Modelling the UV to radio SEDs of nearby star-forming galaxies: new Parsec SSP for Grasil
I.A. Obi, A. Bressan, F. Perrotta, L. Silva, O. Vega, Y. Chen, A. Lapi, C. Mancuso, L. Girardi, G.L. Granato, P. Marigo, A. Slemer
MMNRAS , 000–000 (2017) Preprint 12 November 2018 Compiled using MNRAS L A TEX style file v3.0
Modelling the UV to radio SEDs of nearby star-forminggalaxies: new
PARSEC
SSP for
GRASIL
I.A. Obi (cid:63) , A. Bressan , F. Perrotta , L. Silva O. Vega , Y. Chen , A. Lapi ,C. Mancuso , L. Girardi , G.L. Granato , P. Marigo , and A. Slemer . SISSA, via Bonomea 265, I-34136 Trieste, Italy INAF - Osservatorio Astronomico di Trieste, via Tiepolo 11, 34131 Trieste, Italy INAOE, Luis Enrique Erro 1, 72840 Tonantzintla, Puebla, Mexico Dipartimento di Fisica e Astronomia Galileo Galilei, Universit´a di Padova, Vicolo dell’Osservatorio 3, I-35122 Padova, Italy INAF - Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
By means of the updated
PARSEC database of evolutionary tracks of massive stars,we compute the integrated stellar light, the ionizing photon budget and the supernovarates of young simple stellar populations (SSPs), for different metallicities and IMFupper mass limits. Using
CLOUDY we compute and include in the SSP spectra the neb-ular emission contribution. We also revisit the thermal and non-thermal radio emissioncontribution from young stars. Using
GRASIL we can thus predict the panchromaticspectrum and the main recombination lines of any type of star-forming galaxy, includ-ing the effects of dust absorption and re-emission. We check the new models against thespectral energy distributions (SEDs) of selected well-observed nearby galaxies. Fromthe best-fit models we obtain a consistent set of star formation rate (SFR) calibrationsat wavelengths ranging from ultraviolet (UV) to radio. We also provide analytical cal-ibrations that take into account the dependence on metallcity and IMF upper masslimit of the SSPs. We show that the latter limit can be well constrained by combininginformation from the observed far infrared, 24 µ m, 33 GHz and H α luminosities. An-other interesting property derived from the fits is that, while in a normal galaxy theattenuation in the lines is significantly higher than that in the nearby continuum, inindividual star bursting regions they are similar, supporting the notion that this effectis due to an age selective extinction. Since in these conditions the Balmer decrementmethod may not be accurate, we provide relations to estimate the attenuation fromthe observed 24 µ m or 33 GHz fluxes. These relations can be useful for the analysis ofyoung high redshift galaxies. Key words: radio continuum: galaxies–infrared: galaxies–ISM: dust, extinction–stars:formation–galaxies: high-redshift
Modelling the SEDs of galaxies has proven to be a very pow-erful tool in our current understanding of the different phys-ical processes that come into play in the formation and evo-lution of galaxies. Various physical properties of galaxies likestellar, metal and dust content, star formation rate, dust ob-scuration, etc are estimated by fitting the theoretical SEDsto the observed ones. In the UV to infrared (IR) spectralregions of a SED, dust plays an important role. It absorbs (cid:63)
E-mail: [email protected] (as well as scatters) the UV-near-infrared (NIR) light andre-radiates it in the IR. This IR emission (3 - 1000 µ m) mayarise from (a) the emission from dust heated by young OBstars (neglecting heating from AGN), (b) the emission fromthe circumstellar envelopes of evolved stars and (c) the cirrusemission from dust distributed throughout in the ISM andheated by the general interstellar radiation field. Point (b)leads to wrong estimates of the physical properties relatedto star formation. The radio band which is not sensitive todust attenuation is usually used to check and complementthe interpretations arrived by using the optical/IR bands.Radio emission from normal star-forming galaxies is usu- c (cid:13) a r X i v : . [ a s t r o - ph . GA ] F e b Obi ally dominated by the non-thermal component (up to ≈ ≈ (cid:12) ) endingtheir lifes (Condon 1992). Recent advances in hydrodynam-ical simulations of CCSN have indicated a range of stellarmasses where the stars fail to explode but rather end up di-rectly as a black hole. This raises concern about the widelyaccepted notion that all stars more massive than ≈ (cid:12) end up as a CCSN.Over the years, great progress has been made both inthe development of tools and models use to extract the infor-mation encoded in the SEDs and in multi-wavelength sur-veys that sample the UV to radio SED of local and highredshift galaxies. Furthermore, new observing facilities withunprecedented resolution and sensivity (e.g. SKA, JWST ,EVLT etc) will be put in place in the nearest feature. Atthe same time, semi-analytic models of galaxy formation, inthe context of the current cosmological standard model, areappearing and providing realistic predictions of the physi-cal properties of galaxies with which the results of the SEDfitting can be compared.Stellar population synthesis (SPS) still remains the ba-sis of SED modelling. The most common method used incomputing the SEDs of SSPs is that of isochrone synthesis(Chiosi, Bertelli & Bressan 1988; Maeder & Meynet 1988;Charlot & Bruzual 1991) which uses the locus of stars inan isochrone to integrate the spectra of all stars along anisochrone to get the total flux. This involves computing firstthe stellar evolutionary tracks for different masses and metalcontents and building the isochrones from the tracks. Withthe isochrones, the resulting stellar spectrum is computedusing stellar atmosphere libraries. In recent years, signifi-cant efforts from different research groups have been putinto providing homogeneous sets of evolutionary tracks andimproving the stellar libraries. As a result of these improve-ments, SPS models can remarkably reproduce well the UV-NIR SEDs and high-resolution spectra in the optical wave-length band. However, despite these improvements, there arestill challenges in the field, especially in the treatment of thephases of stellar evolution that are weakly understood. Themost important being the short lived phases: massive stars,thermally pulsing asymptotic giant branch (TP-AGB) stars,blue stragglers and extreme horizontal branch stars. TheTP-AGB stars have however increasingly received attentionleading to a rapid progress in their modelling (Maraston2005; Marigo & Girardi 2007; Marigo et al. 2017).The stellar evolution code used in Padova to computesets of stellar evolutionary tracks that are of wide useage inthe astronomical community has recently been thoroughlyrevised and updated, going by the name,
PARSEC (PAdova-TRieste Stellar Evolution Code). More details of this codecan be found in Bressan et al. (2012, 2013); Chen et al.(2014) and will be briefly discussed later in the text. Inthis paper, our main aim is to use the
PARSEC evolu-tionary tracks of massive stars to compute the quantities(the integrated light, ionizing photon budget and the su-pernova rates) of young SSPs, thereby updating the SSPsused by
GRASIL in predicting the panchromatic spectrum ofstar-forming galaxies. We also revisit the thermal and non-thermal radio emissions. We finally check these new mod- els with selected nearby well-observed galaxies. We performan analysis of the resulting best-fit SEDs, with the aim ofobtaining a new set of SFR calibrations and investigatingthe dependence of the dust attenuation properties on galaxytypes.The structure of the rest of paper is as follows: In Sec-tion 2, we use the new
PARSEC code database of stellarevolutionary tracks of massive stars to compute the ioniz-ing photon budget, the integrated light and the supernovarates predicted by young SSP models. Using the integratedspectra of the SPPs in
CLOUDY , we computed the nebularemissions. In Section 3, we revise (a) the prescription used incomputing the thermal radio emission. (b) the previous non-thermal radio emission model originally described in Bres-san, Silva & Granato (2002, hereafter B02) while taking intoaccount recent advances in CCSN explosion models. In Sec-tion 4, we check our new radio emission models and SSPswith
GRASIL using selected well-observed nearby galaxies.Finally, we discuss the resulting best fit SEDs of all galaxiesstudied in this paper in Section 5. We draw our conclusionsin Section 6.Throughout this paper we adopt 12 + log(O / H) = 8 . . − (cid:12) and -2.5 for ≥ (cid:12) ). The cosmological parameterswe adopt assume H = 70 km s − Mpc − , Ω Λ = 0 . , Ω M =0 . PARSEC
PARSEC is the latest version of the Padova-Trieste stel-lar evolution code with thorough update of the major in-put physics including new and accurate homogenised opac-ity and equation of state tables fully consistent with anyadopted chemical composition. More details may be foundin Bressan et al. (2012, 2013); Chen et al. (2014). The evo-lutionary tracks span a wide range in metallicities, 0 . ≤ Z ≤ .
04, and initial masses, from very low ( M = 0 . (cid:12) )to very massive ( M = 350 M (cid:12) ) stars, starting from thepre-main sequence phase and ending at central carbon ig-nition. Tang et al. (2014) and Chen et al. (2015) computednew evolutionary tracks of massive stars and tables of the-oretical bolometric corrections that allow for the conver-sion from theoretical HR to the observed colour-magnitudediagrams. A preliminary comparison of the new modelswith color-magnitude diagrams of star-forming regions innearby low metallicity dwarf irregular galaxies was per-formed by Tang et al. (2014). The full set of new evolution-ary tracks and the corresponding isochrones may be foundin http://people.sissa.it/~sbressan/parsec.html and http://stev.oapd.inaf.it/cgi-bin/cmd , respectively. To build the integrated spectra of SSPs, we adopt the spec-tral library compilation by Chen et al. (2015) who homog-enized various sets of existing stellar atmosphere librariesencompassing a wide range of parameters of both cool andhot stars (i.e. masses, evolutionary stages and metallici-ties). The atmosphere models adopted by Chen et al. (2015)
MNRAS , 000–000 (2017)
ARSEC SSP for GRASIL are the ATLAS9 models (Kurucz 1993; Castelli & Kurucz2004), suitable for intermediate and low mass stars, and thePhoenix models (Allard et al. 1997) for the coolest stars. Forhot massive stars Chen et al. (2015) generated new windmodels with the
WM-BASIC code Pauldrach, Puls & Ku-dritzki (1986) and adopted new models of WR stars fromthe Potsdam group (see e.g. Sander et al. 2015). Since dif-ferent sets of libraries have different metallicities, they weremerged to obtain homogeneous sets of spectral libraries asdescribed in Girardi et al. (2002) and Chen et al. (2014).The properties of SSP are obtained by integration along thecorresponding isochrones assuming a two-slopes power lawKennicutt initial mass function. Results are presented forthree different values of the upper mass limit, M up of 40,120,350 M (cid:12) . As an example, Figure 1 shows the synthesizedspectra of star clusters at ages of t = 2, 5 and 40 Myr andfor three values of the initial metallicity, Z = 0.02, 0.004 and0.0001. The effect of assuming different M up values, at fixedtotal initial mass, is more pronounced at an age of 2 Myr.At 5 Myr, when stars with masses of 120 M (cid:12) and 350 M (cid:12) already left the main sequence or already died out, the spec-tra of SSP with upper mass limits of 120 M (cid:12) and 350 M (cid:12) are superimposed, while those of 40 M (cid:12) remains distinct. At40 Myr the spectra are almost independent of M up , though itis evident that the spectrum of the SSP with larger M up hasa lower luminosity, because of the higher mass budget storedin massive stars We already note from this figure that theeffects of M up on the number of ionizing photons disappearsat ages larger than about 5 Myr, as discussed below. The number of Lyman ionizing photons per sec (Q(H)) andper unit mass emitted by young stellar populations is con-trolled by hot massive stars, i.e. O-B main sequence starsand Wolf Rayet stars. This number is thus critically depen-dent on the shape of the initial mass function in the domainof massive stars. In Figure 2, we show the time evolutionof Q(H) for selected SSPs with different upper mass limit(M up ) and metallicities. As already said, the adopted IMFis a two-slope power law Kennicutt (1983). The lower limitis M low = 0.1 M (cid:12) and the upper limits are M up = 40 M (cid:12) ,M up = 120 M (cid:12) and M up = 350 M (cid:12) . The slope of the IMF isX = 1.4 between M low and M = 1M (cid:12) and X = 2.5 betweenM = 1M (cid:12) and M up From this figure we may appreciate therole of age, metallicity and IMF on the ionizing photon rateQ(H). For a given Z and M up , Q(H) generally increases to amaximum value and then, once a threshold age is reached, itrapidly decreases to negligible values. At fixed M up , both themaximum value of Q(H) and the threshold age decrease, atincreasing metallicity. In general this is also true at varyingage, i.e. at given M up , Q(H) decreases at increasing metal-licity. However there are some cases where this is not true,in particular for the SSP of solar metallicity. The effect ofM up is strong. A star cluster with M up of 350 M (cid:12) producesabout seven times more ionizing photons than a cluster witha M up of 40 M (cid:12) , at constant total mass. Moreover, the ageto attain the maximum Q(H) becomes lesser at increasingupper mass limit, reflecting the larger relative weight of moremassive stars in the ionizing photon budget. PARSEC’s
SSP
