ff usethermal emission that is sole relevant to our case . In addition,the spectral range used to compute the X-ray luminosity variesfrom one instrument to the other (Table 4), leading to systematicdi ff erences. Nonetheless, accounting for these di ff erences, whichis beyond the scope of this paper, would likely not change theplausibility that dust grains are significantly depleted in ETGsdue to thermal sputtering. Panel (d) of Fig. 8 shows that the dustiness-metallicity rela-tion is non-linear. Rémy-Ruyer et al. (2014) first argued, re-lying on insights from the models of Asano et al. (2013) andZhukovska (2014), that such a trend was the result of di ff erentdust production regimes: (i) at low 12 + log(O / H), dust produc-tion is dominated by condensation in type II Supernova (SN)ejecta, with a low yield; (ii) around a critical metallicity of12 + log(O / H) (cid:39)
8, grain growth in the ISM becomes dominant,causing a rapid increase of Z dust ; (iii) at high 12 + log(O / H), thedust production is dominated by grain growth in the ISM, witha yield about two orders of magnitude higher than SN ii , andis counterbalanced by SN ii blast wave dust destruction. Rémy-Ruyer et al. (2014) argued that the intrinsic scatter of the rela- David et al. (2006), Diehl & Statler (2007), Rosa González et al.(2009) and Kim et al. (2019) extract the thermal emission of the gas.We use these values for the sources in these catalogs. This is a concept introduced by Asano et al. (2013). Its exact valuedepends on the star formation history of each galaxy.Article number, page 17 of 64 & A proofs: manuscript no. manuscript
Table 4.
X-ray luminosity references.
The total number of sources (lastline) is fewer than the sum of each sample size (last column). This isbecause the same sources were observed by di ff erent instruments. Whenit is the case, we keep the most recent estimate. Bibliographic Telescope Range Sizereference [keV]Fabbiano et al. (1992)
Einstein . − ROSAT . − . ROSAT . −
17 83Tajer et al. (2005)
ROSAT . − XMM . −
10 16David et al. (2006)
Chandra . − Chandra . − XMM . − Chandra . −
10 30Akylas & Georgantopoulos(2009)
XMM −
10 19Grier et al. (2011)
Chandra . − XMM −
10 37Liu (2011)
Chandra . − Chandra . − Fig. 9.
Relation of dust mass to X-ray luminosity.
This figure showsthe variation of the dust-to-stellar mass ratio as a function of the X-rayphoton rate per dust grain, for the sample of Table 4. This is a subset ofthe reference run (Sect. 3.2). The color convention is similar to Fig. 8.The Bayesian correlation coe ffi cient of this relation is ρ = − . + . − . ,with CR ( ρ ) = [ − . , − . tion, which could not be explained by SED fitting uncertainties,was due to the fact that each galaxy has a particular Star Forma-tion History (SFH). We will explore this aspect in Sect. 5. In thefollowing paragraphs, we discuss the di ff erent biases that couldhave induced an artificial non-linearity in our empirical trend. Comparison to DLAs.
Fig. 10 shows the evolution of the dust-to-metal mass ratio (DTM) as a function of metallicity. It is an-other way to look at the data in panel (d) of Fig. 8. A constantDTM corresponds to a linear dustiness-metallicity trend. TheSUEs in Fig. 10 are not consistent with a constant DTM (hor-izontal yellow line). However, there are reports in the literatureof objects exhibiting an approximately constant DTM, down tovery low metallicities:
Damped Lyman- α Absorbers (DLA). Wehave overlaid the DLA sample of De Cia et al. (2016). Thesemeasures are performed in absorption on redshifted systems,along the sightline of distant quasars. The metallicity and DTMare derived from a combination of atomic lines of volatile andrefractory elements. We can see that the DLA DTMs vary sig-nificantly less than in our nearby galaxy sample . Such an evo-lutionary behaviour requires a high SN-dust condensation e ffi -ciency coupled to a weak grain growth rate in the ISM ( e.g. DeVis et al. 2017b). Alternatively, the DLA estimates could be bi-ased. It is indeed not impossible that the hydrogen column den-sity of most DLAs includes dust- and element-free circumgalac-tic clouds in the same velocity range. It would result in a typicalsolar metallicity object appearing to have a solar DTM, and atthe same time, an artificially lower metallicity, diluted by the ad-ditional pristine gas along the line of sight.
Fig. 10.
Comparison to DLAs.
This figure shows the relation betweenthe metallicity and the dust-to-metal mass ratio, for the reference run(Sect. 3.2). This figure is very similar to panel (d) of Fig. 8: the onlydi ff erence is that the y -axis has been divided by Z (related to the x -axis through Eq. 1). We have overlaid in magenta the DLA measuresfrom Table 6 of De Cia et al. (2016). The horizontal yellow line cor-responds to the Galactic dust-to-metal mass ratio. The Bayesian corre-lation coe ffi cient of the nearby galaxy sample is ρ = . + . − . , withCR ( ρ ) = [0 . , . We note that metallicities measured in absorption tend to always belower than metallicities measured in emission ( e.g.
Hamanowicz et al.2020)Article number, page 18 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Accounting for the Gas Halo.
The contamination of the gasmass estimate by external, dust- and element-poor gas is alsoa potential issue for our nearby galaxy sample. This is partic-ularly important for low-metallicity, dwarf galaxies, where theIR-emitting region is usually small compared to the whole H i halo ( e.g. Walter et al. 2007; Begum et al. 2008). For instance,Draine et al. (2007) hinted that the trend between Z and Z dust was close to linear, when the gas mass used to estimate Z dust wasintegrated in the same region as the dust mass. They only had9 galaxies below 12 + log(O / H) < .
1. We have addressed thisissue by adopting the interferometric [H i ]
21 cm observations of20 of the lowest metallicity galaxies in our sample, includingthe lowest metallicity system, I Zw 18 (Roychowdhury et al., inprep. ; Sect. 2.2.3). We have integrated the gas mass within thephotometric aperture for these 20 objects. I Zw 18 still lies twoorders of magnitude below the Galactic DTM, despite this cor-rection. On the contrary, it is possible that the DTM of UGCA 20,the lowest SUE in Fig. 10, has been underestimated, as it has notbeen resolved in H i . We have to admit that there is still roomfor improvement as several of the ELMGs are barely resolvedin the IR. Thus, although we corrected for a large fraction ofthe H i halo, there might still be residual gas not associated withthe star forming region within our aperture. We might thereforebe underestimating the dustiness of our ELMGs. This will haveconsequences in Sect. 5. The amplitude of this underestimationis not quantifiable as these sources are not resolved in the far-IR.It is however di ffi cult to imagine that there would still be 99 %of gas not associated with IR emission within our aperture. In-deed, for the most extreme case, I Zw 18, our aperture is only1.5 times the optical radius (Rémy-Ruyer et al. 2013), whichshould be comparable to the IR radius. The overall rising DTMwith 12 + log(O / H) of Fig. 10 is therefore unlikely due to animproper correction of the H i envelopes of ELMGs. Variation of the Grain Opacities.
We have noted in Sect. 3.1.3that our dust mass estimates depend on the rather arbitrary grainopacity we have adopted. This grain opacity has been designedto account for the emission, extinction and depletions of the dif-fuse Galactic ISM ( cf.
Sect. 3.1.1). A systematic variation of theoverall grain opacity with metallicity could change the slope ofthe trend in Fig. 10. In order to move I Zw 18 up to the GalacticDTM, we would need to adopt a grain emissivity diminished byabout two orders of magnitude . Qualitatively, the ISM of anELMG, such as I Zw 18, is ( e.g. Cormier et al. 2019): (i) per-meated by hard UV photons; (ii) very clumpy with a low cloudfilling factor. With more UV photons to evaporate the mantlesand less clouds to grow them back, we could assume that thegrains in such a system would be reduced to their cores ( cf.
Fig-ure 16 of Jones et al. 2013). Demantled, crystalline, compactgrains are indeed among the least emissive grains. However, toour knowledge, there are no interstellar dust analogs having afar-IR opacity two orders of magnitude lower than those usedin the
THEMIS model. The Draine & Li (2007) mixture, whichresembles compact bare grains, is only a factor of (cid:39)
THEMIS ( e.g. Figure 4 of Galliano et al. 2018). Wecould also imagine that the composition of the dust mixture itselfchanges. In particular, the fraction of silicates could be higherin ELMGs, as C / O and O / H are correlated (Garnett et al. 1995).This would have a limited e ff ect, since: (i) a decrease of the largea-C(:H) abundance by 50 % would decrease the global emissiv-ity of THEMIS in the SPIRE bands by 15 −
30 %; (ii) a variation For I Zw 18, CR (DTM) = [2 . × − , . × − ], while DTM (cid:12) (cid:39) . of the forsterite-to-enstatite ratio would change the emissivity byless than 30 %. It is therefore very unlikely that the dependenceof DTM with metallicity is artificially induced by our grain opac-ity assumption. Variation of the Size Distribution.
Another factor that coulda ff ect the trend of Fig. 10 is that we have fixed the size dis-tribution of the large grains. In principle, relaxing this assump-tion and allowing the size distribution to be dominated by VerySmall Grains (VSG) in low-metallicity sources, would raise theDTM of objects such as I Zw 18. Indeed, VSGs are stochas-tically heated. They spend most of their time at very low tem-peratures between successive photon absorptions. Their excur-sion at T (cid:38)
20 K will span only a fraction of their time. Amixture of VSGs would thus appear less emissive than a largergrain at an equilibrium temperature close to the high end oftheir temperature distribution. We have demonstrated this e ff ectin Fig. 11. We have simulated a VSG-dominated SED mimick-ing a typical ELMG, peaking around λ (cid:39) µ m, and with veryweak aromatic feature emission (Fig. 11; panel b ; blue curve).The size distribution needed to produce such a SED is made al-most exclusively of a (cid:39) . a ;blue curve). We have fit this synthetic SED with our reference model (Sect. 3.1.2), keeping the large grain size distributionfixed (Fig. 11; panel a ; red curve), but varying the ISRF distri-bution. This model reproduces very well the photometric fluxes(Fig. 11; panel b ; red circles), but requires a total dust mass a fac-tor of (cid:39) ff ect goes in the rightdirection but is not enough to explain the 2 orders of magnituderequired to account for a constant DTM in Fig. 10. We couldfurther decrease the emissivity of the VSG model by loweringthe size of the grains. However, it would result in a SED peakingshortward λ (cid:39) µ m, inconsistent with our observations. Fi-nally, VSG-dominated ELMGs would not be in agreement withtheoretical dust size distribution evolution models ( e.g. Houet al. 2017; Hirashita & Aoyama 2019; Aoyama et al. 2020).At early stages, these models predict the ISM being populatedof large grains. The reason is that the dust production at thesestages is thought to be dominated by SN- ii -condensed dust, andgrains condensed in core-collapse SN ejecta are essentially largeas the small ones are kinetically sputtered ( e.g. Nozawa et al.2006).
Very Cold Dust.
A significant fraction of the dust mass couldhave been overlooked, hidden in the form of very cold dust( T dust (cid:46)
10 K). The emission of this component would man-ifest as a weakly emissive continuum at submm wavelengths,that we have not accounted for. Very cold dust has been invokedto explain the submm excess in dwarf galaxies ( cf.
Sect. 3.1.3).It could thus be invoked to flatten our dust-to-metal mass ratiotrend, in principle. However, while the excess has been reportedby numerous studies, predominantly in dwarf galaxies ( e.g.
Gal-liano et al. 2003, 2005; Dumke et al. 2004; Bendo et al. 2006;Galametz et al. 2009; Bot et al. 2010), very cold dust does notappear as one of its viable explanations. Indeed, to reach such alow temperature, very cold dust should be shielded from the gen-eral ISRF in massive dense clumps. In the LMC, Galliano et al.(2011) showed that the excess emission at 10 pc scale was di ff useand negatively correlated with the gas surface density, inconsis-tent with the picture of a few dense clumps. Similarly, Galametzet al. (2014) and Hunt et al. (2015) showed that this excess wasmore prominent in the outskirts of late-type disk galaxies, wherethe medium is less dense. In addition, other realistic physical Article number, page 19 of 64 & A proofs: manuscript no. manuscript
Fig. 11.
Demonstration of a VSG-dominated SED.
Panel (a) shows thesize distribution of the two models we are comparing here: the reference model in red, which is simply the
THEMIS model, with the small grainsscaled down to mimic the SED of a typical ELMG; and a VSG model,in blue, which is a log-normal size distribution, peaking at 1 . .
2. The optical properties of the VSG model are thoseof
THEMIS , and we have kept the same silicate-to-carbon grain mass ra-tio. In both cases, the curves represent the size distributions of a-C(:H)and silicates. Panel (b) shows the corresponding SEDs for the two mod-els. The SED of the reference model has been scaled down by a factorof 0 .
30, to fit the VSG SED. It means the VSG SED reproduces thereference model with a dust mass 3 .
33 times higher. The VSG SED isuniformly illuminated by an ISRF with U =
10, while the reference model has a distribution of ISRFs with (cid:104) U (cid:105) = processes to explain this excess have been proposed (Meny et al.2007; Draine & Hensley 2012). Dust analogs also exhibit a flat-ter submm slope that could partly account for this excess (De-myk et al. 2017a). More qualitatively, it is di ffi cult to conceiveof the presence of massive dense clumps in ELMGs, where thedust-poor ISM is permeated by intense UV photons from theyoung stellar populations that are forming. In addition, this dustwould likely be associated with dense gas that we have not ac-counted for, limiting its impact on the estimated dustiness. Systematic Uncertainty on the ELMG’s DTM.
Overall, it ap-pears that none of our model assumptions could be demonstratedto be responsible for artificially inducing the observed variationof the DTM. The trend of Fig. 10, for nearby galaxies, is there-fore likely real. It is however possible that the dustiness of theELMGs has been underestimated. We can quote a rough system-atic uncertainty for an object such as I Zw 18, the followingway. – Since the H i aperture is a factor of (cid:39) . Z dust might be underestimated by a factor at most (cid:39) . = . – We have discussed that the grain opacity could have beenoverestimated by a factor of (cid:39)
2. The systematic uncertaintyon Z dust is thus at most a factor of (cid:39) – We have discussed that our grain size distribution assumptioncould lead to an underestimate of Z dust by a factor of at most (cid:39) (cid:39) √ . + + = . We now focus our discussion on another important dust param-eter, the mass fraction of aromatic feature emitting grains, q AF (Sect. 3.1.1). Note that, in the THEMIS model, all grains are ei-ther pure a-C(:H) or a-C(:H)-coated. All of them therefore po-tentially carry aromatic features. However, only the smallestones ( a (cid:46)
10 nm) will fluctuate to high enough temperatures( T (cid:38)
300 K) to emit these features. Finally, we remind the readerthat, assuming aromatic features are carried by PAHs, q AF is for-mally equivalent to (cid:39) . × q PAH (Sect. 3.1.1).
The strong spatial variability of the aromatic feature strengthhas been known for several decades. Dramatic variations havebeen observed within Galactic and Magellanic H ii regions ( e.g. Boulanger et al. 1998; Madden et al. 2006; Galametz et al. 2013),as well as among nearby galaxies ( e.g.
Galliano et al. 2003, 2005;Engelbracht et al. 2005; Madden et al. 2006). The following sce-narios have been proposed.
Photodestruction.
The aromatic feature strength appears tobe negatively correlated with the presence of intense / hardUV fields. For instance, Boulanger et al. (1998) showedthat their strength in Galactic PDRs is decreasing when theintensity of the ISRF is increasing. Madden et al. (2006)showed that their strength, within Galactic and Magellanic re-gions and within nearby galaxies, is negatively correlated with[Ne iii ] . µ m / [Ne ii ] . µ m , an ISRF hardness indicator. Numer-ous studies confirmed these trends, showing the depletion of aro- Article number, page 20 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution matic features around massive stars, as a result of the photodisso-ciation and photosublimation of small a-C(:H). At the same time,it was also shown that the aromatic feature strength is empiri-cally correlated with metallicity. This is clear in nearby galaxies,as a whole ( e.g.
Engelbracht et al. 2005; Madden et al. 2006), aswell as within extragalactic H ii regions ( e.g. Gordon et al. 2008;Khramtsova et al. 2013). This correlation is not inconsistent withphotodestruction, as most low-metallicity galaxies detected at IRwavelengths to date are actively forming stars. Their ISM, lessopaque due to a lower Z dust , is permeated by an intense UV field,potentially destroying small a-C(:H) on wider scales. It is alsoconsistent with the increasing strength of the 2175 Å bump withmetallicity, comparing sightlines in the Small Magellanic Cloud (SMC), LMC and Milky Way ( e.g.
Gordon et al. 2003). Theextinction bump is indeed thought to be carried by small carbongrains with aromatic bonds (Joblin et al. 1992).
Inhibited formation.
Alternatively, several studies have ex-plored the possibility that small a-C(:H) are less e ffi cientlyformed at low-metallicity. Galliano et al. (2008a) showed that,assuming small a-C(:H) are formed from the carbon producedby AGB stars (on timescales of (cid:39)
400 Myr) and the rest of thegrains are mostly made out of the elements produced by massivestars (on timescales of (cid:39)
10 Myr), the aromatic feature emittersare under-abundant at early stages of galaxy evolution. Anotherscenario, developed by Seok et al. (2014), reproduces the trendof aromatic feature strength with metallicity, assuming small a-C(:H) are the product of the shattering of larger carbon grains(see also Rau et al. 2019; Hirashita & Murga 2020). Finally,Greenberg et al. (2000) have proposed that aromatic feature car-riers could form on grain surfaces in molecular clouds and bephotoprocessed in the di ff use ISM. Sandstrom et al. (2010) andChastenet et al. (2019) show that the spatial distribution of q PAH in the Magellanic clouds is consistent with this scenario. Thisprocess would also explain the fact that these grains are under-abundant in ELMGs, as the molecular gas fraction rises withmetallicity.
The di ff erent processes we have just listed are not exclusive andcould very well compete within the ISM. It is however importantto understand which one controls the overall abundance of smalla-C(:H), at galaxy-wide scales.Fig. 12 shows q AF as a function of the average starlight in-tensity, (cid:104) U (cid:105) (Sect. 3.1.2), and metallicity, in our sample. Sim-ilar relations were previously shown by Draine et al. (2007),Galliano et al. (2008a), Khramtsova et al. (2013) and Rémy-Ruyer et al. (2015). The two SUEs at high (cid:104) U (cid:105) (panel a ) areI Zw 18 and SBS 0335-052. Their SEDs indeed peaks around30 µ m. However, their q AF appear higher than the extrapola-tion of the general trend, with CR ( q AF ) = [0 . , . ( q AF ) = [0 . , . Spitzer -IRS spectroscopy did not detect aromatic fea-tures in these galaxies (Wu et al. 2007; Houck et al. 2004). Thetrue value of q AF is likely lower for these two objects. The reasonof this overestimation lies in the di ffi culty to estimate aromaticfeature strengths solely with broadband fluxes, when the feature-to-continuum ratio is weak. Indeed, in the weak aromatic featureregime, q AF is biased by the color of the mid-IR continuum ( cf. Figure 1 of Galliano et al. 2008a).Overall, we find clear correlations in both panels of Fig. 12,consistent with past studies. However, the relation appears more scattered with (cid:104) U (cid:105) , than with 12 + log(O / H). The correlation co-e ffi cient of panel (a) is only ρ = − . + . − . with CR ( ρ ) = [ − . , − . ρ = . + . − . with CR ( ρ ) = [0 . , .
79] for panel (b) . We could argue that panel (b) of Fig. 12contains only the 376 sources with metallicity measurements(Table 2), while panel (a) contains the 798 sources with pho-tometric fluxes, including very noisy ETG SEDs. If we consideronly the subsample of panel (a) with metallicity measurements,the correlation coe ffi cient does not significantly improve: ρ = − . + . − . with CR ( ρ ) = [ − . , − . ffi cients do not change much: ρ = − . + . − . withCR ( ρ ) = [ − . , − .
35] for panel (a) and ρ = . + . − . with CR ( ρ ) = [0 . , .
80] for panel (b) .We could also question the accuracy of (cid:104) U (cid:105) as an ISRF tracer.Indeed, (cid:104) U (cid:105) is a mass-averaged ISRF intensity, giving a largeweight to the coldest regions within the beam. Rémy-Ruyer et al.(2015) and Nersesian et al. (2019) used sSFR, which is luminos-ity weighted, in place of (cid:104) U (cid:105) and found a good negative corre-lation with q PAH and q AF , respectively. In our sample, the cor-relation coe ffi cient between ln q AF and ln sSFR is not improved: ρ = − . + . − . with CR ( ρ ) = [ − . , − . q AF correlates much more robustlywith metallicity than ISRF indicators, in our sample. This resultis worth noting, especially since several studies focussing on anarrower metallicity range concluded the opposite ( e.g. Gordonet al. 2008; Wu et al. 2011). It probably relies on the fact themetallicities we have adopted (Sect. 2.2.2) correspond to well-sampled galaxy averages, while in the past a single metallicity,often central, was available and may have not been representa-tive of the entire galaxy. This result suggests that photodestruc-tion, although real at the scale of star-forming regions, mightnot be the dominant mechanism at galaxy-wide scales and thatone needs to invoke one of the inhibited formation processes dis-cussed in Sect. 4.2.1.
It can be interesting to have a simple analytical approximationdescribing how Z dust and q AF vary as a function of 12 + log(O / H).To that purpose, we have performed polynomial fits of the rela-tions in panel (d) of Fig. 8 and panel (b) of Fig. 12. These fits aredisplayed in Fig. 13.A 4 th degree polynomial fit of the dustiness-metallicity rela-tion gives, posing x = + log(O / H):log Z dust (cid:39) . − . x + . x − . x + . x . (8)This equation provides a good fit of our trend, for the metal-licity range covered by our sources. However, it gives a risingdustiness trend with decreasing metallicity below I Zw 18. Toimprove this relation, we can assume that the dustiness will beproportional to 12 + log(O / H) at extremelly low-metallicity, aswe will show in Sect. 5.3 that dust evolution in this regime isdominated by SN ii production. We therefore modify Eq. (8), as:log Z dust (cid:39) − . + x for x < . . (9)This fit splits our data in two equal size samples above and be-low. To quantify its uncertainty, we can compute the envelopescorresponding to encompassing 68 % and 95 % of the sources,adding [ − . , + .
29] and [ − . , + .
70] respectively to the fitof log Z dust . Article number, page 21 of 64 & A proofs: manuscript no. manuscript
Fig. 12.
Evolution of small a-C(:H) grains.
The SUEs are color-coded according to the type of galaxy ( cf.
Sect. 3.3). The Milky Way is shown asa yellow star. There are fewer objects with metallicity measurements (376; Table 2), especially among ETGs (panel b ). In the case of q AF , a 1 st degree polynomial gives a satisfac-tory fit as a function of 12 + log(O / H):log q AF (cid:39) − . + . x . (10)Its 68 % and 95 % envelopes are obtained adding [ − . , + . − . , + .
5. EMPIRICAL QUANTIFICATION OF KEY DUSTEVOLUTION PROCESSES
We now analyze the trends of Fig. 8, in a more quantitative way,with the help of a grain evolution model. The goal here is two-fold: (i) by fitting theoretical tracks to our sample, we intend totest if it is possible to account for the variation of the main galaxyparameters, with only a few evolutionary processes; (ii) we aimto give a self-consistent empirical quantification of the main adhoc tuning parameters controlling these evolutionary processes.
Cosmic dust evolution models compute the variation of the dustcontent of a galaxy as a function of time. Dwek & Scalo(1980) presented the first model of this kind, developed as anextension of models computing the elemental enrichment of theISM (Audouze & Tinsley 1976, for an early review). Subse-quent attempts, with various degrees of complexity, followed( e.g. Dwek 1998; Lisenfeld & Ferrara 1998; Hirashita 1999;Morgan & Edmunds 2003; Inoue 2003; Dwek et al. 2007; Gal-liano et al. 2008a; Calura et al. 2008; Valiante et al. 2009; Matts-son & Andersen 2012; Asano et al. 2013; Zhukovska 2014; Feld-mann 2015; De Looze et al. 2020; Nanni et al. 2020). Recently, they can also eventually compute the variation of the grain size dis-tribution and composition with time ( e.g. Hirashita et al. 2015). such models have been used to post-process numerical simula-tions in order to provide a more comprehensive understanding ofgalaxy evolution ( e.g.
Aoyama et al. 2017).
We adopt the one-zone dust evolution model of Rowlands et al.(2014) updated by De Vis et al. (2017b) . It solves the coupleddi ff erential equations accounting for the time evolution of themass of the four following quantities. Stars are made out of the gas, which is partially returned to theISM at the end of their lifetime. The model tracks their evo-lution as a function of their mass, which determines theirlifetime and their elemental and dust yields. The role of thiscomponent therefore relies greatly on the form of the as-sumed IMF ( e.g.
Salpeter 1955; Chabrier 2003).
Gas is depleted by astration and outflow, and is replenished bystellar feedback and by inflow of metal- and dust-free gas.
Heavy elements are injected in the ISM by stars at the endof their lifetime. A fraction of them is recycled into starsthrough astration and lost via outflow.
Dust is produced by three main processes: (i) condensa-tion in
Low- and Intemediate-Mass Star (LIMS) ejecta( m (cid:63) < (cid:12) ) ; (ii) condensation in SN ii ejecta( m (cid:63) ≥ (cid:12) ); (iii) grain growth in the ISM, by accretion We started from the public Python code provided by the authors athttps: // github.com / zemogle / chemevol. We have rewritten it in Fortranfor numerical e ffi ciency, since we needed to generate large grids of mod-els. We have also implemented an adaptative temporal grid to ensurenumerical precision at later stages of evolution. following De Vis et al. (2017b), we assume that LIMSs condense15 % of their heavy elements into dust.Article number, page 22 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution Fig. 13.
Analytical fit of the scaling relations.
The red SUEs show thedata of panel (d) of Fig. 8 and panel (b) of Fig. 12. The blue curve inpanel (a) shows the analytical fit of Eq. (8) modified by Eq. (9). The bluecurve in panel (b) shows the analytical fit of Eq. (10). In both panels, thedashed lines display the envelope encompassing 68 % of the sources,and the dotted lines, the envelope encompassing 95 % of the sources.We show here the decimal logarithm of the Z dust and q AF . of elements onto grain seeds. Dust is removed from the ISMby: (i) destruction by SN ii blast waves; (ii) outflow; (iii) as-tration.The drivers of the evolution of these quantities are: (i) the as-sumed SFH ( i.e. the SFR as a function of time); (ii) the assumedinflow and outflow rates. The e ffi ciencies of individual dust evolution processes arepoorly known (see reviews by Dwek 2005; Draine 2009; Jones2016a,b,c; Galliano et al. 2018). From a theoretical point ofview, these e ffi ciencies depend on the most elusive detailed mi-croscopic dust properties: chemical constitution, structure (crys-talline, amorphous, aggregate, etc. ) and size. Consequently, the-oretical estimates usually span several orders of magnitude.From an observational point of view, unambiguous constraints of the evolution rates are also problematic, because it is nearlyimpossible to isolate a dust source or sink in a telescope beam.Dust evolution models therefore use simple parametric e ffi cien-cies controlled by tuning parameters. Dust condensation in SN-II ejecta.
