WISDOM project -- VI. Exploring the relation between supermassive black hole mass and galaxy rotation with molecular gas
Mark D. Smith, Martin Bureau, Timothy A. Davis, Michele Cappellari, Lijie Liu, Kyoko Onishi, Satoru Iguchi, Eve V. North, Marc Sarzi
MMNRAS , 1–18 (2020) Preprint 20 October 2020 Compiled using MNRAS L A TEX style file v3.0
WISDOM project - VI. Exploring the relation between supermassive blackhole mass and galaxy rotation with molecular gas
Mark D. Smith, ★ Martin Bureau, , Timothy A. Davis, Michele Cappellari, Lijie Liu, Kyoko Onishi, , , Satoru Iguchi, , Eve V. North, and Marc Sarzi Sub-department of Astrophysics, Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford, OX1 3RH, UK Yonsei Frontier Lab and Department of Astronomy, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea School of Physics & Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK Research Center for Space and Cosmic Evolution, Ehime University, Matsuyama, Ehime, 790-8577, Japan Department of Astronomical Science, SOKENDAI (The Graduate University of Advanced Studies), Mitaka, Tokyo 181-8588, Japan National Astronomical Observatory of Japan, National Institutes of Natural Sciences, Mitaka, Tokyo, 181-8588, Japan Armagh Observatory and Planetarium, College Hill, Armagh, BT61 DG, UK
Accepted 2020 October 15. Received 2020 October 5; in original form 2020 February 11
ABSTRACT
Empirical correlations between the masses of supermassive black holes (SMBHs) and properties of their host galaxies arewell-established. Among these is the correlation with the flat rotation velocity of each galaxy measured either at a large radiusin its rotation curve or via a spatially-integrated emission line width. We propose here the use of the de-projected integratedCO emission line width as an alternative tracer of this rotation velocity, that has already been shown useful for the Tully-Fisher (luminosity-rotation velocity) relation. We investigate the correlation between CO line widths and SMBH masses fortwo samples of galaxies with dynamical SMBH mass measurements, with respectively spatially-resolved and unresolved COobservations. The tightest correlation is found using the resolved sample of 24 galaxies as log ( 𝑀 BH / M (cid:12) ) = ( . ± . ) + ( . ± . ) [ log ( 𝑊 / sin 𝑖 km s − ) − . ] , where 𝑀 BH is the central SMBH mass, 𝑊 the full-width at half-maximum of a double-hornedemission line profile, and 𝑖 the inclination of the CO disc. This relation has a total scatter of 0 . . Key words: galaxies: general – galaxies: kinematics and dynamics – galaxies: bulges – galaxies: nuclei – submillimetre: galaxies
Supermassive black holes (SMBHs) are found in the centres of almostall massive galaxies. They are now believed to play an instrumentalrole in the evolution of their hosts, a conclusion drawn from thetight correlations, spanning multiple orders of magnitude, betweenthe SMBH masses and large-scale host properties (for reviews, seee.g. Kormendy & Ho 2013; Graham 2016). This is surprising giventhat, in almost all galaxies following these correlations, the SMBHonly dominates the gravitational potential on very small spatial scales( .
100 pc), and it has a negligible gravitational influence on the scaleson which the host properties are measured. Nevertheless, these tightcorrelations have been used to argue that each SMBH coevolves withits host, invoking mechanisms such as active galactic nucleus (AGN)feedback (e.g. Croton et al. 2006; Bower et al. 2006; Vogelsbergeret al. 2014), major merger-enhanced accretion (e.g. Sanders et al.1988; Cattaneo et al. 1999; Di Matteo et al. 2005), and simple mergeraveraging (e.g. Peng 2007; Hirschmann et al. 2010; Jahnke & Macciò ★ E-mail: [email protected] © a r X i v : . [ a s t r o - ph . GA ] O c t Mark D. Smith et al.
The tightest known correlations are those between the SMBH massand properties of the host galaxy’s bulge - stellar velocity dispersion( 𝜎 ∗ ; e.g. Ferrarese & Merritt 2000; Gebhardt et al. 2000), mass orluminosity ( 𝑀 bulge and 𝐿 bulge ; e.g. Kormendy & Richstone 1995;Magorrian et al. 1998; Marconi & Hunt 2003; Häring & Rix 2004).These host quantities are measures of the stellar mass-dominatedcentral potential of the bulge.The 𝑀 BH − 𝜎 ∗ relation has traditionally been viewed as the tightestcorrelation, with an intrinsic scatter of only ≈ . 𝑅 e ), although the effects of finiteinstrumental apertures can affect this scale.Correlations also exist between the SMBH mass and other prop-erties of the host galaxy. One of the simplest such properties is thetotal stellar mass ( 𝑀 ∗ , tot ; Davis et al. 2018b). Although originallythe total stellar mass (and the disc component in late-type galaxies,LTGs) was thought not to correlate with SMBH mass (Kormendy &Gebhardt 2001; Kormendy et al. 2011), recent works have indicatedthere is a correlation, albeit one weaker than 𝑀 BH − 𝜎 ∗ (e.g. Beifioriet al. 2012; Läsker et al. 2014; Savorgnan & Graham 2016; Mutlu-Pakdil et al. 2018) with 0 .