The integrated spectra of the SSPs are used to calculate thenebular emission from the surrounding H ii regions which isthen added to the original spectrum to obtain the integratedspectra containing both the stellar continuum (with absorp-tion lines and eventually wind emission features) and thenebular features (continuum and lines). For this purpose,star clusters are assumed to be the central ionizing sourcesof the H ii regions that are modelled using the photoioniza-tion code CLOUDY (Ferland 1996). As a further input to the
CLOUDY code, we specify that the H ii region is modelledas a thin shell of gas with constant density, n H = 100 cm − ,placed at a distance R H = 15 pc from the central source.The evolution of the ionizing star clusters is followed from0.1 Myr to 20 Myr, for five different values of the metallic-ity (Z = 0.0001, 0.0005, 0.004, 0.008, 0.008 and 0.02) andthree values of M up of 40, 120 and 350 M (cid:12) . We note thatour goal is not that of providing a detailed dependence of alarge ensemble of emission lines on the critical parameters ofthe H ii nebulae. Instead we aim at obtaining a reasonableestimate of the intensities of the main recombination linesand of free-free emission to increase the diagnostic capabili-ties of our population synthesis codes. Line emission and thecorresponding nebular continuum are much less dependenton the characteristic properties of the H ii regions (e.g. ion-ization parameter, individual abundance of heavy elementsetc.) than e.g. excitation lines, for which a more detailedset of initial parameters would be more appropriate (see e.g.Panuzzo et al. 2003; Wofford et al. 2016). The main outputof this process is a library of emission line intensities, neb-ular continuum properties and electron temperatures (T e )of the H ii regions. Then, emission lines and nebular contin-uum are used to suitably complement the integrated SED ofSSPs from the far-UV to radio wavelengths. Radio emission associated with the presence of young mas-sive stars comprises essentially two components, the thermalradio emission (also referred to as free-free emission) and thenon-thermal radio emission (also referred to as non-thermalradio emission). The former emission comes from the nebu-lar free electrons originating from the ionizing radiation ofmassive stars. The non-thermal emission is instead believedto be synchrotron radiation that originated from the interac-tion of relativistic electrons, produced in the ejecta of core-collapsed supernovae (CSSN), with the ambient magneticfield. The radio continuum is thus a tracer of the numberof massive stars formed (and exploded) and hence an op-timal indicator of the very recent (if not the current) starformation rate.The fact that the radio emission is a good SFR traceris supported by the remarkably tight correlation betweenFIR and non-thermal radio emission. At 1.49 GHz, this cor-relation is quantified by the q-parameter (Helou, Soifer &Rowan-Robinson 1985): q = log F FIR / (3 . × Hz)F ν (1 . / (W m − Hz − ) ≈ . ± . F FIR = 1 . × − (2 . S µ m + S µ m)Wm − MNRAS000
CLOUDY code, we specify that the H ii region is modelledas a thin shell of gas with constant density, n H = 100 cm − ,placed at a distance R H = 15 pc from the central source.The evolution of the ionizing star clusters is followed from0.1 Myr to 20 Myr, for five different values of the metallic-ity (Z = 0.0001, 0.0005, 0.004, 0.008, 0.008 and 0.02) andthree values of M up of 40, 120 and 350 M (cid:12) . We note thatour goal is not that of providing a detailed dependence of alarge ensemble of emission lines on the critical parameters ofthe H ii nebulae. Instead we aim at obtaining a reasonableestimate of the intensities of the main recombination linesand of free-free emission to increase the diagnostic capabili-ties of our population synthesis codes. Line emission and thecorresponding nebular continuum are much less dependenton the characteristic properties of the H ii regions (e.g. ion-ization parameter, individual abundance of heavy elementsetc.) than e.g. excitation lines, for which a more detailedset of initial parameters would be more appropriate (see e.g.Panuzzo et al. 2003; Wofford et al. 2016). The main outputof this process is a library of emission line intensities, neb-ular continuum properties and electron temperatures (T e )of the H ii regions. Then, emission lines and nebular contin-uum are used to suitably complement the integrated SED ofSSPs from the far-UV to radio wavelengths. Radio emission associated with the presence of young mas-sive stars comprises essentially two components, the thermalradio emission (also referred to as free-free emission) and thenon-thermal radio emission (also referred to as non-thermalradio emission). The former emission comes from the nebu-lar free electrons originating from the ionizing radiation ofmassive stars. The non-thermal emission is instead believedto be synchrotron radiation that originated from the interac-tion of relativistic electrons, produced in the ejecta of core-collapsed supernovae (CSSN), with the ambient magneticfield. The radio continuum is thus a tracer of the numberof massive stars formed (and exploded) and hence an op-timal indicator of the very recent (if not the current) starformation rate.The fact that the radio emission is a good SFR traceris supported by the remarkably tight correlation betweenFIR and non-thermal radio emission. At 1.49 GHz, this cor-relation is quantified by the q-parameter (Helou, Soifer &Rowan-Robinson 1985): q = log F FIR / (3 . × Hz)F ν (1 . / (W m − Hz − ) ≈ . ± . F FIR = 1 . × − (2 . S µ m + S µ m)Wm − MNRAS000 , 000–000 (2017)
Obi
Figure 1.
SSP Integrated spectra per solar mass at ages of t = 2, 5 and 40 Myr, for metallicities Z = 0.02, 0.004 and 0.0001 andM up of 40, 120 and 350 M (cid:12) indicated by the solid blue, dotted red and dashed green lines respectively. At 2 Myr, the spectra for thevarious upper mass limits at any of the three metallicities is quite distinguishable. At 5 Myr and Z = 0.02, it is distinguishable only atwavelengths below 912 ˚A, the maximum for the lyman ionizing photons. At this age, notice that the spectra for the M up of 120 and350 M (cid:12) below 912 ˚A are superimposed, owing to the fact they must have evolved off the main sequence at this age. At 5 Myr and Z =0.0001, the reverse is the case, the spectra is distinguishable only at wavelengths above 912 ˚A because at this metallicity, stars lifetimesare a bit longer than at Z = 0.02. At 40 Myr, the spectra for all upper mass limits and metalicities are all superimposed and the Lymanionizing photons are no longer produced. (Young et al. 1989), S µ m and S µ m are IRAS flux den-sities in Jy. At sufficiently high frequency such that free-free self-absorption is negligible, the relation between the specific lu-minosity of free-free emission L ff ( ν ) and the rate of ionizingphotons Q(H) can be written as (Rubin 1968; Condon 1992) L ff = Q(H) C (cid:18) T e K (cid:19) . G dra ( ν, T e ) (2)where T e is the electron temperature, C = √ /π × . × and G dra ( ν, T e ) is the velocity averaged gaunt factor (Draine 2011): G dra ( ν, T e ) =ln (cid:40) exp (cid:34) . − √ π ln (cid:32) Z i ν GHz (cid:18) T e K (cid:19) − . (cid:33)(cid:35) + e (cid:41) (3)where Z i is the charge of the ions in the H ii region. Anapproximate velocity averaged gaunt factor were obtainedearlier by Oster (1961): G ost ( ν, T e ) =ln (cid:20) . × − (cid:16) ν GHz (cid:17) − (cid:21) + 1 . (cid:18) T e K (cid:19) (4)Taking into account that G dra ( ν, T e ) (cid:39) √ /π × G ost ( ν, T e )and adopting a common approximation used in literature, MNRAS , 000–000 (2017)
ARSEC SSP for GRASIL Figure 2.
Variation of the instantenous number of ionizing pho-tons per second per unit ionizing solar mass of the cluster withage (Myr). Different symbols correspond to different metallicitiesas illustrated in the plot . we obtain for the free-free emission (Condon 1992) L ff erg s − Hz − = Q ( H )6 . × (cid:18) T e K (cid:19) . (cid:16) ν GHz (cid:17) − . (5)The latter equation is often used by assuming a fixed elec-tronic temperature (10 K) to provide useful analytical ap-proximations at radio frequencies especially in the lack ofnebular emission (see discussion in B02). Here we directly es-timate the intensity of the thermal radio emission of our SSPfrom Cloudy with the procedure already described in Sec-tion 2.3. In Figure 3, we show the evolution of the 1.49 GHzand 33 GHz thermal radio emission for different metallici-ties, Z = 0.0001, 0.0005, 0.004, 0.008 and 0.02, and differ-ent M up of 40 ,
120 and 350 M (cid:12) . The effects of metallicityand M up on the thermal emission are easily noted. For ex-ample, at Z = 0.0001, the 1.4 GHz thermal emission for M up = 120 M (cid:12) is about 3 - 7 times larger than that for M up = 40 M (cid:12) In general by increasing the metallicity fromZ = 0.0001 to Z = 0.02 the thermal radio emission decreasesby a factor of about 3. Instead by increasing M up from 40 to350 M (cid:12) , thermal emission increases by about one order ofmagnitude. These important factors, that must be consid-ered in the calibration of the relation between star formationrate and thermal radio emission, are discussed below. Equations 2, 3 and 5 contain an explicit dependence onthe electron temperature, that is generally neglected in an-alytical approximations which assume a constant value ofT e = 10 K. Since T e is known to depend on the metallicityof the H ii regions, with a variation of more than a factorof two in the range of the observed values, we provide inAppendix A some useful analytical relations. We first list inTable A1 the values of the electronic temperature derivedusing CLOUDY for our SSP models at various metallicitiesand upper mass limits. In Figure A1 of Appendix A, we showthe relations between oxygen abundance and the electronic
Figure 3.
Variation of the 1.49GHz (red) and 33GHz (blue) ther-mal radio emission with age at different metallicities for differentvalues of M up . The five different line styles correspond to the fivedifferent values of metallicity. temperature. In this figure, crosses, ’X’s and asterisks indi-cate M up = 40, 120 and 350 M (cid:12) respectively. The averageof the empirical fits derived by L´opez-S´anchez et al. (2012)for high-ionization O iii and for low-ionization O iii zones isshown as the dashed black lines. We provide a multiple re-gression fitting relation (Equation A1) between T e , M up andZ that could be easily included in analytical approximations. SFR − Q(H) calibration
In a young stellar system the ionizing photon budget is dom-inated by massive stars and thus there must be a tight rela-tion between the current star formation rate and the rate ofionizing photons, that ultimately produce the thermal radioemission Condon & Yin (1990). In this section, we provide acalibration of the SFR − Q(H) relation. For this purpose weconsider the integrated spectrum of a galaxy up to a time t : f galν ( t, Z ) = (cid:90) t f SSPν ( t − t (cid:48) , Z ) SF R ( t (cid:48) ) dt (cid:48) (6)where SFR(t’) is the star formation rate at time t (cid:48) and f SSPν ( t − t (cid:48) , Z ) is the stellar spectrum of a SSP of age t ssp = t − t (cid:48) and given metallicity Zf SSPν ( t ssp , Z ) = (cid:90) M up M low φ ( m ) f ν ( m, t ssp , Z ) dm (7)In the latter equation, f ν ( m, t ssp , Z ) is the spectrum of anindividual star in a SSP which depends on the fundamen-tal parameters, its mass m , age t ssp , metal abundance Z and the IMF, φ ( m ). Using the SSPs already described, aconstant SFR of 10 M (cid:12) yr − and adopting the Kennicutt(1983) IMF, we obtain the integrated number of ionizingphotons IQ ( H ), shown in figure 4. Since IQ ( H ) is dom-inated by the most massive stars, the number of ionizingphotons emitted by a galaxy with constant SFR will ini-tially grow and soon saturate to a constant maximum value,when there is a balance between the newly formed ionizingmassive stars and the ones that die. Looking at Figure 2we see that, almost independently from the metallicity, the MNRAS000
In a young stellar system the ionizing photon budget is dom-inated by massive stars and thus there must be a tight rela-tion between the current star formation rate and the rate ofionizing photons, that ultimately produce the thermal radioemission Condon & Yin (1990). In this section, we provide acalibration of the SFR − Q(H) relation. For this purpose weconsider the integrated spectrum of a galaxy up to a time t : f galν ( t, Z ) = (cid:90) t f SSPν ( t − t (cid:48) , Z ) SF R ( t (cid:48) ) dt (cid:48) (6)where SFR(t’) is the star formation rate at time t (cid:48) and f SSPν ( t − t (cid:48) , Z ) is the stellar spectrum of a SSP of age t ssp = t − t (cid:48) and given metallicity Zf SSPν ( t ssp , Z ) = (cid:90) M up M low φ ( m ) f ν ( m, t ssp , Z ) dm (7)In the latter equation, f ν ( m, t ssp , Z ) is the spectrum of anindividual star in a SSP which depends on the fundamen-tal parameters, its mass m , age t ssp , metal abundance Z and the IMF, φ ( m ). Using the SSPs already described, aconstant SFR of 10 M (cid:12) yr − and adopting the Kennicutt(1983) IMF, we obtain the integrated number of ionizingphotons IQ ( H ), shown in figure 4. Since IQ ( H ) is dom-inated by the most massive stars, the number of ionizingphotons emitted by a galaxy with constant SFR will ini-tially grow and soon saturate to a constant maximum value,when there is a balance between the newly formed ionizingmassive stars and the ones that die. Looking at Figure 2we see that, almost independently from the metallicity, the MNRAS000 , 000–000 (2017)
Obi
Figure 4.