Dust formed by massivestars ( m (cid:63) ≥ (cid:12) ) is thought to dominate the dust production atearly stages, below the critical metallicity ( cf. Sect. 4.1.3). Thedust evolution model we are using assumes the theoretical dustyields, m SNdust , of Todini & Ferrara (2001), modified by a generaltuning parameter, δ SN (Table 5). These dust yields can also beintegrated over the IMF, φ ( m (cid:63) ): (cid:104) Y SN (cid:105) ≡ (cid:90)
40 M (cid:12) (cid:12) φ ( m (cid:63) ) × m SNdust ( m (cid:63) ) d m (cid:63) (cid:90)
40 M (cid:12) (cid:12) φ ( m (cid:63) ) d m (cid:63) , (11)to provide a single averaged dust yield per SN ii . For bothSalpeter (1955) and Chabrier (2003) IMFs, it is: (cid:104) Y SN (cid:105) (cid:39) . × δ SN M (cid:12) / SN. The dust condensation timescale, τ cond , can be ex-pressed as a function of the SN ii rate, R SN :1 τ cond ( t ) = (cid:104) Y SN (cid:105) R SN ( t ) M dust ( t ) . (12) Table 5.
SN II dust yields.
These values are the Todini & Ferrara (2001)yields, compiled by Rowlands et al. (2014). They are multiplied by thetuning parameter δ SN , used by De Vis et al. (2017b). Individual star mass, m (cid:63) Dust yield, m SNdust . (cid:12) (cid:12) × δ SN (cid:12) .
17 M (cid:12) × δ SN
12 M (cid:12) . (cid:12) × δ SN
15 M (cid:12) . (cid:12) × δ SN
20 M (cid:12) . (cid:12) × δ SN
22 M (cid:12) . (cid:12) × δ SN
25 M (cid:12) . (cid:12) × δ SN
30 M (cid:12) . (cid:12) × δ SN
35 M (cid:12) . (cid:12) × δ SN
40 M (cid:12) . (cid:12) × δ SN Grain growth in the ISM.
The dust build-up by accretion ofgas atoms onto pre-existing dust seeds is a potentially dominantproduction process at late stages, above the critical metallicity (Sect. 4.1.3). We adopt the parametrization of Mattsson et al.(2012), where the grain growth timescale, τ grow , is parametrizedby a tuning parameter, (cid:15) grow :1 τ grow ( t ) = (cid:15) grow ψ ( t ) M gas ( t ) ( Z ( t ) − Z dust ( t )) , (13)where ψ ( t ) is the SFR as a function of time t . This tuning pa-rameter encompasses our uncertainty about grain sizes, stickingcoe ffi cients and the fraction of cold clouds where dust growthoccurs . We did not implement the parameter f c , the fraction of cold clouds,introduced by De Vis et al. (2017b), as its e ff ect can be encompassed in (cid:15) grow and m destgas (Eq. 14). Article number, page 23 of 64 & A proofs: manuscript no. manuscript
Dust destruction by SN II blast waves. SN ii shock waves de-stroy dust by kinetic sputtering and grain-grain collisional va-porization ( e.g. Jones et al. 1994). We adopt the dust destructiontimescale, τ dest , of Dwek & Scalo (1980):1 τ dest ( t ) = m destgas R SN ( t ) M gas ( t ) , (14)where m destgas is a tuning parameter quantifying the e ff ective massof ISM swept by a single SN ii blast wave within which all thegrains are destroyed. We use the dust evolution model of Sect. 5.1 to fit, for eachgalaxy: M dust , M gas , M (cid:63) , SFR and Z . Dust destruction in X-rayemitting gas is not taken into account in this model. We there-fore exclude the ETGs ( T ≤
0) which would not be consistentlyfitted ( cf.
Sect. 4.1.2). The sample we model here contains 556sources.
We have generated a large grid of models that we interpolate tofind the best evolution tracks for each of our sources. We assumea delayed
SFH (Lee et al. 2010): ψ ( t ) = ψ t τ SFH exp (cid:32) − t τ SFH (cid:33) , (15)parametrized by the SFH timescale, τ SFH , and a scaling factor, ψ . We assume a Salpeter (1955) IMF in order to be consistentwith the observed SFR and stellar mass estimates (Sect. 2.2).Exchanges of matter between galaxies and their environmentcan have a significant role in regulating the global dustinessat all redshifts ( e.g. Jones et al. 2018; Ohyama et al. 2019;Sanders et al. 2020; Burgarella et al. 2020). We account for in-flow and outflow, assuming their rates are proportional to SFR: R in / out ( t ) = δ in / out × ψ ( t ). Table 6 gives the parameters of our dustevolution model grid. We perform log-log interpolation of thisgrid in order to estimate the tracks corresponding to any arbi-trary combination of parameters.The SFH we have adopted here, to compute the chemicalevolution, is di ff erent from the SFH used by Nersesian et al.(2019) to model the SEDs and estimate the observed SFR and M (cid:63) ( cf. Sect. 2.2.1). Ideally, adopting the same SFH would bemore consistent. However, adding a second functional form toEq. (15), accounting for a potential recent burst, would pushthis model beyond our current computational capabilities, by in-creasing the number of free parameters. At the same time, theelemental and dust enrichment by this recent burst would prob-ably be negligible. Alternatively, we could have also modelledthe SED, using solely Eq. (15). The problem, in this case, is thatthe use of a single stellar population biases the estimate of M (cid:63) ( cf. Appendix B.2).
To constrain our dust evolution model, we consider the posteriorinference of our reference run (Sect. 3.2) as a set of observa-tional constraints. We fit the four independent, intensive quanti-ties: s M dust , s M gas , sSFR and Z . The complex PDF, including theintricate parameter correlations, is preserved in this process. Wemake the restrictive assumption that the three tuning parameters, Table 6.
Dust evolution parameter grid.
Individual galaxy parameters control the particular SFH of each galaxy.
Common dust evolution pa-rameters are fitted to the whole sample, assuming their values are thesame for each galaxy. The grid step (4 th column) is logarithmic forall parameters except the time grid. The SFR scale is normalized tothe total initial mass of the galaxy, M . All extensive quantities com-puted by the model are proportional to M , while intensive quantitiesare independent of M . In practice, we generate a grid for an arbitrary M = × M (cid:12) . This parameter cancels out in the process, as we arefitting ratios (Sect. 5.2.2). Parameter Notation Range StepIndividual galaxy parametersAge [Gyr] t [0 . ,
15] 0.15SF timescale [Gyr] τ SFH [0 . ,
30] 0.57 (ln)SFR scale [Gyr − ] ψ / M [0 . , .
5] 0.26 (ln)Inflow rate / SFR δ in [0 . ,
4] 0.37 (ln)Outflow rate / SFR δ out [0 . ,
4] 0.13 (ln)Common dust evolution parametersSN condensation δ SN [0 . ,
1] 0.37 (ln)Grain growth (cid:15) grow [100 , (cid:12) ] m destgas [50 , δ SN , (cid:15) grow and m destgas are universal and are therefore identical inevery galaxy. Consequently, we assume that the di ff erence be-tween galaxies is solely the result of their particular individualSFH. We vary the age of the galaxy, t , the two SFH parameters, τ SFH and ψ , and the inflow and outflow rates, δ in and δ out . On the universality of the tuning parameters.
As we haveseen, the three tuning parameters hide e ff ects of the dust con-stitution, size distribution, fraction of cold clouds, etc. Thesequantities could vary across di ff erent environments. However, aswe will show in Sect. 5.3.1, the SN II dust condensation domi-nates in the low-metallicity regime, while grain growth and SNdestruction are important above the critical metallicity. Thus, theparameters that we will constrain are representative of the regimewhere they dominate the dust budget. Exploring their variationwith the environment is probably premature. We will however beable to infer the variation of the timescales across galaxies, fromEqs. (11) – (14). In addition, if we were to infer one set of tuningparameters per galaxy, it would imply that they vary as a func-tion of the galaxy’s global parameters. In order to be consistent,we would then need to implement these variations of the tuningparameters in the dust evolution model, and change their valueat each time step, accordingly. The model prior.
We have built a HB model to infer theseparameters. The prior of the five SFH-related parameters is amultivariate Student’s t distribution controlled by hyperparam-eters, similar to the treatment in HerBIE . We have assumedwide log-normal priors for the three common tuning parame-ters. These priors are centered at ln 0 .
1, ln 1000 and ln 320 M (cid:12) with standard-deviations, 0 .
8, 0 . .
4, for δ SN , (cid:15) grow and m destgas , respectively. These priors were designed so that their ± σ range roughly corresponds to the extent of the values reportedin the literature: 1 % (cid:46) δ SN (cid:46)
100 %, 100 (cid:46) (cid:15) grow (cid:46) and 100 M (cid:12) (cid:46) m destgas (cid:46) (cid:12) . It does not mean that theseparameters can not exceed these limits, but it will be a pri-ori improbable. The reason to adopt weakly informative pri-ors is to avoid unrealistic degeneracies. For instance, there isa well-known degeneracy between grain growth and grain de- Article number, page 24 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution struction ( e.g.
Mattsson & Andersen 2012; De Vis et al. 2017b;De Looze et al. 2020). Indeed, the ratio of the two timescales, τ dest ( t ) /τ grow ( t ) ∝ (cid:15) grow / m destgas × ( Z ( t ) − Z dust ( t )) is not constant,but the metallicity dependence is quite mild in the narrow rangeabove the critical metallicity. This is enough to allow the MCMCto explore unrealistically high values of (cid:15) grow and m destgas , if we as-sume a flat prior. HB run specifications.
Accounting for the missing ancillarydata, we have a total of 1913 observational constraints, for our556 sources. One may note that we are fitting a model with5 × + = + + C =
20 hyper-parameters. This is not an issue in the Bayesian approach ( e.g.
Hogg et al. 2010). Model parameters are rarely completely inde-pendent. Furthermore, the hyperprior is the dominant constraintfor very scattered parameters (G18). Finally, by sampling thefull joint PDF, a Bayesian model clearly delineates the variousdegeneracies, provided the MCMC has converged towards thestationary posterior. We have run 12 parallel MCMCs, startingfrom uniformly distributed random initial conditions within theparameter ranges in Table 6, in order to ensure the uniqueness ofour posterior. The results discussed below are from a 10 lengthMCMC, removing the first 10 steps to account for burn-in. Thelongest integrated autocorrelation time is 6200. The four panels of Fig. 14 present the same relations as in Fig. 8,for the subsample of 556 sources. The posterior PDF of thedust evolution tracks is displayed as colored density contours,marginalizing over the SFH of individual galaxies.
Qualitative inspection.
At first glance, we can see that thetracks of Fig. 14 reproduce the data quite well. Apart from a fewoutliers, there are however two notable systematic discrepancies.1. The s M dust -sSFR trend of panel (c) is poorly reproduced. Theinitial rise of s M dust at sSFR (cid:38) . − undershoots sev-eral of the starbursting dwarf galaxies. Overall, this discrep-ancy is quite mild, as most of the SUEs in this area are lessthan 2 σ away from the trend. The recent burst of star for-mation, that is not accounted for by the chemical evolutionmodel, is likely responsible for the enhanced observed SFR.On the contrary, a starburst occuring in more evolved ob-jects, on the left of this trend, might simply contribute tothe general scatter of the relation and go unnoticed. BelowsSFR (cid:46) . − , there is a general decreasing trend ofs M dust with decreasing sSFR, but our model is essentiallyflat. This is the most troublesome discrepancy of our analy-sis. We will discuss it fully below.2. In panel (a) , several high-gas-fraction sources are undershotby the model, although most of them are only less than 2 σ away from the tracks. Those are the irregular galaxies aroundthe critical metallicity regime. They are in the stage wherethe dustiness changes rapidly, due to the increased contribu-tion of grain growth. These outliers can be seen in panel (b) ,around s M gas (cid:39)
10, in panel (c) , around sSFR (cid:39) − ,and in panel (d) , around 12 + log(O / H) (cid:39)
8. The model poorlyreproduces the rapid dustiness rise around the critical metal-licity, in panel (d) . On the s M dust -sSFR relation. The quasi-linear trend of s M dust with sSFR, for sSFR (cid:46) . − (panel (c) of Fig. 14), is not accounted for by our model. N20 argue that outflows is respon-sible for this trend . Indeed, outflow depletes the dust contentproportionally to SFR, without a ff ecting the stellar content. Itseems like a natural explanation. The outflow rate, δ out , is a freeparameter in our model. However, it does not produce a linears M dust -sSFR relation. Fig. 15 shows the same data as in panel (c) of Fig. 14. We have overlaid several dust evolution tracks corre-sponding to our maximum a posteriori parameters, varying δ out .This figure is similar to Fig. 6 of N20. We note the following.1. We can see that no single track can reproduce the trend. Itcould be a satisfactory explanation if galaxies were rapidlyevolving o ff the main trend, staying only a small fractionof their lifetime on the horizontal branch. However, look-ing at the top axis of Fig. 15, we realize that a galaxy shouldspend about half of its lifetime on the horizontal branch. Ifour model was correct, there should have been, statistically, asignificant number of sources deviating from the main trend.2. The range of δ out values that can account for most of the trendis quite narrow (Fig. 15). It would mean that the outflow hasto be precisely regulated. It seems unlikely.3. If this trend was solely due to outflow, the specific gas masswould follow it closely, which is not the case. This point hasalso been discussed by Cortese et al. (2012).In summary, it appears our failure at reproducing the s M dust -sSFR relation is rather an incapacity of our model to producea realistic trend, rather than a fitting issue. As we will see inSect. 5.3.3, this is not an IMF-related issue. Since the othertrends are acceptably reproduced, the problem might lie in theonly quantity represented in panel (c) of Fig. 14 not appearing inthe other panels: the SFR. Our adopted SFH (Eq. 15) and our in-flow and outflow prescriptions might be too simplistic to accountfor the wealth of data we have here ( cf. e.g. Leja et al. 2019, fora discussion on the limitations of the delayed SFH).
The importance of fitting dust evolution models.
We stress theimportance of actually fitting, in a consistent way, dust evolu-tion models, rather than simply performing visual comparisons.Here, we have attempted to fit M (cid:63) , M gas , M dust , Z and SFR foreach galaxy. This rigorous process highlights the model limi-tations. Most past studies have merely overlaid tracks on theirdata, producing a convincing but inconsistent interpretation. Forinstance, De Vis et al. (2017b), who used the same dust evolu-tion model as we use, and compared it to a similar sample asours, were able to produce tracks accounting for most of the ob-servations in the panels (a) and (d) of our Fig. 14. However, twoquantities of a given galaxy, such as the dust and stellar masses,were usually explained with di ff erent values of the dust evolu-tion parameters, at di ff erent ages. On the contrary, our approachallows us to avoid mutually inconsistent explanations of di ff erenttrends and correlations. Overall, performing a rigorous fit doesnot help getting better solutions, but it definitely helps avoidingbad ones. We now discuss the parameters inferred from the fit ofSect. 5.2.3. We note that N20 do not have sources below s M dust (cid:46) − , while itis where our fit gets the most problematic.Article number, page 25 of 64 & A proofs: manuscript no. manuscript
Fig. 14.
Fitted dust evolution tracks, assuming a Salpeter (1955) IMF. The four panels represent the same quantities as Fig. 8. The black SUEsrepresent the 556 galaxies of our subsample. The yellow star is the Milky Way. The colored density contours represent the posterior PDF of dustevolution tracks, marginalizing over the individual SFH of each galaxy.
The fits of Fig. 14 allow us to infer the common dust evolutiontuning parameters, as well as the individual SFH-related param-eters (Table 6).
The dust evolution tuning parameters.
The PDF of thethree common dust evolution tuning parameters is displayed inFig. 16. We infer the following values: – (cid:104) Y SN (cid:105) (cid:39) . + . − . × − M (cid:12) / SN; – (cid:15) grow (cid:39) − ; – m destgas (cid:39) + − M (cid:12) / SN.
Article number, page 26 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Fig. 15. E ff ect of outflow on the s M dust -sSFR relation. The data isidentical to panel (c) of Fig. 14. The colored lines represent our dustevolution model. We have fixed all the parameters close to their maxi-mum a posterior values, except the outflow rate, δ out : τ SFH = . ψ =
40 M (cid:12) / yr, δ in = . δ SN = . (cid:15) grow = m destgas = (cid:12) / SN. The di ff erent lines correspond to di ff erent values of δ out .The top axis displays the age of the galaxy corresponding to the partic-ular SFH of the model run. We have used a Salpeter (1955) IMF. The relatively small uncertainties on these parameters reflectthe fitting uncertainties. They indicate the values we infer arenot ambiguous. However, they do not include the assumption-dependent uncertainties. In particular, the precise value of (cid:104) Y SN (cid:105) relies mainly on our estimate of the dustiness of the few ELMGsin our sample. In Sect. 4.1.3, we have extensively discussed thedi ff erent systematic e ff ects that could have biased these esti-mates. If some of these e ff ects are, at some point, proven to berelevant, our inference of (cid:104) Y SN (cid:105) would have to be revised ac-cordingly. To first order, the SN dust yield is proportional to thedustiness of the lowest metallicity objects: (cid:104) Y SN (cid:105) (cid:39) .
007 M (cid:12) / SN × Z dust (I Zw 18)1 . × − . (16)We also notice that δ SN and m destgas are peaking at the tail of theirprior. It means our data carries a large weight evidence. It alsomeans the values we infer are probably an upper limit for δ SN and a lower limit for m destgas . Since m destgas and (cid:15) grow are correlated,our inference of (cid:15) grow is also probably a lower limit. We haveestimated in Sect. 4.1.3 that the dustiness of ELMGs could havebeen underestimated by a factor of at most (cid:39) .
25, the conserva-tive conclusions we can draw from our analysis are thus that: – (cid:104) Y SN (cid:105) (cid:46) .
03 M (cid:12) / SN; – (cid:15) grow (cid:38) – m destgas (cid:38) (cid:12) / SN.
The SFH-related parameters.
Fig. 17 displays the corner plotof the five parameters controlling the individual SFH of each
Fig. 16.
Posterior distribution of the tuning parameters, assuming aSalpeter (1955) IMF. The three central panels with colored contours dis-play the bidimensional posterior PDF of pairs of parameters, marginal-izing over all the other ones. The three margin plots show the poste-rior PDF of each tuning parameter. The PDFs are scaled (divided bytheir maximum). The displayed ranges encompass every single param-eter draw after burn-in. galaxy. The displayed PDF is the posterior of the parameters ofevery galaxy. There is a relatively large scatter of these param-eters, implying that our di ff erent galaxies have di ff erent SFHs.Note that the interpolation between models does not produce aperfectly smooth distribution. The edges of our model grid arevisible in this corner plot. This does not however impact the re-sults as our grid samples well enough the PDF. It is possible to estimate the posterior PDF of the dust evolu-tion timescales of each galaxy, from the inferred parameters ofFigs. 16 – 17, using Eqs. (11) – (14). Fig. 18 displays thesetimescales as a function of metallicity. Although there is somescatter due to the di ff erent SFH and age of galaxies in a givenmetallicity bin, we note that these timescales evolve. The SN II dust condensation timescale (panel (a) of Fig. 18)is around τ cond (cid:39)
100 Myr for ELMGs, implying that dustcan be dominated by stardust in this regime. It rises up to τ cond (cid:39) ffi cient to account for all ISM dust in evolvedsystems. The grain growth timescale (panel (b) of Fig. 18) is quite scat-tered. It starts around τ grow (cid:39) τ grow (cid:39)
50 Myr around solar metallicity.The average value of our sample at 12 + log(O / H) ≥ . τ grow (cid:39)
45 Myr. It is another way to show that dust formationis dominated by grain growth around solar metallicity.
The SN II dust destruction timescale (panel (c) of Fig. 18) isalso scattered but stays around τ dest (cid:39)
300 Myr across ourmetallicity range.
Article number, page 27 of 64 & A proofs: manuscript no. manuscript
Fig. 17.
Posterior distribution of the SFH-related parameters.
The plotting conventions are identical to Fig. 16. The displayed PDF is the distributionof the individual parameters of every galaxy, marginalizing over the dust evolution tuning parameters.
The Milky Way value displayed in the three panels is consistentwith the cloud of points in the highest metallicity domain.There is a common misconception that dust destruction bySN II blast waves is unimportant at early-stages, because thedustiness is so low that few grains are destroyed by a singleSN II. However, we show here that this is not the case as: (i) theSN II rate is on average higher at low-metallicity; (ii) the fractionof grains destroyed by a single SN II is dustiness-independent.
As we discussed in Sects. 2.2.3 – 2.2.4, the main uncertainty onour estimated M (cid:63) and SFR comes from our IMF assumptions.Those were derived with a Salpeter (1955) IMF. Here, we ex-plore the sensitivity of our results assuming a Chabrier (2003)IMF. To be consistent, we first need to correct our estimated M (cid:63) and SFR. According to Madau & Dickinson (2014, Sect. 3.1),we need to multiply SFR by 0.63 and M (cid:63) by 0.61. We havethen generated another grid of models similar to Table 6 withthe Chabrier (2003) IMF, and performed the fitting process of Article number, page 28 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Fig. 18.
Dust evolution timescales, assuming a Salpeter (1955) IMF.The three panels display the posterior PDF of the three dust evolutiontimescales. The SUEs represent the value of these timescales as a func-tion of metallicity, for each galaxy. The yellow star represents the MilkyWay, at the maximum a posteriori of the three tuning parameters.
Sect. 5.2.3. The full results are given in Appendix G. The upshotis that the inferred tuning parameters are roughly consistent withour estimates in Sect. 5.3.1: – (cid:104) Y SN (cid:105) (cid:39) . + . − . × − M (cid:12) / SN; – (cid:15) grow (cid:39) + − ; – m destgas (cid:39) + − M (cid:12) / SN.The di ff erences can be explained by the di ff erent relative con-tribution from LIMSs. The only value that di ff ers sensibly is (cid:104) Y SN (cid:105) . This di ff erence is however simply due to the fact the low-metallicity dustiness is overshot by the model with the Chabrier(2003) IMF.This agreement was expected. The reason is that, to first or-der, LIMSs represent a dead weight in both the SED and thechemical enrichment. The total power emitted by stellar popu-lations is dominated by massive stars. This is the reason whySFR and M (cid:63) estimates are so dependent on the IMF assump-tion. From the dust evolution modelling, the elemental and star-dust enrichment is also dominated by massive stars. The onlyquantity for which we infer a di ff erent value is logically ψ . Itis (cid:39)
50 % higher to generate the same number of massive stars,compensating for the 0.63 correction factor.
Our SN II dust yield is lower than the most recent estimates insitu . Measuring the dust mass produced by a single SN II is quitedi ffi cult, as it implies disentangling the freshly-formed dust fromthe surrounding ISM. It also carries the usual uncertainty aboutdust optical properties. A decade ago, the largest dust yield evermeasured was Y SN (cid:39) .
02 M (cid:12) (in SN 2003gd; Sugerman et al.2006). The
Herschel space telescope has been instrumental inestimating the cold mass of
SuperNova Remnants (SNR). Theyields of the three most well-studied SNRs are now an order ofmagnitude higher:
Cassiopeia A: Y SN (cid:39) . − . (cid:12) (Barlow et al. 2010; Arendtet al. 2014; De Looze et al. 2017; Bevan et al. 2017; Priestleyet al. 2019); The Crab nebula: Y SN (cid:39) . − .
23 M (cid:12) (Gomez et al. 2012;Temim & Dwek 2013; De Looze et al. 2019);
SN 1987A: Y SN (cid:39) . − . (cid:12) (Dwek & Arendt 2015; Mat-suura et al. 2015).In all these cases, the newly-formed grains have not yet experi-enced the reverse shock (Bocchio et al. 2016). The net yield isthus expected to be significantly lower.Even if (cid:39) −
20 % of the dust condensed in an SN II ejectasurvives its reverse shock ( e.g.
Nozawa et al. 2006; Micelottaet al. 2016; Bocchio et al. 2016), we have to also consider thefact that massive stars are born in clusters. The freshly-formeddust injected by a particular SN II, having survived the reverseshock, will thus be exposed to the forward shock waves of nearbySNe II ( e.g.
Martínez-González et al. 2018). This e ff ect is not ac-counted for by Eq. (14), as it does not account for clustering, nordoes it account for the excess dustiness around these stars due tothe recent grain production. Our estimate of (cid:104) Y SN (cid:105) is therefore ane ff ective empirical yield, that probably accounts for this e ff ect. Our analysis confirms the long-lasting consensus that Milky Waydust is essentially grown in the ISM (Sect. 1). The apparentlyparadoxical fact here is that we have drawn this conclusion fromthe low-metallicity domain. It is because dust production is dom-inated by SN II condensation below the critical metallicity thatwe could constrain its e ffi ciency and show it is unimportant at so-lar metallicity. The relevance of dwarf galaxies here is not neces-sarily that they can be considered as analogs of primordial distantgalaxies, but that they sample a particular, key, dust productionregime. Article number, page 29 of 64 & A proofs: manuscript no. manuscript
High-redshift ( z (cid:38)
6) objects exhibiting copious amounts ofdust ( (cid:39) − M (cid:12) ), close to the reionization era, have beenchallenging grain formation scenarios ( e.g. Dwek et al. 2007;Valiante et al. 2009; Dwek et al. 2014; Laporte et al. 2017).These objects are indeed only a few 100 Myr old, but have aroughly Galactic dustiness. SN II dust condensation would needto have a high e ffi ciency ( (cid:39) (cid:12) / SN) to account for the ob-served dust mass (Dwek et al. 2007, 2014). AGB star yield canexplain this dust content for z (cid:39) z (cid:39) (cid:39)
100 Myr (panel (b) of Fig. 18), wellbelow the age of these systems. Consequently, these very distantgalaxies may not be the best laboratories to constrain the SN IIdust yield.
As stated in Sects. 1 and 5.2.3, past studies have not been rig-orously fitting cosmic dust evolution models to observations ofgalaxies. Recently, N20 and De Looze et al. (2020, hereafterDL20) have addressed this issue. N20 have adopted a relativelycoarse dust evolution model grid with a frequentist fitting ap-proach. Although interesting, their approach does not allow themto rigorously quantify parameter degeneracies and uncertainties.The comparison with their results is therefore limited. We havediscussed the main discrepancies between the present work andtheirs in Sects. 2.1.2 and Sect. 5.2.3.DL20 have analyzed the JINGLE galaxy sample, follow-ing a methodology similar to ours, fitting the IR SED of eachgalaxy, and subsequently fitting one-zone dust evolution tracksto their derived M (cid:63) , M gas , M dust , Z and SFR. They adopted anon-hierarchical Bayesian approach. To our knowledge, this isthe first article, similar to ours, to perform a rigorous fit of dustevolution models, with clearly quantified parameter uncertain-ties. Their results however qualitatively di ff er from ours. DL20find an overall high SN II dust yield, and a low grain growth e ffi -ciency (the tuning parameters are not assumed universal in theirstudy). In our opinion, the discrepancy between our results andthose of DL20 comes from the two following points.1. DL20’s metallicity coverage is more limited than ours. Theyhave only one source below 12 + log(O / H) = .