66 dex scatter (Davis et al. 2018b). Thisallows total stellar mass (or luminosity) to be invoked as a convenientproxy for SMBH mass where the dynamical 𝜎 ∗ is unavailable or hardto measure.The total stellar mass/luminosity can also be linked to a dynamicalquantity via the shape of the rotation curve, as indicated for spiralsby the Tully-Fisher relation (Tully & Fisher 1977). Such rotationcurves are observed from the line-of-sight projected velocities of(rotating) dynamical tracers (e.g. Pease 1918; Burbidge et al. 1959;Rubin & Ford 1970, see Sofue & Rubin 2001 for a review), and havebeen extensively used to study the structure of galaxies. Each galac-tic rotation curve is a probe of the gravitational potential, from theSMBH-dominated central region (occasionally spatially-resolvablewith modern high-resolution observations; e.g. Greenhill et al. 1995;Gao et al. 2017; North et al. 2019), through a stellar-mass dominatedregime, to outer parts dominated by a putative dark halo. A rotationcurve can be decomposed into contributions from these componentsof the galactic potential (e.g. Martinsson et al. 2013). Disc galax-ies often exhibit rotation curves that are (almost) flat over most ofthe stellar-dominated regimes and into the halo-dominated regimes,providing evidence for the ‘disc-halo conspiracy’ (e.g. van Albada& Sancisi 1986; Williams et al. 2009). The rotation curves of someelliptical and lenticular galaxies peak within 1 𝑅 e before decliningwith increasing radius, some then flattening in the outer parts (e.g.Noordermeer et al. 2007; Cappellari et al. 2013). Both 𝑀 ∗ , tot and 𝜎 ∗ are widely known to correlate with the spatially-integrated line width of neutral hydrogen (H i; e.g. Whitmore et al.1979; Courteau et al. 2014; Serra et al. 2016) . However, each hasalso been linked to the line width of CO. Throughout this discussionwe refer to the spatially-integrated width of an emission line as Δ 𝑉 ,with a subscript denoting the emitting atom/molecule. The Tully-Fisher relation (TFR), relating the asymptotic velocity ofa rotationally-supported disc to its host galaxy’s absolute magnitude,is widely used to measure distances to extragalactic sources. For thelast two decades, since initial proposals by Dickey & Kazes (1992)and Sofue (1992), millimetre-wave emission from CO molecules hasbeen used as an alternative to radio H i or optical H 𝛼 emission to tracethe asymptotic rotation velocity (e.g. Ho 2007b; Davis et al. 2011,2016; Tiley et al. 2016; Topal et al. 2018; Tiley et al. 2019), includingin early-type galaxies (ETGs) where such rotationally-supported COdiscs are still reasonably common (e.g. Davis et al. 2013a).Although CO discs do not usually extend as far as neutral hydrogendiscs, they have been found to extend to the flat part of the rotationcurve in ≈
70% of CO-rich ETGs (Davis et al. 2013a), and theyappear to in most LTGs (e.g. Leung et al. 2018; Levy et al. 2018).The potential at the radii probed by CO, however, is still dominatedby the stellar component (Cappellari et al. 2013), and thus CO gasdoes not trace the same halo-dominated potential as H i. We discussthis in further detail in Section 1.3.Nevertheless, Davis et al. (2019b) combined the CO TFR of Tileyet al. (2019) with the 𝑀 BH − 𝑀 ∗ , tot correlation of Davis et al. (2018b)to yield a prediction of 𝑀 BH ∝ Δ 𝑉 . ± . . For spiral galaxies,the disc-halo conspiracy enables the replacement of the CO linewidths in the Tiley et al. (2019) TFR with those of H i. The sameargument cannot be made for ETGs, as we discuss in Section 1.4.In a sample of 48 spiral galaxies with dynamically-measured SMBHmasses and H i line widths, Davis et al. (2019b) obtained a relation of 𝑀 BH ∝ Δ 𝑉 . ± .
37H i , consistent with the prediction. Notably, boththe predicted and the observed relation are substantially steeper thanfound in earlier works (e.g. Beifiori et al. 2012; Sabra et al. 2015). 𝜎 ∗ A correlation between spatially-integrated H i emission line widthsand 𝜎 ∗ was initially suggested for disc galaxies by Whitmoreet al. (1979) and Whitmore & Kirshner (1981), where a constant Δ 𝑉 H i / 𝜎 ∗ ≈ . Δ 𝑉 H i − 𝜎 ∗ correlation for ETGs was obtained using spatially-resolved rotationcurves from the ATLAS survey. Serra et al. (2016) found a lin-ear relation, Δ 𝑉 H i / 𝜎 ∗ = .
33, and 12% total scatter consistent withthe measurement errors. We must once more emphasise that thesecorrelations physically correspond to a correlation between a haloproperty and a property measured on baryon-dominated scales, dis-cussed further in Section 1.4.In addition to that of large-scale H i, other emission line widthson smaller spatial scales have been proposed to potentially correlatewith 𝜎 ∗ . Nelson & Whittle (1999) showed for a sample of Seyfertgalaxies that the full-width at half-maximum (FWHM) of the nuclear[O iii] emission correlates with its 𝜎 ∗ when the latter is measured on asimilar scale, with Δ 𝑉 [ O iii ] / 𝜎 ∗ = .
35. Nelson (2000) later adoptedthis relation to use the [O iii] FWHM as a proxy for 𝜎 ∗ to investigatethe 𝑀 BH − 𝜎 ∗ relation among active galaxies, for which there werefew 𝜎 ∗ measurements available.Shields et al. (2006) proposed the use of the CO line width as aproxy for 𝜎 ∗ to study whether the 𝑀 BH − 𝜎 ∗ relation was already inplace in a sample of quasars at redshifts 2 < 𝑧 < Δ 𝑉 CO / 𝜎 ∗ = .