Evolution of the integrated number of ionizing photonsper second per unit solar mass initially formed as a function of theage in yr. Different line colors represents different metallciities.The variation of Q(H) with metallicity decreasis at increasingIMF upper mass limit. characteristic time of the saturation is set by the rapid dropof IQ ( H ) above about 6 Myr. The effect of M up on IQ ( H )is a direct consequence of the variation of the Q ( H ) of SSPsshown in Figure 2. The variation of IQ(H) with metallicitydecreases with increasing upper mass limit. After denotingby C the calibration coefficient between SFR and Q(H) inthe equation below (cid:18) SFRM (cid:12) yr − (cid:19) = C × (cid:18) IQ ( H )s − (cid:19) (8)we collect in Table A1 the values of C obtained with ourconstant SFR models, for different SSPs parameters. To il-lustrate the significant variations of C with metallicity ata given M up , we show in Figure A2 the plot of C againstmetallicity for M up = 40, 120 and 350 M (cid:12) Using the valuesof C given in Table A1 for different M up and Z , we providea multiple regression fitting relation between C , M up andmetallicity ( Z ), Equation A2. As an example, using this fit-ting relation, for M up = 120 M (cid:12) and Z = 0.02 Equation 8is: (cid:18) SFRM (cid:12) yr − (cid:19) = (cid:18) IQ ( H ) s − (cid:19) (9)We may compare equation 9 with the one obtained by Mur-phy et al. (2012) using the Starburst99 stellar populationmodel with a Kroupa (2001) IMF, a metallicity of Z = 0.02and a constant star formation over 100 Myr. (cid:18) SFRM (cid:12) yr − (cid:19) = (cid:18) IQ ( H ) s − (cid:19) (10)We see that the Murphy et al. (2012) calibration constant isfairly in agreement with ours. L ff Calibration
By combining equation 8 and equation 2, we derive the re-lation between the SFR and thermal radio emission:SFRM (cid:12) yr − = L ff C (cid:18) T e K (cid:19) − . (cid:18) G dra (cid:19) (11) where C = 1 / ( C × C ). The values of the coefficient C for different SSP parameters are provided in Table A1 andthe variation of C with metallicity and M up is shown inFigure A3. Using these values of C given in Table A1 fordifferent M up and Z , we also, as we did for the case C ,provide a multiple regression fitting relation between C , M up and metallicity ( Z ), Equation A3. As an example, usingthis fitting relation for M up = 120 M (cid:12) and Z = 0.02 andassuming the already quoted approximation for the Gauntfactor, Equation 11 becomesSFRM (cid:12) yr − = (cid:18) L ff . × (cid:19) (cid:18) T e K (cid:19) − . (cid:16) ν GHz (cid:17) . (12)A similar equation is provided by Murphy et al. (2012):SFRM (cid:12) yr − = (cid:18) L ff . × (cid:19) (cid:18) T e K (cid:19) − . (cid:16) ν GHz (cid:17) . (13) α and H β calibrations Using well-known relations between IQ ( H ) and the inten-sity of recombination lines (Osterbrock 1989), we may alsoobtain the corresponding calibrations for the SFR. For H α and H β we have (cid:18) IQ(H)s − (cid:19) = 7 . × (cid:18) L ( Hα )erg s − (cid:19) (14) (cid:18) IQ(H)s − (cid:19) = 0 . × (cid:18) L ( Hβ )erg s − (cid:19) (15)Using the above relations in equation 8, we write in Ap-pendix A analytical equations for the SFR-H α (equation A6)and SFR-H β (equation A7) calibrations, as a function of Zand M up . For the case with M up = 120 M (cid:12) and Z = 0.02we obtain with these analytical equations (cid:18) SFRM (cid:12) yr − (cid:19) = 4 . × − (cid:18) L ( Hα )erg s − (cid:19) (16) (cid:18) SFRM (cid:12) yr − (cid:19) = 0 . × − (cid:18) L ( Hβ )erg s − (cid:19) (17)Our calibration coefficient in equation 16 is in good agree-ment with the value of 4 . × − obtained by Bicker &Fritze-v. Alvensleben (2005) using GALEV synthesis code.
We know quite little about the source of non-thermal (NT)radio emission in star-forming galaxies. The mechanism isbelieved to be synchrotron emission from relativistic elec-trons that are accelerated by ISM shocks in the outskirts ofCCSN explosions (Condon 1992). B02 derived the followingrelation between NT radio emission L NT and the CCSN rate L NT / ν CCSN yr − erg s − Hz − = E SNR . ( ν .
49 ) − . + E NT . ( ν .
49 ) − α (18)In the above equation ν CCSN is the CCSN rate, E SNR . isthe average non thermal radio luminosity due to a youngSupernova Remnant (SNR) and E NT . is the average injected MNRAS , 000–000 (2017)
ARSEC SSP for GRASIL energy in relativistic electrons per CCSN event. Moreover,B02 estimated that, at 1.49 GHz, E SNR ≈ . E NT . (19) E NT . can be estimated from observations. For our GalaxyB02 adopt L NT = 6 . × W Hz − (Berkhuijsen 1984) at0.4GHz and ν CCSN = 0 . α ( − d logS ν − d log ν ) = 0 .
8, a value of E NT . = 1.44. We note that thefinal fate of massive stars is a critical assumption for estimat-ing their contribution to thermal radio emission. The forma-tion of NSs and BHs depends on the amount of mass lost bythe massive star through stellar winds and on the hydrody-namics of the explosion. One of the the most troublesomefacts is that the variations shown by these pre-supernovastars in their structural properties, like for e.g. the Fe-coreand O-core masses, are non-monotonic and pronounced evenwithin small differences in the ZAMS masses (Sukhbold &Woosley 2014). Some recent works in the attempt to char-acterize the parameters of successful and failed supernovaehave yielded some structural parameters that can be utilizedin predicting the fate of SNe (eg. Ertl et al. 2015; Uglianoet al. 2012; Janka 2012; O’Connor & Ott 2011). Using theseparameters, Spera, Mapelli & Bressan (2015) and Slemeret al. 2017 (to be submitted) were able to characterize thefinal fate of PARSEC massive stars for the different crite-ria adopted for successful CCSN explosion. Following Spera,Mapelli & Bressan (2015) and Slemer et al. 2017 we assumethat stars with initial mass above about M = 30 M (cid:12) do notcontribute to non thermal radio emission, contrary to B02where all stars of masses above M = 8 M (cid:12) were thought toexplode as CCSN. The region between about 24 −
30 M (cid:12) iscritical because the explosion criterion by O’Connor & Ott(2011) produces a much higher number of NSs than thatproduced by Ertl et al. (2015) criterion. Finally we stressthat we assume that progenitors undergoing pair-instabilitySNe either collapse to a BH or are completely incineratedby a thermonuclear explosion without producing relativisticelectrons, similarly to what is assumed for SNIa. This as-sumption on the CCSN distribution with initial mass mod-ifies the expected non thermal luminosity of star-forminggalaxies and requires a re-calibration of the GRASIL model.After accounting for the failed and successful SNe in theevaluation of non thermal emission from Equation 18, weshow in Figure 5 the variation of the 1.49 GHz non-thermalradio emissions with age, for different upper mass limits andmetallicities. We note that non-thermal radio emission is notsensitive to the upper mass limit of the IMF, as long as it islarger than the assumed threshold for failed SN, M = 30 M (cid:12) .In this case non thermal emission begins at an age of ∼ ∼ GRASIL code.
GRASIL
In the previous sections, we described a new suite of SSPsthat will supersede the ones used in the current version of
GRASIL . The new suite differs in many aspects from theprevious one as we briefly list in the followings. (1) TheSSP are based on the most recent
PARSEC stellar evolution-ary tracks with an updated physics, in particular new mass-loss recipes and finer and wider coverage in initial mass andmetallicity; (2) they include the most recent advances in ourunderstanding of the CCSN explosion mechanism and ac-count for the so called ” failed SN ”; (3) a more accurate gauntfactor and metallicity-dependent electron temperature wereincorporated in the relation between the integrated ioniza-tion photon luminosity and thermal radio luminosity (4) inthe current suite, we may adopt several values of the IMFupper mass limit Because of all these differences, we need tocheck and recalibrate some parameters of the SED producedby
GRASIL , in particular to check whether we are able toreproduce the canonical value of q . GHz = 2 .
35, observedin a prototype normal star-forming galaxiy, see Eq. 1. Forthis purpose, in the next section we will use
GRASIL withthe new SSPs to reproduce the SEDs of a some selected wellstudied galaxies.
GRASIL
GRASIL is a spectro-phometric code able to predict the SEDof galaxies from the FUV to the radio, including state-of-the-art treatment of dust reprocessing (Silva et al. 1998, 2011;Granato et al. 2000), production of radio photons by thermaland non-thermal processes (BO2) and an updated treatmentof PAH emission (Vega et al. (2005)). The reader is referredto these original papers for a fully detailed description ofthe code. It is also worth noting that nebular emission wasalready included in
GRASIL by Panuzzo et al. (2003) butwith a completely different procedure which also accountedfor different electron densities. In this respect our procedureis more simple because nebular emission is added directly tothe SSPs, but it allows a more versatile use of
GRASIL .For sake of convenience, we briefly summarise here themain features of
GRASIL . The first step is to compute achemical evolution model that provides the star formationhistory (SFH) and the metallicity and mass of the gas.Other quantities are computed by the code
CHE − EVO ,such as mass in stars, SN rates, detailed elemental abun-dances, but they are not used for the spectro-photometricsynthesis.
GRASIL’s main task is to compute the SED re-sulting from the interaction between the stellar radiationfrom CHE − EVO and dust, using a relatively flexible andrealistic geometry where stars and dust are distributed ina spheroidal and/or a disk profiles. A spherical symmet-ric distribution with a King profile is adopted in the caseof spheroidal systems while, for disk-like systems, a doubleexponential of the distance from the polar axis and fromthe equatorial plane is adopted. The dusty environmentsare made up of dust (i) in interstellar HI clouds heated bythe general interstellar radiation of the galaxy (refered toas the cirrus component), (ii) associated with star-formingmolecular clouds (MC) and (iii) in the circumstellar shellsof Asymptotic Giant Branch (AGB) stars.
GRASIL per-
MNRAS000
MNRAS000 , 000–000 (2017)
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Figure 5.
Variation of the 1.49 GHz and 33 GHz non-thermal (free-free) emission with age at different metallicities and different IMFupper mass limits. The red lines indicate thermal radio emission and the blue lines non-thermal radio emission. The plot for the thermalradio emission has already been shown in Figure 3 but added here for comparison with the non-thermal radio emission. As easily noticedin the figure, the non-thermal emission is almost unchanged for each of the different IMF upper mass limits, owing to the fact thatmasses above 30 M (cid:12) collapse directly to BH and do not explode to produce non-thermal emission. For this same reason, the non thermalemission for all plots starts at about an age of 7 Myr. For comparison purposes, the plot of the thermal radio emission is included toshow it’s pronounced variation with upper mass limits. At 1.4 GHz (upper panel), the non-thermal radio emission dominates that at33 GHz (lower panel) whereas at 33 GHz, the thermal emission dominates. forms the radiative transfer of starlight through these en-vironments. We remind the reader that the reprocessing ofstarlight by dust in envelopes of AGB stars is already takeninto account in our SSPs. For the intrinsic dust properties,
GRASIL adopts grains (graphite and silicate) in thermalequilibrium and a mixture of smaller grains and PAHs fluc-tuating in temperature. The dust parameters are tuned inorder to match with the observed emissivity and extinctionproperties of the local ISM (Vega et al. 2005).