0, and nonebelow 12 + log(O / H) = . e.g. their figure 7). Conse-quently, they do not sample the stardust regime, below thecritical metallicity. Disentangling SN II dust condensation,grain growth and shock destruction, with their data, is there-fore rendered di ffi cult.2. The posterior distribution of the dust evolution parametersinferred by DL20, as seen in their figures G.7 to G.12 (theyfocus their analysis on their galaxy bins 3 and 4), rarely goesdown to zero probability within the range allowed by theiruniform prior. It means the weight of evidence provided bytheir data is relatively mild. Our inference of (cid:15) grow and m destgas are consistent with their PDF, as they fall in a high proba-bility domain in all their models. We simply have a smalleruncertainty, thanks to our low-metallicity coverage. This ismore pronounced for their distribution of δ SN (their f survival ).DL20 would have also benefitted from extending their prior range down to smaller values, as they do not consider yieldsbelow δ SN =
10 %, while we infer a value around δ SN (cid:39)
6. SUMMARY AND CONCLUSION
This article has presented an observational study aimed at con-straining the timescales of the main processes controlling theevolution of interstellar dust in galaxies. The principal highlightsare the following.1. We have gathered the 3- µ m-to-1-mm photometry and ancil-lary data of 798 nearby galaxies from the DustPedia (Davieset al. 2017) and DGS (Madden et al. 2013) surveys. Wehave attempted to create the most conservative, homoge-neous sample, by controlling the factors that could lead tosystematic biases (Sect. 2):(a) the DustPedia and DGS IR data reduction and photome-try have been performed consistently;(b) the stellar mass and SFR have been estimated using thesame IMF;(c) the metallicities have been estimated using one uniformcalibration;(d) the total gas masses have been derived from [H i ]
21 cm and CO(J = → . observations, when available. WhenCO data was not available, the molecular gas mass wasestimated from a scaling relation.(e) Resolved interferometric [H i ]
21 cm observations of 20 ofthe lowest metallicity objects were used in order to ex-tract the gas mass corresponding exactly to the IR photo-metric aperture.2. We have performed a hierarchical Bayesian dust SED fitof the 798 galaxies, using the code
HerBIE (G18) with the
THEMIS grain properties (Jones et al. 2017).(a) This allowed us to infer the dust mass, M dust , meanstarlight intensity, (cid:104) U (cid:105) , and the mass fraction ofaromatic-feature-emitting grains, q AF , in each galaxy(Sect. 3.2). The inferred parameters are given in Ta-ble H.1.(b) We have compared our inferred parameters to a series ofadditional runs, as well as to independent literature stud-ies, in order to demonstrate the influence of the di ff erentassumptions of our model and assess the robustness ofour results (Sects. 3.3 – 3.4).3. We have displayed several well-known scaling relations in-volving M (cid:63) , M gas , M dust , 12 + log(O / H), SFR, q AF and (cid:104) U (cid:105) ,for our sample (Sect. 4).(a) We have shown that there is a drastic evolution withmetallicity of the dust-to-metal mass ratio (by two ordersof magnitude). We have extensively discussed the dif-ferent biases that could artificially produce such a trend,concluding they were unlikely (Sect. 4.1.3).(b) We have noticed that early-type galaxies have a system-atically lower dust-to-gas mass ratio than other types inthe same gas-to-stellar mass ratio range. We have inves-tigated the possibility that this was resulting from theenhanced dust destruction due to thermal sputtering inthe hot X-ray emitting gas permeating these objects. Thisscenario is supported by a rough negative correlation be-tween the dust-to-star mass ratio and the X-ray photonrate per dust grain (Sect. 4.1.2).(c) We have displayed the well-known trends of q AF with12 + log(O / H) and (cid:104) U (cid:105) . Our data indicate the correlationwith 12 + log(O / H) is significantly better (Sect. 4.2). It
Article number, page 30 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution implies that, at the scale of a galaxy, the overall abun-dance of small a-C(:H) grains might be principally con-trolled by the e ffi ciency of their formation (stardust pro-duction and / or shattering of larger carbon grains). Thephotodestruction of small a-C(:H) might overall be cir-cumscribed around star forming regions.4. We have performed a hierarchical Bayesian fit of a one-zone dust evolution model to the derived M (cid:63) , M gas , M dust ,12 + log(O / H) and SFR of a subsample of 556 late-type andirregular objects (Sect. 5).(a) We have inferred the e ffi ciency of the three main dustevolution tuning parameters (Sect. 5.3): (i) the IMF-av-eraged SN II dust yield is (cid:104) Y SN (cid:105) (cid:46) .
03 M (cid:12) / SN; (ii) thegrain growth e ffi ciency parameter (Mattsson et al. 2012)is (cid:15) grow (cid:38) (iii) the average gas mass cleared of dustby a single SN II shock wave is m destgas (cid:38) (cid:12) / SN.Our results therefore imply that dust production is domi-nated by grain growth in the ISM above a critical metal-licity of 12 + log(O / H) (cid:39) .
0. They also suggest that themassive amounts of dust detected in high redshift sys-tems ( z (cid:38)
6) likely grew in the ISM.(b) We have shown that ELMGs were crucial in constrain-ing these parameters, as they sample a regime where dustproduction is dominated by SN II condensation. A steep,strongly non-linear, dustiness-metallicity relation, suchas the one we have found, is the unambiguous evidencethat stardust can not dominate the content of solar metal-licity systems.(c) We have shown and explained why these conclusionswere, to first order, independent of our IMF assumption(Sect. 5.3.3).(d) Our model fails at reproducing the relation between thesSFR and the dust-to-star mass ratio. We suspect this isdue to the oversimplicity of our SFH, inflow and outflowprescriptions.Several of the limitations of our study could be addressedby spatially resolving star forming regions. Performing a simi-lar analysis on (cid:39)
100 pc scales within galaxies would allow usto access another important parameter: the density of the ISM.This quantity drives mantle growth and coagulation. Local vari-ations of the dust-to-metal mass ratio are good indications ofgrain growth and can help us break the degeneracy with SN IIdestruction (Sect. 5.2.2). In addition, spatial resolution would bea way to address the origin of the trend of q AF with metallicity(Sect. 4.2), as well as resolving ETGs to quantify the grain sput-tering timescale (Sect. 4.1.2). Numerous spatially resolved duststudies have already been published ( e.g. Galliano et al. 2011;Mattsson & Andersen 2012; Draine & Hensley 2013; Hunt et al.2015; Roman-Duval et al. 2017; Aniano et al. 2020). We are cur-rently preparing several papers of a resolved subsample, with thesame consistent approach as employed in the present manuscript(Roychowdhury et al.; Casasola et al., in prep. ). The main ob-servational challenge in order to address these degeneracies ishowever to obtain spatial resolution in ELMGs, at far-IR wave-lengths. The data are currently very limited, because the sensitiv-ity of
Herschel was not high enough.
SPICA (van der Tak et al.2018) was the only observatory on the horizon to have the sen-sitivity to produce resolved far-IR maps of ELMGs. Its suddencancellation by ESA might leave the important open questionsraised in this paper unanswered for several decades.
Acknowledgements.
We thank Marc-Antoine M iville -D esch ˆ enes for useful dis-cussions about SED fitting, and about Planck and
IRAS data, Albrecht P oglitsch for discussions about PACS calibration, and Joana F rontera -P ons for her exper- tise about M-estimators. We also thank Vianney L ebouteiller and Julia R oman -D uval for insightful interpretations of absorption line measurements in DLAsystems. Finally, we thank the referee, Denis B urgarella , for his numerouscomments that helped clarify the text of this article and strengthen the relia-bility of our stellar mass estimates. DustPedia is a collaborative focused researchproject supported by the European Union under the Seventh Framework Pro-gramme (2007–2013) call (proposal no. 606847, PI J. I. Davies). The data usedin this work is publicly available at http: // dustpedia.astro.noa.gr. This work wassupported by the Programme National “Physique et Chimie du Milieu Inter-stellaire” (PCMI) of CNRS / INSU with INC / INP co-funded by CEA and CNES(France). It has also been supported by the
Programme National de Cosmolo-gie et Galaxies (PNCG) CNRS / INSU with INC / IN2P3 co-funded by CEA andCNES (France). Simone B ianchi and Viviana C asasola acknowledge fundingfrom the INAF mainstream 2018 program “Gas-DustPedia: A definitive viewof the ISM in the Local Universe". Ilse D e L ooze acknowledges support fromEuropean Research Council (ERC) Starting Grant 851622 DustOrigin. MaudG alametz has received funding from the European Research Council (ERC)under the European Union Horizon 2020 research and innovation programme(MagneticYSOs project, grant agreement No 679937, PI: Maury). AleksandrM osenkov acknowledges financial support from the Russian Science Founda-tion (grant no. 20-72-10052). This work has made extensive use of the HDF5library, developed by The HDF Group and by the National Center for Super-computing Applications at the University of Illinois at Urbana-Champaign. Thisresearch has made use of the NASA / IPAC Extragalactic Database (NED), whichis operated by the Jet Propulsion Laboratory, California Institute of Technology,under contract with the National Aeronautics and Space Administration. Thisresearch has made use of the VizieR catalogue access tool, CDS, Strasbourg,France (DOI: 10.26093 / cds / vizier). The original description of the VizieR ser-vice was published in Ochsenbein et al. (2000). References
Akylas, A. & Georgantopoulos, I. 2009, A&A, 500, 999Aloisi, A., Clementini, G., Tosi, M., et al. 2007, ApJ, 667, L151Andersson, B.-G., Lazarian, A., & Vaillancourt, J. E. 2015, ARA&A, 53, 501Aniano, G., Draine, B., Hunt, L., et al. 2020, Astrophysical Journal, 889Aoyama, S., Hirashita, H., & Nagamine, K. 2020, MNRAS, 491, 3844Aoyama, S., Hou, K.-C., Shimizu, I., et al. 2017, MNRAS, 466, 105Arendt, R. G., Dwek, E., Kober, G., Rho, J., & Hwang, U. 2014, ApJ, 786, 55Asano, R. S., Takeuchi, T. T., Hirashita, H., & Inoue, A. K. 2013, Earth, Planets,and Space, 65, 213Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481Assef, R. J., Stern, D., Noirot, G., et al. 2018, ApJS, 234, 23Astropy Collaboration, Price-Whelan, A. M., Sip˝ocz, B. M., et al. 2018, AJ, 156,123Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558,A33Audouze, J. & Tinsley, B. M. 1976, ARA&A, 14, 43Baes, M. & Dejonghe, H. 2001, MNRAS, 326, 733Balog, Z., Müller, T., Nielbock, M., et al. 2014, Experimental Astronomy, 37,129Barlow, M. J., Krause, O., Swinyard, B. M., et al. 2010, A&A, 518, L138Barnard, J., McCulloch, R., & Meng, X.-L. 2000, Statistica Sinica, 10, 1281Beers, T. C., Flynn, K., & Gebhardt, K. 1990, AJ, 100, 32Begum, A., Chengalur, J. N., Karachentsev, I. D., Sharina, M. E., & Kaisin, S. S.2008, MNRAS, 386, 1667Bell, A. C., Onaka, T., Galliano, F., et al. 2019, PASJ, 71, 123Bendo, G. J., Buckalew, B. A., Dale, D. A., et al. 2006, ApJ, 645, 134Bevan, A., Barlow, M. J., & Milisavljevic, D. 2017, MNRAS, 465, 4044Bianchi, S., Casasola, V., Baes, M., et al. 2019, A&A, 631, A102Bianchi, S., De Vis, P., Viaene, S., et al. 2018, A&A, 620, A112Bianchi, S. & Schneider, R. 2007, MNRAS, 378, 973Bocchio, M., Marassi, S., Schneider, R., et al. 2016, A&A, 587, A157Bocchio, M., Micelotta, E. R., Gautier, A.-L., & Jones, A. P. 2012, A&A, 545,A124Bolatto, A. D., Wolfire, M., & Leroy, A. K. 2013, ARA&A, 51, 207Boquien, M., Burgarella, D., Roehlly, Y., et al. 2019, A&A, 622, A103Bot, C., Ysard, N., Paradis, D., et al. 2010, A&A, 523, A20 + Boulanger, F., Boisssel, P., Cesarsky, D., & Ryter, C. 1998, A&A, 339, 194Brauher, J. R., Dale, D. A., & Helou, G. 2008, ApJS, 178, 280Brightman, M. & Nandra, K. 2011, MNRAS, 413, 1206Brinkmann, W., Siebert, J., & Boller, T. 1994, A&A, 281, 355Bron, E., Le Bourlot, J., & Le Petit, F. 2014, A&A, 569, A100Brown, M. J. I., Jarrett, T. H., & Cluver, M. E. 2014, Publications of the Astro-nomical Society of Australia, 31, e049Buat, V., Heinis, S., Boquien, M., et al. 2014, A&A, 561, A39Burgarella, D., Nanni, A., Hirashita, H., et al. 2020, A&A, 637, A32
Article number, page 31 of 64 & A proofs: manuscript no. manuscript
Calura, F., Pipino, A., & Matteucci, F. 2008, A&A, 479, 669Camps, P., Misselt, K., Bianchi, S., et al. 2015, A&A, 580, A87Camps, P., Trayford, J. W., Baes, M., et al. 2016, MNRAS, 462, 1057Camps, P., Trˇcka, A., Trayford, J., et al. 2018, ApJS, 234, 20Cappi, M., Panessa, F., Bassani, L., et al. 2006, A&A, 446, 459Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245Cartledge, S. I. B., Clayton, G. C., Gordon, K. D., et al. 2005, ApJ, 630, 355Casasola, V., Bianchi, S., De Vis, P., et al. 2020a, A&A, 633, A100Casasola, V., co-I1, co-I2, et al. 2020b, in prep.
Chabrier, G. 2003, PASP, 115, 763Chastenet, J., Sandstrom, K., Chiang, I. D., et al. 2019, ApJ, 876, 62Clark, C. J. R., De Vis, P., Baes, M., et al. 2019, MNRAS, 489, 5256Clark, C. J. R., Dunne, L., Gomez, H. L., et al. 2015, MNRAS, 452, 397Clark, C. J. R., Verstocken, S., Bianchi, S., et al. 2018, A&A, 609, A37 (C18)Clayton, G. C., Gordon, K. D., Salama, F., et al. 2003, ApJ, 592, 947Cohen, M., Megeath, S. T., Hammersley, P. L., Martín-Luis, F., & Stau ff er, J.2003, AJ, 125, 2645Compiègne, M., Verstraete, L., Jones, A., et al. 2011, A&A, 525, A103 + Cormier, D., Abel, N. P., Hony, S., et al. 2019, A&A, 626, A23Cormier, D., Madden, S. C., Lebouteiller, V., et al. 2015, A&A, 578, A53Cortese, L., Ciesla, L., Boselli, A., et al. 2012, A&A, 540, A52Crinklaw, G., Federman, S. R., & Joseph, C. L. 1994, ApJ, 424, 748Dale, D. A., Cook, D. O., Roussel, H., et al. 2017, ApJ, 837, 90Dale, D. A., Helou, G., Contursi, A., Silbermann, N. A., & Kolhatkar, S. 2001,ApJ, 549, 215David, L. P., Jones, C., Forman, W., Vargas, I. M., & Nulsen, P. 2006, ApJ, 653,207Davies, J. I., Baes, M., Bianchi, S., et al. 2017, PASP, 129, 044102Davies, J. I., Nersesian, A., Baes, M., et al. 2019, A&A, 626, A63De Cia, A., Ledoux, C., Mattsson, L., et al. 2016, A&A, 596, A97De Looze, I., Barlow, M. J., Bandiera, R., et al. 2019, MNRAS, 488, 164De Looze, I., Barlow, M. J., Swinyard, B. M., et al. 2017, MNRAS, 465, 3309De Looze, I., Lamperti, I., Saintonge, A., et al. 2020, MNRAS, 496, 3668 (DL20)De Vis, P., Dunne, L., Maddox, S., et al. 2017a, MNRAS, 464, 4680De Vis, P., Gomez, H. L., Schofield, S. P., et al. 2017b, MNRAS, 471, 1743De Vis, P., Jones, A., Viaene, S., et al. 2019, A&A, 623, A5Demyk, K., Meny, C., Leroux, H., et al. 2017a, A&A, 606, A50Demyk, K., Meny, C., Lu, X. H., et al. 2017b, A&A, 600, A123Diehl, S. & Statler, T. S. 2007, ApJ, 668, 150Draine, B. T. 1978, ApJS, 36, 595Draine, B. T. 2009, in Astronomical Society of the Pacific Conference Series,Vol. 414, Astronomical Society of the Pacific Conference Series, ed. T. Hen-ning, E. Grün, & J. Steinacker, 453– + Draine, B. T. 2011, in EAS Publications Series, Vol. 46, EAS Publications Series,ed. C. Joblin & A. G. G. M. Tielens, 29–42Draine, B. T., Dale, D. A., Bendo, G., et al. 2007, ApJ, 663, 866Draine, B. T. & Hensley, B. 2012, ApJ, 757, 103Draine, B. T. & Hensley, B. 2013, ApJ, 765, 159Draine, B. T. & Li, A. 2007, ApJ, 657, 810 (DL07)Draine, B. T. & Salpeter, E. E. 1979, ApJ, 231, 438Dumke, M., Krause, M., & Wielebinski, R. 2004, A&A, 414, 475Dupac, X., Bernard, J.-P., Boudet, N., et al. 2003, A&A, 404, L11Dwek, E. 1998, ApJ, 501, 643Dwek, E. 2005, in AIP Conf. Proc. 761: The Spectral Energy Distributions ofGas-Rich Galaxies: Confronting Models with Data, ed. C. C. Popescu & R. J.Tu ff s, 103Dwek, E. & Arendt, R. G. 2015, ApJ, 810, 75Dwek, E., Galliano, F., & Jones, A. P. 2007, ApJ, 662, 927Dwek, E. & Scalo, J. M. 1980, ApJ, 239, 193Dwek, E., Staguhn, J., Arendt, R. G., et al. 2014, ApJ, 788, L30Efron, B. & Morris, C. 1977, Scientific American, 236, 119Engelbracht, C. W., Blaylock, M., Su, K. Y. L., et al. 2007, PASP, 119, 994Engelbracht, C. W., Gordon, K. D., Rieke, G. H., et al. 2005, ApJ, 628, L29Ercolano, B., Barlow, M. J., & Sugerman, B. E. K. 2007, MNRAS, 375, 753Eskew, M., Zaritsky, D., & Meidt, S. 2012, AJ, 143, 139Fabbiano, G., Kim, D. W., & Trinchieri, G. 1992, ApJS, 80, 531Fanciullo, L., Guillet, V., Boulanger, F., & Jones, A. P. 2017, A&A, 602, A7Feldmann, R. 2015, MNRAS, 449, 3274Fitzpatrick, E. L. 1986, AJ, 92, 1068Galametz, M., Albrecht, M., Kennicutt, R., et al. 2014, MNRAS, 439, 2542Galametz, M., Hony, S., Galliano, F., et al. 2013, MNRAS, 431, 1596Galametz, M., Madden, S., Galliano, F., et al. 2009, A&A, 508, 645Galametz, M., Madden, S. C., Galliano, F., et al. 2011, A&A, 532, A56Galliano, F. 2018, MNRAS, 476, 1445 (G18)Galliano, F., Dwek, E., & Chanial, P. 2008a, ApJ, 672, 214Galliano, F., Galametz, M., & Jones, A. P. 2018, ARA&A, 56, 673Galliano, F., Hony, S., Bernard, J.-P., et al. 2011, A&A, 536, A88Galliano, F., Madden, S. C., Jones, A. P., Wilson, C. D., & Bernard, J.-P. 2005,A&A, 434, 867Galliano, F., Madden, S. C., Jones, A. P., et al. 2003, A&A, 407, 159 Galliano, F., Madden, S. C., Tielens, A. G. G. M., Peeters, E., & Jones, A. P.2008b, ApJ, 679, 310Garnett, D. R., Skillman, E. D., Dufour, R. J., et al. 1995, ApJ, 443, 64Gelman, A., Carlin, J., Stern, H., & Rubin, D. 2004, Bayesian Data Analysis(Chapman & Hall)Geman, S. & Geman, D. 1984, IEEE Trans. Pattern Anal. Mach. Intell., 6, 721Gomez, H. L., Krause, O., Barlow, M. J., et al. 2012, ApJ, 760, 96González-Martín, O., Masegosa, J., Márquez, I., Guainazzi, M., & Jiménez-Bailón, E. 2009, A&A, 506, 1107Gordon, K. D., Clayton, G. C., Misselt, K. A., Landolt, A. U., & Wol ff , M. J.2003, ApJ, 594, 279Gordon, K. D., Engelbracht, C. W., Fadda, D., et al. 2007, PASP, 119, 1019Gordon, K. D., Engelbracht, C. W., Rieke, G. H., et al. 2008, ApJ, 682, 336Gordon, K. D., Roman-Duval, J., Bot, C., et al. 2014, ApJ, 797, 85Gould, R. J. & Salpeter, E. E. 1963, ApJ, 138, 393Grebel, E. K. 1999, in The Stellar Content of Local Group Galaxies, ed. P. White-lock & R. Cannon, Vol. 192, 17Greenberg, J. M., Gillette, J. S., Muñoz Caro, G. M., et al. 2000, ApJ, 531, L71Grier, C. J., Mathur, S., Ghosh, H., & Ferrarese, L. 2011, ApJ, 731, 60Gri ffi n, M. J., North, C. E., Schulz, B., et al. 2013, MNRAS, 434, 992Hahn, R. 2005, Pierre Simon Laplace, 1749-1827: A Determined Scientist (Har-vard University Press)Hamanowicz, A., Péroux, C., Zwaan, M. A., et al. 2020, MNRAS, 492, 2347Hirashita, H. 1999, ApJ, 510, L99Hirashita, H. 2012, MNRAS, 422, 1263Hirashita, H. & Aoyama, S. 2019, MNRAS, 482, 2555Hirashita, H. & Murga, M. S. 2020, MNRAS, 492, 3779Hirashita, H., Nozawa, T., Villaume, A., & Srinivasan, S. 2015, MNRAS, 454,1620Hogg, D. W., Bovy, J., & Lang, D. 2010, arXiv e-prints, arXiv:1008.4686Hou, K.-C., Hirashita, H., Nagamine, K., Aoyama, S., & Shimizu, I. 2017, MN-RAS, 469, 870Houck, J. R., Charmandaris, V., Brandl, B. R., et al. 2004, ApJS, 154, 211Hunt, L. K., Draine, B. T., Bianchi, S., et al. 2015, A&A, 576, A33Hunter, D. A. & Gallagher, J. S., I. 1989, Science, 243, 1557Inoue, A. K. 2003, PASJ, 55, 901James, A., Dunne, L., Eales, S., & Edmunds, M. G. 2002, MNRAS, 335, 753Janowiecki, S., Salzer, J. J., van Zee, L., Rosenberg, J. L., & Skillman, E. 2017,ApJ, 836, 128Jarrett, T. H., Cohen, M., Masci, F., et al. 2011, ApJ, 735, 112Jaynes, E. T. 1976, Confidence Intervals vs Bayesian Intervals (W. L. Harper andC. A. Hooker), 175Jenkins, E. B. 2009, ApJ, 700, 1299Joblin, C., Leger, A., & Martin, P. 1992, ApJ, 393, L79Jones, A. P. 2016a, Royal Society Open Science, 3, 160221Jones, A. P. 2016b, Royal Society Open Science, 3, 160223Jones, A. P. 2016c, Royal Society Open Science, 3, 160224Jones, A. P., Fanciullo, L., Köhler, M., et al. 2013, A&A, 558, A62Jones, A. P., Köhler, M., Ysard, N., Bocchio, M., & Verstraete, L. 2017, A&A,602, A46Jones, A. P., Tielens, A. G. G. M., Hollenbach, D. J., & McKee, C. F. 1994, ApJ,433, 797Jones, T., Stark, D. P., & Ellis, R. S. 2018, ApJ, 863, 191Kelly, B. C., Shetty, R., Stutz, A. M., et al. 2012, ApJ, 752, 55Khramtsova, M. S., Wiebe, D. S., Boley, P. A., & Pavlyuchenkov, Y. N. 2013,MNRAS, 431, 2006Kim, D.-W., Anderson, C., Burke, D., et al. 2019, ApJS, 241, 36Kim, S.-H., Martin, P. G., & Hendry, P. D. 1994, ApJ, 422, 164Kimura, H. 2016, MNRAS, 459, 2751Kirchschlager, F., Schmidt, F. D., Barlow, M. J., et al. 2019, MNRAS, 489, 4465Köhler, M., Jones, A., & Ysard, N. 2014, A&A, 565, L9Köhler, M., Ysard, N., & Jones, A. P. 2015, A&A, 579, A15Kunth, D. & Östlin, G. 2000, A&A Rev., 10, 1Laigle, C., Davidzon, I., Ilbert, O., et al. 2019, MNRAS, 486, 5104Lamperti, I., Saintonge, A., De Looze, I., et al. 2019, MNRAS, 489, 4389Laporte, N., Ellis, R. S., Boone, F., et al. 2017, ApJ, 837, L21Lax, D. 1975, An Interim Report of a Monte Carlo Study of Robust Estimatorsof Width (Department of Statistics, Princeton University)Lee, S.-K., Ferguson, H. C., Somerville, R. S., Wiklind, T., & Giavalisco, M.2010, ApJ, 725, 1644Leja, J., Carnall, A. C., Johnson, B. D., Conroy, C., & Speagle, J. S. 2019, ApJ,876, 3Lianou, S., Barmby, P., Mosenkov, A. A., Lehnert, M., & Karczewski, O. 2019,A&A, 631, A38 (L19)Lisenfeld, U. & Ferrara, A. 1998, ApJ, 496, 145Liu, F. K. & Zhang, Y. H. 2002, A&A, 381, 757Liu, J. 2011, ApJS, 192, 10Lopes, A. R., Telles, E., & Melnick, J. 2020, MNRASMadau, P. & Dickinson, M. 2014, ARA&A, 52, 415Madden, S. C., Galliano, F., Jones, A. P., & Sauvage, M. 2006, A&A, 446, 877 Article number, page 32 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Madden, S. C., Rémy-Ruyer, A., Galametz, M., et al. 2013, PASP, 125, 600Madden, S. C., Rémy-Ruyer, A., Galametz, M., et al. 2014, PASP, 126, 1079Makarov, D., Prugniel, P., Terekhova, N., Courtois, H., & Vauglin, I. 2014, A&A,570, A13Malhotra, S., Helou, G., Stacey, G., et al. 1997, ApJ, 491, L27Malhotra, S., Kaufman, M. J., Hollenbach, D., et al. 2001, ApJ, 561, 766Marassi, S., Schneider, R., Limongi, M., et al. 2019, MNRAS, 484, 2587Martínez-González, S., Wünsch, R., Palouš, J., et al. 2018, ApJ, 866, 40Mathews, W. G. & Brighenti, F. 2003, ARA&A, 41, 191Mathis, J. S., Mezger, P. G., & Panagia, N. 1983, A&A, 128, 212Matsuura, M., Dwek, E., Barlow, M. J., et al. 2015, ApJ, 800, 50Mattsson, L. & Andersen, A. C. 2012, MNRAS, 423, 38Mattsson, L., Andersen, A. C., & Munkhammar, J. D. 2012, MNRAS, 423, 26McGrayne, S. 2011, The Theory That Would Not Die: How Bayes’ Rule Crackedthe Enigma Code, Hunted Down Russian Submarines, and Emerged Tri-umphant from Two Centuries of Controversy (Yale University Press)Meny, C., Gromov, V., Boudet, N., et al. 2007, A&A, 468, 171Micelotta, E. R., Dwek, E., & Slavin, J. D. 2016, A&A, 590, A65Mitchell, P. D., Lacey, C. G., Baugh, C. M., & Cole, S. 2013, MNRAS, 435, 87Morgan, H. L. & Edmunds, M. G. 2003, MNRAS, 343, 427Mosteller, F. & Tukey, J. W. 1977, Data analysis and regression. A secondcourse in statistics (Addison-Wesley Series in Behavioral Science: Quanti-tative Methods, Reading, Mass.: Addison-Wesley, 1977)Nanni, A., Burgarella, D., Theulé, P., Côté, B., & Hirashita, H. 2020, A&A, 641,A168 (N20)Nersesian, A., Xilouris, E. M., Bianchi, S., et al. 2019, A&A, 624, A80Nozawa, T., Kozasa, T., & Habe, A. 2006, ApJ, 648, 435Ochsenbein, F., Bauer, P., & Marcout, J. 2000, A&AS, 143, 23Ohyama, Y., Sakamoto, K., Aalto, S., & Gallagher, John S., I. 2019, ApJ, 871,191O’Sullivan, E., Forbes, D. A., & Ponman, T. J. 2001, MNRAS, 328, 461Parvathi, V. S., Sofia, U. J., Murthy, J., & Babu, B. R. S. 2012, ApJ, 760, 36Pei, Y. C. 1992, ApJ, 395, 130Pilyugin, L. S. & Grebel, E. K. 2016, MNRAS, 457, 3678Planck Collaboration, Abergel, A., Ade, P. A. R., et al. 2014, A&A, 571, A11Planck Collaboration, Adam, R., Ade, P. A. R., et al. 2016, A&A, 594, A8Priestley, F. D., Barlow, M. J., & De Looze, I. 2019, MNRAS, 485, 440Rau, S.-J., Hirashita, H., & Murga, M. 2019, MNRAS, 489, 5218Reach, W. T., Megeath, S. T., Cohen, M., et al. 2005, PASP, 117, 978Rémy-Ruyer, A., Madden, S. C., Galliano, F., et al. 2014, A&A, 563, A31Rémy-Ruyer, A., Madden, S. C., Galliano, F., et al. 2013, A&A, 557, A95Rémy-Ruyer, A., Madden, S. C., Galliano, F., et al. 2015, A&A, 582, A121Rieke, G. H., Lebofsky, M. J., & Low, F. J. 1985, AJ, 90, 900Rodriguez-Gomez, V., Snyder, G. F., Lotz, J. M., et al. 2019, MNRAS, 483, 4140Röllig, M., Abel, N. P., Bell, T., et al. 2007, A&A, 467, 187Roman-Duval, J., Bot, C., Chastenet, J., & Gordon, K. 2017, ApJ, 841, 72Rosa González, D., Terlevich, E., Jiménez Bailón, E., et al. 2009, MNRAS, 399,487Rowlands, K., Gomez, H. L., Dunne, L., et al. 2014, MNRAS, 441, 1040Roychowdhury, S., Galliano, F., Roychowdhury, S., et al. 2020, in prep.