35. Although Shields et al. (2006) thereby concludedthat 𝑀 BH − 𝜎 ∗ does not hold at high redshifts, a subsequent analysis MNRAS , 1–18 (2020)
ISDOM: The Δ 𝑉 CO − 𝑀 BH relation by Wu (2007) showed that by de-projecting Δ 𝑉 CO and assuming thequasars were viewed almost face-on, the CO line widths could bebrought into agreement with the local 𝑀 BH − 𝜎 ∗ relation. In his anal-ysis of Seyfert galaxies, Wu (2007) found a steeper Δ 𝑉 CO − 𝜎 ∗ corre-lation than Shields et al. (2006) had assumed, Δ 𝑉 CO /( sin 𝑖 km s − ) = (− . ± . ) + ( . ± . )( 𝜎 ∗ / km s − ) , where 𝑖 is the incli-nation of the CO disc. Although this relation still has substantialscatter, it dramatically outperforms the simpler approximation ofShields et al. (2006). The spectral profile of a broad spatially-integrated emission lineis dominated by Doppler-broadening, and thus tells us about thekinematics of the galaxy rather than the physical state of its emittinggas. Thus both H i and CO line widths trace the rotation curve.However, as hinted at above, these emission lines originate fromvery different regions of the galaxy. H i emission primarily traces theouter parts, where the rotation curve is typically very flat and thepotential dominated by non-luminous matter.In contrast, CO emission typically extends to only ≈ . 𝑅 e (Daviset al. 2013a), emphatically in baryon-dominated regions. It thus tracesthe depth of the central, stellar, potential in a manner similar to 𝜎 ∗ .As previously discussed (Section 1.2.1), in LTGs this distinction ismade smaller by the disc-halo conspiracy. However, this conspiracyis not known to hold in ETGs (Young et al. 2008; Cappellari et al.2013). Furthermore, ETG rotation curves are not ubiquitously flat intheir outer parts, with recent kinematic modelling indicating that therotation curves often decline (from some maximum) with increasingradius, such that the asymptotic velocities traced by H i are typically ≈
25% lower than those found by central tracers at 0 . 𝑅 e (Serra et al.2016), as previously found in early-type disc galaxies (Noordermeeret al. 2007). This indicates the existence of an inner maximum in therotation curve (hereafter 𝑉 max ). The ATLAS survey constructedJeans Anisotropic Models (JAMs) of ETGs, and from these generateda rotation curve for each object. Cappellari et al. (2013) showed thatboth the outer asymptotic circular velocity and 𝑉 max correlate tightlywith 𝜎 ∗ , the latter with an intrinsic scatter of only 7%.However, if one simply measures the width of an emission line,it is not trivial to identify which of these two velocities (asymptoticcircular velocity or 𝑉 max ) is traced by CO emission (e.g. Noordermeer& Verheijen 2007). Lavezzi & Dickey (1997) have argued that theshapes of the emission line profiles can be used to select those thatreach beyond 𝑉 max , i.e. the profiles must be ‘boxy’ or ‘sharp-edged’.With different specific implementations, this criterion is now widelyused in the absence of spatially-resolved emission (e.g. Davis et al.2011; Tiley et al. 2016; Topal et al. 2018).However, even when 𝑉 max has not been reached such profiles canalso be produced by sharply-truncated discs. Modern interferometricobservations have revealed populations of (potentially low-surfacebrightness) CO discs in ETGs that are truncated at the edge of theassociated circumnuclear dust discs (e.g. Barth et al. 2016b; Boizelleet al. 2017; Davis et al. 2018a; Boizelle et al. 2019). It is worth notingthat some of these galaxies have nearly-flat rotation curves within the 𝑉 max defined by luminous mass models, due to the contribution of thecentral SMBHs, also leading to double-horned profiles, but spatially-resolved observations are nevertheless essential to determine whichscales the CO emission probes. Following the discovery of the first SMBH mass-host property cor-relations, studies began to investigate whether the underlying coevo-lution was with the bulge, or whether a more fundamental corre-lation existed with another structural component. Particular interestrevolved around the halo mass, with the asymptotic value of the ro-tation curve invoked as a suitable observable proxy. Initial work byFerrarese (2002) and later Pizzella et al. (2005) appeared to show anon-linear relationship between the SMBH and (dark) halo masses.However, this was really a correlation between the rotation velocityand 𝜎 ∗ of each galaxy, and it relied on invoking the 𝑀 BH − 𝜎 ∗ relationand the assumption that the asymptotic rotation velocity measuredcorrelates with the (dark) halo mass.The later analysis of Kormendy & Bender (2011) showed thatthere was no correlation unless the galaxy also hosted a classicalbulge - thus the apparent correlation was merely an ‘indirect resultof the rotation curve conspiracy’. Moreover, they argued that a loosecorrelation between these parameters cannot be taken to imply co-evolution - on the simple principle that a larger galaxy contains largerstructural components. Kormendy et al. (2011) went on to challengethe assumption that 𝜎 ∗ closely traces 𝑀 BH in pseudobulges, andhence the inference that haloes drive the growth of SMBHs.Nevertheless, interest in these correlations has not subsided, notleast because although weak correlations should not be taken asimplying co-evolution, they can enable simple observable proxiesto be used as estimators of SMBH masses. Davis et al. (2018b),for instance, suggested that their 𝑀 ∗ , tot correlation is ‘beneficial forestimating 𝑀 BH from pipeline data or at higher redshift, conditionsthat are not ideal for the isolation of the bulge’.However, we must be cautious. In Section 1.2.2 we argued that thespatially-integrated