The galaxy M100 was selected from the Spitzer NearbyGalaxies Survey (SINGS) (Kennicutt et al. 2003), a collec-tion of 75 nearby galaxies with a rich data coverage from thefar-UV to the radio, because it is one of the best sampledobjects, including the intensities of main emission lines. Thiswill provide the opportunity to check, for the first time in
GRASIL , the consistency of the SED continuum and emis-sion lines fitting. To obtain the chemical evolution modelwe adopt the parameters of the chemical evolution code
CHE-EVO given by Silva et al. (1998) who was able to well-reproduce M100. They are infall time scale t inf = 4 . ν sch = 0 . m inf = 2 × M (cid:12) . Figure 7shows the SFH resulting from the adopted chemical evo-lution parameters. The SFH is indicated by the solid blueline and the gas mass history by the dotted purple line. Toperform the SED fit, we consider several time steps alongthe chemical evolution of the galaxy for which we built alibrary of SED models with different GRASIL parameters.We note that since the observed SED refers to the wholegalaxy, the derived parameters correspond to a luminosityaverage of the physical properties, as commonly obtained bythis kind of fitting process. As a particular check, we alsoinvestigate the effect of changing the upper mass limit of the
MNRAS , 000–000 (2017)
ARSEC SSP for GRASIL IMF, M up = 40,120 and 350 M (cid:12) , on some physical quan-tities derived from our best-fit SED, in particular the SFR.The main GRASIL parameters varied are the molecular gasfraction f mol , the escape time t esc and the optical depthof molecular clouds (MC) at 1 µ m τ . The best fits were ob-tained by minimizing the merit function χ which is givenby χ = 1 N N (cid:88) i =1 (cid:18) F mod ( i ) − F obs ( i ) Err ( i ) (cid:19) (20)where F mod ( i ), F obs ( i ) and Err ( i ) are the model flux values,the observed fluxes and observational errors respectively. N is the number of photometric bands used to obtain the bestfit. Our GRASIL best-fit SEDs of M100 for M up = 40 M (cid:12) and M up = 120 M (cid:12) , are shown in the left and right pan-els of Figure 6 respectively, while the corresponding best fitparameters are summarized in Table 1. We do not showthe case with M up = 350 M (cid:12) , because its thermal-radioemission was significantly exceeding the observed one. Thisdiscrepancy could not be cured by varying any other param-eter in the fit. This result is, by itself, quite interesting andshows that for a normal star-forming galaxy it is difficultto have an average IMF extending up to such high initialmasses. The different dust components in diffuse medium(cirrus) and molecular clouds are shown and indicated bythe blue and red dashed lines, respectively. The thermal andnon-thermal radio emission components are indicated by thecyan and purple dashed dotted lines, respectively. The ther-mal component can be seen to be negligible for the case of M up = 40 M (cid:12) . We include, for the first time in GRASIL , se-lected emission lines in the SED. The labels in the plots referto some important quantities derived from our best fit: thebolometric luminosity from UV to radio (BOL), the total IRluminosity from 3 - 1000 µ m (FIR), the predicted extinctionuncorrected H α luminosity (Ha gra ), the observed H α lumi-nosity (Ha dat ), H α attenuation (A(H α )), attenuation in theV(0 . µ m) band (A(V)), the SFR averaged over the last 100Myr ( < SFR > ), the q-parameter as defined by equation 1(q(1.4GHz)), the coefficients of the SFR(H α ) and SFR(IR)calibrations ( < SFR / Ha > and < SFR / FIR > respectively).A summary of other important quantities derived from ourbest fit is provided in Tables B1 and B2. For both valuesof the adopted M up , the best fits match very well the over-all observed UV-radio SEDs. However, for M up = 120 M (cid:12) ,the model over-predicts by factor of ∼ α lu-minosity, 1 . × ergs s − (taken from Kennicutt et al.(2009)). This upper mass limit also produces a higher UVemission and a slight excess of thermal emission. On theother hand, the observed H α luminosity is well reproducedin the case of M up = 40 M (cid:12) . The over-predicted H α lu-minosity resulting from adopting M up = 120 M (cid:12) could belowered by increasing the escape time of young stars in theirparent clouds, leading to a larger absorption in the MCs.This will also lower the predicted far-UV emission which,in the current best fit, is slightly larger than the observedvalue. However, a larger absorption from MCs will increasethe predicted 24 µ m flux above the observed one. Note thatat 24 µ m the cirrus component has a pronounced minimumand its contribution to the overall MIR emission is only asmall fraction of the total. Thus, the 24 µ m flux, being dom- inated by the MC emission, is indeed a strong diagnostic forthe amount of light reprocessed by the MC component. Fromour best fit, we obtain a CCSN rate to NT radio luminosityratio (Equation 18) that is about a factor of 1.35 larger thanthe value obtained by B02 using the previous radio model.That is, E NT . (Thiswork) = 1 .
944 = E
NT1 . (B02) × .
35 (21)We anticipate here that this value is confirmed by all sub-sequent SED fits. We also note that this value is almostindependent from the adoption of M up for the reasons al-ready discussed previously. The predicted average SFR re-sulting from the panchromatic fit is only slightly affected bythe adoption of a different value of M up . By increasing M up from 40 to 120 M (cid:12) the average SFR decreases by about16 per cent. In the previous section we were able to reproduce fairly wellthe observed SEDs of the prototype galaxy M100, in particu-lar, we used the best fit model to calibrate the constant E NT of the non-thermal radio emission model. In this section wewish to check the thermal component of our radio emissionmodel. For this purpose, we compare our synthetic SEDswith those of selected extranuclear regions of NGC 6946, awell studied starburst galaxy at a distance of 6.8 Mpc. Thisgalaxy is dominated by very young starburst regions andshows relatively large thermal over non-thermal ratios (egIsrael & Kennicutt 1980; Heckman et al. 1983), and thus isparticularly well suited for a test of the free-free emissionoriginating from star formation. Murphy et al. (2010) ob-served these regions at 1.4, 1.5, 1.7, 4.9, 8.5 and 33 GHz andcomplemented their full SEDs with existing data from theUV to the submm range. For eight observed regions Mur-phy et al. (2010) estimated an average 33 GHz thermal com-ponent of ≈
85 per cent of the total, while for one region(named extra-nuclear region 4), this percentage was found tobe significantly lower, ≈
42 per cent, likely for the presenceof a so-called anomalous dust emission component whichsuppresses the thermal component. Particulary interestingfor our purpose is that Murphy et al. (2010) also providethe intensity of the H α emission for each region, that can bedirectly compared to the predictions of our model.To model the SEDs of the extra-nuclear star-formingregions of NGC 6946 we adopt a spherical symmetric dis-tribution with a King profile for the stars and dust. Mostimportant, we use the data not corrected for the local back-ground emission of the galaxy, though (Murphy et al. 2011)provide also data corrected for this emission. We thus adopt,for each region, a chemical evolution model composed by astar-burst superimposed to a quiescent star formating com-ponent. Our choice is dictated by the fact that the subtrac-tion by (Murphy et al. 2011) may bias our results and we pre-fer to eventually split the contribution of the starburst andthe old disk components directly from our fits. For purposesof clarity we show in Figure 8 a plot of the star formationhistory of the extra-nuclear region (cid:93) M up = 40 M (cid:12) .The corresponding chemical evolution model parameters arelabelled in the left side of the figure. For these models, thegalaxy is observed at a given age t gal = 11 Gyr. The ongo-ing starburst has an exponentially declining SFR that begins MNRAS000
42 per cent, likely for the presenceof a so-called anomalous dust emission component whichsuppresses the thermal component. Particulary interestingfor our purpose is that Murphy et al. (2010) also providethe intensity of the H α emission for each region, that can bedirectly compared to the predictions of our model.To model the SEDs of the extra-nuclear star-formingregions of NGC 6946 we adopt a spherical symmetric dis-tribution with a King profile for the stars and dust. Mostimportant, we use the data not corrected for the local back-ground emission of the galaxy, though (Murphy et al. 2011)provide also data corrected for this emission. We thus adopt,for each region, a chemical evolution model composed by astar-burst superimposed to a quiescent star formating com-ponent. Our choice is dictated by the fact that the subtrac-tion by (Murphy et al. 2011) may bias our results and we pre-fer to eventually split the contribution of the starburst andthe old disk components directly from our fits. For purposesof clarity we show in Figure 8 a plot of the star formationhistory of the extra-nuclear region (cid:93) M up = 40 M (cid:12) .The corresponding chemical evolution model parameters arelabelled in the left side of the figure. For these models, thegalaxy is observed at a given age t gal = 11 Gyr. The ongo-ing starburst has an exponentially declining SFR that begins MNRAS000 , 000–000 (2017) Obi
Figure 6.
M100
GRASIL best-fit SED for M up = 40 M (cid:12) (right panel) and M up = 120 M (cid:12) (left panel). The different dust components,diffuse medium and molecular clouds are represented by the dashed blue and red lines respectively. The thermal and non thermal radiocomponents are represented by the cyan and purple dashed dotted lines. The thermal component can be seen to be negligible for the caseof M up = 40 M (cid:12) . For the different M up , note the differences in the predicted quantities labelled in the plots (see text for more details),in particular the H α luminosities, attenuations (A(H α )) and SFR(H α ) calibration coefficient. We estimated E NT . = 1 . Figure 7.
Star formation history of M100 adopted in our
CHE-EVO model. The model parametrs are labelled: galaxy’s age(solid red line) , infall time (dashed green line) and schmidt-law efficiency. These parameters were adopted by Silva et al.(1998) based on constraints to reproduce the observed final massof M100. The SFH is indicated by the solid blue lines while thegas mass history by the dotted purple line. at t = t gal − t sb , where t sb is the age of the starburst. TwoSFR examples are given for a starburst age of t sb = 5 Myrand t sb = 14 Myr respectively. In the first case we are not ex-pecting any contribution to the non-thermal emission fromthe starburst while, in the second case since the age is largerthan 7 Myr (see Figure 5) we expect a contribution to thenon-thermal radio emission also from the starburst. Thusany age between t sb = 7 and 30 Myr can provide SEDswith different percentages of thermal vs non-thermal radioemission. We note that this can be used to mimic possi-ble different contributions of non thermal emission from theunderlying disk. To obtain the GRASIL best fit models wemainly varied the following parameters: the escape time ofyoung stars from their birth clouds t esc , the optical depth Figure 8.
SFH of one of the 8 extranuclear regions,NGC 6946 enuc 3 for M up = 40 M (cid:12) case. A starburst age of t sb = 14 Myr (green solid line) produced the best fit but we added t sb = 5 Myr (blue dotted line) case only to illustrate that we donot expect any contribution to the non-thermal emission from thestarburst at this age according to our radio model in Figure 5.At burst ages between 7 and 30 Myr, we expect a contribution tothe non-thermal radio emission also from the starburst. The reddotted-dashed line indicates the age (11.000 Gyr) at which theSED of this region was observed. of molecular clouds at 1 µ m τ , molecular gas fraction f mol ,the submm dust emissivity index β and the start time of theburst t (represented by the starburst age t sb ). The param-eters of the best fit SEDs are shown in Table 1 while, thecorresponding plots, are shown in Figure 9. In this figure, leftpanels show the results obtained adopting M up = 40 M (cid:12) and right panels show those for M up = 120 M (cid:12) . For allregions the observed IR SED can be fairly well reproducedby using either of the IMF upper mass limits. In general,the value of q . is found to lie between 2.5 and 2.6. This isabout 0.2 dex larger than the value observed in the normalstar-forming galaxy M100 ( q . = 2.35) implying that, inthese star-forming regions, the ratio between radio and FIRluminosity is about a factor 1.6 lower than in the normal MNRAS , 000–000 (2017)
ARSEC SSP for GRASIL Figure 9.
GRASIL best fit SEDs for the extra-nuclear regions of NGC 6946 (red diamonds) for upper mass limit of 40 (left panels)and 120 M (cid:12) (right panels). To test our radio decomposition, we over-plotted on top our thermal radio component (dotted-dashed cyanlines) the local background subtracted radio data flux (cyan diamonds) by Murphy et al. (2011).MNRAS000
GRASIL best fit SEDs for the extra-nuclear regions of NGC 6946 (red diamonds) for upper mass limit of 40 (left panels)and 120 M (cid:12) (right panels). To test our radio decomposition, we over-plotted on top our thermal radio component (dotted-dashed cyanlines) the local background subtracted radio data flux (cyan diamonds) by Murphy et al. (2011).MNRAS000 , 000–000 (2017) Obi
Figure 9 – continued MNRAS , 000–000 (2017)
ARSEC SSP for GRASIL star-forming galaxy M100. The estimated young starburstages support the notion that this is due to a lack of non-thermal radio emission as predicted by the original modelsby B02. This is also evident from the radio slope which isfound to be flatter than the value observed in the normalstar-forming galaxy ( α (cid:39) - 0.8). It is worth reminding herethat we adopted the calibration ( E NT . ) of non-thermal ra-dio luminosity obtained from the fits to M100. We note alsothat since the radio emission is dominated by the thermalcomponent, which has no free parameters, the SFR in theseregions is very well determined by the 33 GHz point, modulothe IMF. Another characteristics of the fits is the difficultyof reproducing the UV data, in spite of a fairly well fit in allthe other bands from mid-IR to radio bands. In particularthe runs with M up = 40 M (cid:12) tend to show larger UV fluxesthan the corresponding cases made with M up = 120 M (cid:12) ,which is against what could be expected from the depen-dence of the UV luminosity on the IMF. This can be notedin Figure 9 where we see that adopting M up = 120 M (cid:12) we either reproduce or underpredic the far-UV data while,adopting M up = 40 M (cid:12) , we either reproduce or overpre-dict them. At the same time, the average SFR in the modelswith M up = 40 M (cid:12) is about two to three times larger thanthat obtained with the models that adopt M up = 120 M (cid:12) .This is in evident contrast with what we have found in thefits of normal galaxies where we see that the SFR, obtainedwith different values of M up , differ by 20 per cent at maxi-mum and it is a consequence of the young age of such starbursting regions, where the bolometric luminosity is dom-inated by the most massive stars. Finally, the attenuationin the models with M up = 40 M (cid:12) is always lower thanthat obtained with the models adopting M up = 120 M (cid:12) .As the non-thermal radio emission starts about 7 Myr afterthe beginning of the burst of star formation (see Figure 5),we have the opportunity to perform an accurate decomposi-tion of the radio flux into thermal and non thermal compo-nents. We present in Table B2 the thermal fraction resultingfrom this decomposition and we show the two radio compo-nents in Figure 9. To show the quality of our decomposi-tion, we also show in Figure 9 and only for the case with M up = 120 M (cid:12) , the background subtracted radio datafluxes (cyan diamonds) by Murphy et al. (2011). In the nextsection, we will discuss the SFR calibrations derived usingour best fit model of the galaxies studied in this work. In this section we discuss the results obtained from the bestfits of the SEDs of M100 and the extra-nuclear regions ofNGC 6946. We begin with the SFR calibrations obtainedwith the new SSPs and then discuss the impact of the newlyadded emission line prediction on the resulting attenuation.