Salpeter, E. E. 1955, ApJ, 121, 161Sanders, R. L., Shapley, A. E., Jones, T., et al. 2020, arXiv e-prints,arXiv:2009.07292Sandstrom, K. M., Bolatto, A. D., Draine, B. T., Bot, C., & Stanimirovi´c, S.2010, ApJ, 715, 701Savage, B. D. & Mathis, J. S. 1979, ARA&A, 17, 73Schirmer, T., Abergel, A., Verstraete, L., et al. 2020, arXiv e-prints,arXiv:2003.05902Seok, J. Y., Hirashita, H., & Asano, R. S. 2014, MNRAS, 439, 2186Shetty, R., Kau ff mann, J., Schnee, S., & Goodman, A. A. 2009, ApJ, 696, 676Slavin, J. D., Dwek, E., & Jones, A. P. 2015, ApJ, 803, 7Smith, M. W. L., Gomez, H. L., Eales, S. A., et al. 2012, ApJ, 748, 123Stansberry, J. A., Gordon, K. D., Bhattacharya, B., et al. 2007, PASP, 119, 1038Stein, C. 1956, in Proceedings of the Third Berkeley Symposium on Mathe-matical Statistics and Probability, Volume 1: Contributions to the Theory ofStatistics (Berkeley, Calif.: University of California Press), 197–206Stepnik, B., Abergel, A., Bernard, J., et al. 2003, A&A, 398, 551Sugerman, B. E. K., Ercolano, B., Barlow, M. J., et al. 2006, Science, 313, 196Tajer, M., Trinchieri, G., Wolter, A., et al. 2005, A&A, 435, 799Temim, T. & Dwek, E. 2013, ApJ, 774, 8Temim, T., Dwek, E., Arendt, R. G., et al. 2017, ApJ, 836, 129Tielens, A. G. G. M. 1998, ApJ, 499, 267Todini, P. & Ferrara, A. 2001, MNRAS, 325, 726Trayford, J. W., Camps, P., Theuns, T., et al. 2017, MNRAS, 470, 771Trˇcka, A., Baes, M., Camps, P., et al. 2020, MNRAS, 494, 2823Valiante, R., Schneider, R., Bianchi, S., & Andersen, A. C. 2009, MNRAS, 397,1661van der Tak, F. F. S., Madden, S. C., Roelfsema, P., et al. 2018, PASA, 35, e002Viaene, S., Fritz, J., Baes, M., et al. 2014, A&A, 567, A71 Villani, M. & Larsson, R. 2006, Communications in Statistics-Theory and Meth-ods, 35, 1123Wagenmakers, E.-J., Lee, M., Lodewyckx, T., & Iverson, G. J. 2008, BayesianVersus Frequentist Inference (New York, NY: Springer New York), 181–207Walter, F., Cannon, J. M., Roussel, H., et al. 2007, ApJ, 661, 102Wheelock, S. L., Gautier, T. N., Chillemi, J., et al. 1994, IRAS sky survey atlas:Explanatory supplement, Tech. rep., IRSAWitt, A. N. & Gordon, K. D. 2000, ApJ, 528, 799Witt, A. N., Thronson, Harley A., J., & Capuano, John M., J. 1992, ApJ, 393,611Wu, R., Hogg, D. W., & Moustakas, J. 2011, ApJ, 730, 111Wu, Y., Charmandaris, V., Hunt, L. K., et al. 2007, ApJ, 662, 952Ysard, N., Köhler, M., Jones, A., et al. 2016, A&A, 588, A44Ysard, N., Köhler, M., Jones, A., et al. 2015, A&A, 577, A110Zhukovska, S. 2014, A&A, 562, A76Zubko, V., Dwek, E., & Arendt, R. G. 2004, ApJS, 152, 211 Article number, page 33 of 64 & A proofs: manuscript no. manuscript
Appendix A: CALIBRATION UNCERTAINTIES
The HB approach is one of the only methods allowing a rigoroustreatment of the photometric calibration uncertainties. These un-certainties are indeed systematic e ff ects, with both spectral andspatial correlations. Some studies account for their spectral cor-relations, but ignore their spatial correlations ( e.g. Gordon et al.2014). In the present paper, following G18, we assume that cal-ibration uncertainties are perfectly correlated between sources,and partially correlated between wavelengths. In this section, wediscuss the values of these uncertainties and of their correlationcoe ffi cients.The DustPedia photometric fluxes, given in the archive , F ν ( λ ) at wavelength λ , are accompanied with a total uncer-tainty being the quadratic sum of noise and calibration errors: σ C18 ν ( λ ) = (cid:114)(cid:16) σ noise ν ( λ ) (cid:17) + (cid:16) δ C18cal ( λ ) × F ν ( λ ) (cid:17) , (A.1)where δ C18cal ( λ ) is the calibration uncertainty (Table 1 of C18). HerBIE treats the noise and calibration uncertainties separately.Therefore, we keep the noise uncertainty, σ noise ν ( λ ), but we builda covariance matrix of the absolute calibration uncertainties, V cal , to replace the δ C18cal coe ffi cients. Appendix A.1: The Full Covariance Matrix
Using the separation strategy (Barnard et al. 2000), we decom-pose the covariance matrix of the absolute calibration uncertain-ties as: V cal = S cal R cal S cal , (A.2)where S cal is the diagonal matrix of standard-deviations and R cal the correlation matrix. The non-trivial elements of S cal and R cal are given in Tables A.1 – A.2. We describe, in the followingsections A.2 to A.8, how we obtained these values from the lit-erature. Appendix A.2: Spitzer/IRAC
The calibration of IRAC data is presented by Reach et al. (2005).It is performed using a subsample of the stellar catalog of Co-hen et al. (2003). The components entering in the uncertaintyon the absolute calibration are given by Eq. (13) of Reach et al.(2005) and the corresponding values in their Table 7. The firstterm is the correlated uncertainty, σ abs = . (cid:113) ( σ − σ ) / n = .
87 %, with σ ground = . n =
4. Finally, there is an uncorrelated term introduced by thedispersion of the IRAC observations of the calibrators: σ rms / √ n ,where σ rms = . . . . (Sect. 4.11), these factors have a 10 % un-certainty. We include this extra source of uncertainty, assumingit is uncorrelated. These correction factors have been applied byC18 for all the DustPedia galaxies and by Rémy-Ruyer et al. http: // dustpedia.astro.noa.gr / Photometry https: // irsa.ipac.caltech.edu / data / SPITZER / docs / irac / iracinstrument-handbook / Table A.1.
Absolute calibration uncertainties (diagonal of S cal ;Eq. A.2). See Table 1 for waveband naming conventions. Waveband label Calibration uncertaintyIRAC1 10 . . . . . . . . . . . . . . . . . . . . . . . .
90 %(2015) for half of the DGS galaxies, the other half being nearlypoint sources. The IRAC calibration uncertainties will thus beoverestimated for about 15 of our sources.
Appendix A.3: Spitzer/MIPS
MIPS calibration has been independently performed for each ofits three wavebands. The 24 µ m calibration is presented by En-gelbracht et al. (2007). It is primarily based on observations ofA stars. The authors recommend adopting a net calibration un-certainty of 4 %. The 70 µ m calibration is presented by Gordonet al. (2007). It is primarily based on observations of B and Mstars. The authors recommend using a calibration uncertaintyof 5 %, dominated by repeatability scatter. Finally, the 160 µ mcalibration, presented by Stansberry et al. (2007) is performedon observations of asteroids, simulatenously in the three MIPSbands. This 160 µ m calibration uncertainty is therefore tied to24 and 70 µ m. The authors estimate a 7 % uncertainty tied tothese bands, for a total uncertainty of 11 . . Appendix A.4: Herschel/PACS
PACS calibration is performed on five stars, used as primary cal-ibrators (Balog et al. 2014). The absolute calibration uncertaintyfor point sources appears to be dominated by the stellar modeluncertainty of 5 %, correlated between bands. In addition, thereis a 2 % repeatability uncertainty, uncorrelated between bands.The extended source calibration uncertainty is not quantified bythe instrument team.
Article number, page 34 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution T a b l e A . . C o rr e l a ti on s o f t h ea b s o l u t eca li b r a ti onun ce r t a i n ti e s ( R ca l m a t r i x ; E q . A . ) . S ee T a b l e f o r w a v e b a ndn a m i ng c onv e n ti on s . I R A C M I PSP A C SSP I R E W I S E I R A S H F I I R A C . . . . . . I R A C . . . . . . I R A C . . . . . . I R A C . . . . . . M I PS . . M I PS . M I PS . . . P A C S . . P A C S . . P A C S . . SP I R E . . . . SP I R E . . . . SP I R E . . . . W I S E . . . . . . W I S E . . . . . . W I S E . . . . . . W I S E . . I R A S . . . I R A S . . . I R A S . . . I R A S . . . H F I . . . . H F I . . . . H F I Article number, page 35 of 64 & A proofs: manuscript no. manuscript
Appendix A.5: Herschel/SPIRE
SPIRE calibration, presented by Gri ffi n et al. (2013) is per-formed on Neptune. The uncertainty comes from three sources.There is a 4 % correlated uncertainty on Neptune’s model. Thereis also a 1 . Appendix A.6: WISE
WISE data have been calibrated by Jarrett et al. (2011) using ob-servations of a network of stars in both ecliptic poles (Cohenet al. 2003) and an additional red source, the galaxy NGC 6552.These calibrators have been observed with
Spitzer / IRAC and
Spitzer / MIPS, and compared to
WISE . It appears that the rela-tive
WISE calibration, tied to
Spitzer , is accurate to 2 . . . . (cid:39) WISE is not discussedby Jarrett et al. (2011). We can simply assume that each
WISE band will be tied to the closest
Spitzer band: WISE1 withIRAC1; WISE2 with IRAC2; WISE3 with IRAC4; WISE4 withMIPS1. We can thus quadratically add the
Spitzer calibrationuncertainties to these bands and assume that this term will becorrelated with the
Spitzer bands. However, we do not includethe IRAC uncertainty on the extended source correction (Ap-pendix A.2), as these calibrators are point sources.
Appendix A.7: IRAS
The
IRAS flux calibration is presented by Wheelock et al. (1994,Sect. VI.C.2) . The 12 µ m flux is calibrated on observations ofthe star α -Tau, assuming the absolute flux value derived fromthe ground-based 10 µ m photometry by Rieke et al. (1985), ac-curate within 3 %. An additional source of error comes from theuncertainty of 2 % on the model used to extrapolate the flux at12 µ m. The 25 and 60 µ m fluxes are calibrated by extrapolat-ing the 12 µ m flux, using stellar models, normalized to the Sun.The uncertainty in this extrapolation, based on the scatter of in-dividual stars, is estimated to be 4 % and 5 . µ m uncertainty, which is a fully correlatedterm. The 100 µ m calibration is based on observations of aster-oids, where the 60 µ m flux is extrapolated to 100 µ m, assum-ing that the 25 /
60 and 60 /
100 color temperatures are identical.Wheelock et al. (1994) estimate that the total relative calibrationuncertainty at 100 µ m is 10 %, due to the model uncertainty andscatter of the asteroid observations. This uncertainty is correlatedwith the 60 µ m.For extended sources, uncertainties in the frequency re-sponse and the e ff ective detector area have to be considered(Wheelock et al. 1994, Sect. VI.C.4). The uncertainty on the fre-quency response is not fully quantified, except that it should be7 % / µ m of the central bandwidth, with an uncertainty of 0.3 µ mon the bandwidth (Sect. VI.C.3 of Wheelock et al. 1994). It is https: // irsa.ipac.caltech.edu / IRASdocs / exp.sup / toc.html also specified that the 100 µ m uncertainty can be significant forobjects cooler than 30 K, which is our case. The uncertainty onthe detector areas is given by Table IV.A.1 of Wheelock et al.(1994) showing the flux dispersion of each individual detector,during a cross-scan of the planetary nebula NGC 6543. The av-erage dispersions of 6 . . . Appendix A.8: Planck/HFI
The calibration of the HFI data used by C18 is presentedby Planck Collaboration et al. (2016). The two short wave-length bands (350 and 550 µ m) are calibrated on Neptuneand Uranus. The uncertainty on the model is 5 % includ-ing 2 % spectrally independent. The statistical errors on theobservations of the calibrators are 1 . . // ftp.sciops.esa.int / pub / hsc-calibration / PlanetaryModels / ), respectively. Both models di ff eronly by 0.3–0.6 % in the SPIRE and HFI bands. They will thusinduce correlation. To simplify, we assume that the HFI cali-bration factors derived from Neptune (correlated with SPIRE)and Uranus (not correlated with SPIRE) are averaged. We obtaincalibration uncertainties (cid:39)
30 % lower than Planck Collabora-tion et al. (2016), as they have opted for the more conservative,linear addition of independent errors. We choose here the morerigorous quadratrical addition.The four long wavelength bands of HFI are calibrated onthe CMB dipole. The first source of uncertainty is the scatterof individual bolometers: 0 .
78 %, 0 .
16 %, 0 .
07 % and 0 .
09 % at850 µ m, 1.38, 2.1 and 3.0 mm. The second source of uncer-tainty comes from the gain variations: 0 .
03 %, 0 .
04 %, 0 .
05 %and 0 .
05 %, respectively. These di ff erent uncertainties can beconsidered independent. Appendix B: HOMOGENEITY OF THE SAMPLE
Appendix B.1: DustPedia and DGS Photometry
Fig. B.1 displays the comparison, in the 6
Herschel bands, of thephotometry of the sources of the DGS that are part of the Dust-Pedia sample. The DustPedia photometry has been estimated byC18 ( cf.
Sect. 2.1.1), and the DGS photometry, by Rémy-Ruyeret al. (2015, cf.
Sect. 2.1.2). Both are in very good agreement.
Appendix B.2: Derivation of the Stellar Mass
To further investigate the discrepancy between the
CIGALE fitsof N20 and the Eskew et al. (2012) approximation used by Mad-den et al. (2014), discussed in Sect. 2.2.1, we have comparedthe two estimators on our sample. To close the controversy, wehave modelled the UV-to-mm SED of the 35 DGS galaxies thatwere not in DustPedia, with
CIGALE , using the same settings asNersesian et al. (2019, i.e. using two stellar populations). Wetherefore have
CIGALE -derived M (cid:63) for our whole sample. Thisis shown in panel (a) of Fig. B.2. The stellar mass derived using CIGALE with two stellar populations are in very good agreementwith the Eskew et al. (2012) approximation.Panel (b) of Fig. B.2 compares the same
CIGALE -two-population estimates with the values of M (cid:63) reported by N20.The main di ff erences are the following, noting that the stellar Article number, page 36 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Fig. B.1.
Comparison between the DustPedia and DGS photometry.
The13 sources of the DGS which are part of the DustPedia catalog are com-pared in the 3 PACS and 3 SPIRE bands (one color per filter). The x axis shows the photometry estimated by C18, while the y axis showsthe photometry estimated by Rémy-Ruyer et al. (2015). The dashed linerepresents the 1:1 relation. masses quoted by N20 come from the SED modelling presentedby Burgarella et al. (2020).1. Nersesian et al. (2019) used the UV-optical photometryof Clark et al. (2018), which have been homogenized( cf. Sect. 2.1), whereas Burgarella et al. (2020) gathered UV-optical data from the
NASA / IPAC Extragalactic Database (NED). The latter is a compilation of data from the literaturethat can be inhomogeneous in terms of photometric aperture,extinction correction and removal of foreground stars.2. Nersesian et al. (2019) used
CIGALE with two stellar popula-tions: (i) an old exponentially decreasing SFH; (ii) a youngburst. In contrast, Burgarella et al. (2020) used a single de-layed SFH, which can lead to underestimating the mass, be-cause of the outshining e ff ect of the recent star formation( e.g. Lopes et al. 2020). For instance, Buat et al. (2014) con-ducted a large comparison of stellar mass estimates and con-cluded that models using two stellar populations were pro-viding the best fits. This can explain why the IRAC1 andIRAC2 fluxes are systematically underestimated by the meanmodel of N20 ( cf. their figure A.1), while it is not the case forNersesian et al. (2019, http: // dustpedia.astro.noa.gr / Cigale).Yet, these bands sample the spectral range where the bulkof the stellar mass dominates the emission. In addition, mostof the galaxies of the DGS are
Blue Compact Dwarf galax-ies (BCD). These galaxies are known to be actively form-ing stars and have an old underlying stellar population ( e.g.
Hunter & Gallagher 1989; Grebel 1999; Kunth & Östlin2000; Aloisi et al. 2007; Janowiecki et al. 2017).3. Nersesian et al. (2019) used a Salpeter (1955) IMF, whereasBurgarella et al. (2020) used a Chabrier (2003) IMF leadingto a systematic scaling by a factor 0.61.
Fig. B.2.
Comparison of stellar mass estimators.
Panel (a) compares the
CIGALE estimates of M (cid:63) , using two stellar populations ( x -axis), with theEskew et al. (2012, y -axis) empirical approximation, both assuming aSalpeter (1955) IMF. Panel (b) compares the same x -axis as panel (a) tothe CIGALE estimates, using a single stellar population and a Chabrier(2003) IMF, by N20. In both panels, the blue symbols correspond tothe values presented in Nersesian et al. (2019), and the red symbolscorrespond to the values estimated for this study, with the same
CIGALE settings. The solid yellow line represents the 1:1 relation. The dashedyellow line in panel (b) represents the 1:0.61 relation that accounts forthe di ff erence in IMFs. The comparison of these two estimates, in panel (b) of Fig. B.2,shows that the stellar masses of N20 are most of the time system-atically lower than those of Nersesian et al. (2019), sometimesdrastically.
Appendix C: ADDITIONAL DISCUSSION ON THEPARAMETRIZATION OF
THEMIS
We have presented the way we parametrize the
THEMIS size dis-tribution in Sect. 3.1.1. It consists in linearly scaling the fractionsof a-C(:H) smaller than 7 Å, and between 7 and 15 Å. We call itthe linear parametrization. It is controlled by the two parameters q AF and f VSAC , introduced in Sect. 3.1.1. In the present appendix,we demonstrate, on an example, that this parametrization is flex-
Article number, page 37 of 64 & A proofs: manuscript no. manuscript ible enough to mimic the original parametrization of
THEMIS .The
THEMIS size distribution of small a-C(:H) is a power-law,with minimum cut-o ff size a min = α = non-linear parametrization.Varying a min and α is probably more physical than our linear method, as it preserves the continuity of the size distribution.However, it produces SEDs with very similar shapes. Fig. C.1.
THEMIS parametrization comparison.
The two panels displaythe same quantities as Fig. 1. On each panel, the red curve shows
THEMIS , non-linearly parametrized, i.e. varying the minimum cut-o ff radius, a min , and the index of the power-law1 size distribution, α . Theblue curve shows THEMIS , linearly parametrized, with the method de-scribed in Sect. 3.1.1. The dots on the two SED curves (panel b ) repre-sent the synthetic photometry, i.e. the model integrated in the filters ofTable 1. This is demonstrated on Fig. C.1. This figure displays thesame quantities as Fig. 1, but compares the two parametriza-tions. The red curves show the size distribution (panel a ) and thecorresponding SED (panel b ), for the non-linear method, with a min = α =
4. The blue curves show the same quantities,with the linear method. We see that the broadband fluxes (dotsin panel b ) produced by these two parametrizations are very sim-ilar. The fact that they are not exactly the same is not importanthere. What is relevant is that the two methods can alter the SEDwith the same dynamical range. Appendix D: POSTERIOR PREDICTIVE P-VALUE
We have estimated the posterior predictive p-value (PPP; e.g.
Gelman et al. 2004) of our reference run (Sect. 3.2). PPPs arethe Bayesian equivalent to a chi-squared test. They allow us toquantify the goodness of our fit. PPPs are estimated by generat-ing sets of replicated observables, noted D rep , from our posteriordistribution, conditional on the actual data (Sect. 2), noted D : p ( D rep | D ) = (cid:90) p ( D rep | X ) p ( X | D ) d X , (D.1)where X are the model parameters. In practice, these replicatedsets are simply estimated by computing the SED model for sam-ples of the parameters drawn from the MCMC. The comparisonto the data requires the assumption of a test statistic, T ( D , X ).We adopt the commonly-used χ discrepancy quantity: T ( D , X ) ≡ (cid:88) i (cid:2) D i − µ ( D i | X ) (cid:3) σ ( D i | X ) , (D.2)where the index i represents every observable of every galaxy,and the quantities µ ( D i | X ) and σ ( D i | X ) are the mean andstandard-deviation of the replicated data. We then need to es-timate the probability: p B ≡ P (cid:16) T ( D rep | X ) ≥ T ( D | X ) | D (cid:17) . (D.3)If the di ff erence between the replicated set and the data is solelydue to statistical fluctuations, this probability should be on aver-age 50 %. A model passes the test, at the 98 % credence level, if1 % < p B <
99 %.In our case, we get p B = .
68 %, indicating our model failsthis test (it passes the 99 % credence level, though). Investigatingthe cause of this low p -value, we notice that a few observationsare responsible for large deviations. Fig. D.1 displays the SEDscontaining the 9 most deviant fluxes. IC 0319 and NGC 4322: the problematic flux is PACS1. ForIC 0319, it clearly lies above the rest of the observations,but has a small error bar. There is likely a problem with thisparticular measure. The problem is more di ffi cult to assessfor NGC 4322. However, the model is pulled well below thisflux by the three SPIRE upper limits. UGC 05336 and PGC 041994: the problems come from sev-eral far-IR upper limits. We display 3 σ upper limits whenthe value of the measured flux is smaller than its 1 σ noiselevel. In the case of the highlighted bands, the actual valueof the fluxes are negative, either because of statistical fluctu-ations, or background over-subtraction. Since the modelledflux can not be negative, we have T ( D rep | X ) (cid:28) T ( D | X ) forall replicated sets, pulling p B to the tail of the distribution. Article number, page 38 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Fig. D.1.
SEDs of the 4 galaxies causing the maximum deviations of thePPP.
The black circles with error bars are the observables. Most of themare upper limits. The blue line is the maximum a posteriori model, andthe purple dots are the synthetic photometry. The problematic fluxes areidentified by a red circle.
In summary, we are not in the case where the model would pro-vide a poor fit on average. A few discrepant data, that are treatedas outliers by the model ( i.e. which have a very limited impacton the results), are responsible for failing the PPP test. Excludingthese 9 observables, which represent only 0 .
07 % of our sample,we get p B = . . < ¯ χ < .
05. This is because the more data we have, thesmaller the statistical fluctuations should be.
Appendix E: DERIVED TEMPERATURE-EMISSIVITYRELATION
Fig. E.1 shows the β − T d relation derived from the HB MBB fitto the sample of Sect. 2 ( cf. Sect. 3.3.2). We can see that mostsources are clustered around ( T d ; β ) (cid:39) (cid:16) . + . − . K; 2 . + . − . (cid:17) ,with ± σ distribution widths ∆ T d = (cid:104) . + . −− . K , . + . −− . K (cid:105) and ∆ β = (cid:104) . + . − . , . + . − . (cid:105) . The correlation coe ffi -cient is ρ (ln T d , β ) (cid:39) − . + . − . , and CR ( ρ (ln T d , β )) = [ − . , − . IRAS µ m detection and three SPIRE upper limits.This trend is consistent with the Galactic di ff use ISM (yellowstar). This relation appears intrinsically scattered, with irregulars(in blue) being significantly hotter than ETGs (in red), them- Fig. E.1.