width of a CO line traces the baryonic componentof a galaxy, since CO emission does not extend to halo-dominatedscales. Moreover, since it is unclear whether the disc-halo conspiracyholds in lenticulars (or an analogous relation in ellipticals), we arguethat the discussion in this paper of a correlation between CO linewidths and SMBH masses should not be taken as implying anythingabout SMBH-halo coevolution. The discussion in Sections 1.1 and 1.2 implies that it is reasonable toinvestigate a correlation between the deprojected, spatially-integratedCO line widths of galaxies, tracing their rotation curves within thebaryon-dominated regions, and their SMBH masses. Such a correla-tion may prove an alternative to the 𝑀 BH − 𝜎 ∗ relation. To this end,we fit double-horned emission line profiles to new and archival COobservations of galaxies to measure their line widths. We then showthat these CO line widths correlate sufficiently well with the SMBHmasses to be used as proxies to estimate SMBH masses. We alsocontribute to the extensive literature on CO line width correlationswith 𝜎 ∗ , by finding a reasonably tight correlation.This paper exploits three recent improvements: (1) we use only themost robust SMBH masses measured dynamically, (2) we derive ourtightest relation with spatially-resolved, high spectral resolution andhigh signal-to-noise ratio (SNR) CO observations from the AtacamaLarge Millimetre/sub-millimetre Array (ALMA) and other interfer-ometers (and show the negative impact of instead using unresolvedsingle-dish spectra) and (3) we fit our spatially-integrated CO emis-sion lines with ‘Gaussian double-peak’ line profiles, that have beenshown to recover well the intrinsic line widths (Tiley et al. 2016).In Section 2, we describe the observational data used in this study. MNRAS , 1–18 (2020)
Mark D. Smith et al.
This is accompanied by Appendix A, detailing new single-dish ob-servations. Section 3 goes on to measure the CO line widths andexplore potential correlations. In Section 4, we discuss the conclu-sions that can be drawn from this study and the limitations of thesample used. We conclude in Section 5.
SMBH masses have been measured in around 200 local galaxiesover the last three decades, using a variety of dynamical tracers ofthe galaxies’ central potentials. These results, as compiled in van denBosch (2016), are used as the starting point for this work, to which afew more recent measurements are added. In addition to robust mea-surements, there are also a large number of upper limits, principallyfrom ionised gas. In this work, we exclude such upper limits, leaving aparent sample of 196 galaxies with well-constrained SMBH masses.As most SMBH mass measurements require spatially-resolved trac-ers, these objects are typically well-studied local galaxies. Almost allhave now been observed in CO using single-dish telescopes (thoughonly 75 were detected), and 73 have been observed with interferom-eters (of which 58 were detected).Investigating a correlation with CO line widths requires that weare able to recover these widths precisely. This is of particular impor-tance since, while among massive galaxies the asymptotic rotationvelocities span less than one order of magnitude (100 −
500 km s − ),the corresponding SMBH masses vary over four (10 − M (cid:12) ).Thus, a comparatively small uncertainty of a few tens of km s − in aline width will translate to a large uncertainty in the predicted SMBHmass. The significance of this potentially large line width uncertaintyis somewhat mitigated by the fact that even a dynamically-measuredSMBH mass can exhibit a relatively large uncertainty.The data required to constrain the line widths need to be of highquality to obtain robust line width measurements. Available ob-servations comprise (intrinsically spatially-integrated) spectra fromsingle-dish telescopes and spatially-resolved data cubes from eitherinterferometers or mosaics of multiple pointings by single-dish tele-scopes. Although spatially-resolving the CO is formally unnecessaryto measure spatially-integrated line widths, resolved observations of-fer multiple advantages. First, we can verify that the molecular gasdiscs are in ordered rotation, and thus that the line widths truly mea-sure the depths of the potentials. Second, the achieved sensitivitiesare generally significantly higher, due to the arrays’ larger total col-lecting areas compared to single dishes, and the similar (or longer)integration times. Third, the use of smaller individual antennae leadsto array primary beams that are much larger than those of single-dish telescopes, avoiding the data potentially missing some emissionat large galactic radii. Pointing errors for single-dish telescopes canalso cause extended emission to be missed, leading to erroneouslyasymmetric (and potentially artificially narrowed) line profiles. Suchpointing errors are trivially diagnosed with spatially-resolved images,and are in any case generally unimportant due to the large primarybeams. This is particularly important for our sample, as the galaxiesused are all sufficiently local (and thus extended on the sky) thattheir SMBH masses could be measured by resolving spatial scaleson which the SMBHs dominate the potentials. These advantages arecountered by the significantly higher complexity in obtaining, cali-brating and imaging interferometric observations, although modernobserving, data reduction and data analysis pipelines have now some-what mitigated this challenge. For these reasons, observations thatspatially resolve the CO discs are preferable.Although spatially-resolved observations are to be preferred, such Table 1.