GRASIL best fits
We first show in Table B1 the luminosities of the best fitmodels in the selected photometric bands, from the UV toradio wavelengths. The upper panel refers to the results ob-tained adopting M up = 40 M (cid:12) while, the lower panel refers Table 1.
GRASIL best fit parameters (for upper mass limits of40 and 120 M (cid:12) ) for the modelled SEDs of M100 and NGC 6956SF regions.ID t gal /t sb t esc β τ f mol (Gyr/Myr) (Myr)(1) (2) (3) (4) (5) (6) M up = 40 M (cid:12) M100 12.0 2.5 2.0 12.0 0.10NGC 6946 1 8.0 1.0 2.1 9.07 0.30NGC 6946 2 9.0 0.5 1.7 12.00 0.05NGC 6946 3 8.0 1.0 2.0 24.48 0.20NGC 6946 5 8.0 0.3 2.0 4.15 0.25NGC 6946 6 12.0 1.2 2.2 5.33 0.40NGC 6946 7 7.0 1.0 2.1 14.81 0.30NGC 6946 8 7.0 0.6 2.1 6.12 0.22NGC 6946 9 8.0 1.0 2.1 5.33 0.30 M up = 120 M (cid:12) M100 12.0 0.9 2.0 14.81 0.10NGC 6946 1 11.0 0.6 2.2 5.33 0.12NGC 6946 2 11.0 1.0 1.7 16.60 0.15NGC 6946 3 8.0 0.9 2.2 12.00 0.14NGC 6946 5 18.0 1.0 1.8 18.75 0.50NGC 6946 6 11.0 0.7 2.2 5.33 0.12NGC 6946 7 8.0 1.0 2.2 5.33 0.16NGC 6946 8 8.0 0.9 2.2 5.33 0.12NGC 6946 9 9.0 0.6 2.2 5.33 0.12Column (2) gives the age of the galaxy ( t gal ) in Gyr for thenormal star-forming galaxy M100 and the age of the burst ( t sb )in Myr for the NGC 6946 star-bursting regions. Parameters inother columns are as described in text. to those obtained with M up = 120 M (cid:12) . The FIR luminos-ity in column 11 was obtained by integrating the IR specificluminosity from 3 to 1000 µ m. We also show the predictedintrinsic (suffix int ) and transmitted (suffix tra ) intensitiesof the H β and H α emission lines, the value of q . (Equa-tion 1), the relative contribution to the 3 - 1000 µ m FIRluminosity by the molecular clouds component and by thecirrus component, and the ratio between the 3 - 1000 µ mFIR and the bolometric luminosity. In the columns of radioluminosities, we enclose in parenthesis the fractional contri-bution of the thermal radio component to the total radioemission, derived from the models. Effects of Mup
By construction, i.e. since we are discussing best fits SEDs,the predicted luminosities obtained with the two different M up are very similar, but for those in the emission lines andin the UV bands. These are the most difficult to model be-cause they are the most sensitive to the attenuation. Thisis not the only reason however, because even the intrinsicH α and H β luminosity differs by a significant factor in thetwo M up cases. Indeed, in the two cases the ionizing photonflux (and the far and near-UV) differ much more than thecorresponding bolometric luminosities. Said in another way,one may be able to obtain the same bolometric flux withtwo different IMF upper limits but the amount of ionizingphotons may be significantly different, and this mainly af-fect the intensity of the recombination lines and the free-free MNRAS000
By construction, i.e. since we are discussing best fits SEDs,the predicted luminosities obtained with the two different M up are very similar, but for those in the emission lines andin the UV bands. These are the most difficult to model be-cause they are the most sensitive to the attenuation. Thisis not the only reason however, because even the intrinsicH α and H β luminosity differs by a significant factor in thetwo M up cases. Indeed, in the two cases the ionizing photonflux (and the far and near-UV) differ much more than thecorresponding bolometric luminosities. Said in another way,one may be able to obtain the same bolometric flux withtwo different IMF upper limits but the amount of ionizingphotons may be significantly different, and this mainly af-fect the intensity of the recombination lines and the free-free MNRAS000 , 000–000 (2017) Obi
Figure 10.
Comparisons between our model’s transmitted in-tensities of the H α emission lines with the observed ones, for M up = 40 M (cid:12) (red daimonds) and M up = 120 M (cid:12) (blue tri-angles) cases. The solid line indicates the one-to-one correlationwhereas the horizontal lines indicate the errors in the observed H α line. The green daimond indicates the case with M up = 350 M (cid:12) for the extra-nuclear region 8. radio emission. Note however that the 33 GHz luminositydoes not show the same strong dependence on the adoptedMup as that shown by the recombination lines, and this islikely due to the fact that a non negligible contribution ofthe non-thermal luminosity is present even at this high ra-dio frequency, which should be larger in the case of lower M up . The best fit transmitted intensities of the H α emissionlines are compared with the observed ones in Figure 10, forboth cases of M up . We do not include M100 in this plot tobetter show the case of the star-forming regions. The solidline indicates the one-to-one correlation. We see that, in thecase of extra-nuclear regions, the predicted values of the casewith M up = 40 M (cid:12) are larger than those of the case with M up = 120 M (cid:12) . In general our best fit models are ableto reproduce the observed values with an accuracy of about50 per cent. Looking to individual regions, we see that re-gions (cid:93) (cid:93) (cid:93) (cid:93) (cid:93) M up = 40 M (cid:12) while, for regions (cid:93) (cid:93)
7, a larger value of M up seemssuggested, up to M up = 120 M (cid:12) . From the figure it alsoappears that, in order to fit region (cid:93)
8, an even higher IMFupper mass limit (see the green daimond in Figure 10 for thecase of M up = 350 M (cid:12) ) should be used. Furhermore, wenote that the in all cases where we are able to reproduce theobserved H α emission we are also able to reproduce fairlywell the observed FUV luminosity, which is also strictly re-lated to the intrinsic ionizing photon flux. On the contrarythe NUV flux is not well reproduced by our models, likelyindicating that its origin is not strictly related to the starformation process. Since all model reproduce the observedbolometric luminosity and, in particular, the 24 µ m and the33 GHz data, we conclude that, by combining in a consistentway this relevant information, it is possible to obtain a fairlyrobust estimate of the upper mass limit of the IMF . Indeedwe stress that the FIR luminosity and those at H α , 33 GHzand 24 µ m bracket, on one side, the intrinsic ionizing photonflux and, on the other, the attenuation and re-emission bymolecular clouds where the stars reside during their initial phase, which are the most sensitive to the fractional contri-bution of the most massive stars.As far as the prototype normal galaxy M100 is con-cerned, we remind that the observed H α luminosity wasmatched by the model with M up = 40 M (cid:12) . It is impor-tant, at this stage, to remind that these conclusions shouldbe taken with care because the current SSP adopted do notaccount for binary evolution. Indeed it is known that binaryevolution can produce more ionizing photons at later stagesthan single star evolution, because of the loss of the envelopeby binary interaction (Wofford et al. 2016). In particular wemay say that regions (cid:93) (cid:93) (cid:93) (cid:93) (cid:93) M up and/or significanteffects by binary evolution. The latter effect could insteadexplain the location of region number (cid:93) M up = 350 M (cid:12) , as indicated by thegreen diamond in Figure 11). This effect, which add a newdimension to the problem, is under study in PARSEC andit will be included in the nearest future.
The q ratio.
The second thing that we note by inspecting Table B1 is thatthe value of the q . does not significantly depend on the up-per limit of the IMF. This is because a significant fraction ofboth the bolometric luminosity and the radio luminosity arecontributed by stars less massive than M = 40 M (cid:12) . Indeedafter a few Myr, the upper mass of the SSP is already signif-icantly lower than M = 120 M (cid:12) . Furthermore, the q . ratiois generally higher in the extranuclear regions of NGC 6946than in the normal SF galaxy M100, by a factor of (cid:39) M (cid:12) ≤ M ≤ M (cid:12) and the individual star-bursting re-gions have an age which is younger than the threshold forCCSN production. Thus they did not yet reach a station-ary equilibrium for non-thermal radio emission and not onlytheir radio slopes appear flatter but also their q . are higherthan that of normal star-forming galaxies B02. The SFR calibration.
Using the luminosity in the different bands, as presented inTable B1, and the average SFR obtained from the
GRASIL fits, we show in Table B2, the corresponding SFR calibra-tions C(b) = SFR/L(b), where b indicates the band. Theaverage SFR is derived by considering the last 100 Myr timeinterval for the normal star-forming galaxy M100, and theage of the burst in the star-forming regions of NGC 6946,which is shown in column 16 of Table B2 for the NGC 6946extranuclear regions. This choice is suggested by the factthat within an entire galaxy, the star-forming regions dis-tribute continuously with time while, this is obviously notthe case for individual regions. The average SFR (M (cid:12) yr − )so computed is shown in the second column of Table B2.These calibrations are directly obtained by GRASIL . Forsake of comparison, we also add, in Table B2, some cali-brations that can be obtained by using the un-attenuatedfluxes derived from
GRASIL best fit models, either directlyor by using the analytical relations obtained by means ofthe SSPs. These are useful to compare the differences be-tween the SFR derived from a panchromatic fit that real-istically account for ISM processes to analytical fits madewith SSP fluxes. For example, the FUV, H β and H α val-ues shown in column 3, 4 and 6, refer to the calibrations MNRAS , 000–000 (2017)
ARSEC SSP for GRASIL obtained by dividing the average SFR by the correspondingun-attenuated intrinsic fluxes of the models, listed in Ta-ble B1. For H β and H α we also show, in columns 5 and 7,the values obtained by inserting their corresponding intrin-sic fluxes in the analytical calibrations obtained from simpleSSPs models, Equations A7 and A6 respectively. For the33 GHz radio emission, we add in column 15, the value ofthe calibration C(33) SSP = SFR/L(33 GHz), directly de-rived from the SSP models (Equation A5). The last rows inthe first and second sections, indicated by < NGC > ,show the median values of all SFR calibrations derived fromthe star-bursting regions of NGC 6946. In the third sectionwe collect some common SFR calibrations from the liter-ature, with the corresponding bibliographic sources givenin the caption. In Figure 11 we plot the calibration con-stants C( ν ) at ν = 1.4, 4.9, 8.5 and 33.0 GHz, in units ofM (cid:12) Yr − erg − sHz, against the corresponding radio fre-quencies, for both the star-bursting regions (left panel) andM100 (right panel) and for both cases of M up . The relations(in logarithmic units) are almost linear above 1.4 GHz, andwe show the best fit regressions as solid lines. Concerningthe dependence on M up , there is a clear difference betweenthe starburst and the normal star formation regime in thesense that, in the former case the constant is about a factorof three larger independently from the frequency. Again thiseffect is due to the young age of the starburst regions coupledwith the dependence of the thermal radio emission on M up .Indeed for the normal SFR regime, the dependence on M up becomes significant only at high frequencies, where the ther-mal emission start dominating. From the fits we derive thefollowing general relations between SFR (in M (cid:12) yr − ) andradio luminosity (in erg s − Hz − ). For Star-bursting regions,with average metallicity ∼ ν ) tot = 0 .
43 log( ν ) − .
96 log( M up
120 ) − .
91 (22)while, for the normal star-forming galaxy, M100, withslightly more than solar metallicity, we have for the totalradio emissionlog( SFRL ν ) tot = 0 .
73 log( ν ) − .
16 log( M up
120 ) − .
31 (23)and for the non-thermal radio emission, we havelog( SFRL ν ) nth = 0 .
58 log( ν ) − .
43 log( M up
120 ) − .