Modified black body results.
The SUEs show the relation be-tween the temperature, T d , and the emissivity index, β , derived fromthe β -free MBB run presented in Sect. 3.3.2. Galaxies are color-codedaccording to their type ( cf. Sect. 3.3.2). The di ff use ISM of the MilkyWay ( T MWd =
20 K, β MW = .
6; Planck Collaboration et al. 2014) isdisplayed as a yellow star. selves hotter than LTGs (in green). There is a significant β − T d negative correlation (such as shown by e.g. Dupac et al. 2003).We show this plot as a reference for comparison to other studies,since the MBB is the most commonly used model. Nonetheless,we emphasize that its physical interpretation is rendered di ffi -cult by the fact that β is degenerate with the mixing of physicalconditions ( cf. Sect. 2.3.1 of Galliano et al. 2018, for a review).
Appendix F: UNCERTAINTY REPRESENTATION
We detail here the way we display uncertainties in correlationplots throughout this article.
Appendix F.1: Skewed Uncertainty Ellipses
Our HB model computes the full posterior distribution of the pa-rameters of each source. Such a distribution is usually asymmet-ric and correlations between parameters can be strong. Display-ing this marginalized posterior distribution as density contours,for several hundreds of sources, is visually ine ff ective. In 2Dcorrelation plots, uncertainty ellipses are a widely-used deviceto display the extent of the posterior and show the correlationbetween parameters. However, it does not account for its skew-ness. To address this issue, we display each posterior as a SkewedUncertainty Ellipse (SUE), which is the 1 σ contour of a Bivari-ate Split-Normal distribution (BSN; Villani & Larsson 2006),having the same means, variances, skewnesses and correlationcoe ffi cient as the posterior. We add a central dot correspondingto the mode of this BSN. Fig. F.1 demonstrates the di ff erent waysof displaying uncertainties, for a typical PDF (orange density).Panel (c) shows the corresponding SUE. It has the advantage of Article number, page 39 of 64 & A proofs: manuscript no. manuscript retaining a lot of information from the posterior, with only onedot and one contour.Displaying a SUE is not straightforward. Indeed, a BSN isparametrized by its position vector, −→ X = ( x , y ), its scale vec-tor, −→ Λ = ( λ x , λ y ), its shape vector, −→ T = ( τ x , τ y ), and its rotationangle, − π/ < θ < π/
2. If we call −→ X = ( x , y ) our original coor-dinates and −→ X (cid:48) = ( x (cid:48) , y (cid:48) ) the coordinates in the centered, rotated,reference frame ( ←→ R being the rotation matrix): −→ X (cid:48) = (cid:32) x (cid:48) ( x , y ) y (cid:48) ( x , y ) (cid:33) = ←→ R T ( −→ X − −→ X ) = (cid:32) ( x − x ) cos θ + ( y − y ) sin θ − ( x − x ) sin θ + ( y − y ) cos θ (cid:33) , (F.1)the BSN PDF can be expressed as: p ( x , y ) = N × exp − (cid:32) x (cid:48) ( x , y ) λ x (cid:33) − (cid:32) y (cid:48) ( x , y ) λ y (cid:33) if x (cid:48) ( x , y ) < y (cid:48) ( x , y ) < − (cid:32) x (cid:48) ( x , y ) λ x τ x (cid:33) − (cid:32) y (cid:48) ( x , y ) λ y (cid:33) if x (cid:48) ( x , y ) ≥ y (cid:48) ( x , y ) < − (cid:32) x (cid:48) ( x , y ) λ x (cid:33) − (cid:32) y (cid:48) ( x , y ) λ y τ y (cid:33) if x (cid:48) ( x , y ) < y (cid:48) ( x , y ) ≥ − (cid:32) x (cid:48) ( x , y ) λ x τ x (cid:33) − (cid:32) y (cid:48) ( x , y ) λ y τ y (cid:33) if x (cid:48) ( x , y ) ≥ y (cid:48) ( x , y ) ≥ , (F.2)where the normalization constant is: N = πλ x λ y (1 + τ x )(1 + τ y ) . (F.3)We start by estimating the means ( (cid:104) x (cid:105) , (cid:104) y (cid:105) ), standard-deviations ( σ x , σ y ), skewnesses ( γ x , γ y ) and the correlation co-e ffi cient ( ρ ) of the posterior. We detail how we estimate thesemoments in Appendix F.2. These moments can be expressed asa function of the BSN’s parameters ( x , y , λ x , λ y , τ x , τ y , θ ): (cid:104) x (cid:105) = (cid:114) π (cid:104) λ x ( τ x −
1) cos θ − λ y ( τ y −
1) sin θ (cid:105) + x (F.4) (cid:104) y (cid:105) = (cid:114) π (cid:104) λ x ( τ x −
1) sin θ + λ y ( τ y −
1) cos θ (cid:105) + y (F.5) σ x = λ x B ( τ x ) cos θ + λ y B ( τ y ) sin θ (F.6) σ y = λ x B ( τ x ) sin θ + λ y B ( τ y ) cos θ (F.7) ρσ x σ y = (cid:16) λ x B ( τ x ) − λ y B ( τ y ) (cid:17) cos θ sin θ (F.8) γ x σ x = (cid:114) π (cid:16) λ x C ( τ x ) cos θ − λ y C ( τ y ) sin θ (cid:17) (F.9) γ y σ y = (cid:114) π (cid:16) λ x C ( τ x ) sin θ + λ y C ( τ y ) cos θ (cid:17) , (F.10)with: B ( τ ) = (cid:32) − π (cid:33) ( τ − + τ (F.11) C ( τ ) = (cid:34)(cid:32) π − (cid:33) τ + (cid:32) − π (cid:33) τ + π − (cid:35) ( τ − . (F.12) Fig. F.1.
Uncertainty display.
The orange density contours in the threepanels represent an arbitrary bivariate PDF of two variables x and y .Panel (a) shows the corresponding traditional error bar: the dot is themean and the bars show the ± σ extent along both axes. Panel (b) shows the widely-used uncertainty ellipse, which can be viewed asthe mode and 1 σ contour of a bivariate normal distribution having thesame means, standard-deviations and correlation coe ffi cient as the PDF.Panel (c) shows the concept of SUE introduced in Appendix F.1.Article number, page 40 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution We then simply need to solve the system of Eqs. (F.4) – (F.10).To do that, we first solve θ : θ =
12 arctan ρσ x σ y σ x − σ y . (F.13)We then solve numerically for τ x and τ y , independently, from thetwo equations: C ( τ x ) B ( τ x ) / = (cid:114) π γ x σ x cos θ + γ x σ x sin θ cos θ + sin θ × cos θ − sin θσ x cos θ − σ y sin θ / (F.14) C ( τ y ) B ( τ y ) / = (cid:114) π γ y σ y cos θ − γ x σ x sin θ cos θ + sin θ × cos θ − sin θσ y cos θ − σ x sin θ / . (F.15)We derive the remaining parameters, using the following equa-tions: λ x = (cid:115) B ( τ x ) σ x cos θ − σ y sin θ cos θ − sin θ (F.16) λ y = (cid:115) B ( τ y ) σ y cos θ − σ x sin θ cos θ − sin θ (F.17) x = (cid:104) x (cid:105) − (cid:114) π (cid:104) λ x ( τ x −
1) cos θ − λ y ( τ y −
1) sin θ (cid:105) (F.18) y = (cid:104) y (cid:105) − (cid:114) π (cid:104) λ x ( τ x −
1) sin θ + λ y ( τ y −
1) cos θ (cid:105) . (F.19) Appendix F.2: Robust Estimate of the Posterior DistributionMoments
We estimate the moments of Eqs. (F.4) – (F.10) numerically,from the marginalized posterior. Some outliers can be presentdue to incomplete burn-in removal, requiring robust estimators.We choose
M-estimators (Mosteller & Tukey 1977), which area generalization of maximum-likelihood estimators. They havebeen popularized in astrophysics by Beers et al. (1990). Loca-tion and scale M-estimators, using
Tukey’s biweight loss func-tion were presented by Lax (1975). Posing u i = ( x i − l x ) / ( c × s x ),where l x = med( X ) is the median of the sample X = { x i } i = ... N , s x = . × med( | X − med( X ) | ) is the Median Absolute Devi-ation (MAD) of X , and c is a tuning parameter, the M-estimatorof the mean is:ˆ µ ( X ) = l x + (cid:80) | u i | < ( x i − l x )(1 − u i ) (cid:80) | u i | < (1 − u i ) , (F.20)and for the variance:ˆ V ( X ) = N × (cid:80) | u i | < ( x i − l x ) (1 − u i ) (cid:104)(cid:80) | u i | < (1 − u i )(1 − u i ) (cid:105) (cid:104)(cid:80) | u i | < (1 − u i )(1 − u i ) − (cid:105) . (F.21)Considering a second sample Y = { y i } i = ... N , an M-estimator ofthe covariance is presented by Mosteller & Tukey (1977). Posing v i = ( y i − l y ) / ( c × s y ), the covariance can be estimated as:ˆ V ( X , Y ) = N × (cid:80) | u i | < , | v i | < ( x i − l x )(1 − u i ) ( y i − l y )(1 − v i ) (cid:104)(cid:80) | u i | < (1 − u i )(1 − u i ) (cid:105) (cid:104)(cid:80) | v i | < (1 − v i )(1 − v i ) (cid:105) . (F.22)These estimators are implemented in the Python astropy module (Astropy Collaboration et al. 2013, 2018). We have de-signed our own skewness W-estimator:ˆ γ ( X ) = (cid:80) | u i | < u i (1 − u i ) (cid:80) | u i | < (1 − u i ) . (F.23)We have also slightly improved astropy ’s implementation byiterating on Eqs. (F.20) – (F.23), replacing l x , l y , s x and s y withˆ µ ( X ), ˆ µ ( Y ), (cid:112) ˆ V ( X ) and (cid:112) ˆ V ( Y ), respectively, until a 10 − relativeaccuracy is reached. The tuning parameter is usually taken as c = c = Appendix G: DUST EVOLUTION RESULTSASSUMING A CHABRIER IMF
We have performed the modelling of Sect. 5.2.2, assuming aChabrier (2003) IMF. The data have been corrected accordingly: M (cid:63) has been multiplied by 0.61 and SFR by 0.63 (Madau &Dickinson 2014), as these two quantities were derived assum-ing a Salpeter (1955) IMF. Fig. G.1 shows the fit of the scalingrelations; it is the equivalent of Fig. 14. Figs. G.2 – G.3 dis-play the PDF of the dust evolution and SFH-related parameters,respectively; they are the equivalent of Figs. 16 – 17. The in-ferred timescales are displayed in Fig. G.4; it is the equivalent ofFig. 18. Appendix H: REFERENCE RUN PARAMETERS
Table H.1 gives the mean and standard-deviation of the most rel-evant parameters derived with the reference run ( cf.
Sect. 3.2),for each galaxy of the sample presented in Sect. 2.
Article number, page 41 of 64 & A proofs: manuscript no. manuscript
Fig. G.1.
Fitted dust evolution tracks, assuming a Chabrier (2003) IMF. This is the equivalent of Fig. 14.Article number, page 42 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Fig. G.2.
Posterior distribution of the tuning parameters, assuming aChabrier (2003) IMF. This is the equivalent of Fig. 16. Article number, page 43 of 64 & A proofs: manuscript no. manuscript
Fig. G.3.
Posterior distribution of the SFH-related parameters, assuming a Chabrier (2003) IMF. This is the equivalent of Fig. 17.Article number, page 44 of 64. Galliano et al.: A Nearby Galaxy Perspective on Dust Evolution
Fig. G.4.
Posterior distribution of the tuning parameters, assuming aChabrier (2003) IMF. This is the equivalent of Fig. 18. Article number, page 45 of 64 & A p r oo f s : m a nu s c r i p t no . m a nu s c r i p t Table H.1.
Main inferred quantities for each galaxy, with the reference run. For each quantity, we quote the mean ± the standard-deviation of the posterior PDF. Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)ESO 149-013 5 . ± . − . ± . − . ± .
21 8 . ± .
023 . . . 8 . ± .
19 . . . . . .NGC 0007 6 . ± .
17 0 . ± . − . ± .
11 9 . ± .
03 . . . 9 . ± . − . ± .
11 . . .ESO 410-005 3 . ± . . ± . − . ± . . ± .
14 . . . . . .IC 0010 5 . ± .
20 0 . ± . − . ± .
16 8 . ± .
06 . . . 8 . ± . − . ± .
31 8 . ± . . ± .
12 0 . ± . − . ± .
08 9 . ± .
04 . . . 9 . ± . − . ± .
10 . . .ESO 410-012 5 . ± . − . ± . − . ± .
21 8 . ± .
029 . . . 8 . ± . − . ± .
14 . . .NGC 0131 6 . ± .
07 0 . ± . − . ± .
04 9 . ± .
005 . . . 9 . ± . − . ± .
11 . . .UGC 00300 5 . ± . − . ± . − . ± .
16 8 . ± .
022 . . . 8 . ± . − . ± .
13 8 . ± . . ± .
13 0 . ± . − . ± .
07 8 . ± .
06 . . . 9 . ± . − . ± .
11 8 . ± . . ± . − . ± . − . ± .
11 9 . ± .
07 . . . 8 . ± . − . ± .
11 . . .NGC 0148 5 . ± .
25 0 . ± . − . ± .
14 . . . . . . 10 . ± .
05 . . . . . .NGC 0150 7 . ± .
020 0 . ± . − . ± .
007 9 . ± .
04 . . . 10 . ± . − . ± .
10 . . .ESO 411-013 5 . ± . − . ± . − . ± .
17 . . . . . . 8 . ± . − . ± .
24 . . .NGC 0254 5 . ± .
20 0 . ± . − . ± .
13 . . . . . . 10 . ± . − . ± . . ± .
24 0 . ± . − . ± .
13 8 . ± .
10 . . . 8 . ± . − . ± .
14 . . .NGC 0289 7 . ± .
04 0 . ± . − . ± .
029 10 . ± .
015 . . . 10 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
20 . . . . . . 8 . ± . − . ± .
19 . . .ESO 411-027 5 . ± . − . ± . − . ± .
20 . . . . . . 8 . ± . − . ± .
27 . . .NGC 0300 6 . ± . − . ± . − . ± .
05 9 . ± .
03 . . . 9 . ± . − . ± .
12 8 . ± . . ± .
06 0 . ± . − . ± .
05 9 . ± .
022 . . . 9 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± . . ± .
004 . . . 2 . ± .
29 . . . . . .IC 1613 4 . ± .
16 0 . ± . − . ± .
17 7 . ± . . ± . − . ± .
11 7 . ± . . ± .
08 0 . ± . − . ± .
07 9 . ± . . ± . − . ± .
06 8 . ± . . ± . − . ± . − . ± .
25 8 . ± .
007 . . . 7 . ± . − . ± .
24 . . .NGC 0448 6 . ± .
22 0 . ± . − . ± .
11 . . . . . . 10 . ± .
07 . . . . . .NGC 0493 7 . ± .
06 0 . ± . − . ± .
031 9 . ± . . ± . − . ± .
09 8 . ± . . ± . . ± . − . ± .
17 9 . ± .
06 . . . 8 . ± . − . ± .
21 8 . ± . . ± .
06 1 . ± . − . ± .
009 . . . . . . 10 . ± . − . ± .
07 . . .NGC 0584 6 . ± .
20 0 . ± . − . ± .
13 . . . . . . 10 . ± . − . ± . . ± .
09 0 . ± . − . ± .
06 . . . . . . 9 . ± . − . ± .
31 . . .NGC 0613 8 . ± .
017 0 . ± . − . ± .
011 10 . ± . − . ± .
19 10 . ± . − . ± .
13 8 . ± . . ± .
12 0 . ± . − . ± .
07 8 . ± .
023 . . . 8 . ± . − . ± .
13 8 . ± . . ± .
07 0 . ± . − . ± .
04 10 . ± . − . ± .
15 10 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
06 9 . ± .
11 . . . 10 . ± . − . ± . . ± . . ± . − . ± .
21 . . . . . . 11 . ± . − . ± . . ± .
09 0 . ± . − . ± .
05 . . . . . . 9 . ± . − . ± . . ± .
09 0 . ± . − . ± .
07 8 . ± .
030 . . . 8 . ± . − . ± .
21 . . .PGC 008962 5 . ± . . ± . − . ± .
16 9 . ± .
028 . . . 8 . ± . − . ± .
16 8 . ± . . ± .
04 0 . ± . − . ± .
011 10 . ± .
019 . . . 10 . ± . − . ± .
09 8 . ± . . ± .
008 0 . ± . − . ± .
013 10 . ± . − . ± .
14 10 . ± . − . ± .
30 . . .NGC 0925 7 . ± . − . ± . − . ± .
07 10 . ± . − . ± .
14 9 . ± . − . ± .
09 8 . ± . . ± .
23 0 . ± . − . ± .
06 . . . . . . 9 . ± . − . ± .
12 . . .NGC 1056 7 . ± .
03 0 . ± . − . ± .
019 9 . ± .
021 . . . 10 . ± . − . ± .
14 8 . ± . . ± .
019 0 . ± . − . ± .
010 10 . ± . − . ± .
14 10 . ± . − . ± .
10 8 . ± . A r ti c l e nu m b e r , p a g e ff
10 8 . ± . A r ti c l e nu m b e r , p a g e ff . G a lli a no e t a l . : AN ea r by G a l a xy P e r s p ec ti v e on D u s t E vo l u ti on Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 1140 6 . ± .
09 0 . ± . − . ± .
07 9 . ± . − . ± .
17 9 . ± . − . ± .
11 8 . ± . . ± . − . ± . − . ± .
16 7 . ± . . ± .
17 . . . . . .UGC 02392 6 . ± .
17 0 . ± . − . ± .
11 9 . ± .
008 . . . 9 . ± . − . ± .
13 . . .NGC 1189 7 . ± . − . ± . − . ± .
07 . . . . . . 9 . ± . − . ± .
12 . . .NGC 1222 6 . ± .
019 1 . ± . − . ± .
013 9 . ± .
05 . . . 9 . ± . − . ± .
11 . . .PGC 166071 6 . ± . . ± . − . ± .
15 . . . . . . 10 . ± .
15 . . . . . .ESO 116-012 7 . ± .
29 0 . ± . − . ± .
04 . . . . . . . . . . . . . . .NGC 1266 6 . ± .
03 1 . ± . − . ± .
010 . . . . . . 9 . ± . − . ± .
11 . . .PGC 012608 5 . ± .
30 0 . ± . − . ± .
15 . . . . . . 9 . ± . − . ± .
15 . . .NGC 1317 6 . ± .
027 0 . ± . − . ± .
014 . . . . . . 10 . ± . − . ± .
16 . . .NGC 1336 5 . ± . − . ± . − . ± .
13 . . . . . . 9 . ± . − . ± . . ± . . ± . − . ± .
26 . . . . . . 8 . ± . − . ± .
17 . . .NGC 1351A 6 . ± . − . ± . − . ± .
04 8 . ± . − . ± .
15 9 . ± . − . ± .
16 . . .NGC 1351 6 . ± . . ± . − . ± .
15 . . . . . . 10 . ± . − . ± . . ± .
18 0 . ± . − . ± .
10 . . . . . . 8 . ± . − . ± .
22 . . .PGC 013084 5 . ± . − . ± . − . ± .
16 . . . . . . 9 . ± . − . ± .
17 . . .PGC 013097 5 . ± . . ± . − . ± .
20 . . . . . . 8 . ± . − . ± . . ± . − . ± . − . ± .
18 . . . . . . 9 . ± . − . ± . . ± . . ± . − . ± .
17 8 . ± .
05 . . . 8 . ± . − . ± .
16 . . .ESO 358-016 5 . ± . − . ± . − . ± .
17 . . . . . . 8 . ± . − . ± .
21 . . .NGC 1365 8 . ± .
020 0 . ± . − . ± .
019 10 . ± . − . ± .
14 10 . ± . − . ± .
19 8 . ± . . ± . − . ± . − . ± .
18 . . . . . . 9 . ± . − . ± . . ± . − . ± . − . ± .
22 . . . . . . 8 . ± .
19 . . . . . .NGC 1373 5 . ± . − . ± . − . ± .
17 . . . . . . 9 . ± . − . ± . . ± .
26 0 . ± . − . ± .
09 . . . . . . 10 . ± . − . ± .
17 . . .IC 0335 5 . ± .
29 0 . ± . − . ± .
15 . . . . . . 10 . ± . − . ± . . ± .
26 0 . ± . − . ± .
15 . . . . . . 10 . ± . − . ± . . ± . . ± . − . ± .
20 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
16 . . . . . . 9 . ± . − . ± . . ± .
016 0 . ± . − . ± .
006 . . . . . . 10 . ± . − . ± . . ± . . ± .
25 0 . ± . − . ± .
13 . . . . . . 9 . ± . − . ± . . ± . − . ± . − . ± .
15 . . . . . . 9 . ± . − . ± . . ± .
06 0 . ± . − . ± .
04 . . . . . . 10 . ± . − . ± .
27 . . .NGC 1389 6 . ± .
28 0 . ± . − . ± .
15 . . . . . . 10 . ± . − . ± .
29 . . .ESO 358-042 5 . ± . − . ± . − . ± .
21 . . . . . . 8 . ± .
10 . . . . . .ESO 358-043 6 . ± . − . ± . − . ± .
14 . . . . . . 9 . ± . − . ± . . ± . . ± . − . ± . . ± . − . ± .
21 . . .NGC 1404 5 . ± .
30 0 . ± . − . ± .
05 . . . . . . 11 . ± . − . ± .
22 . . .NGC 1427A 6 . ± . − . ± . − . ± .
08 9 . ± .
05 . . . 8 . ± . − . ± .
11 8 . ± . . ± .
25 0 . ± . − . ± .
13 9 . ± .
12 . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
14 . . . . . . 10 . ± . − . ± .
29 . . .ESO 358-050 5 . ± . − . ± . − . ± .
13 . . . . . . 9 . ± . − . ± .
25 . . .ESO 358-051 6 . ± .
19 0 . ± . − . ± .
04 8 . ± .
12 . . . 8 . ± . − . ± .
12 8 . ± . . ± . . ± . − . ± .
16 . . . . . . 10 . ± . − . ± . A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . m a nu s c r i p t Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 1428 5 . ± .
29 0 . ± . − . ± .
14 . . . . . . 9 . ± . − . ± .
29 . . .PGC 013635 5 . ± . − . ± . − . ± .
12 . . . . . . 9 . ± . − . ± .
13 . . .ESO 358-054 6 . ± . − . ± . − . ± .
09 8 . ± .
04 . . . 8 . ± . − . ± .
10 8 . ± . . ± . . ± . − . ± .
18 . . . . . . 8 . ± .
22 . . . . . .ESO 358-056 5 . ± .
29 0 . ± . − . ± .
17 . . . . . . 8 . ± . − . ± . . ± . − . ± . − . ± .
026 8 . ± . − . ± .
14 9 . ± . − . ± .
21 8 . ± . . ± .
07 0 . ± . − . ± .
03 . . . . . . 10 . ± . − . ± .
23 . . .ESO 358-059 5 . ± . − . ± . − . ± .
16 . . . . . . 9 . ± . − . ± . . ± . − . ± . − . ± .
24 7 . ± .
026 . . . 7 . ± . − . ± .
30 7 . ± . . ± . − . ± . − . ± .
20 6 . ± .
09 . . . 7 . ± . − . ± .
21 . . .NGC 1437B 6 . ± . − . ± . − . ± .
04 . . . . . . 8 . ± . − . ± .
26 . . .ESO 358-063 7 . ± .
031 0 . ± . − . ± .
013 9 . ± . − . ± .
14 9 . ± . − . ± .
16 . . .IC 0342 7 . ± .
05 0 . ± . − . ± .
025 . . . . . . 10 . ± . − . ± .
08 8 . ± . . ± . − . ± . − . ± .
19 . . . . . . 8 . ± .
12 . . . . . .ESO 359-002 5 . ± . − . ± . − . ± .
17 . . . . . . 9 . ± . − . ± . . ± .
012 1 . ± . − . ± .
007 . . . . . . 9 . ± . − . ± .
10 . . .ESO 549-035 6 . ± . − . ± . − . ± .
13 9 . ± .
05 . . . 9 . ± . − . ± .
13 . . .NGC 1510 5 . ± .
20 0 . ± . − . ± .
10 . . . . . . 8 . ± . − . ± .
12 8 . ± . . ± .
029 0 . ± . − . ± .
05 9 . ± . − . ± .
19 9 . ± . − . ± .
13 8 . ± . . ± .
12 0 . ± . − . ± .
08 9 . ± .
26 . . . 9 . ± .
11 . . . . . .NGC 1569 5 . ± .
14 1 . ± . − . ± .
06 8 . ± . − . ± .
17 8 . ± . − . ± .
10 7 . ± . . ± . − . ± . − . ± .
04 . . . . . . 9 . ± . − . ± . . ± .
05 0 . ± . − . ± .
023 . . . . . . 10 . ± . − . ± . . ± . . ± . − . ± .
15 8 . ± .
04 . . . 8 . ± . − . ± .
17 . . .ESO 157-049 7 . ± .
13 0 . ± . − . ± .
018 9 . ± .
020 . . . 9 . ± . − . ± .
12 8 . ± . . ± .
16 0 . ± . − . ± .
10 8 . ± .
022 . . . 8 . ± . − . ± .
10 8 . ± . . ± .
08 0 . ± . − . ± .
021 8 . ± .
016 . . . 8 . ± . − . ± .
11 8 . ± . . ± .
028 1 . ± . − . ± .
021 10 . ± . − . ± .
17 10 . ± . − . ± .
13 . . .NGC 1924 7 . ± .
04 0 . ± . − . ± .
029 9 . ± .
05 . . . 10 . ± . − . ± .
19 . . .NGC 2146 8 . ± .
011 1 . ± . − . ± .
005 . . . . . . 10 . ± . − . ± .
16 . . .NGC 2273 7 . ± .
021 0 . ± . − . ± .
011 9 . ± . − . ± .
16 10 . ± . − . ± .
19 . . .PGC 2807061 3 . ± . − . ± . − . ± . . ± .
06 . . . 6 . ± .
20 . . . . . .UGC 03701 6 . ± .
18 0 . ± . − . ± .
10 9 . ± .
05 . . . 9 . ± . − . ± .
13 8 . ± . . ± .
24 1 . ± . − . ± .
06 . . . . . . . . . . . . . . .NGC 2403 7 . ± .
06 0 . ± . − . ± .
024 9 . ± . − . ± .
14 9 . ± . − . ± .
07 8 . ± . . ± .
08 0 . ± . − . ± .
03 . . . . . . 10 . ± .
12 . . . . . .UGC 03960 5 . ± . . ± . − . ± .
15 . . . . . . 10 . ± . − . ± . . ± .
06 0 . ± . − . ± .
030 . . . . . . 9 . ± . − . ± .
18 . . .ESO 209-009 7 . ± .
04 0 . ± . − . ± .
04 9 . ± .