Sample size after applying each selection criterion.Selection criterion Spatially- Spatially- Sectionresolved unresolvedsample sample(1) (2) (3) (4)Observed 73 162 2.1/2.2CO detected 58 75 2.1/2.2Regular rotation ∗
37 – 2.1Boxy profile 29 53 1.3, 2.1/2.2Accepted fit 27 24 3.1Not omitted 25 21 4.3
Notes:
Column 1 lists each selection criterion applied to the samples,described in the main text. Column 2 lists the number of galaxies withspatially-resolved observations that remain after each criterion is applied,while Column 3 lists the corresponding number of galaxies with unresolvedobservations. Column 4 lists the section(s) in which each criterion is dis-cussed. The criterion marked with a ∗ only applies to the spatially-resolvedsample. observations are not available for most galaxies. We therefore divideour objects into two samples, galaxies with respectively spatially-resolved and unresolved CO observations. We fit both samples usingidentical procedures, and in Section 4.1 discuss the negative effectsof using unresolved data.From the parent sample of 196 candidate galaxies, we obtain COspectra as described in Sections 2.1 and 2.2. The final samples areselected from these observations, applying the criteria discussed inSections 2.1, 2.2 and 3.1. Finally, a few galaxies that are clear outliersare excluded, and these are justified in Section 4.3. Table 1 liststhe number of galaxies that remain after each selection criterion isapplied.The CO spectra of the galaxies in the final samples, and all thosetaken in our new observations, are available online via Zenodo ,excluding those that are already public from the Spectrographic ArealUnit for Research on Optical Nebulae (SAURON) and ATLAS surveys (Combes et al. 2007; Young et al. 2011) . Data cubes (right ascension, declination, and velocity) are producedfrom either interferometric observations or by mosaicking multiplepointings of a single-dish telescope. We obtain such cubes fromthe ALMA archive, the Berkeley-Illinois-Maryland Association Sur-vey of Nearby Galaxies (BIMA-SONG; Helfer et al. 2003) andthe ATLAS survey (Alatalo et al. 2013). ALMA observationshave been calibrated and imaged automatically either by the ALMApipeline or manually by ALMA Regional Centre staff, and the cubesused are those provided on the archive, with the exception of obser-vations taken by our own WISDOM programme and its precursorstudies, for which the data reduction and calibration (and the proper-ties of the data cubes) are described in the associated papers (Daviset al. 2013b; Onishi et al. 2017; Davis et al. 2017a, 2018a; Smithet al. 2019; North et al. 2019; Smith et al. 2020). BIMA-SONG and https://dx.doi.org/10.5281/zenodo.4067034 SAURON and ATLAS https://ned.ipac.caltech.edu/level5/March02/SONG/SONG.html , 1–18 (2020) ISDOM: The Δ 𝑉 CO − 𝑀 BH relation ATLAS data cubes are used as provided on the associated web-sites. We visualise each cube and manually select only those thatappear to show overall rotation, leaving 37 galaxies.We then convert each data cube into a spectrum by integrating eachchannel over the two spatial dimensions. The emission in any givenchannel typically extends over only a few pixels, with the remainderpopulated by noise. To simply sum all pixels together blindly wouldneedlessly include all this noise in our sum, degrading the sensitivityof the resultant spectrum. We can do better by summing only thepixels contained within a mask encompassing all the emission.Such a mask can be generated using the ‘smooth-masking’ tech-nique (Dame 2011), originally developed to make high-quality mo-ment maps. Each cube is first smoothed spatially by the beam andHanning-smoothed spectrally. Pixels with values exceeding a noisethreshold in the smoothed cube are included in the mask; we use athreshold of 5 times the rms noise measured in the original cube. Themask is then applied to the original, unsmoothed cube, and shouldencompass all high-surface brightness pixels, assumed to correspondto real emission, as well as small regions around them that may in-clude lower surface brightness emission. An integrated spectrum isthen produced by summing all pixels included in the mask.The resulting spectra are of generally significantly higher qualitythan those obtained by single-dish telescopes. However, the uncer-tainty on the total flux in each channel must be considered carefully.In a normal single-dish spectrum, we can simply measure the rmsnoise in line-free channels, and assume that it is constant acrossthe full bandpass. However, in integrated spectra derived from datacubes, the uncertainty in each channel is instead a function of thenumber of pixels included in the mask in that channel. We estimatethis in each channel by assuming the noise to be Gaussian with stan-dard deviation 𝜎 px . The sum of 𝑁 mask normal random variables isthen 𝜎 px √ 𝑁 mask , where 𝑁 mask is the number of pixels in the maskin that channel. This formalism is only valid in channels where themask is non-zero.In channels where the mask is zero (i.e. 𝑁 mask = h 𝑁 mask i ) as therepresentative spatial scale over which undetected emission would bedistributed. The uncertainty is thus given by 𝜎 void = 𝜎 px √︁ h 𝑁 mask i ,and it is therefore constant for line-free channels.The resulting spectra are all visually inspected, and those thatdo not have a boxy line profile are rejected. This can occur evenwhen the dynamics appear to exhibit overall rotation, (e.g. if the COdistribution does not sample the velocity field well). Applying thiscriterion leaves 29 galaxies with spatially-resolved CO observations. Line widths can also be measured directly from the spectra ob-tained in single-dish observations. Such observations are simplerthan spatially-resolved observations, but typically have lower SNRs.The other challenge with these spectra in local galaxies is the rel-atively small primary beams of the large telescopes used, that maynot extend far enough into the galaxies to reach the flat parts oftheir rotation curves in single pointings. For these reasons, thereare two concerns with the line widths obtained from the objects inthis unresolved galaxy sample: the uncertainties are larger fractionsof the channel width than those estimated for the resolved sample galaxies, and we cannot be certain whether the line widths measuredencompass the full widths of the rotation curves.The literature contains single-dish CO observations in two forms.Most commonly, spectra are shown in figures only, with the quanti-tative information needed for other astronomers to use the data rarelyavailable. We then use the public tool