33 (24)Relations similar to Equations 22, 23 and 24 above wereprovided by Murphy et al. (2011), assuming Kroupa IMF(with M up = 100 M (cid:12) ), solar metallicity and a constantSFR over a timescale of 100 Myr. For total radio emission (cid:18) SF RLν (cid:19) totMur = 10 − (cid:18) . ν − . ( T e ) . + 15 . ν − . (cid:19) − (25)and for non-thermal radio emission (cid:18) SF RLν (cid:19) nthMur = 10 − (6 . × − ν . ) (26)These relations are in between our relations in 22 and 23,running only (cid:46)
20 per cent lower than our one for normalstar-forming galaxies, below 33 GHz. However at frequen-cies higher than 33 GHz the difference grows rapidly and at 100 GHz our values are ∼
40 per cent and ∼
200 per centhigher than that of Murphy et al. (2011) for starburst andnormal galaxies, respectively. Interestingly, the relation de-rived by Schmitt et al. (2006) with Starburst99, assuming aSalpeter IMF (with M up = 100 M (cid:12) ), solar metallicity anda continuous SFR of 1 M (cid:12) yr − (cid:18) SF RLν (cid:19) totSch = 10 − (8 . ν − . + 1 . ν − . ) (27)agrees well with our relations in 22 and 23 at frequenciesfrom about 33 GHz to 100 GHz. Above 100 GHz the dustemission contribution becomes dominant.It is interesting to compare the GRASIL calibration at33 GHz with that derived from the SSP models (Equa-tion A5), i.e. columns 14 and column 15 in Table B2. Thevalues show some discrepancies, especially for normal galax-ies. However we remind that the values in column 15 refer tofree-free emission alone while the 33 GHz flux in column 14may include a non negligible contribution by synchrotronemission. If we take this contamination into account, usingthe percentage contribution of the thermal radio componentenclosed in parenthesis, the corrected values of column 14are in fair agreement with those predicted by Equation A5.This is expected because, at these wavelengths, attenuation,including also the free-free one (Vega et al. 2008), shouldnot be important. The above overall agreement indicate asurprising robustness of the radio calibration, irrespective ofthe differences in the underlying models. This will be par-ticularly important for the high redshift galaxies especiallyin their early evolutionary phases.As a further comparison, we provide at the bottom ofTable B2 other SFR calibrations taken from the literature.We remind the reader that, in this work, we adopt a Kenni-cutt (1983) IMF and a typical time-scale for averaging theSFR rate of 100 Myr for normal galaxies and equal to theage of the starburst in the extra-nuclear star bursting re-gions. The details on the parameters adopted by differentauthors may be found in the quoted papers.
It has been already shown in (Silva et al. 1998; Granatoet al. 2000) that the attenuation is the result of the inter-play between the extinction properties of dust grains andthe distribution between dust and stars in space and in time.Further discussion can also be found in (Charlot & Fall 2000;Panuzzo et al. 2003). We now investigate the properties ofthe attenuation curves of the galaxies studied here, with par-ticular interest to understand its dependence on the galaxytype, i.e. starburst vs. normal regime, and also the effectsof using different parameters in the analysis, such as M up inthe IMF.We first show in Figure 12, the attenuation curves,A λ /A V , of M100 (green solid line) and of the NGC 6946extra-nuclear regions studied in this work (black solid lines).They are simply derived by comparing the transmittedgalaxy flux to the intrinsic one, as a function of the wave-length. The top panel refers to the case of M up = 40 M (cid:12) while the case with M up = 120 M (cid:12) is shown in thebottom panel. The dotted blue lines represent the mediancurve of the NGC 6946 extra-nuclear regions obtained by MNRAS000
It has been already shown in (Silva et al. 1998; Granatoet al. 2000) that the attenuation is the result of the inter-play between the extinction properties of dust grains andthe distribution between dust and stars in space and in time.Further discussion can also be found in (Charlot & Fall 2000;Panuzzo et al. 2003). We now investigate the properties ofthe attenuation curves of the galaxies studied here, with par-ticular interest to understand its dependence on the galaxytype, i.e. starburst vs. normal regime, and also the effectsof using different parameters in the analysis, such as M up inthe IMF.We first show in Figure 12, the attenuation curves,A λ /A V , of M100 (green solid line) and of the NGC 6946extra-nuclear regions studied in this work (black solid lines).They are simply derived by comparing the transmittedgalaxy flux to the intrinsic one, as a function of the wave-length. The top panel refers to the case of M up = 40 M (cid:12) while the case with M up = 120 M (cid:12) is shown in thebottom panel. The dotted blue lines represent the mediancurve of the NGC 6946 extra-nuclear regions obtained by MNRAS000 , 000–000 (2017) Obi
Figure 11.
Left panel : SFR calibration constants C( ν ), in units of M (cid:12) yr − erg − s Hz, at ν = 1.4, 4.9, 8.5 and 33.0GHz (Ta-ble B2), for the star-bursting regions and using the total radio emission. Triangles and daimonds indicate cases of M up = 40 M (cid:12) and M up = 120 M (cid:12) respectively. Right panel : The same as in the left panel but for M 100 and using both the total radio (crosses) andnon-thermal radio emission (xs). In both panels, all red symbols and lines indicate cases of M up = 40 M (cid:12) and blue symbols and linescases of M up = 120 M (cid:12) . Also all lines represent least-square fits. sampling the curves of individual regions at selected wave-lengths. The median values of the quantities E ( B − V ) andR V = A V /E(B-V) for the star-bursting regions are also givenin the labels. We have also labelled some prominent emis-sion lines ( Hα line is in brown). For comparison purposes,we added the attenuation curves of Calzetti et al. (2000)(red dashed lines) and Cardelli, Clayton & Mathis (1989)(purple dotted-dashed lines). We also collect in Columns (2- 9) of Table B3 the attenuation in H α , H β , in the FUV(0.16 µ m) and NUV (0.20 µ m), in the B -band(0.45 µ m),and in the interpolated continuum at H β (named A48), inthe V -band(0.55 µ m) and in the interpolated continuum atH α (named A65). Columns 10 and 11 give the optical depthof the molecular cloud at 1 µ m derived from GRASIL andthe R V ratio, respectively. In Column 12 we show the dif-ference A -A which corresponds to E (48 − Hβ and Hα lines, we alsoobtained the same quantity, E ( Hβ − Hα ): E ( Hβ − Hα ) = 1 . (cid:18) ln( Hβ int Hα int ) − ln( Hβ tra Hα tra ) (cid:19) (28)and show its value in Column 13. We assume an intrinsic lineintensity ratio, ( Hα int /Hβ int ) = 2.86, which is valid for T e =10,000 K (Hummer & Storey 1987). Column 14 gives theescape time of young stars from their birth cloud in Myr.Column 15 gives the FIR flux in ergs s − cm − in the 40- 120 µ m interval derived using the 60 and 120 µ m fluxes(Helou et al. 1988).Several points can be noted by inspection of Figure 12and Table B3. First of all, we see that, while in normal galax-ies the attenuation in the lines is significantly higher thanthat in the surrounding continuum, (a factor of 4 on aver-age for M100), this is not true for the star bursting regionswhere this factor is not more than 1.3. The fact that the at-tenuation in the lines is significantly higher than that in thesurrounding continuum is well known and it is a manifesta-tion that young stars are more dust enshrouded than olderstars. However, in the case of the star-bursting regions theunderlying continuum is essentially produced by the samestellar populations, with a small contribution from the olderpopulations, so that the attenuation in the lines is not much different from that in the continuum. To get more insightsfrom the models we compare the characteristic R values inthe lines and in the nearby continuum. We see that for star-forming galaxies, R Hα = A Hα / (A Hβ -A Hα ) is much largerthan the value obtained in the corresponding interpolatedunderlying continuum regions (R = A / ( A − A ). Forexample, for M100, R Hα = 16(10) while R = 4(4), forM up = 40(120) M (cid:12) . In the starburst regions, R Hα and R have similar values between 6 and 10. The high values sodetermined for R Hα would suggest a high neutral absorp-tion in these objects but this is not the case because wehave not modified the grain size distribution which, by de-fault in GRASIL is the one of the Galactic ISM. We alsosee that in M100, R , in the continuum, has a value of ∼ τ µ m in Table B3) that the emission of young stars is almostcompletely absorbed, until they escape from the clouds. Thiseffect mimics the neutral absorption. This effect is enhancedfor the emission lines because they are generated only bystars younger than about 6 Myr, so that the fraction of lineflux absorbed by molecular clouds with respect to the totalone, is even higher. Adopting a t esc larger than 7 Myr willerase line emission in our model, irrespective of the galaxytypes considered here. A major consequence of the age se-lective attenuation described above is that it leads to wrongestimates of the attenuation in the line emission, if one usesmethods involving attenuation-affected observables, like theBalmer decrement method. A more accurate method to esti-mate the intrinsic H α luminosity (hence the H α attenuation)is by using the 33 GHz and 24 µ m luminosities, since theyare optimal tracers of the radiation emitted by the mostmassive. Adopting a median value of 78.5 per cent as thepercentage contribution of the thermal radio component inyoung star-bursts, we first obtain the thermal radio emissioncomponent of our model’s 33 GHz total radio emission lumi-nosity. Using the analytical relation given in Equation 2 (T e and gaunt factors used here are as given in Equations A1 MNRAS , 000–000 (2017)
ARSEC SSP for GRASIL Figure 12.
Attenuation curves, A λ /A V , for M100 and NGC 6946extra-nuclear regions, for the cases of M up = 40 (top panel) and M up = 120 M (cid:12) (bottom panel). The black solid lines are theattenuations curve of the eight regions of NGC 6946 while thedotted blue line represents the median of these curves. The me-dian values of R V and E ( B − V ) for the star-forming regions arealso given in the labels. The green line is the attenuations curve ofM100. For comparison purposes, we added the attenuation curvesof Calzetti et al. (2000) (red dashed line) and Cardelli, Clayton &Mathis (1989) (purple dotted-dashed line) The later attenuationseems to agree very well with that of M100 at wavelengths above ∼ and 3 respectively), we derive the number of ionizing pho-tons corresponding to this luminosity. With Equation A2,we then estimate the corresponding intrinsic H α luminosity.A plot of the estimated intrinsic H α luminosity (in erg s − )against our model’s 33 GHz thermal radio luminosity (L in erg s − Hz − ) is presented in Figure 13. We added inthis figure also the normal SF galaxy M100, with an av-erage thermal fraction of 16.0 per cent(42.0 per cent) forM up = 40 M (cid:12) (M up = 120 M (cid:12) ), respectively. The fittingrelation (solid line) considering only the star bursting re-gions for both cases of M up , is given bylog(L intH α ) = log(0 . .
10 (29)The corresponding attenuation at H α can be obtained by Figure 13.
Plot of our model’s 33 GHz thermal radio luminosityagainst the intrinsic H α luminosity. Solid line represents linear fitfor the star-bursting regions. The H α luminosity here is derivedfrom the thermal radio luminosity using Equations 2 and A2. Weadopted a median thermal fraction of 78.5 per cent in estimatingthe thermal radio component of the 33 GHz total radio luminosity.We also added in this plot the M100 which has an average thermalfraction of 16.0 per cent(42.0 per cent) for M up = 40 M (cid:12) (M up = 120 M (cid:12) ).luminosity (L33 in erg s?1Hz?1) is presented in Figure 12. using the intrinsic value provided by equation 29A H α = − . (cid:18) Hα obs . (cid:19) + 35 .
25 (30)As mentioned earlier, this attenuation is larger than the onethat can be obtained with the Balmer decrement methodbecause the latter might not accounts for the strong obscu-ration in the early life of massive stars (see Table B3). Thus,in presence of an estimate of the radio flux at 33 GHz, Equa-tion 30 should be preferred for young starbursts. A similarrelation, though with somewhat larger scatter, can be ob-tained for the 24 µ m flux, which is shown in Figure 14. Therelation between the model’s intrinsic H α (in erg s − ) and24 µ m luminositiy, L = λ L λ in erg s − , islog(L intH α ) = 0 . ) + 15 .
73 (31)almost independently from M up . Correspondingly, the de-rived attenuation in H α isA H α = − . (cid:18) Hα obs . (cid:19) + 39 .
33 (32)It is also interesting to provide a relation between the at-tenuation at 1600 ˚A (Column 4 of Table B3) and the ratioof FIR (Column 11 of Table B1) to F tra (Column 3 of Ta-ble B1). The plot is shown in Figure 15, along with the linearfitting relation obtained for the star-bursting regions (solidline), for both M up cases. A = 1 . (cid:18) F IRF obs (cid:19) + 0 .
254 (33)We note that the normal galaxy M100 is out from the re-lation. This may likely be due to the non negligible contri-bution to the FIR intermediate age stellar populations thatare not contributing to the far UV.
MNRAS000
MNRAS000 , 000–000 (2017) Obi
Figure 14.
Plot of the 24 µ m luminosity against the intrinsicH α luminosity, both extracted directly from our best-fit models.Solid line represents linear fit. We excluded M100 in this plot soas to better represent the star-bursting regions. Figure 15.