020 . . . 10 . ± .
10 . . . . . .IC 2233 6 . ± . − . ± . − . ± .
13 9 . ± .
05 . . . 9 . ± . − . ± .
06 8 . ± . . ± .
22 0 . ± . − . ± .
13 . . . . . . 10 . ± . − . ± . . ± .
23 0 . ± . − . ± .
15 8 . ± .
022 . . . 8 . ± . − . ± .
11 7 . ± . . ± .
27 0 . ± . − . ± .
14 . . . . . . 10 . ± .
05 . . . . . .NGC 2592 5 . ± . − . ± . − . ± .
16 . . . . . . 10 . ± . − . ± . A r ti c l e nu m b e r , p a g e ff
16 . . . . . . 10 . ± . − . ± . A r ti c l e nu m b e r , p a g e ff . G a lli a no e t a l . : AN ea r by G a l a xy P e r s p ec ti v e on D u s t E vo l u ti on Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)ESO 495-021 6 . ± .
018 1 . ± . − . ± .
010 8 . ± .
021 . . . 8 . ± . − . ± .
15 8 . ± . . ± . . ± . − . ± .
18 7 . ± .
022 . . . 6 . ± . − . ± .
22 7 . ± . . ± . . ± . − . ± .
16 . . . . . . 10 . ± . − . ± . . ± .
09 0 . ± . − . ± .
04 9 . ± .
04 . . . 9 . ± . − . ± .
10 8 . ± . . ± . . ± . − . ± .
17 . . . . . . 10 . ± . − . ± .
21 . . .NGC 2685 6 . ± . − . ± . − . ± .
04 . . . . . . 10 . ± . − . ± .
14 . . .NGC 2655 6 . ± . − . ± . − . ± .
08 9 . ± .
09 . . . 10 . ± . − . ± .
12 . . .UGC 04684 6 . ± .
11 0 . ± . − . ± .
06 9 . ± .
005 . . . 9 . ± . − . ± .
11 8 . ± . . ± .
03 0 . ± . − . ± .
013 . . . . . . 10 . ± . − . ± .
12 . . .NGC 2768 6 . ± . . ± . − . ± .
13 . . . . . . 11 . ± . − . ± .
28 . . .NGC 2778 5 . ± .
27 0 . ± . − . ± .
15 . . . . . . 10 . ± . − . ± .
22 . . .NGC 2787 5 . ± .
27 0 . ± . − . ± .
13 9 . ± .
13 . . . 10 . ± . − . ± . . ± .
04 0 . ± . − . ± .
027 10 . ± .
04 . . . 10 . ± . − . ± .
30 . . .NGC 2841 7 . ± .
05 0 . ± . − . ± .
12 10 . ± .
022 . . . 11 . ± . − . ± .
11 8 . ± . . ± .
10 0 . ± . − . ± .
06 . . . . . . 9 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
11 10 . ± .
18 . . . 10 . ± . − . ± . . ± .
17 0 . ± . − . ± .
12 8 . ± .
030 . . . 8 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
10 10 . ± .
15 . . . 10 . ± . − . ± . . ± .
24 0 . ± . − . ± .
13 . . . . . . 9 . ± . − . ± .
30 . . .ESO 373-008 7 . ± . − . ± . − . ± .
07 9 . ± .
021 . . . 9 . ± .
11 . . . . . .UGC 05139 4 . ± . − . ± . − . ± .
18 8 . ± .
022 . . . 7 . ± . − . ± .
15 7 . ± . . ± . − . ± . − . ± .
031 . . . . . . . . . . . . . . .NGC 2950 5 . ± . . ± . − . ± .
18 . . . . . . 10 . ± . − . ± .
09 . . .PGC 090942 5 . ± . − . ± . − . ± .
23 9 . ± .
025 . . . 9 . ± . − . ± . . ± .
011 1 . ± . − . ± .
007 9 . ± . − . ± .
21 10 . ± . − . ± .
10 . . .NGC 2993 6 . ± .
013 1 . ± . − . ± .
006 . . . . . . 9 . ± . − . ± .
10 . . .NGC 2976 6 . ± .
05 0 . ± . − . ± .
023 8 . ± . − . ± .
16 8 . ± . − . ± .
10 8 . ± . . ± .
09 0 . ± . − . ± .
03 9 . ± . − . ± .
20 9 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
03 9 . ± . − . ± .
14 10 . ± . − . ± .
17 8 . ± . . ± .
007 1 . ± . − . ± .
010 9 . ± . − . ± .
17 10 . ± . − . ± .
10 . . .UGC 05340 5 . ± . − . ± . − . ± .
21 9 . ± . . ± . − . ± .
15 . . .PGC 028759 3 . ± . − . ± . − . ± . . ± .
12 . . . 6 . ± . − . ± . . ± . − . ± . − . ± .
30 . . . . . . . . . . . . 8 . ± . . ± .
09 0 . ± . − . ± .
017 9 . ± .
07 . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
029 10 . ± .
06 . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
18 7 . ± .
022 . . . 7 . ± . − . ± .
10 7 . ± . . ± .
19 0 . ± . − . ± .
11 8 . ± .
06 . . . 9 . ± . − . ± .
25 . . .NGC 3079 7 . ± .
025 0 . ± . − . ± .
013 10 . ± . − . ± .
15 10 . ± . − . ± .
12 . . .NGC 3077 6 . ± .
06 0 . ± . − . ± .
04 9 . ± . − . ± .
16 9 . ± . − . ± . . ± . . ± .
28 0 . ± . − . ± .
14 7 . ± .
10 . . . 7 . ± . − . ± .
14 . . .UGC 05454 5 . ± .
27 0 . ± . − . ± .
14 9 . ± .
006 . . . 8 . ± . − . ± .
13 8 . ± . . ± . − . ± . − . ± .
21 7 . ± .
022 . . . 6 . ± . − . ± .
26 7 . ± . . ± .
017 0 . ± . − . ± .
013 10 . ± . − . ± .
15 11 . ± . − . ± .
27 . . .NGC 3185 6 . ± .
07 0 . ± . − . ± .
03 9 . ± . − . ± .
17 10 . ± . − . ± .
20 . . . A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . m a nu s c r i p t Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 3155 7 . ± .
09 0 . ± . − . ± .
04 9 . ± .
030 . . . 9 . ± . − . ± .
11 . . .NGC 3187 7 . ± . − . ± . − . ± .
06 9 . ± .
005 . . . 9 . ± . − . ± .
09 8 . ± . . ± .
04 0 . ± . − . ± .
014 9 . ± . − . ± .
16 10 . ± .
07 . . . . . .NGC 3184 7 . ± .
04 0 . ± . − . ± .
020 9 . ± . − . ± .
15 10 . ± . − . ± .
08 8 . ± . . ± .
16 0 . ± . − . ± .
07 9 . ± . − . ± .
19 10 . ± . − . ± .
12 8 . ± . . ± .
03 0 . ± . − . ± .
04 10 . ± . − . ± .
21 10 . ± . − . ± .
09 8 . ± . . ± . . ± . − . ± .
14 . . . . . . 9 . ± . − . ± . . ± . − . ± . − . ± .
10 9 . ± .
024 . . . 9 . ± . − . ± .
09 . . .IC 0610 6 . ± .
04 0 . ± . − . ± .
020 9 . ± .
16 . . . 10 . ± . − . ± . . ± . . ± . − . ± . − . ± .
12 9 . ± .
006 . . . 9 . ± . − . ± .
14 8 . ± . . ± . − . ± . − . ± .
16 9 . ± .
08 . . . 8 . ± . − . ± .
11 . . .NGC 3254 7 . ± . − . ± . − . ± .
04 10 . ± .
014 . . . 10 . ± . − . ± .
08 . . .UGC 05686 6 . ± .
31 0 . ± . − . ± .
15 9 . ± .
05 . . . 8 . ± . − . ± .
20 . . .UGC 05689 7 . ± .
10 0 . ± . − . ± .
05 9 . ± .
09 . . . 9 . ± . − . ± .
12 . . .NGC 3283 7 . ± .
09 0 . ± . − . ± .
11 . . . . . . 11 . ± .
14 . . . . . .UGC 05720 6 . ± .
08 1 . ± . − . ± .
018 9 . ± . − . ± .
21 9 . ± . − . ± .
10 8 . ± . . ± .
10 0 . ± . − . ± .
05 9 . ± . − . ± .
19 10 . ± . − . ± .
29 . . .NGC 3252 6 . ± .
10 0 . ± . − . ± .
05 9 . ± .
05 . . . 9 . ± . − . ± .
14 . . .NGC 3287 6 . ± .
03 0 . ± . − . ± .
03 8 . ± .
05 . . . 9 . ± . − . ± .
10 8 . ± . . ± .
009 0 . ± . − . ± .
010 9 . ± . − . ± .
14 10 . ± . − . ± .
08 8 . ± . . ± .
18 0 . ± . − . ± .
11 9 . ± .
21 . . . 10 . ± . − . ± .
17 . . .NGC 3338 7 . ± .
05 0 . ± . − . ± .
05 10 . ± . − . ± .
15 10 . ± . − . ± .
11 8 . ± . . ± .
04 0 . ± . − . ± .
04 9 . ± . − . ± .
17 9 . ± . − . ± .
08 8 . ± . . ± .
04 0 . ± . − . ± .
05 9 . ± . − . ± .
15 10 . ± . − . ± .
12 8 . ± . . ± . − . ± . − . ± .
19 . . . . . . 8 . ± . − . ± .
13 . . .NGC 3353 6 . ± .
04 1 . ± . − . ± .
015 . . . . . . 9 . ± . − . ± .
09 8 . ± . . ± .
029 0 . ± . − . ± .
010 10 . ± . − . ± .
14 10 . ± . − . ± .
09 8 . ± . . ± . . ± . − . ± .
20 . . . . . . 11 . ± . − . ± .
18 . . .NGC 3380 5 . ± .
08 0 . ± . − . ± .
03 7 . ± .
10 . . . 8 . ± . − . ± .
12 . . .NGC 3381 7 . ± .
05 0 . ± . − . ± .
011 9 . ± .
003 . . . 9 . ± . − . ± .
07 8 . ± . . ± .
07 0 . ± . − . ± .
026 9 . ± .
04 . . . 10 . ± . − . ± .
11 . . .UGC 05958 6 . ± . − . ± . − . ± .
09 8 . ± .
025 . . . 9 . ± . − . ± .
12 8 . ± . . ± . − . ± . − . ± .
14 10 . ± .
20 . . . 11 . ± . − . ± .
06 . . .NGC 3413 6 . ± .
10 0 . ± . − . ± .
06 9 . ± . . ± . − . ± .
13 8 . ± . . ± .
026 0 . ± . − . ± .
018 9 . ± .
021 . . . 10 . ± . − . ± .
10 . . .UGC 05955 5 . ± . − . ± . − . ± .
15 . . . . . . 9 . ± . − . ± . . ± .
026 0 . ± . − . ± .
011 10 . ± .
08 . . . 10 . ± . − . ± .
10 8 . ± . . ± .
021 0 . ± . − . ± .
011 9 . ± . − . ± .
13 10 . ± . − . ± .
08 8 . ± . . ± .
12 0 . ± . − . ± .
06 8 . ± .
021 . . . 9 . ± . − . ± .
09 8 . ± . . ± .
13 0 . ± . − . ± .
06 9 . ± .
06 . . . 9 . ± . − . ± .
09 8 . ± . . ± .
08 0 . ± . − . ± .
05 9 . ± .
011 . . . 9 . ± . − . ± .
09 . . .UGC 06016 5 . ± . − . ± . − . ± .
17 9 . ± .
10 . . . 8 . ± . − . ± .
15 8 . ± . . ± .
04 0 . ± . − . ± .
019 9 . ± .
010 . . . 9 . ± . − . ± .
08 8 . ± . . ± .
09 0 . ± . − . ± .
08 8 . ± .
06 . . . 9 . ± . − . ± .
12 8 . ± . A r ti c l e nu m b e r , p a g e ff
12 8 . ± . A r ti c l e nu m b e r , p a g e ff . G a lli a no e t a l . : AN ea r by G a l a xy P e r s p ec ti v e on D u s t E vo l u ti on Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 3455 7 . ± .
06 0 . ± . − . ± .
03 9 . ± . . ± . − . ± .
08 . . .NGC 3448 6 . ± .
020 0 . ± . − . ± .
010 10 . ± .
010 . . . 9 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
19 . . . . . . 10 . ± . − . ± . . ± .
10 0 . ± . − . ± .
07 9 . ± . − . ± .
22 9 . ± . − . ± .
11 8 . ± . . ± .
06 0 . ± . − . ± .
017 9 . ± .
06 . . . 9 . ± . − . ± .
08 8 . ± . . ± .
05 0 . ± . − . ± .
04 9 . ± . − . ± .
17 10 . ± . − . ± .
09 . . .NGC 3504 7 . ± .
009 1 . ± . − . ± .
005 9 . ± . − . ± .
20 10 . ± . − . ± .
11 8 . ± . . ± .
05 0 . ± . − . ± .
013 9 . ± . − . ± .
17 9 . ± . − . ± .
08 8 . ± . . ± .
04 0 . ± . − . ± .
018 10 . ± . − . ± .
14 10 . ± . − . ± .
18 8 . ± . . ± .
09 0 . ± . − . ± .
06 9 . ± . − . ± . . ± . − . ± .
12 8 . ± . . ± .
04 0 . ± . − . ± .
017 9 . ± .
006 . . . 9 . ± . − . ± .
07 8 . ± . . ± . − . ± . − . ± .
16 9 . ± .
09 . . . 10 . ± . − . ± .
21 . . .NGC 3592 6 . ± . − . ± . − . ± .
07 8 . ± .
028 . . . 9 . ± . − . ± .
16 8 . ± . . ± .
030 0 . ± . − . ± .
019 10 . ± . − . ± .
14 10 . ± . − . ± .
09 8 . ± . . ± .
08 1 . ± . − . ± .
020 . . . . . . 10 . ± . − . ± .
13 . . .PGC 034407 6 . ± . − . ± . − . ± .
17 . . . . . . 8 . ± . − . ± . . ± . . ± . − . ± .
19 . . . . . . 10 . ± . − . ± . . ± .
05 0 . ± . − . ± .
04 9 . ± .
022 . . . 10 . ± . − . ± .
14 8 . ± . . ± .
22 0 . ± . − . ± .
13 8 . ± .
015 . . . 8 . ± . − . ± .
14 . . .NGC 3610 6 . ± . . ± . − . ± .
18 . . . . . . 11 . ± . − . ± . . ± . − . ± . − . ± .
17 . . . . . . 11 . ± . − . ± . . ± . − . ± . − . ± .
13 9 . ± .
12 . . . 10 . ± . − . ± .
29 8 . ± . . ± .
24 0 . ± . − . ± .
13 . . . . . . 9 . ± . − . ± .
21 . . .UGC 06341 5 . ± . − . ± . − . ± .
16 8 . ± .
010 . . . 8 . ± . − . ± .
19 8 . ± . . ± .
07 0 . ± . − . ± .
05 9 . ± .
11 . . . 10 . ± . − . ± . . ± .
07 0 . ± . − . ± .
014 9 . ± .
021 . . . 9 . ± . − . ± .
08 8 . ± . . ± .
030 0 . ± . − . ± .
025 9 . ± . − . ± .
17 10 . ± . − . ± .
16 8 . ± . . ± .
014 0 . ± . − . ± .
018 10 . ± . − . ± .
14 10 . ± . − . ± .
28 8 . ± . . ± . − . ± . − . ± .
06 9 . ± . . ± . − . ± .
07 8 . ± . . ± .
030 0 . ± . − . ± .
024 . . . . . . 9 . ± . − . ± .
09 8 . ± . . ± . . ± . − . ± .
24 . . . . . . 11 . ± . − . ± .
16 . . .NGC 3655 7 . ± .
015 0 . ± . − . ± .
009 9 . ± . − . ± .
13 9 . ± . − . ± .
09 . . .NGC 3659 6 . ± .
06 0 . ± . − . ± .
008 9 . ± . − . ± .
13 9 . ± . − . ± .
09 8 . ± . . ± .
04 0 . ± . − . ± .
04 9 . ± . − . ± .
13 9 . ± . − . ± .
10 8 . ± . . ± .
07 0 . ± . − . ± .
06 . . . . . . 11 . ± . − . ± .
07 . . .NGC 3674 5 . ± . . ± . − . ± .
15 . . . . . . 10 . ± . − . ± .
21 . . .NGC 3681 7 . ± . − . ± . − . ± .
04 9 . ± . − . ± .
14 10 . ± . − . ± .
10 . . .IC 2828 5 . ± .
15 0 . ± . − . ± .
06 8 . ± .
008 . . . 8 . ± . − . ± .
10 8 . ± . . ± .
05 0 . ± . − . ± .
03 9 . ± . − . ± .
18 9 . ± . − . ± .
10 8 . ± . . ± .
017 0 . ± . − . ± .
009 9 . ± . − . ± .
16 10 . ± . − . ± .
10 8 . ± . . ± .
026 0 . ± . − . ± .
017 9 . ± . − . ± .
15 9 . ± . − . ± .
08 8 . ± . . ± .
07 0 . ± . − . ± .
031 8 . ± .
016 . . . 9 . ± . − . ± .
07 8 . ± . . ± .
06 0 . ± . − . ± .
031 9 . ± .
06 . . . 10 . ± . − . ± .
10 . . .NGC 3718 8 . ± . − . ± . − . ± .
03 . . . . . . 11 . ± . − . ± .
11 . . . A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . m a nu s c r i p t Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 3729 7 . ± .
030 0 . ± . − . ± .
009 9 . ± . − . ± .
15 10 . ± . − . ± .
15 8 . ± . . ± . − . ± . − . ± .
20 9 . ± .
05 . . . 8 . ± . − . ± .
17 . . .UGC 06575 7 . ± . − . ± . − . ± .
08 9 . ± .
05 . . . 9 . ± . − . ± .
10 8 . ± . . ± .
10 0 . ± . − . ± .
07 10 . ± .
023 . . . 9 . ± . − . ± .
09 8 . ± . . ± .
031 0 . ± . − . ± .
026 9 . ± . − . ± .
16 10 . ± . − . ± .
11 8 . ± . . ± .
28 0 . ± . − . ± .
14 . . . . . . 10 . ± . − . ± .
22 . . .NGC 3773 5 . ± .
10 0 . ± . − . ± .
014 8 . ± .
020 . . . 9 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
05 9 . ± .
05 . . . 9 . ± . − . ± .
14 8 . ± . . ± .
21 0 . ± . − . ± .
11 . . . . . . 10 . ± . − . ± .
15 . . .NGC 3794 6 . ± .
07 0 . ± . − . ± .
024 9 . ± .
018 . . . 9 . ± . − . ± .
10 8 . ± . . ± .
026 0 . ± . − . ± .
016 9 . ± . − . ± .
14 10 . ± . − . ± .
08 8 . ± . . ± . − . ± . − . ± .
14 . . . . . . 10 . ± .
06 . . . . . .NGC 3846A 6 . ± .
11 0 . ± . − . ± .
06 . . . . . . 9 . ± . − . ± .
09 8 . ± . . ± .
06 0 . ± . − . ± .
031 8 . ± .
05 . . . 8 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
04 . . . . . . 11 . ± . − . ± .
07 . . .NGC 3938 7 . ± .
031 0 . ± . − . ± .
018 10 . ± . − . ± .
14 10 . ± . − . ± .
09 8 . ± . . ± .
24 0 . ± . − . ± .
17 9 . ± .
11 . . . 10 . ± . − . ± .
09 . . .NGC 3945 7 . ± . − . ± . − . ± .
11 . . . . . . 11 . ± . − . ± .
05 . . .NGC 3952 6 . ± .
10 0 . ± . − . ± .
05 . . . . . . 9 . ± . − . ± .
10 8 . ± . . ± .
05 0 . ± . − . ± .
04 9 . ± . − . ± .
17 10 . ± . − . ± . . ± . − . ± . − . ± .
03 9 . ± .
05 . . . 9 . ± . − . ± .
08 8 . ± . . ± . − . ± . − . ± .
022 . . . . . . . . . . . . 8 . ± . . ± .
017 0 . ± . − . ± .
008 . . . . . . 10 . ± . − . ± .
06 8 . ± . . ± . − . ± . − . ± .
10 . . . . . . 9 . ± . − . ± . . ± . . ± .
28 0 . ± . − . ± .
16 . . . . . . 9 . ± .
028 . . . . . .NGC 4013 7 . ± .
017 0 . ± . − . ± .
014 9 . ± . − . ± .
14 10 . ± . − . ± . . ± .
010 0 . ± . − . ± .
006 10 . ± . − . ± .
18 10 . ± . − . ± .
09 8 . ± . . ± .
08 0 . ± . − . ± .
04 9 . ± .
04 . . . 9 . ± . − . ± .
06 8 . ± . . ± .
24 0 . ± . − . ± .
14 9 . ± .
004 . . . 9 . ± . − . ± .
13 8 . ± . . ± .
14 0 . ± . − . ± .
08 9 . ± . . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
05 8 . ± .
06 . . . 9 . ± . − . ± .
12 8 . ± . . ± .
13 0 . ± . − . ± .
09 . . . . . . 10 . ± . − . ± . . ± .
07 0 . ± . − . ± .
07 9 . ± . − . ± .
15 9 . ± . − . ± .
14 8 . ± . . ± .
08 0 . ± . − . ± .
05 9 . ± . − . ± .
21 10 . ± . − . ± .
08 . . .UGC 07086 7 . ± .
07 0 . ± . − . ± .
04 9 . ± .
025 . . . 9 . ± . − . ± .
19 . . .UGC 07089 6 . ± . − . ± . − . ± .
14 . . . . . . 8 . ± . − . ± .
17 8 . ± . . ± .
016 0 . ± . − . ± .
010 9 . ± . − . ± .
13 10 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
15 8 . ± .
04 . . . 8 . ± . − . ± .
17 8 . ± . . ± .
009 1 . ± . − . ± .
024 . . . . . . 10 . ± . − . ± .
13 . . .NGC 4111 6 . ± .
17 0 . ± . − . ± .
10 9 . ± .
13 . . . 10 . ± .
06 . . . . . .NGC 4116 7 . ± . − . ± . − . ± .
06 9 . ± . − . ± .
13 9 . ± . − . ± .
10 8 . ± . . ± .
19 0 . ± . − . ± .
11 8 . ± .
09 . . . 9 . ± . − . ± . . ± .
25 0 . ± . − . ± .
15 . . . . . . 11 . ± . − . ± .
04 . . .NGC 4119 6 . ± .
15 0 . ± . − . ± .
09 . . . . . . 10 . ± . − . ± .
16 8 . ± . A r ti c l e nu m b e r , p a g e ff
16 8 . ± . A r ti c l e nu m b e r , p a g e ff . G a lli a no e t a l . : AN ea r by G a l a xy P e r s p ec ti v e on D u s t E vo l u ti on Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 4123 7 . ± .
04 0 . ± . − . ± .
04 9 . ± . − . ± .
21 9 . ± . − . ± .
11 8 . ± . . ± . − . ± . − . ± .
17 . . . . . . 9 . ± . − . ± . . ± .
07 0 . ± . − . ± .
04 9 . ± .
07 . . . 10 . ± . − . ± .
15 8 . ± . . ± .
29 0 . ± . − . ± .
15 9 . ± .
028 . . . 9 . ± . − . ± .
15 8 . ± . . ± .
07 0 . ± . − . ± .
07 8 . ± . − . ± .
17 8 . ± . − . ± .
07 8 . ± . . ± . . ± . − . ± .
21 7 . ± .
005 . . . 7 . ± . − . ± .
14 7 . ± . . ± .
03 0 . ± . − . ± .
017 10 . ± . − . ± .
13 9 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
16 9 . ± .
003 . . . 8 . ± . − . ± .
17 8 . ± . . ± . − . ± . − . ± .
17 8 . ± .
007 . . . 8 . ± . − . ± .
14 . . .UGC 07184 6 . ± .
18 0 . ± . − . ± .
11 9 . ± .
006 . . . 9 . ± . − . ± .
12 8 . ± . . ± .
10 0 . ± . − . ± .
07 9 . ± .
08 . . . 10 . ± . − . ± .
13 8 . ± . . ± . − . ± . − . ± .
04 10 . ± . − . ± .
14 10 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
15 8 . ± .
003 . . . 8 . ± . − . ± .
13 8 . ± . . ± . − . ± . − . ± .
22 . . . . . . 10 . ± . − . ± . . ± .
020 0 . ± . − . ± .
010 9 . ± .
12 . . . 10 . ± . − . ± .
14 8 . ± . . ± . − . ± . − . ± .
05 9 . ± .
06 . . . 9 . ± . − . ± .
11 8 . ± . . ± .
030 0 . ± . − . ± .
015 9 . ± . − . ± .
15 9 . ± . − . ± .
10 8 . ± . . ± .
03 0 . ± . − . ± .
019 9 . ± . − . ± .
15 10 . ± . − . ± .
18 . . .NGC 4191 6 . ± .
16 0 . ± . − . ± .
10 9 . ± .
04 . . . 10 . ± . − . ± .
19 8 . ± . . ± .
05 0 . ± . − . ± .
05 9 . ± .
04 . . . 10 . ± . − . ± .
13 8 . ± . . ± .
20 0 . ± . − . ± .
12 8 . ± .
05 . . . 9 . ± . − . ± .
18 8 . ± . . ± . . ± . − . ± .
15 9 . ± .
005 . . . 8 . ± . − . ± .
14 8 . ± . . ± .
06 0 . ± . − . ± .
05 9 . ± . . ± . − . ± .
08 8 . ± . . ± . − . ± . − . ± .
14 . . . . . . 9 . ± . − . ± .
08 . . .IC 3059 6 . ± .
25 0 . ± . − . ± .
14 8 . ± .
006 . . . 8 . ± . − . ± .
15 . . .IC 3061 7 . ± .
09 0 . ± . − . ± .
05 9 . ± .
006 . . . 9 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
04 9 . ± .
08 . . . 10 . ± . − . ± .
15 . . .IC 3065 5 . ± . − . ± . − . ± .
20 . . . . . . 9 . ± . − . ± .
30 . . .NGC 4206 7 . ± . − . ± . − . ± .
05 9 . ± . − . ± .
13 9 . ± . − . ± .
08 . . .NGC 4207 6 . ± .
020 0 . ± . − . ± .
005 8 . ± . − . ± .
20 9 . ± . − . ± .
17 8 . ± . . ± .
10 0 . ± . − . ± .
05 8 . ± . − . ± .
17 8 . ± . − . ± .
09 8 . ± . . ± .
015 0 . ± . − . ± .
010 9 . ± . − . ± .
22 10 . ± . − . ± .
07 8 . ± . . ± .
022 0 . ± . − . ± .
014 9 . ± . − . ± .
18 10 . ± . − . ± .
26 8 . ± . . ± .
026 0 . ± . − . ± .
03 9 . ± . − . ± .
13 10 . ± . − . ± . . ± . . ± . − . ± . − . ± .
15 . . . . . . 10 . ± . − . ± .
10 . . .IC 3077 4 . ± . − . ± . − . ± .