GraphClick to manuallydigitise these figures, obtaining flux measurements by interpolatingfrom the axis scales.These data are given variously in the antenna ( 𝑇 ∗ A ), radiation ( 𝑇 ∗ R )and main beam ( 𝑇 mb ) temperature scales. For the sake of homogene-ity, we transform them all to the same flux density scale (Jy) as thespectra obtained for our resolved galaxy sample, using observatory-specific appropriate beam efficiencies listed in Table 2. We assumethat the emission is point-like and do not account for the spatially-varying responses of the telescopes. This would be valid only if thegas is centrally concentrated. As we have argued above, and dis-cuss further in Section 4.1, the relatively small extents of the beamscompared to the very large extents of these local galaxies imply thisassumption may be invalid. With no a priori information on the gasdistributions, however, we cannot make more appropriate conver-sions. Moreover, since this is a spectrally-constant conversion, anychange will not affect the line widths measured, the only quantitiesused in this paper.For all spectra except those of Maiolino et al. (1997) (for whicha direct conversion from 𝑇 ∗ R is provided), we therefore first convertfrom 𝑇 mb or 𝑇 ∗ R to 𝑇 ∗ A using the efficiencies in Table 2, and thenconvert from 𝑇 ∗ A to flux densities using 𝑆 ( Jy ) = 𝑘 B 𝜂 A 𝜋𝐷 𝑇 ∗ A , (1)where 𝑘 B is Boltzmann’s constant, 𝜂 A the telescope aperture effi-ciency (relating the geometric area of the telescope dish to its effec-tive area) and 𝐷 the telescope diameter.In addition to observations published by other authors, we acquirednew observations at the Institut de Radioastonomie Millimétrique(IRAM) 30-m telescope under programme 191-18 and at the On-sala Space Observatory (OSO) 20-m telescope under programme2018-04a. Fifty-one galaxies were observed with the IRAM 30-mtelescope, of which twenty-two were detected. Nine were observedat the OSO 20-m telescope, of which four were detected. Theseobservations are described in detail in Appendices A1 and A2, re-spectively. Associated noise estimates, integrated line fluxes and totalmolecular gas masses are listed in Tables A1 and A2, and the spectraand telescope beam extents are shown in Figures A1 and A2, that arecontinued as Figures A3 and A4 in the supplemental material.Combining observations from the literature and from our pro-grammes, there are unresolved CO detections of 75 of the galaxiesin our parent sample. From these, those without a boxy line profileare rejected, leaving 53 galaxies. Estimates of the noise levels in allthese spectra are obtained from the emission-free channels at eitherend of the CO lines, and are assumed to be spectrally constant. We discussed in Section 1.2.1 the role of the CO Tully-Fisher relationto interpret our proposed CO line width–SMBH mass correlation.However, different methods of measuring the CO line width froma spectrum have been proposed. The simplest scheme is simply to , 1–18 (2020) Mark D. Smith et al.
Table 2.
Adopted conversions from literature units to flux densities, assumingpoint sources. Telescope CO line ConversionsIRAM 30-M CO(1-0) 𝑇 ∗ A = . 𝑇 mb 𝑆 Jy = . 𝑇 ∗ A CO(2-1) 𝑇 ∗ A = . 𝑇 mb 𝑆 Jy = . 𝑇 ∗ A NRAO 12-M CO(1-0) 𝑇 ∗ R = . 𝑇 mb 𝑆 Jy = 𝑇 ∗ R adopt the width at which the observed flux first falls below somefraction of the maximum (e.g. Davis et al. 2011). Using 20% ofthe maximum flux appears to yield a tighter CO TFR correlation(Ho 2007b), but 50% would be preferable at low SNRs where asmaller fraction cannot be accurately determined. This approach canbe particularly unreliable with very low SNR spectra, where althoughthe line can be visually identified as a consistently-positive sequenceof channels, the line edges are ill-defined. A profile fit to the lineis therefore now generally preferred. This latter method also allowsspectra with anomalous line shapes to be rejected when poorly fit bya suitably physically-motivated profile. Tiley et al. (2016) investigated appropriate choices of line profilesand determined that the ‘Gaussian double peak’ profile, consistingof a quadratic function bounded by half-Gaussian wings, gave themost reliable line width measurements with least sensitivity to SNRand inclination. We therefore adopt the full-width at half-maximum(FWHM; equivalent to the 50% criterion defined above) of such aprofile as our measure of the line width, fitting each spectrum withthe Tiley et al. (2016) function 𝑓 ( 𝑣 ) = 𝐴 G × 𝑒 −[ 𝑣 −( 𝑣 − 𝑤 )] 𝜎 𝑣 ≤ 𝑣 − 𝑤𝐴 C + 𝑎 ( 𝑣 − 𝑣 ) 𝑣 − 𝑤 ≤ 𝑣 ≤ 𝑣 + 𝑤𝐴 G × 𝑒 −[ 𝑣 −( 𝑣 + 𝑤 )] 𝜎 𝑣 + 𝑤 ≤ 𝑣 , (2)where 𝐴 G (the flux of each peak), 𝐴 C (the flux of the central ex-tremum), 𝑣 (the velocity of the central extremum), 𝑤 (the velocityhalf-width of the quadratic function) and 𝜎 (the velocity width ofboth half-Gaussian functions) are all free parameters, and 𝑎 is deter-mined by the continuity conditions at 𝑣 ± 𝑤 . The corresponding linewidth at the half-maximum is then given by 𝑊 = ( 𝑤 + 𝜎 √ ) . (3)We note that in cases for which 𝐴 C > 𝐴 G , this equation will notyield the FWHM, yielding instead slightly broader line widths. Wedescribe below that galaxies for which 𝐴 C > ( / ) 𝐴 G (those thatwould be most affected by this effect) are in any case rejected fornot being double-horned profiles, and in the few cases where thiscondition occurs in the remaining galaxies this broadening effect isnegligible due to the sharp edges of the spectral lines and 𝐴 C beingonly very slightly greater than 𝐴 G .The fits are performed using the Python package lmfit , min- https://lmfit.github.io/lmfit-py/
400 300 200 100 0 100 200 300 400Velocity (kms )0.0250.0000.0250.0500.0750.1000.1250.1500.175 F l u x ( J y ) Figure 1.