Plot of attenuation at 1600 ˚A against the ratio,
F IR/F , both extracted from our best-fit models. The solidblack line represents our linear fit as given in Equation 33. Thered crosses and blue ’X’s indicate M up = 40 and 120 M (cid:12) casesrespectively. In this paper we have used the recent
PARSEC tracks tocompute the integrated stellar light, the ionizing photonbudget and the supernova rates predicted by young SSPmodels for different IMF upper mass limits. The SSPs spansa wide range in metallicities, from 0.0001 to 0.04 and initialmasses ranging from 0.1 to 350M (cid:12) . In building the inte-grated spectra, we have adopted the spectral library com-piled by Chen et al. (2015). This library is a result of ho-mogenising different sets of libraries through a process fullydescribed in Girardi et al. (2002) and Chen et al. (2014).Using this integrated spectra in the photoionization code
CLOUDY , we have also calculated and included in the in-tegrated spectra the nebular continum and the intensitiesof some selected emission lines. With the new SSPs we can then be able to predict the panchromatic spectrum and themain recombination lines of star-forming galaxies of anytype, with
GRASIL .We made also two major revisions in the radio emissionmodel. First, we revisited the relation between free-free radioemission, number of ionizing photons and radio frequencyand came up with a relation that (a) takes into account thefull dependence of the electron temperature on the metallic-ity and the effect of considering different IMF upper masslimits and (b) incorporated a more accurate gaunt factorterm. The free-free radio emission shows a significant vari-ation with metallicity and IMF upper mass limit, decreas-ing by a factor of about 3 when Z increases from 0.0001 to0.02 and inceasing by more than an order of of magnitudewhen the mass limit is increased from 40 to 350 M (cid:12) , atconstant total mass. These differences cannot be negelected,especially when calibrating SFRs using tracers that dependstrongly on the ionizing photon budget. Hence, the corre-sponding SFR calibrations (H α , H β and thermal radio emis-sion) take into account this dependence on metallicity andIMF upper limits.Second, we revised the non-thermal radio emissionmodel originally described by B02, taking into account re-cent advances in the CCSN explosion mechanisms which in-dicates a range of stellar masses where the stars fail to ex-plode, the so called Failed SNe . We adopt a threshold valueof 30 M (cid:12) , above which stars do not produce non-thermal ra-dio emission. This has two immediate effects: (a) the begin-ning of the non-thermal radio emission is delayed by about7 Myr, ∼ the lifetime of a 30 M (cid:12) star; (b) the non-thermalradio emission is independent from the IMF upper mass limitas long as it is above 30 M (cid:12) . It is also assumed that pair-instability SNe, discussed by Slemer et al. (2017) do notproduce synchrotron radiation.With these revisions in the new SSPs and in the radioemission model, there is the need to check some parametersof the GRASIL code. We first re-calibrate the proportionalityconstant between the supernova rate and the correspondingnon-thermal radio luminosity, E NT . ), using one of the best-sampled nearby normal star-forming galaxy, M100. We areable to reproduce very well the far-UV to radio SED of thisgalaxy, for IMF upper mass limits of 40 M (cid:12) and 120 M (cid:12) ,with an average q . of 2.42. We obtain a value of E NT . =1.94 which is larger than that obtained previously by B02by a factor of 1.35, but it is similar to that obtained byVega et al. (2005). We find that using M up = 350 M (cid:12) produces a thermal radio emission that significantly exceedsthe observed one. This excess thermal radio emission cannotbe cured by varying any other parameter in the fit. Thisresult suggests that, for a normal star-forming galaxy, it isdifficult to have an average IMF extending up to such highinitial masses. What depends strongly on the upper masslimit of the IMF is the number of ionizing photons, whichbeqars on the intensity of the recombination lines and onthe thermal radio emission. Indeed, in spite of being able toreproduce the FIR and 1.4 GHz radio emission, the modelthat adopts M up = 120 M (cid:12) over predicts the H α emissionby a factor of about three while, in the case of M up = 40 M (cid:12) ,the discrepancy is only of a few percent.We then check the new thermal radio emission modelagainst the well studied thermal radio dominated star-forming regions in NGC 6946. Even in this case we are able MNRAS , 000–000 (2017)
ARSEC SSP for GRASIL to reproduce very well the observed SEDs from NIR to ra-dio wavelengths for both cases of the IMF upper mass lim-its. In fitting the SEDs of these thermal radio-dominantedstar-bursting regions, we adopt the value of E NT . result-ing from the non-thermal radio calibration with the normalstar-forming galaxy M100. The estimated values of the q . ratio in these regions lie between 2.5 and 2.6, implying arelatively lower non-thermal emission than in normal star-forming galaxies. The additional evidence of flatter radioslopes supports the notion that there is lack of the non-thermal emission as predicted by the original non-thermalradio emission models by B02. The resulting ages of thebursts, range from 7 to 12 Myr, confirming that these obser-vations can be used to determine the star-burst ages. The fitobtained with the two IMF upper mass limits exhibit inter-esting differences, in particular in the predicted H α and UVluminosities which are the most sensitive to the IMF and todust attenuations. We show that, by combining informationfrom the FIR, 24 µ m, 33 GHz and H α , we can determine thepreferred value for M up . This is the first time, to the bestof our knowledge, that the IMF upper mass limit can beconsistently determined. However, for region (cid:93) α flux even with M up = 350 M (cid:12) .This could be a case where binary evolution, which is knownto produce an excess of ionizing photons due to the loss ofthe envelope of massive stars by binary interaction, may berequired.With luminosities and averaged SFR extracted from ourbest fit models (Table B1), we derive SFR calibrations in dif-ferent bands for both normal galaxies and star-burst regions(Table B2). Since thermal radio emission and that in the re-combination lines depend strongly on the upper mass limitof the IMF, we provide multiple regression fitting relationswith M up and metallicity (e.g. Equations A5, A6 A7).Finally, exploiting the realistic treatment of dust per-formed by GRASIL , we investigate the properties of the at-tenuation curves of the galaxies studied in this work withthe aim of understanding their dependence on the galaxytype. We find that, while in the normal SF galaxy M100the attenuation in the lines is significantly higher than thatin the surrounding continuum, for the star bursting regionsof NGC 6946 the two attenuations are similar. A commonproperty is that the predicted R values obtained for the Hα line is large, mimicking a significant neutral absorption. Forstar bursting regions, large values are found also for the con-tinuum while, in the case of M100, the R value of the con-tinuum is normal. Large R values have been found in highredshift star-forming galaxies by Fan et al. (2014), using acompletely different population synthesis tool. A major dis-turbing consequence of the age selective attenuation, whichcould not be revealed in a foreground screen model, is that itleads to wrong estimates of attenuation when using methodsinvolving observed line fluxes, like the Balmer decrement. Ofcourse, more accurate methods are those that combine UVor line fluxes with fluxes that are not affected by attenu-ation, such as the well known relation between the FUV(at 1600 ˚A) attenuation and the flux ratio ratio, FIR/F .For the star-forming regions we revisit the former relation(Equation 33) and we provide new relations between the H α attenuation and the observed H α and 24 µ m (Equation 30)or 33 GHz (Equation 32) fluxes. The above mentioned rela-tions, which we show to be almost independent from M up , can be extremely useful in estimating the attenuations inyoung high redshift galaxies. For this purpose we are work-ing on a larger galaxy sample to increase the statistical sig-nificance of our results. ACKNOWLEDGMENTS
We thank ?? for helpful discussions. A. Bressan andL. Girardi acknowledge financial support from INAFthrough grants PRIN-INAF-2014-14. P. Marigo and Y.Chen acknowledge support from ERC Consolidator Grant”STARKEY”, G.A. n. 615604. F. Perrotta was supportedby the RADIOFOREGROUNDS grant of the EuropeanUnion’s Horizon 2020 research and innovation programmeCOMPET-05-2015, grant agreement number 687312.
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APPENDIX A: VARIATION OF ELECTRONTEMPERATURE AND THE CONSTANTS, C AND C , WITH IMF UPPER MASS LIMITSAND METALLICITY In Figure A1, we show the plot of electron temperature T e (ob-tained from CLOUDY ) against metallicity Z for M up = 40, 120and 350. The oxygen abundance corresponding to the metallicityZ, written as x = 12 + log(O / H) where O / H = O / H (cid:12) +log(Z / Z (cid:12) , is shown on the upper axis. To convert from Z to Table A1.
Calibration constants, C and C , for different metal-licities and upper mass limits.Z IQ ( H ) C T e C (10 (10 − ) (10 ) (10 )(1) (2) (3) (4) (5) M up = 40 M (cid:12) M up = 120 M (cid:12) M up = 350 M (cid:12) C ) of the SFR-IQ(H) relation as given in equation 8. Col-umn(4): electron temperature in K computed using CLOUDY .Column(5): calibration constant ( C ) of the SF R - L ff relationas given in equation 11. Figure A1.
Plot of electron temperature T e (obtained from CLOUDY ) against metallicity Z for M up = 40, 120 and 350 M (cid:12) indicated by the red ’X’s, blue crosses and green xterisks respec-tively. The lower axis is the metallicity while the upper one is thecorresponding oxygen abundance, x = 12 + log(O / H). The bluedashed-dotted line indicates the metallicity at Z = 0.0134 whichwe adopted in this work as the solar metallicity. The average ofthe empirical fits derived by L´opez-S´anchez et al. (2012) for high-ionization O iii and for low-ionization O ii zones is shown by theblack dashed line. MNRAS , 000–000 (2017) ARSEC SSP for GRASIL Figure A2.
Variation of the constant C with age at differentmetallicities (Z = 0.0001, 0.0005, 0.004, 0.008 and 0.02) and differ-ent upper mass limits. The symbols used to indicate the different M up are as in Figure A1. These variations of C , depending onthe set of upper limits used, can severely underestimate or over-estimate the estimated SFR using the thermal radio luminosityas a tracer. As clearly noticed, there is a large difference between C obtained with M up = 40 M (cid:12) and M up = 120 M (cid:12) and thatobtained with M up = 120 M (cid:12) and M up = 350 M (cid:12) . C is asdefined in equation 8. Figure A3.
Same as in Figure A2 but for the constant C . C is as defined in equation 11.(O/H), we adopt the solar oxygen abundance given by As-plund et al. (2009), x (cid:12) = 12 + log(O / H) (cid:12) = 8 . ± .
05 and Z (cid:12) = 0 . iii and for low-ionization O ii zones,using the MAPPINGS III code (Sutherland & Dopita 1993), isshown as the dashed black lines. In this figure, our T e values(’X’s, crosses and xterisks) computed with CLOUDY for differ-ent metallicities are compared with the above-mentioned empiri-cal fit obatined by L´opez-S´anchez et al. (2012). It can be seen that our T e values start deviating from those of L´opez-S´anchez et al.(2012) at low metallicities. A multiple regression fitting relationbetween T e , M up and Z that can be easily included in analyticalapproximations, is provided by equation A1.log (cid:18) T e (Z , M up )10 K (cid:19) = − . − . / . . up / C and C in equations 8and 11, obtained with our constant SFR models for different SSPsparameters. These values are shown in Figure A2. The multipleregression fitting relation is given by Equation A2.log(C ) = 0 . / . − . up / − .
18 (A2)Table A1 also lists the values of the constants C in equation 11.These values are shown in Figure A3. The corresponding multipleregression fitting relation is given by Equation A3.log(C ) = 0 . up / − . / .
02) + 26 .
61 (A3)Using the relation A2 in Equation 8 we obtain the integratedionizing photon flux of a star-forming region of arbitrary constantmetallicity and IMF upper mass limit log(IQ(H)) = − . / .
02) + 0 . up / .
18] + log(SFR) (A4)while, using the relation A3 in Equation 11 (T e in this Equationis in 10 K ), we may get the corresponding SFR-thermal radiocalibration:log(SFR / L( ν ) ff ) = 0 . up / − . / . − log(G dra ) − .
57 (A5)where SFR and ν are in units of M (cid:12) yr − and GHz respectively.Similarly for SFR vs. H α calibration we may write:log(SFR / H α ) = 0 . / . − . up / − .
32 (A6)and for SFR vs. H β calibration:log(SFR / H β ) = 0 . / . − . up / − .
87 (A7)Comparisons between SFR calibrations derived using EquationsA5 , A6 and A7 above and those obtained directly from our modelare given in Table B2 and discussed in Section 5.1. The formercase is indicated by the superscript ssp in this table.MNRAS000
87 (A7)Comparisons between SFR calibrations derived using EquationsA5 , A6 and A7 above and those obtained directly from our modelare given in Table B2 and discussed in Section 5.1. The formercase is indicated by the superscript ssp in this table.MNRAS000 , 000–000 (2017) O b i Table B1.