17 7 . ± .
16 . . . 8 . ± . − . ± .
23 8 . ± . . ± . − . ± . − . ± .
07 9 . ± .
06 . . . 9 . ± . − . ± .
11 8 . ± . . ± . − . ± . − . ± .
05 10 . ± .
18 . . . 11 . ± . − . ± . . ± . − . ± . − . ± .
024 . . . . . . 9 . ± . − . ± .
12 8 . ± . . ± .
22 0 . ± . − . ± .
14 7 . ± .
06 . . . 8 . ± . − . ± . . ± . . ± . − . ± . − . ± .
25 . . . . . . 7 . ± . − . ± .
16 . . .NGC 4233 6 . ± .
23 0 . ± . − . ± .
14 . . . . . . 10 . ± . − . ± . . ± .
04 0 . ± . − . ± .
010 9 . ± . − . ± .
14 9 . ± . − . ± .
08 8 . ± . . ± .
16 0 . ± . − . ± .
12 9 . ± .
008 . . . 9 . ± . − . ± .
12 8 . ± . A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . m a nu s c r i p t Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 4235 6 . ± .
18 0 . ± . − . ± .
05 . . . . . . 10 . ± . − . ± . . ± . . ± .
021 0 . ± . − . ± .
007 8 . ± . − . ± .
14 10 . ± . − . ± .
15 . . .NGC 4239 5 . ± . − . ± . − . ± .
14 . . . . . . 9 . ± . − . ± .
15 . . .IC 3102 7 . ± . − . ± . − . ± .
14 9 . ± .
15 . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
26 . . . . . . 7 . ± . − . ± .
27 . . .NGC 4244 6 . ± . − . ± . − . ± .
09 9 . ± . − . ± .
14 9 . ± . − . ± .
11 8 . ± . . ± .
23 0 . ± . − . ± .
15 8 . ± .
022 . . . 8 . ± . − . ± .
10 7 . ± . . ± . − . ± . − . ± .
08 9 . ± .
005 . . . 9 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
15 9 . ± .
004 . . . 9 . ± . − . ± .
07 . . .NGC 4251 6 . ± . − . ± . − . ± .
16 . . . . . . 10 . ± . − . ± .
09 . . .NGC 4252 6 . ± .
17 0 . ± . − . ± .
12 8 . ± .
009 . . . 9 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
22 7 . ± .
16 . . . 8 . ± .
16 . . . . . .NGC 4254 7 . ± .
025 0 . ± . − . ± .
016 9 . ± . − . ± .
15 10 . ± . − . ± .
08 8 . ± . . ± . − . ± . − . ± .
20 . . . . . . 9 . ± . − . ± .
25 . . .NGC 4255 5 . ± . − . ± . − . ± .
15 . . . . . . 10 . ± . − . ± .
06 . . .NGC 4259 6 . ± . . ± . − . ± .
16 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
09 . . . . . . 10 . ± . − . ± .
31 . . .NGC 4266 6 . ± . − . ± . − . ± .
14 . . . . . . . . . . . . . . .NGC 4267 6 . ± . − . ± . − . ± .
16 . . . . . . 10 . ± . − . ± . . ± .
04 1 . ± . − . ± .
27 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
15 9 . ± .
13 . . . 10 . ± .
05 . . . . . .NGC 4273 7 . ± .
007 0 . ± . − . ± .
005 9 . ± . − . ± .
14 10 . ± . − . ± .
08 8 . ± . . ± . − . ± . − . ± .
19 . . . . . . 9 . ± . − . ± .
23 . . .NGC 4276 6 . ± .
08 0 . ± . − . ± .
04 9 . ± .
013 . . . 9 . ± . − . ± .
11 8 . ± . . ± . − . ± . − . ± .
09 9 . ± .
019 . . . 9 . ± . − . ± .
21 8 . ± . . ± . − . ± . − . ± .
20 . . . . . . 8 . ± . − . ± .
30 . . .PGC 039799 4 . ± . − . ± . − . ± .
26 7 . ± .
007 . . . 7 . ± . − . ± .
15 . . .NGC 4281 6 . ± .
19 0 . ± . − . ± .
15 . . . . . . 10 . ± . − . ± . . ± .
21 0 . ± . − . ± .
14 9 . ± .
010 . . . 9 . ± . − . ± .
14 8 . ± . . ± .
10 0 . ± . − . ± .
07 8 . ± .
08 . . . 9 . ± . − . ± .
14 . . .NGC 4289 7 . ± .
08 0 . ± . − . ± .
13 10 . ± .
020 . . . 10 . ± . − . ± .
17 . . .NGC 4292 5 . ± .
13 0 . ± . − . ± .
13 . . . . . . 9 . ± . − . ± . . ± .
05 0 . ± . − . ± .
04 9 . ± .
04 . . . 9 . ± . − . ± .
08 8 . ± . . ± . − . ± . − . ± .
19 . . . . . . 9 . ± . − . ± . . ± . . ± . − . ± .
16 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
14 . . . . . . 9 . ± . − . ± . . ± .
07 0 . ± . − . ± .
04 9 . ± . − . ± .
15 9 . ± . − . ± .
09 8 . ± . . ± .
11 0 . ± . − . ± .
12 . . . . . . 10 . ± . − . ± .
12 . . .UGC 07422 5 . ± .
10 0 . ± . − . ± .
10 8 . ± .
14 . . . 9 . ± . − . ± . . ± . . ± . . ± . − . ± .
16 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
18 . . . . . . 9 . ± . − . ± . . ± .
05 0 . ± . − . ± .
03 9 . ± . − . ± .
18 10 . ± . − . ± . . ± . . ± . − . ± .
21 7 . ± .
028 . . . 7 . ± . − . ± .
25 . . .NGC 4309 6 . ± .
16 0 . ± . − . ± .
05 9 . ± .
19 . . . 9 . ± . − . ± . A r ti c l e nu m b e r , p a g e ff
19 . . . 9 . ± . − . ± . A r ti c l e nu m b e r , p a g e ff . G a lli a no e t a l . : AN ea r by G a l a xy P e r s p ec ti v e on D u s t E vo l u ti on Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)UGC 07436 4 . ± . − . ± . − . ± .
23 . . . . . . 8 . ± . − . ± .
07 . . .PGC 040074 4 . ± . − . ± . − . ± .
27 . . . . . . 8 . ± .
15 . . . . . .NGC 4303A 6 . ± .
12 0 . ± . − . ± .
12 9 . ± . . ± . − . ± .
07 8 . ± . . ± .
06 0 . ± . − . ± .
025 8 . ± . − . ± .
19 9 . ± . − . ± .
26 8 . ± . . ± .
07 0 . ± . − . ± .
08 8 . ± . − . ± .
17 9 . ± . − . ± . . ± .
05 0 . ± . − . ± .
03 9 . ± . − . ± .
30 10 . ± . − . ± .
18 . . .IC 3229 6 . ± .
17 0 . ± . − . ± .
11 8 . ± .
013 . . . 8 . ± . − . ± .
11 8 . ± . . ± .
05 0 . ± . − . ± .
03 10 . ± . − . ± .
17 10 . ± . − . ± .
11 8 . ± . . ± . − . ± . − . ± .
21 8 . ± .
08 . . . 8 . ± . − . ± .
27 . . .NGC 4324 6 . ± . − . ± . − . ± .
10 9 . ± .
07 . . . 10 . ± . − . ± .
12 . . .NGC 4330 6 . ± .
07 0 . ± . − . ± .
06 9 . ± . − . ± .
20 9 . ± . − . ± .
12 8 . ± . . ± .
28 0 . ± . − . ± .
15 . . . . . . 10 . ± . − . ± .
07 . . .NGC 4340 5 . ± . − . ± . − . ± .
13 . . . . . . 10 . ± . − . ± .
05 . . .NGC 4343 7 . ± .
05 0 . ± . − . ± .
030 9 . ± .
30 . . . 10 . ± . − . ± .
21 . . .IC 3258 5 . ± .
12 0 . ± . − . ± .
11 8 . ± .
008 . . . 8 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
08 8 . ± .
04 . . . 9 . ± . − . ± .
13 8 . ± . . ± . − . ± . − . ± .
17 . . . . . . 9 . ± . − . ± . . ± .
19 0 . ± . − . ± .
11 . . . . . . 10 . ± . − . ± .
04 . . .NGC 4351 6 . ± .
08 0 . ± . − . ± .
07 8 . ± .
06 . . . 9 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
18 . . . . . . 9 . ± . − . ± . . ± .
10 0 . ± . − . ± .
06 9 . ± .
03 . . . 9 . ± . − . ± .
10 8 . ± . . ± .
09 0 . ± . − . ± .
08 9 . ± .
005 . . . 9 . ± . − . ± .
06 8 . ± . . ± . − . ± . − . ± .
05 9 . ± . − . ± .
16 9 . ± . − . ± .
10 8 . ± . . ± .
11 0 . ± . − . ± .
09 8 . ± .
16 . . . 9 . ± . − . ± .
30 . . .NGC 4365 6 . ± . . ± . − . ± .
25 . . . . . . 11 . ± . − . ± .
15 . . .NGC 4370 6 . ± .
07 0 . ± . − . ± .
09 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
17 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
16 . . . . . . 9 . ± . − . ± . . ± .
26 0 . ± . − . ± .
13 . . . . . . 10 . ± . − . ± .
30 . . .NGC 4376 6 . ± .
08 0 . ± . − . ± .
09 8 . ± .
008 . . . 9 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
08 9 . ± .
06 . . . 11 . ± . − . ± .
07 . . .NGC 4380 7 . ± . − . ± . − . ± .
016 8 . ± . − . ± .
17 10 . ± . − . ± .
23 . . .IC 3311 6 . ± . − . ± . − . ± .
10 8 . ± .
019 . . . 9 . ± . − . ± .
13 8 . ± . . ± . − . ± . − . ± .
18 . . . . . . 10 . ± . − . ± . . ± .
16 0 . ± . − . ± .
008 9 . ± .
028 . . . 9 . ± . − . ± .
09 8 . ± . . ± .
021 0 . ± . − . ± .
012 9 . ± . − . ± .
23 10 . ± . − . ± .
12 8 . ± . . ± .
06 0 . ± . − . ± .
04 9 . ± .
08 . . . 9 . ± . − . ± .
06 8 . ± . . ± .
07 0 . ± . − . ± .
05 8 . ± .
020 . . . 9 . ± . − . ± .
15 8 . ± . . ± . − . ± . − . ± .
06 9 . ± .
04 . . . 10 . ± . − . ± .
09 . . .NGC 4396 6 . ± . − . ± . − . ± .
04 9 . ± . − . ± . . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
22 . . . . . . 8 . ± . − . ± .
20 8 . ± . . ± .
029 0 . ± . − . ± .
011 9 . ± . − . ± .
24 9 . ± . − . ± .
22 8 . ± . . ± . . ± . − . ± .
21 . . . . . . 11 . ± . − . ± .
27 . . .NGC 4411A 6 . ± . − . ± . − . ± .
08 9 . ± .
003 . . . 9 . ± . − . ± .
12 8 . ± . A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . m a nu s c r i p t Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 4413 6 . ± .
06 0 . ± . − . ± .
03 8 . ± .
26 . . . 9 . ± . − . ± .
09 8 . ± . . ± .
027 0 . ± . − . ± .
009 9 . ± . − . ± .
23 10 . ± . − . ± .
08 8 . ± . . ± . − . ± . − . ± .
18 . . . . . . 9 . ± . − . ± . . ± .
05 0 . ± . − . ± .
05 9 . ± . − . ± .
15 10 . ± . − . ± .
08 8 . ± . . ± .
30 0 . ± . − . ± .
15 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
26 5 . ± .
022 . . . 5 . ± . − . ± .
13 7 . ± . . ± . − . ± . − . ± .
19 . . . . . . 8 . ± . − . ± .
20 . . .PGC 040759 5 . ± . − . ± . − . ± .
20 . . . . . . 8 . ± . − . ± .
13 . . .NGC 4419 6 . ± .
020 0 . ± . − . ± .
007 9 . ± . − . ± .
20 10 . ± . − . ± . . ± . . ± .
026 0 . ± . − . ± .
011 9 . ± . − . ± .
19 9 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
13 9 . ± . − . ± .
20 9 . ± . − . ± .
09 8 . ± . . ± .
06 0 . ± . − . ± .
05 7 . ± . − . ± .
14 8 . ± . − . ± .
24 8 . ± . . ± . − . ± . − . ± .
21 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
28 . . . . . . . . . . . . . . .IC 3371 6 . ± .
26 0 . ± . − . ± .
15 9 . ± .
004 . . . 9 . ± . − . ± .
11 8 . ± . . ± .
05 0 . ± . − . ± .
06 9 . ± . − . ± .
24 10 . ± . − . ± .
09 8 . ± . . ± .
16 0 . ± . − . ± .
06 . . . . . . 10 . ± . − . ± .
22 . . .PGC 040821 1 . ± . − . ± . − . ± . . ± . − . ± .
23 . . .NGC 4434 5 . ± .
31 0 . ± . − . ± .
17 . . . . . . 10 . ± . − . ± .
27 . . .NGC 4435 6 . ± .
022 0 . ± . − . ± .
026 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
13 . . . . . . 9 . ± . − . ± . . ± .
03 0 . ± . − . ± .
014 9 . ± . − . ± . . ± . − . ± .
15 . . .NGC 4440 5 . ± . − . ± . − . ± .
17 . . . . . . 10 . ± . − . ± .
30 . . .UGC 07579 6 . ± .
09 0 . ± . − . ± .
10 9 . ± .
029 . . . 9 . ± . − . ± .
10 8 . ± . . ± . . ± . − . ± .
19 . . . . . . 10 . ± .
04 . . . . . .NGC 4449 6 . ± .
03 0 . ± . − . ± .
031 9 . ± . − . ± .
18 8 . ± . − . ± .
03 8 . ± . . ± . − . ± . − . ± .
19 . . . . . . 9 . ± . − . ± . . ± .
07 0 . ± . − . ± .
08 8 . ± .
16 . . . 9 . ± . − . ± .
25 . . .IC 3391 6 . ± .
07 0 . ± . − . ± .
04 8 . ± .
025 . . . 9 . ± . − . ± .
08 8 . ± . . ± .
023 0 . ± . − . ± .
029 9 . ± . − . ± .
19 10 . ± . − . ± .
12 . . .UGC 07596 4 . ± . . ± . − . ± .
19 6 . ± .
08 . . . 7 . ± . − . ± .
22 . . .NGC 4451 6 . ± .
04 0 . ± . − . ± .
023 9 . ± . − . ± .
22 9 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
18 . . . . . . 9 . ± . − . ± .
30 . . .IC 3392 6 . ± .
05 0 . ± . − . ± .
014 8 . ± . − . ± .
20 9 . ± . − . ± .
23 8 . ± . . ± . . ± . − . ± .
15 . . . . . . 9 . ± . − . ± .
24 . . .NGC 4460 5 . ± .
08 0 . ± . − . ± .
04 8 . ± .
09 . . . 9 . ± . − . ± .
19 . . .NGC 4454 6 . ± .
23 0 . ± . − . ± .
05 . . . . . . 10 . ± . − . ± .
15 . . .NGC 4458 5 . ± . − . ± . − . ± .
18 . . . . . . 9 . ± . − . ± .
21 . . .NGC 4457 6 . ± .
06 0 . ± . − . ± .
05 9 . ± .
16 . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
17 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
15 . . . . . . 9 . ± . − . ± . . ± . − . ± . − . ± .
16 . . . . . . 9 . ± . − . ± .
29 . . .NGC 4469 6 . ± .
09 0 . ± . − . ± .
12 9 . ± . . ± . − . ± . . ± . − . ± . − . ± .
15 . . . . . . 9 . ± . − . ± . A r ti c l e nu m b e r , p a g e ff
15 . . . . . . 9 . ± . − . ± . A r ti c l e nu m b e r , p a g e ff . G a lli a no e t a l . : AN ea r by G a l a xy P e r s p ec ti v e on D u s t E vo l u ti on Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 4470 6 . ± .
06 0 . ± . − . ± .
010 8 . ± . − . ± .
22 9 . ± . − . ± .
10 8 . ± . . ± . . ± . − . ± .
24 . . . . . . 11 . ± . − . ± .
031 . . .NGC 4473 6 . ± .
30 0 . ± . − . ± .
17 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
20 . . . . . . 10 . ± . − . ± . . ± .
09 0 . ± . − . ± .
04 . . . . . . 9 . ± . − . ± .
25 . . .UGC 07636 4 . ± . − . ± . − . ± . . ± . − . ± .
24 . . .NGC 4477 6 . ± .
24 0 . ± . − . ± .
13 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
14 . . . . . . 9 . ± . − . ± .
25 . . .NGC 4478 5 . ± .
28 0 . ± . − . ± .
16 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
17 . . . . . . 9 . ± . − . ± .
26 . . .NGC 4480 7 . ± .
05 0 . ± . − . ± .
06 9 . ± . − . ± .
23 10 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
17 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
17 . . . . . . 9 . ± . − . ± . . ± .
18 1 . ± . − . ± .
07 . . . . . . 8 . ± . − . ± .
27 . . .NGC 4492 7 . ± . − . ± . − . ± .
14 9 . ± . − . ± . . ± . − . ± .
15 . . .NGC 4494 6 . ± . − . ± . − . ± .
23 . . . . . . 10 . ± .
07 . . . . . .NGC 4497 5 . ± . − . ± . − . ± .
16 . . . . . . 9 . ± . − . ± . . ± .
04 0 . ± . − . ± .
03 9 . ± . − . ± .
25 9 . ± . − . ± .
10 8 . ± . . ± .
04 0 . ± . − . ± .
010 9 . ± .
12 . . . 9 . ± . − . ± .
07 8 . ± . . ± .
06 0 . ± . − . ± .
016 8 . ± .
013 . . . 9 . ± . − . ± .
07 8 . ± . . ± . − . ± . − . ± . . ± . − . ± . . ± .
025 0 . ± . − . ± .
031 9 . ± . − . ± .
17 10 . ± . − . ± .
11 8 . ± . . ± .
30 0 . ± . − . ± .
14 . . . . . . 10 . ± .
04 . . . . . .NGC 4506 5 . ± .
18 0 . ± . − . ± .
09 . . . . . . 9 . ± . − . ± .
28 8 . ± . . ± . − . ± . − . ± .
16 . . . . . . 9 . ± . − . ± .
12 . . .UGC 07688 5 . ± . − . ± . − . ± .
19 . . . . . . 9 . ± .
07 . . . . . .UGC 07700 7 . ± .
12 0 . ± . − . ± .
08 9 . ± .
04 . . . 9 . ± . − . ± .
10 8 . ± . . ± . . ± . − . ± .
17 9 . ± .
06 . . . 10 . ± . − . ± .
28 . . .IC 3476 6 . ± .
06 0 . ± . − . ± .
021 8 . ± . − . ± .
14 8 . ± . − . ± .
05 8 . ± . . ± . − . ± . − . ± .
04 9 . ± . − . ± . . ± . − . ± .
12 8 . ± . . ± .
22 0 . ± . − . ± .
11 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
14 . . . . . . 9 . ± . − . ± .
12 . . .NGC 4522 6 . ± .
05 0 . ± . − . ± .
026 9 . ± . − . ± .
17 9 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
19 . . . . . . 9 . ± . − . ± . . ± . − . ± . − . ± .
04 8 . ± . − . ± .
15 8 . ± . − . ± .
12 8 . ± . . ± .
09 0 . ± . − . ± .
027 8 . ± .
10 . . . 9 . ± . − . ± .
08 8 . ± . . ± .
030 0 . ± . − . ± .
07 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
17 . . . . . . 9 . ± . − . ± . . ± .
015 0 . ± . − . ± .
027 10 . ± . − . ± .
14 10 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
19 . . . . . . 9 . ± . − . ± .
27 . . .NGC 4531 6 . ± . − . ± . − . ± .
10 . . . . . . 10 . ± . − . ± . . ± .
06 0 . ± . − . ± .
03 9 . ± . − . ± .
20 9 . ± . − . ± .
08 8 . ± . . ± .
019 0 . ± . − . ± .
026 9 . ± . − . ± .
21 10 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
10 8 . ± .
009 . . . 9 . ± . − . ± .
10 8 . ± . A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . m a nu s c r i p t Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 4536 7 . ± .
018 0 . ± . − . ± .
020 9 . ± . − . ± .
15 10 . ± . − . ± .
09 . . .IC 3517 5 . ± .
17 0 . ± . − . ± .
14 7 . ± .
03 . . . 8 . ± . − . ± .
11 8 . ± . . ± . − . ± . − . ± .
19 . . . . . . 8 . ± . − . ± . . ± .
05 0 . ± . − . ± .
04 8 . ± . − . ± .
23 9 . ± . − . ± .
10 8 . ± . . ± .
20 0 . ± . − . ± .
11 . . . . . . 10 . ± . − . ± . . ± .
19 0 . ± . − . ± .
12 . . . . . . 10 . ± . − . ± .
28 . . .NGC 4562 6 . ± . − . ± . − . ± .
11 8 . ± .
008 . . . 8 . ± . − . ± .
10 . . .NGC 4551 5 . ± . − . ± . − . ± .
15 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
22 . . . . . . 11 . ± . − . ± .
31 . . .PGC 041994 4 . ± . − . ± . − . ± .
23 9 . ± .
010 . . . . . . . . . . . .NGC 4559 7 . ± . − . ± . − . ± .
14 9 . ± . − . ± .
15 9 . ± . − . ± .
10 8 . ± . . ± .
11 0 . ± . − . ± .
027 9 . ± .
023 . . . 9 . ± . − . ± .
10 8 . ± . . ± . . ± . − . ± .
16 . . . . . . 10 . ± . − . ± . . ± . . ± . − . ± .
17 7 . ± .
11 . . . 8 . ± . − . ± .
15 8 . ± . . ± .
05 0 . ± . − . ± .
05 9 . ± . − . ± .
16 10 . ± . − . ± .
28 . . .NGC 4570 6 . ± . − . ± . − . ± .
18 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
17 . . . . . . 9 . ± . − . ± . . ± .
09 0 . ± . − . ± .
05 9 . ± . − . ± .
14 10 . ± . − . ± .
15 . . .NGC 4589 6 . ± . . ± . − . ± .
18 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
25 . . . . . . 8 . ± . − . ± . . ± .
29 0 . ± . − . ± .
15 . . . . . . 10 . ± . − . ± . . ± .
16 0 . ± . − . ± .
12 8 . ± .
014 . . . 8 . ± . − . ± .
07 8 . ± . . ± .
07 0 . ± . − . ± .
07 9 . ± .
25 . . . 11 . ± . − . ± .
24 8 . ± . . ± . − . ± . − . ± .
17 8 . ± .
005 . . . 8 . ± . − . ± .
12 8 . ± . . ± .
04 0 . ± . − . ± .
014 . . . . . . 10 . ± . − . ± .
24 . . .NGC 4584 5 . ± .
13 0 . ± . − . ± .
08 8 . ± .
18 . . . 9 . ± . − . ± .
25 8 . ± . . ± . − . ± . − . ± .
11 8 . ± .
016 . . . 9 . ± . − . ± .
14 8 . ± . . ± .
19 0 . ± . − . ± .
07 8 . ± . − . ± .
15 10 . ± . − . ± . . ± .
29 0 . ± . − . ± .
14 8 . ± .
06 . . . 9 . ± . − . ± .
26 8 . ± . . ± .
06 0 . ± . − . ± .
04 9 . ± .
04 . . . 10 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
05 9 . ± .
024 . . . 9 . ± . − . ± .
04 8 . ± . . ± .
27 0 . ± . − . ± .
14 . . . . . . 9 . ± . − . ± .
09 . . .NGC 4595 6 . ± .
05 0 . ± . − . ± .
026 8 . ± . − . ± .
20 9 . ± . − . ± .
09 8 . ± . . ± .
19 0 . ± . − . ± .
11 . . . . . . 10 . ± . − . ± .
31 . . .NGC 4606 6 . ± .
11 0 . ± . − . ± .
06 8 . ± .
19 . . . 9 . ± . − . ± .
15 8 . ± . . ± .
04 0 . ± . − . ± .
007 9 . ± . − . ± .
16 9 . ± . − . ± .
17 . . .NGC 4608 6 . ± . − . ± . − . ± .
19 . . . . . . 10 . ± .
05 . . . . . .NGC 4612 6 . ± . − . ± . − . ± .
15 . . . . . . 10 . ± . − . ± . . ± .
04 0 . ± . − . ± .
026 9 . ± .
013 . . . 9 . ± . − . ± .
05 8 . ± . . ± .
14 0 . ± . − . ± .
07 . . . . . . 8 . ± . − . ± .
09 8 . ± . . ± .
08 0 . ± . − . ± .
14 10 . ± . − . ± .
15 10 . ± . − . ± .
08 8 . ± . . ± .
03 0 . ± . − . ± .
008 9 . ± . − . ± .
17 9 . ± . − . ± .
10 8 . ± . . ± .
15 0 . ± . − . ± .
12 . . . . . . 9 . ± . − . ± .
20 8 . ± . . ± . − . ± . − . ± .
10 8 . ± .
004 . . . 9 . ± . − . ± .
11 8 . ± . A r ti c l e nu m b e r , p a g e ff
11 8 . ± . A r ti c l e nu m b e r , p a g e ff . G a lli a no e t a l . : AN ea r by G a l a xy P e r s p ec ti v e on D u s t E vo l u ti on Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 4636 5 . ± . − . ± . − . ± .
20 . . . . . . 11 . ± . − . ± .
06 . . .NGC 4639 7 . ± .
04 0 . ± . − . ± .
04 9 . ± .
11 . . . 10 . ± . − . ± .
07 8 . ± . . ± . − . ± . − . ± .
10 9 . ± .
22 . . . 10 . ± . − . ± .
10 . . .NGC 4651 7 . ± .
04 0 . ± . − . ± .
031 10 . ± . − . ± .
22 10 . ± . − . ± .
06 8 . ± . . ± .
026 0 . ± . − . ± .
032 10 . ± . − . ± .
20 10 . ± . − . ± .
12 8 . ± . . ± .
05 0 . ± . − . ± .
09 8 . ± .
027 . . . 8 . ± . − . ± .
09 7 . ± . . ± . − . ± . − . ± .
14 . . . . . . . . . . . . . . .NGC 4660 5 . ± .
28 0 . ± . − . ± .
16 . . . . . . 10 . ± . − . ± .
20 . . .IC 3718 4 . ± .
26 0 . ± . − . ± .
15 7 . ± .
07 . . . 8 . ± . − . ± .
20 . . .NGC 4624 5 . ± . − . ± . − . ± .
17 . . . . . . 10 . ± . − . ± .
20 . . .NGC 4666 7 . ± .
015 0 . ± . − . ± .
010 9 . ± . − . ± .
15 10 . ± . − . ± .
09 8 . ± . . ± .
09 0 . ± . − . ± .
09 8 . ± .
04 . . . 9 . ± . − . ± .
07 8 . ± . . ± . . ± . − . ± .
17 8 . ± .
015 . . . 8 . ± . − . ± .