Example Gaussian double peak profile fit (green) overlaid on aspectrum synthesised from the CARMA data cube of NGC3665 (blue). Themean noise estimate ( ± 𝜎 ) is shown in the top-left corner. The red verticallines are at 𝑣 (solid) and bound 𝑊 (dashed), defined in Equation 3, whilethe grey bands indicate the 67% confidence interval in 𝑊 . The originaldata cube had already had the galaxy’s systemic velocity subtracted. Fits tothe other spectra of spatially-resolved galaxies are shown in Figure 9 in thesupplemental material. )0.020.010.000.010.020.030.04 F l u x ( J y ) Figure 2.
Example Gaussian double peak profile fit (green) overlaid on theIRAM 30-m spectrum of NGC 1497. The mean noise estimate ( ± 𝜎 ) isshown in the top-left corner. The red vertical lines are at 𝑣 (solid) and bound 𝑊 (dashed), defined in Equation 3, while the grey bands indicate the 67%confidence interval in 𝑊 . The velocity axis is the observed velocity, andincludes the galaxy’s systemic velocity. Fits to the other spectra of unresolvedgalaxies are shown in Figure 10 in the supplemental material. imising the chi-squared statistic: 𝜒 = ∑︁ 𝑖 (cid:18) data 𝑖 − model 𝑖 𝜎 𝑖 (cid:19) , (4)where 𝑖 denotes each velocity bin (i.e. channel) of the spectrum, and 𝜎 𝑖 is the uncertainty on the flux at each velocity bin as describedin Section 2. Each spectrum is fit 30 times, with initial conditionsselected randomly from a uniform distribution within reasonablephysical limits, to ensure a global minimum is found. The fit withthe smallest reduced chi-square is then selected as the best-fittingsolution. The associated line width and uncertainty is then estimatedfrom the uncertainties on 𝜎 and 𝑤 (determined by the lmfit routines) MNRAS , 1–18 (2020)
ISDOM: The Δ 𝑉 CO − 𝑀 BH relation through Monte Carlo methods: ( 𝜎 , 𝑤 ) pairs are generated as normalrandom variables with means given by the best-fitting ( 𝜎 , 𝑤 ) andstandard deviations obtained from the lmfit -derived uncertainties.The corresponding 𝑊 are then calculated from Equation 3, and themedian and standard deviation adopted as the best-fitting line widthand uncertainty respectively.We also investigated the systematics affecting our line width mea-surements. We generate 150 realisations of the best-fitting modelwith random normally-distributed noise of magnitude equal to thenoise in the data added to each. Each realisation is then fit by thesame Gaussian double peak profile using the parameters best-fittingthe data as initial conditions. The standard deviations of the distribu-tions of line widths from these fits are comparable to the uncertaintiesestimated by lmfit for the spectra in our unresolved sample, but theyare much smaller (and also much smaller than the channel width) forour spatially-resolved sample due to the much higher signal-to-noiseratios. This suggests that reducing the noise in the spectra of the unre-solved sample would yield smaller line width uncertainties, whereasadopting smaller channel widths will yield the greatest improvementfor galaxies in the spatially-resolved sample.Since not all profiles are well-reproduced by a Gaussian doublepeak profile, we also fit each profile with a simple Gaussian. We im-mediately reject a spectrum if either the Gaussian profile has a lowerreduced 𝜒 or the Gaussian double peak profile has 𝐴 C > ( / ) 𝐴 G ,the latter corresponding to the flux at the centre of the spectrumbeing at least 50% higher than that of the bounding half-Gaussians,in which case one might more naturally fit the spectrum with a sin-gle Gaussian (e.g. Tiley et al. 2016). Both criteria correspond to aviolation of the ‘boxy’ criterion outlined previously, and imply thatthe observed CO gas is unlikely to have reached the flat part of therotation curve.Finally, every spectrum is manually inspected to ensure a good fitwas achieved. This leaves final samples of 27 galaxies with spatially-resolved observations and 24 galaxies with unresolved observationsthat satisfy our selection criteria. These galaxies, and the associatedline width measurements, inclinations and SMBH masses, are listedin Tables 3 and 4, respectively. Example profile fits to interferometricand single-dish observations are shown in Figures 1 and 2 respec-tively, and all data and associated fits are shown in Figures 9 and 10in the supplemental material.Since we observe the line-of-sight projection of each line width,rather than the intrinsic width, we de-project 𝑊 determined by thefit by sin 𝑖 . Uncertainties in the inclination, which can be significant,are propagated by Monte Carlo sampling as before. The inclinationsare determined either from fits to dust features or the resolved COdiscs in the literature, ellipse fits to dust discs in archival HubbleSpace Telescope ( HST ) images, or, where the other methods are notpossible, by using the apparent flattenings of the 25 mag arcsec − 𝐵 -band isophotes and assuming morphology-dependent intrinsic thick-nesses as given in HyperLEDA . Davis et al. (2011) discuss therelative merits (and dangers) of using these methods to infer theinclination