GRASIL
Best-fit model luminosities.ID
F UV i F UV t Hβ i Hβ t Hα i Hα data Hα t
24 70
F IR . . . q . MC CIR F IR/BOL (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19)10 M up = 40 M (cid:12) M100 653.10 319.0 102.15 33.70 298.61 123.0 105.0 130.0 616.0 167.0 793.0 (2) 285.0 (5) 186.0 (8) 71.6 (18) 2.38 19 81 0.39NGC 6946 1 4.52 2.03 1.92 0.95 5.48 3.96 2.88 0.77 2.81 0.66 2.28 (24) 1.1 (44) 0.87 (54) 0.55 (75) 2.53 25 75 0.62NGC 6946 2 10.65 6.73 5.01 3.47 14.28 12.10 10.30 1.34 4.50 1.02 4.11 (37) 2.3 (59) 1.89 (68) 1.33 (85) 2.46 35 65 0.44NGC 6946 3 4.52 2.20 1.92 1.02 5.48 4.86 3.07 0.47 2.85 0.60 2.28 (24) 1.1 (44) 0.87 (54) 0.55 (75) 2.53 28 72 0.58NGC 6946 5 2.71 1.54 1.15 0.76 3.29 2.90 2.28 0.20 1.28 0.30 1.37 (24) 0.7 (44) 0.52 (54) 0.33 (75) 2.42 12 88 0.50NGC 6946 6 12.47 5.22 4.86 2.17 13.87 7.87 6.59 2.92 8.41 2.01 7.99 (16) 3.6 (32) 2.68 (42) 1.55 (65) 2.47 27 73 0.66NGC 6946 7 13.93 5.79 6.47 2.87 18.40 7.81 8.67 2.96 9.42 2.26 5.36 (36) 3.0 (58) 2.45 (67) 1.71 (84) 2.69 37 63 0.66NGC 6946 8 9.90 4.99 4.59 2.66 13.08 2.73 8.02 1.42 5.75 1.29 3.81 (36) 2.1 (58) 1.74 (67) 1.21 (84) 2.61 21 80 0.57NGC 6946 9 10.80 4.86 4.61 2.29 13.10 5.08 6.92 2.07 6.58 1.58 5.47 (24) 2.7 (44) 2.09 (54) 1.33 (75) 2.52 24 76 0.62 M up = 120 M (cid:12) M100 729.94 379.0 260.66 131.0 759.97 123.0 406.0 120.0 687.0 175.0 734.0 (7) 291.0 (15) 204.0 (21) 98.4 (42) 2.45 18 82 0.42NGC 6946 1 3.77 1.29 1.82 0.63 5.17 3.96 1.94 0.83 3.33 0.70 2.26 (24) 1.1 (44) 0.87 (54) 0.55 (76) 2.60 212 78 0.69NGC 6946 2 6.76 3.29 4.53 2.07 12.95 12.10 6.23 1.29 4.29 0.95 4.23 (35) 2.3 (57) 1.91 (66) 1.33 (84) 2.44 42 58 0.60NGC 6946 3 3.01 0.99 1.85 0.71 5.28 4.86 2.19 0.57 3.02 0.63 1.96 (30) 1.0 (52) 0.82 (61) 0.55 (81) 2.62 21 79 0.70NGC 6946 5 1.74 0.68 1.02 0.38 2.92 2.90 1.16 0.27 1.25 0.30 1.48 (21) 0.7 (40) 0.54 (49) 0.33 (72) 2.38 29 71 0.70NGC 6946 6 10.69 3.49 5.12 1.55 14.66 7.87 4.79 2.85 9.27 2.02 6.32 (24) 3.1 (44) 2.43 (54) 1.55 (76) 2.60 26 74 0.70NGC 6946 7 9.24 2.80 5.73 1.87 16.24 7.81 5.79 2.57 8.99 2.01 6.06 (30) 3.2 (52) 2.55 (61) 1.71 (81) 2.61 24 76 0.72NGC 6946 8 6.57 2.28 4.07 1.61 11.55 2.73 4.97 1.54 6.26 1.32 4.30 (30) 2.2 (52) 1.81 (61) 1.21 (81) 2.60 21 79 0.68NGC 6946 9 9.15 3.03 4.51 1.43 12.82 5.08 4.43 2.41 8.06 1.75 5.00 (28) 2.5 (49) 2.02 (58) 1.33 (79) 2.64 26 74 0.69Col.(1): ID. Col.(2-7): luminosities at FUV (0.16 µ m), Hβ and Hα . i and t indicates intrinsic and attenuated transmitted luminosities respectively. Col.(8): observed attenuationuncorrected Hα luminosity. Cols.(9 and 10): luminosities at 24 µ m and 70 µ m. Col.(11): total (3-1000 µ m)IR luminosity. Cols.(12-15): radio luminosities at 1.4, 4.9, 8.5 and 33 GHz.Enclosed in parenthesis is the fraction in per cent of the thermal radio component to the total radio emission. Col.(16): q-parameter as defined by equation 1. Cols.(17 and 18) are theMC and cirrus contribution (in per cent) to the total IR luminosity respectively. Col.(19): ratio of the total IR and the bolometric luminosities All UV, optical and infrared luminositiesare in erg s − while all radio luminosities are in erg s − Hz − . The corresponding SFR calibrations at these luminosities are given in Table B2. APPENDIX B: BEST-FITS DERIVED QUANTITIES FOR M100 AND NGC 6946 STAR-FORMING REGIONS M N R A S , ( ) A R S E C SS P f o r G R A S I L Table B2.
GRASIL
Best-fit derived SFRs and their calibrations at various bands.
ID < SF R > C ( F UV i ) C ( Hβ i ) C ( Hβ i ) ssp C ( Hα i ) C ( Hα i ) ssp C (24) C (70) C ( F IR ) C (1 . C (4 . C (8 . C (33) C (33) ssp t (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)10 − − − − − − − − − − − − − M up = 40 M (cid:12) M100 5.58 0.85 54.67 45.22 18.70 16.04 4.30 0.91 3.35 0.70 (2) 1.96 (5) 3.00 (8) 7.79 (18) 25.71 12.0NGC 6946 1 0.09 1.88 44.33 31.96 15.5 11.34 11.01 3.02 12.80 3.72 (24) 7.62 (44) 9.72 (54) 15.4 (76) 14.77 8.0NGC 6946 2 0.20 1.85 39.31 31.95 13.8 11.33 14.70 4.38 19.30 4.79 (37) 8.64 (59) 10.40 (68) 14.9 (85) 14.75 9.0NGC 6946 3 0.09 1.88 44.22 31.96 15.5 11.34 18.01 2.98 14.20 3.72 (24) 7.62 (44) 9.72 (54) 15.4 (76) 14.77 8.0NGC 6946 5 0.05 1.88 44.28 31.96 15.5 11.34 25.63 3.98 17.00 3.72 (50) 7.62 (71) 9.72 (78) 15.3 (90) 14.77 8.0NGC 6946 6 0.20 1.58 40.51 31.99 14.2 11.35 6.75 2.34 9.79 2.47 (24) 5.53 (44) 7.36 (54) 12.8 (76) 14.79 12.0NGC 6946 7 0.29 2.06 44.38 31.95 15.6 11.34 9.70 3.05 12.70 5.36 (17) 9.70 (33) 11.70 (42) 16.8 (66) 14.76 7.0NGC 6946 8 0.20 2.06 44.46 31.95 15.6 11.34 14.37 3.55 15.80 5.36 (37) 9.70 (59) 11.70 (68) 16.8 (85) 14.76 7.0NGC 6946 9 0.20 1.88 44.06 31.96 15.5 11.34 9.81 3.09 12.90 3.72 (37) 7.62 (59) 9.72 (68) 15.4 (85) 14.77 8.0 < NGC > up = 120 M (cid:12) M100 4.80 0.66 18.43 15.92 6.32 5.65 4.00 0.70 2.74 0.65 (24) 1.65 (44) 2.36 (54) 4.88 (76) 8.90 12.0NGC 6946 1 0.03 0.80 16.44 11.46 5.80 4.07 3.61 0.90 4.30 1.34 (9) 2.73 (19) 3.48 (26) 5.48 (48) 5.27 11.0NGC 6946 2 0.07 1.02 15.22 11.27 5.33 4.00 5.35 1.61 7.25 1.63 (26) 2.98 (46) 3.62 (56) 5.20 (77) 5.13 11.0NGC 6946 3 0.03 0.90 14.62 11.46 5.11 4.07 4.78 0.89 4.27 1.38 (37) 2.64 (59) 3.27 (68) 4.88 (85) 5.26 8.0NGC 6946 5 0.02 0.92 15.75 11.32 5.48 4.02 5.84 1.28 5.23 1.07 (32) 2.28 (53) 2.95 (63) 4.79 (82) 5.16 18.0NGC 6946 6 0.09 0.80 16.59 11.46 5.80 4.07 2.98 0.92 4.19 1.34 (37) 2.73 (59) 3.48 (68) 5.48 (85) 5.27 11.0NGC 6946 7 0.08 0.90 14.48 11.46 5.11 4.07 3.23 0.92 4.15 1.38 (23) 2.64 (42) 3.27 (52) 4.88 (74) 5.26 8.0NGC 6946 8 0.06 0.90 14.51 11.46 5.11 4.07 3.83 0.94 4.48 1.38 (26) 2.64 (46) 3.27 (56) 4.88 (77) 5.26 8.0NGC 6946 9 0.07 0.82 16.63 11.46 5.85 4.07 3.11 0.93 4.29 1.51 (32) 2.97 (53) 3.72 (63) 5.68 (82) 5.26 9.0 < NGC > a h b d g b a e e a c h h a e h f h Col.(1): ID. Col.(2): average SFR (in M (cid:12) yr − ) derived by considering the last 100 Myr time interval for the normal star-forming galaxy M100 and the age of the burst in thestar-forming regions of NGC 6946 Cols.(3-15): SFR calibrations obtained using the above averaged SFR and the luminosities (intrinsic values for FUV, H α and H β ) given in Table B1.In Cols.5, 7 and 15, we rather present the calibrations obtained from simple SSPs models, Equations A7 , A6 and A5 respectively for H β , H α and 33GHz. The later refers to free-freeemission. For the radio -based SFR calibration, we enclosed in parenthesis the percentage contribution of the thermal radio component to the total radio emission. Col.(16): age of thegalaxy in Gyr for M100 or the age of the burst in Myr, for NGC 6946 extranuclear regions. The last row in the first and second panels (with ID, < NGC > ) gives the medianvalues of all quantities given for NGC 6946 star-bursting regions. The values of the SFR calibrations given in the 3rd panel were taken from the literature. The superscript on thesevalues indicates the reference as described below: a Murphy et al. (2011), b Kennicutt (1998), c Calzetti et al. (2007), d Zhu et al. (2008), e Schmitt et al. (2006), f Li et al. (2010), g Lawtonet al. (2010), h Panuzzo et al. (2003). These authors adopted different IMF and evolutionary synthesis models. M N R A S , ( ) O b i Table B3.
GRASIL
Best-fit derived quantities related to dust attenuation. ID A Hα A Hβ A F UV A NUV A B A A V A τ R V E ( Hβ − Hα ) c E ( Hβ − Hα ) l t esc (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) M up = 40 M (cid:12) M100 1.13 1.20 0.78 0.83 0.30 0.28 0.24 0.23 17.79 4.17 0.055 0.093 2.5NGC 6946 1 0.70 0.76 0.87 0.91 0.60 0.63 0.54 0.57 12.66 8.08 0.060 0.059 1.0NGC 6946 2 0.36 0.40 0.50 0.53 0.31 0.33 0.27 0.29 15.38 6.03 0.041 0.037 0.5NGC 6946 3 0.63 0.69 0.78 0.82 0.53 0.56 0.47 0.51 26.84 7.34 0.056 0.055 1.0NGC 6946 5 0.40 0.45 0.61 0.65 0.43 0.42 0.39 0.37 8.43 9.14 0.053 0.054 0.3NGC 6946 6 0.81 0.88 0.95 0.99 0.67 0.71 0.60 0.66 8.51 8.62 0.056 0.067 1.2NGC 6946 7 0.82 0.88 0.96 0.99 0.67 0.73 0.59 0.66 17.67 7.71 0.062 0.059 1.0NGC 6946 8 0.53 0.59 0.75 0.79 0.53 0.54 0.48 0.48 9.63 9.48 0.059 0.053 0.6NGC 6946 9 0.70 0.76 0.87 0.91 0.60 0.63 0.54 0.57 8.79 8.08 0.060 0.060 1.0 M up = 120 M (cid:12) M100 0.68 0.75 0.71 0.77 0.30 0.30 0.24 0.23 20.16 4.18 0.070 0.087 0.9NGC 6946 1 1.07 1.16 1.18 1.24 0.82 0.95 0.75 0.78 9.28 9.48 0.173 0.088 0.6NGC 6946 2 0.79 0.85 0.78 0.84 0.53 0.77 0.45 0.58 19.10 5.28 0.188 0.055 1.0NGC 6946 3 0.96 1.04 1.20 1.26 0.86 0.93 0.78 0.79 16.11 10.38 0.136 0.087 0.9NGC 6946 5 0.99 1.06 1.01 1.08 0.73 0.96 0.65 0.77 21.31 7.51 0.190 0.062 1.0NGC 6946 6 1.21 1.30 1.21 1.28 0.84 1.01 0.75 0.81 9.05 8.92 0.201 0.084 0.7NGC 6946 7 1.13 1.22 1.30 1.36 0.91 1.02 0.82 0.87 9.08 9.71 0.152 0.086 1.0NGC 6946 8 0.92 1.01 1.15 1.21 0.82 0.89 0.74 0.76 9.26 10.03 0.135 0.085 0.9NGC 6946 9 1.16 1.25 1.20 1.27 0.83 1.00 0.75 0.80 9.11 9.10 0.194 0.087 0.6Col.(1) :ID. Cols.(2 - 9) give the attenuations in H α , H β , FUV (0.16 µ m), NUV (0.20 µ m), B -band(0.45 µ m), the interpolated continum at H β , V -band(0.55 µ m)and the interpolated continum at H α . They were derived using the ratio of the intrinsic unattenuated and attenuated (observed) fluxes. Col.(10): opticaldepth of the molecular cloud at 1 µ m. Col.(11): R V . Col.(12):The reddening given simply by A - A . Col.(13):The reddening derived using the balmerdecrement method as given by Equation 28. Col.(14): escape time of young stars from their birth cloud in Myr. M N R A S , ( ) ARSEC SSP for GRASIL This paper has been typeset from a TEX/L A TEX file prepared bythe author.MNRAS000