26 8 . ± . . ± .
10 1 . ± . − . ± .
07 . . . . . . 10 . ± . − . ± .
30 8 . ± . . ± .
016 0 . ± . − . ± .
014 9 . ± . − . ± .
14 10 . ± . − . ± .
25 . . .NGC 4688 6 . ± . − . ± . − . ± .
10 9 . ± . − . ± .
13 9 . ± . − . ± .
08 8 . ± . . ± .
04 1 . ± . − . ± .
018 . . . . . . 8 . ± . − . ± .
12 8 . ± . . ± .
11 0 . ± . − . ± .
11 9 . ± .
05 . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
18 . . . . . . 11 . ± . − . ± .
08 . . .NGC 4701 6 . ± .
08 0 . ± . − . ± .
12 9 . ± . − . ± .
22 9 . ± . − . ± .
09 8 . ± . . ± .
03 0 . ± . − . ± .
021 9 . ± .
23 . . . 10 . ± . − . ± . . ± . . ± . − . ± . − . ± .
13 9 . ± .
024 . . . 9 . ± . − . ± .
21 8 . ± . . ± .
04 0 . ± . − . ± .
05 9 . ± . − . ± .
17 9 . ± . − . ± .
07 8 . ± . . ± . − . ± . − . ± .
04 9 . ± . − . ± .
14 10 . ± . − . ± .
08 . . .UGC 07991 6 . ± . − . ± . − . ± .
11 8 . ± .
023 . . . 9 . ± . − . ± .
17 8 . ± . . ± .
07 0 . ± . − . ± .
03 . . . . . . 9 . ± . − . ± .
10 8 . ± . . ± .
04 0 . ± . − . ± .
03 9 . ± . − . ± .
15 10 . ± . − . ± .
15 8 . ± . . ± . − . ± . − . ± .
08 9 . ± . − . ± .
14 9 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
10 . . . . . . 9 . ± . − . ± .
12 . . .NGC 4747 6 . ± .
04 0 . ± . − . ± .
03 9 . ± .
004 . . . 9 . ± . − . ± .
13 8 . ± . . ± .
03 0 . ± . − . ± .
016 9 . ± . − . ± .
13 10 . ± . − . ± .
08 8 . ± . . ± .
26 0 . ± . − . ± .
16 . . . . . . 10 . ± . − . ± . . ± .
11 0 . ± . − . ± .
19 . . . . . . 11 . ± . − . ± . . ± . − . ± . − . ± .
06 8 . ± .
011 . . . 9 . ± . − . ± .
13 8 . ± . . ± .
04 0 . ± . − . ± .
013 9 . ± . . ± . − . ± .
05 8 . ± . . ± . − . ± . − . ± .
08 9 . ± . − . ± .
16 9 . ± . − . ± .
13 . . .NGC 4772 7 . ± . − . ± . − . ± .
12 9 . ± .
07 . . . 10 . ± . − . ± .
26 8 . ± . . ± .
06 0 . ± . − . ± .
025 9 . ± . − . ± .
30 9 . ± . − . ± .
09 . . .NGC 4779 7 . ± .
05 0 . ± . − . ± .
028 9 . ± .
17 . . . 10 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
19 8 . ± . . ± . − . ± .
15 . . .NGC 4793 7 . ± .
009 0 . ± . − . ± .
006 9 . ± . − . ± .
19 10 . ± . − . ± .
10 8 . ± . . ± .
15 0 . ± . − . ± .
09 9 . ± .
11 . . . 9 . ± . − . ± .
11 . . .UGC 08032 6 . ± . − . ± . − . ± .
08 8 . ± .
15 . . . 9 . ± . − . ± .
13 8 . ± . . ± .
29 0 . ± . − . ± .
15 10 . ± .
10 . . . 11 . ± . − . ± .
09 . . . A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . m a nu s c r i p t Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)UGC 08042 6 . ± . − . ± . − . ± .
12 8 . ± .
027 . . . 9 . ± . − . ± .
12 8 . ± . . ± .
05 0 . ± . − . ± .
05 9 . ± .
07 . . . 10 . ± . − . ± .
10 . . .NGC 4808 7 . ± .
020 0 . ± . − . ± .
028 9 . ± . − . ± .
14 9 . ± . − . ± .
09 8 . ± . . ± .
04 0 . ± . − . ± .
030 9 . ± . − . ± .
17 10 . ± . − . ± . . ± .
027 0 . ± . − . ± .
06 9 . ± . − . ± .
30 10 . ± . − . ± .
11 . . .PGC 044532 5 . ± .
14 0 . ± . − . ± .
13 9 . ± .
022 . . . 8 . ± . − . ± .
11 7 . ± . . ± . − . ± . − . ± .
08 10 . ± .
07 . . . 11 . ± . − . ± .
10 . . .NGC 4904 6 . ± .
04 0 . ± . − . ± .
018 9 . ± . − . ± .
16 9 . ± . − . ± .
08 8 . ± . . ± .
029 0 . ± . − . ± .
022 9 . ± . − . ± .
20 10 . ± . − . ± .
07 8 . ± . . ± . − . ± . − . ± .
17 8 . ± .
005 . . . 8 . ± . − . ± .
11 8 . ± . . ± .
006 0 . ± . − . ± .
008 9 . ± . − . ± .
17 10 . ± . − . ± .
27 8 . ± . . ± .
05 0 . ± . − . ± .
04 9 . ± .
008 . . . 9 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
21 . . . . . . 7 . ± . − . ± .
03 . . .NGC 4981 7 . ± .
027 0 . ± . − . ± .
019 9 . ± . − . ± .
15 10 . ± . − . ± .
12 8 . ± . . ± . − . ± . − . ± .
13 9 . ± . . ± . − . ± .
12 8 . ± . . ± .
06 0 . ± . − . ± .
012 7 . ± .
15 . . . 8 . ± . − . ± .
10 8 . ± . . ± .
029 0 . ± . − . ± .
018 9 . ± .
04 . . . 10 . ± . − . ± .
11 . . .NGC 5016 7 . ± .
04 0 . ± . − . ± .
04 9 . ± . − . ± .
13 10 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
06 9 . ± .
004 . . . 9 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
12 8 . ± .
05 . . . 8 . ± . − . ± .
10 8 . ± . . ± .
008 1 . ± . − . ± .
005 . . . . . . 10 . ± . − . ± .
21 8 . ± . . ± .
024 0 . ± . − . ± .
012 10 . ± . − . ± .
14 10 . ± . − . ± .
14 8 . ± . . ± . − . ± . − . ± .
17 9 . ± .
022 . . . 8 . ± . − . ± .
12 8 . ± . . ± . − . ± . − . ± .
19 8 . ± .
009 . . . 8 . ± . − . ± .
10 7 . ± . . ± .
05 0 . ± . − . ± .
024 9 . ± .
026 . . . 10 . ± . − . ± .
09 8 . ± . . ± .
11 0 . ± . − . ± .
07 9 . ± .
003 . . . 9 . ± . − . ± .
08 8 . ± . . ± .
27 0 . ± . − . ± .
14 . . . . . . 10 . ± .
11 . . . . . .PGC 046875 6 . ± .
28 0 . ± . − . ± .
14 9 . ± .
05 . . . 9 . ± .
15 . . . . . .NGC 5145 7 . ± .
016 0 . ± . − . ± .
005 . . . . . . 10 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
025 . . . . . . 10 . ± . − . ± . . ± . . ± .
06 0 . ± . − . ± .
012 9 . ± . − . ± .
28 9 . ± . − . ± .
04 8 . ± . . ± .
07 0 . ± . − . ± .
04 9 . ± .
030 . . . 10 . ± . − . ± .
09 . . .IC 0902 7 . ± .
05 0 . ± . − . ± .
026 9 . ± .
05 . . . 9 . ± . − . ± .
20 8 . ± . . ± .
019 0 . ± . − . ± .
021 10 . ± . − . ± .
15 10 . ± . − . ± .
10 8 . ± . . ± .
020 0 . ± . − . ± .
017 9 . ± . − . ± .
14 10 . ± . − . ± .
10 8 . ± . . ± .
11 0 . ± . − . ± .
06 9 . ± .
005 . . . 9 . ± . − . ± .
10 8 . ± . . ± .
21 0 . ± . − . ± .
13 9 . ± .
014 . . . 9 . ± . − . ± .
11 8 . ± . . ± .
18 0 . ± . − . ± .
07 . . . . . . 10 . ± . − . ± . . ± .
11 0 . ± . − . ± .
06 9 . ± .
008 . . . 9 . ± . − . ± .
10 8 . ± . . ± .
04 0 . ± . − . ± .
016 9 . ± .
09 . . . 10 . ± . − . ± .
13 . . .NGC 5301 7 . ± .
031 0 . ± . − . ± .
022 9 . ± . − . ± .
19 10 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
03 9 . ± . − . ± .
27 9 . ± . − . ± .
07 8 . ± . . ± .
10 0 . ± . − . ± .
05 9 . ± .
24 . . . 9 . ± . − . ± .
16 . . .NGC 5334 7 . ± . − . ± . − . ± .
04 10 . ± . − . ± .
25 10 . ± . − . ± .
07 8 . ± . A r ti c l e nu m b e r , p a g e ff
07 8 . ± . A r ti c l e nu m b e r , p a g e ff . G a lli a no e t a l . : AN ea r by G a l a xy P e r s p ec ti v e on D u s t E vo l u ti on Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 5350 7 . ± .
027 0 . ± . − . ± .
05 9 . ± .
04 . . . 10 . ± . − . ± .
09 . . .NGC 5338 5 . ± .
16 0 . ± . − . ± .
04 8 . ± .
11 . . . 8 . ± . − . ± .
28 8 . ± . . ± . − . ± . − . ± .
17 9 . ± .
029 . . . 10 . ± . − . ± .
08 . . .NGC 5358 6 . ± . − . ± . − . ± .
14 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
07 9 . ± .
004 . . . 9 . ± . − . ± .
10 . . .NGC 5356 7 . ± . − . ± . − . ± .
030 8 . ± . − . ± .
22 9 . ± . − . ± .
27 . . .NGC 5360 6 . ± .
18 0 . ± . − . ± .
12 8 . ± .
12 . . . 9 . ± . − . ± .
26 8 . ± . . ± .
09 0 . ± . − . ± .
09 11 . ± .
24 . . . 12 . ± . − . ± . . ± .
04 0 . ± . − . ± .
03 9 . ± . − . ± .
20 10 . ± . − . ± .
13 . . .UGC 08857 5 . ± .
20 0 . ± . − . ± .
12 . . . . . . 8 . ± . − . ± .
28 8 . ± . . ± .
10 0 . ± . − . ± .
05 8 . ± .
014 . . . 8 . ± . − . ± .
10 8 . ± . . ± .
05 0 . ± . − . ± .
016 10 . ± . − . ± .
13 10 . ± . − . ± .
06 8 . ± . . ± .
21 1 . ± . − . ± .
12 8 . ± . . ± . − . ± . . ± . − . ± . − . ± .
06 9 . ± .
06 . . . 9 . ± . − . ± .
10 8 . ± . . ± .
24 0 . ± . − . ± .
15 8 . ± .
008 . . . 7 . ± . − . ± .
09 7 . ± . . ± .
19 0 . ± . − . ± .
13 . . . . . . 9 . ± . − . ± .
14 . . .NGC 5481 5 . ± .
10 1 . ± . − . ± .
21 . . . . . . 10 . ± .
05 . . . . . .NGC 5485 6 . ± .
22 0 . ± . − . ± .
12 . . . . . . 10 . ± . − . ± .
30 . . .NGC 5486 6 . ± .
10 0 . ± . − . ± .
06 . . . . . . 9 . ± . − . ± .
10 8 . ± . . ± . . ± . − . ± .
17 . . . . . . 9 . ± . − . ± .
24 . . .ESO 097-013 7 . ± .
05 0 . ± . − . ± .
07 9 . ± . − . ± .
15 10 . ± . − . ± .
25 8 . ± . . ± .
05 1 . ± . − . ± .
27 9 . ± .
14 . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
05 10 . ± .
06 . . . 11 . ± . − . ± .
08 . . .NGC 5560 6 . ± .
05 0 . ± . − . ± .
029 9 . ± . − . ± .
17 9 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
12 8 . ± .
006 . . . 9 . ± . − . ± .
11 8 . ± . . ± . − . ± . − . ± .
14 . . . . . . 10 . ± .
07 . . . . . .NGC 5574 5 . ± .
30 0 . ± . − . ± .
15 . . . . . . 10 . ± . − . ± .
26 . . .NGC 5577 7 . ± . − . ± . − . ± .
04 9 . ± . − . ± . . ± . − . ± .
12 8 . ± . . ± .
05 0 . ± . − . ± .
03 9 . ± . − . ± .
17 10 . ± . − . ± .
07 8 . ± . . ± .
14 0 . ± . − . ± .
09 . . . . . . 9 . ± . − . ± .
07 8 . ± . . ± . − . ± . − . ± .
13 10 . ± . . ± . − . ± .
14 8 . ± . . ± . − . ± . − . ± .
06 . . . . . . 9 . ± . − . ± .
26 8 . ± . . ± . − . ± . − . ± .
11 9 . ± .
006 . . . 9 . ± . − . ± .
13 . . .NGC 5667 7 . ± .
05 0 . ± . − . ± .
024 9 . ± .
04 . . . 9 . ± . − . ± .
09 8 . ± . . ± .
06 0 . ± . − . ± .
05 9 . ± .
025 . . . 9 . ± . − . ± .
09 8 . ± . . ± .
06 0 . ± . − . ± .
06 9 . ± . − . ± .
23 9 . ± . − . ± .
08 8 . ± . . ± .
08 0 . ± . − . ± .
04 9 . ± . − . ± .
30 9 . ± . − . ± .
09 8 . ± . . ± .
15 0 . ± . − . ± .
07 10 . ± .
19 . . . 11 . ± . − . ± . . ± . − . ± . − . ± .
18 8 . ± .
023 . . . 8 . ± . − . ± .
10 8 . ± . . ± .
19 0 . ± . − . ± .
04 . . . . . . 9 . ± . − . ± .
11 8 . ± . . ± . − . ± . − . ± .
16 . . . . . . 8 . ± . − . ± .
16 . . .NGC 5690 7 . ± .
019 0 . ± . − . ± .
010 10 . ± . − . ± .
19 9 . ± . − . ± .
13 8 . ± . . ± .
04 0 . ± . − . ± .
009 9 . ± . − . ± .
24 9 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
05 10 . ± .
015 . . . 10 . ± . − . ± .
13 8 . ± . A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . m a nu s c r i p t Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 5705 7 . ± . − . ± . − . ± .
05 9 . ± .
06 . . . 9 . ± . − . ± .
06 8 . ± . . ± .
011 0 . ± . − . ± .
007 9 . ± . − . ± .
14 9 . ± . − . ± .
09 8 . ± . . ± .
017 0 . ± . − . ± .
016 10 . ± . − . ± .
15 10 . ± . − . ± .
18 . . .UGC 09470 6 . ± .
16 0 . ± . − . ± .
10 9 . ± .
009 . . . 9 . ± . − . ± .
10 8 . ± . . ± .
020 0 . ± . − . ± .
027 . . . . . . 10 . ± . − . ± .
15 8 . ± . . ± . . ± . − . ± .
15 9 . ± .
007 . . . 9 . ± . − . ± .
15 8 . ± . . ± .
07 0 . ± . − . ± .
024 9 . ± . − . ± .
17 10 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
018 10 . ± .
11 . . . 11 . ± .
05 . . . 8 . ± . . ± .
06 0 . ± . − . ± .
05 9 . ± .
20 . . . 10 . ± . − . ± .
25 8 . ± . . ± .
04 0 . ± . − . ± .
017 10 . ± .
04 . . . 10 . ± . − . ± .
11 . . .NGC 5866 6 . ± .
011 0 . ± . − . ± .
04 . . . . . . 10 . ± . − . ± . . ± . − . ± . − . ± .
025 9 . ± .
07 . . . 10 . ± . − . ± .
10 . . .NGC 5899 7 . ± .
018 0 . ± . − . ± .
016 10 . ± .
05 . . . 10 . ± . − . ± .
14 . . .NGC 5907 7 . ± .
008 0 . ± . − . ± .
018 10 . ± . − . ± .
16 10 . ± . − . ± .
09 8 . ± . . ± .
05 0 . ± . − . ± .
012 . . . . . . 10 . ± . − . ± .
11 . . .NGC 6221 7 . ± .
010 0 . ± . − . ± .
022 9 . ± . − . ± .
28 10 . ± . − . ± .
12 . . .NGC 6300 7 . ± .
03 0 . ± . − . ± .
04 9 . ± .
08 . . . 10 . ± . − . ± .
22 . . .UGC 10854 6 . ± .
25 0 . ± . − . ± .
13 9 . ± .
05 . . . 9 . ± . − . ± .
13 8 . ± . . ± .
31 0 . ± . − . ± .
17 9 . ± .
22 . . . 10 . ± .
13 . . . . . .NGC 6703 6 . ± . − . ± . − . ± .
17 10 . ± .
23 . . . 11 . ± .
06 . . . . . .NGC 6798 6 . ± . . ± . − . ± .
16 . . . . . . 10 . ± . − . ± . . ± .
03 0 . ± . − . ± .
028 9 . ± . − . ± .
15 10 . ± . − . ± .
11 . . .NGC 6946 7 . ± .
018 0 . ± . − . ± .
007 10 . ± . − . ± .
15 10 . ± . − . ± .
10 8 . ± . . ± . . ± . − . ± .
26 6 . ± .
05 . . . 6 . ± . − . ± .
19 . . .NGC 7090 7 . ± . − . ± . − . ± .
04 9 . ± .
03 . . . 9 . ± . − . ± .
12 . . .NGC 7213 7 . ± .
07 0 . ± . − . ± .
07 10 . ± . − . ± .
25 . . . . . . . . .ESO 289-020 5 . ± . − . ± . − . ± .
23 . . . . . . 7 . ± . − . ± .
29 . . .ESO 405-014 5 . ± . − . ± . − . ± .
19 . . . . . . 8 . ± . − . ± .
17 . . .PGC 166755 7 . ± .
18 0 . ± . − . ± .
07 9 . ± .
018 . . . 10 . ± .
12 . . . . . .NGC 7314 7 . ± .
018 0 . ± . − . ± .
009 9 . ± .
26 . . . 10 . ± . − . ± .
11 . . .NGC 7331 7 . ± .
017 0 . ± . − . ± .
011 10 . ± . − . ± .
15 10 . ± . − . ± .
15 8 . ± . . ± .
16 0 . ± . − . ± .
05 9 . ± .
04 . . . 9 . ± . − . ± .
19 . . .ESO 603-031 6 . ± .
19 0 . ± . − . ± .
10 . . . . . . 9 . ± . − . ± .
11 . . .ESO 406-031 6 . ± . − . ± . − . ± .
11 . . . . . . 9 . ± . − . ± .
23 . . .IC 5270 7 . ± .
05 0 . ± . − . ± .
018 10 . ± .
006 . . . 9 . ± . − . ± .
11 . . .UGC 12313 6 . ± . − . ± . − . ± .
16 9 . ± .
004 . . . 8 . ± . − . ± . . ± .
07 0 . ± . − . ± .
019 9 . ± .
008 . . . 9 . ± . − . ± .
14 . . .ESO 407-002 6 . ± .
08 0 . ± . − . ± .
03 . . . . . . 9 . ± . − . ± .
26 . . .NGC 7552 7 . ± .
03 1 . ± . − . ± .
026 10 . ± . − . ± .
15 10 . ± . − . ± .
15 8 . ± . . ± .
030 0 . ± . − . ± .
021 9 . ± . − . ± .
14 9 . ± . − . ± .
14 8 . ± . . ± .
24 0 . ± . − . ± .
14 9 . ± . . ± . − . ± .
08 8 . ± . . ± . − . ± . − . ± .
23 7 . ± .
09 . . . 7 . ± . − . ± .
18 . . .ESO 240-004 6 . ± . − . ± . − . ± .
17 . . . . . . 8 . ± . − . ± .
18 . . .NGC 7690 6 . ± .
05 0 . ± . − . ± .
016 9 . ± .
04 . . . 9 . ± . − . ± .
09 . . . A r ti c l e nu m b e r , p a g e ff
09 . . . A r ti c l e nu m b e r , p a g e ff . G a lli a no e t a l . : AN ea r by G a l a xy P e r s p ec ti v e on D u s t E vo l u ti on Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)NGC 7694 6 . ± .
06 0 . ± . − . ± .
04 8 . ± .
04 . . . 8 . ± . − . ± .
09 . . .NGC 7689 7 . ± .
04 0 . ± . − . ± .
010 9 . ± .
019 . . . 9 . ± . − . ± .
10 . . .IC 5334 7 . ± . − . ± . − . ± .
09 10 . ± .
06 . . . 10 . ± . − . ± .
15 . . .NGC 7710 6 . ± . − . ± . − . ± .
13 . . . . . . 10 . ± . − . ± . . ± .
04 1 . ± . − . ± .
004 9 . ± .
005 . . . 9 . ± . − . ± .
08 . . .NGC 7715 6 . ± . − . ± . − . ± .
15 . . . . . . 9 . ± . − . ± .
031 . . .NGC 7716 7 . ± .
05 0 . ± . − . ± .
023 9 . ± .
019 . . . 10 . ± . − . ± .
09 8 . ± . . ± . − . ± . − . ± .
11 9 . ± .
004 . . . 9 . ± . − . ± .
09 8 . ± . . ± .
030 0 . ± . − . ± .
014 10 . ± . − . ± .
13 10 . ± . − . ± .
10 8 . ± . . ± . − . ± . − . ± .
14 9 . ± .
019 . . . 9 . ± . − . ± .
09 . . .ESO 471-006 4 . ± . − . ± . − . ± .
22 7 . ± .
022 . . . 7 . ± . − . ± .
17 7 . ± . . ± .
12 0 . ± . − . ± .
10 9 . ± .
018 . . . 9 . ± . − . ± .
11 . . .NGC 7755 7 . ± .
03 0 . ± . − . ± .
022 10 . ± .
06 . . . 10 . ± . − . ± .
11 8 . ± . . ± .
06 0 . ± . − . ± .
04 9 . ± .
031 . . . 9 . ± . − . ± .
04 . . .NGC 7764 6 . ± .
07 0 . ± . − . ± .
05 9 . ± .
04 . . . 9 . ± . − . ± .
12 . . .NGC 7793 6 . ± . − . ± . − . ± .
12 9 . ± . − . ± .
14 9 . ± . − . ± .
10 8 . ± . + . ± .
14 1 . ± . − . ± .
06 . . . . . . 9 . ± . − . ± .
15 . . .HS 2352 + . ± .
09 2 . ± . − . ± .
28 . . . . . . 8 . ± .
16 . . . . . .Mrk 153 4 . ± .
08 1 . ± . − . ± .
07 . . . . . . 8 . ± . − . ± .
20 . . .Tol 1214-277 5 . ± . . ± . − . ± .
15 . . . . . . 7 . ± . − . ± .
19 7 . ± . + . ± .
23 1 . ± . − . ± .
11 . . . . . . 7 . ± .
14 . . . . . .SBS 1159 +
545 4 . ± . . ± . − . ± .
17 . . . . . . 7 . ± . − . ± .
15 7 . ± . . ± .
14 0 . ± . − . ± .
18 . . . . . . 6 . ± . − . ± .
15 . . .Haro 11 6 . ± .
06 2 . ± . − . ± .
08 8 . ± .
19 . . . 9 . ± . − . ± . . ± . . ± .
04 1 . ± . − . ± .
04 9 . ± .
07 . . . 10 . ± . − . ± .
16 8 . ± . . ± .
06 1 . ± . − . ± .
12 8 . ± .
07 . . . 8 . ± . − . ± .
22 8 . ± . . ± .
12 2 . ± . − . ± .
13 7 . ± .
07 . . . 7 . ± . − . ± .
16 7 . ± . . ± .
09 1 . ± . − . ± .
05 9 . ± .
07 . . . 9 . ± . − . ± .
19 8 . ± . +
574 5 . ± .
09 1 . ± . − . ± .
13 9 . ± .
07 . . . 8 . ± . − . ± .
18 8 . ± . +
540 3 . ± . . ± . − . ± .
16 7 . ± .
07 . . . 6 . ± . − . ± .
31 7 . ± . . ± .
04 1 . ± . − . ± .
14 8 . ± .
07 . . . 8 . ± . − . ± .
18 8 . ± . . ± .
07 1 . ± . − . ± .
04 10 . ± .
07 . . . 9 . ± . − . ± .
19 8 . ± . − . ± . − . ± . − . ± . . ± .
07 . . . . . . . . . 7 . ± . . ± .
17 1 . ± . − . ± .
14 7 . ± .
07 . . . 7 . ± . − . ± .
19 7 . ± . . ± .
23 1 . ± . − . ± .
08 8 . ± .
07 . . . 7 . ± . − . ± .
20 7 . ± . + . ± . . ± . − . ± .
13 8 . ± .
07 . . . 7 . ± . − . ± .
14 7 . ± . . ± .
12 0 . ± . − . ± .
07 8 . ± .
07 . . . 7 . ± . − . ± .
15 7 . ± . +
493 5 . ± . . ± . − . ± .
13 9 . ± .
07 . . . 8 . ± . − . ± .
21 7 . ± . . ± .
13 1 . ± . − . ± . . ± .
07 . . . . . . . . . 7 . ± . . ± .
16 1 . ± . − . ± .
09 7 . ± .
07 . . . 6 . ± . − . ± .
27 7 . ± .
08I Zw 18 2 . ± .
06 2 . ± . − . ± .
12 8 . ± .
07 . . . 6 . ± . − . ± .
21 7 . ± . . ± .
13 3 . ± . − . ± .
11 8 . ± .
07 . . . 7 . ± . − . ± .
21 7 . ± . +
437 3 . ± .
20 2 . ± . − . ± .
16 8 . ± .
07 . . . 7 . ± . − . ± .
21 7 . ± . . ± .
06 0 . ± . − . ± .
04 10 . ± .
07 . . . 9 . ± . − . ± .
20 8 . ± . A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . m a nu s c r i p t Table H.1. continued.
Galaxy log M dust / M (cid:12) log (cid:104) U (cid:105) log q AF log M gas / M (cid:12) log f H log M (cid:63) / M (cid:12) log sSFR / yr − + log(O / H)HS 1222 + . ± . . ± . − . ± .
10 . . . . . . 8 . ± . − . ± .
20 . . .HS 1236 + . ± . − . ± . − . ± .
28 . . . . . . . . . . . . . . .HS 1304 + . ± .
12 1 . ± . − . ± .
09 . . . . . . 8 . ± . − . ± .
16 7 . ± . + . ± . . ± . − . ± .
12 . . . . . . 7 . ± . − . ± .
21 . . .HS 1330 + . ± .
16 0 . ± . − . ± .
09 . . . . . . 8 . ± . − . ± .
13 8 . ± . . ± . . ± . − . ± .
19 . . . . . . 10 . ± . − . ± .
18 . . . A r ti c l e nu m b e r , p a g e ff