of a molecular gas disc. Where the B -band isophotesare used, the uncertainties in both the apparent flattenings and themorphological T-types listed in HyperLEDA are propagated into theinclination uncertainties by Monte Carlo sampling. This approachdoes not work for the face-on galaxy NGC 4388, which appears to beflatter than the inferred intrinsic thickness given its morphological The formula for this inclination and for the assumed intrinsic thickness isgiven online at https://leda.univ-lyon1.fr/leda/param/incl.html classification, so we adopt a typical inclination uncertainty of 5 ° . Wenote this has a negligible effect on the deprojected line width. Given our derived line widths, and the associated SMBH masses andstellar velocity dispersions, we now investigate the correlations be-tween these parameters. We use the
HYPER-FIT package (Robotham& Obreschkow 2015) via its web interface to fit both line width toSMBH mass and line width to stellar velocity dispersion. HYPER-FIT seeks to maximise the likelihood function that takes into account themultivariate Gaussian uncertainties on each data point, and allowsfor the possibility of intrinsic scatter. The use of this approach, incontrast to the traditional forward and/or reverse fits used in manyTully-Fisher relation works (e.g. Tiley et al. 2016), allows us to in-clude the significant uncertainties on both 𝑀 BH and 𝑊 , and tominimise the scatter orthogonal to the best-fitting line (rather thanonly the vertical or horizontal scatter).To reduce the covariance between the slope and the intercept, andthe error in the intercept, we follow the approach of Tremaine et al.(2002), as is now common practice, and translate the data to bringthe median line width closer to zero. We therefore translate the linewidths by 2 . 𝑦 = 𝑎 (cid:20) log (cid:18) 𝑊 sin 𝑖 km s − (cid:19) − . (cid:21) + 𝑏 , (5)where the variable 𝑦 is an observable quantity - for this work eitherthe SMBH mass or the stellar velocity dispersion. We also determinethe total scatter as the root-mean-square deviation (along the 𝑦 -axis)of the data from the best-fitting relation assuming zero measurementerrors. Anticipating that the principal application for these relationswill be estimating 𝑀 BH from a measured Δ 𝑉 CO , we use the projectionof the intrinsic scatter onto the 𝑦 -axis to quantify the tightness of eachfit.We omit from the fits a small number of galaxies that, although hav-ing well-constrained SMBH masses and sufficiently double-hornedline profiles to yield a robust measurement of 𝑊 , are neverthelessnot considered sufficiently reliable to use. These are indicated inTables 3 and 4 and are discussed in detail in Section 4.3.Table 5 lists the results of our fits for both relations (discussed inSections 3.3 and 3.4) and for two-different morphologically-selectedsub-samples (ETGs and LTGs), in addition to our spatially-resolvedand unresolved galaxy samples (and all data/galaxies taken together;see Section 4.1). Seven galaxies are included in both the resolved andunresolved samples, as there are both interferometric and single-dishobservations available. The fits for ‘all’ galaxies use the line widthwith the smaller uncertainty only, almost always from the resolvedobservations.In the following two subsections, we present our results for eachcorrelation and evidence for a morphological dependence. In Section4, we describe the impacts of using spatially-resolved or unresolveddata, compare our results with other host property correlations, andexplore the implications of the Δ 𝑉 CO − 𝑀 BH correlation. Δ 𝑉 CO − 𝑀 BH correlation Figure 3 shows the Δ 𝑉 CO − 𝑀 BH correlation of all our data and thebest-fitting relation derived using only the galaxies with spatially-resolved observations. This is the tightest correlation we find, with http://hyperfit.icrar.org/ MNRAS , 1–18 (2020) Mark D. Smith et al.
Table 3.
CO data, best-fitting line widths and host galaxy properties for our spatially-resolved galaxies. All galaxies listed have a well-determined CO line width,but one (NGC 5055) is excluded from the final correlations. This omission is justified in Section 4.3.Name T-type CO transition 𝑊 Inclination log ( 𝑀 BH / M (cid:12) ) SMBH method Notes(km s − ) ( ° )(1) (2) (3) (4) (5) (6) (7) (8)Circinus 3.3 1-0 . ± . ± (M) 6 . ± . masers 𝑀 BH − 𝜎 ∗ outlierNGC 383 -2.9 2-1 . ± . ± (M) 9 . ± . CONGC 524 -1.2 2-1 . ± . ± (D) 8 . ± . CONGC 1332 -2.9 2-1 . ± . ± (M) 8 . ± . CONGC 1386 -0.7 1-0 . ± . ± (D) 6 . ± . masers 𝑀 BH − 𝜎 ∗ outlierNGC 3081 0.0 2-1 . ± . ± (D) 7 . ± . ionised gasNGC 3245 -2.1 2-1 . ± . ± (K) 8 . ± . ionised gasNGC 3258 -4.3 2-1 . ± . ± (M) 9 . ± . CONGC 3504 2.1 2-1 . ± . ± (M) 7 . ± . CO OmittedNGC 3557 -4.9 2-1 . ± . ± (M) 8 . ± . CONGC 3607 -3.2 2-1 . ± . ± (D) 8 . ± . starsNGC 3627 3.1 1-0 . ± . ± (D) 6 . ± . starsNGC 3665 -2.1 2-1 . ± . ± (M) 8 . ± . CONGC 4258 4.0 1-0 . ± . ± (B) 7 . ± . masersNGC 4303 4.0 2-1 . ± . ± (M) 6 . ± . ionised gasNGC 4429 -0.8 1-0 . ± . . ± . (M) 8 . ± . CONGC 4459 -1.6 1-0 . ± . ± (D) 7 . ± . ionised gasNGC 4526 -1.9 2-1 . ± . ± (M) 8 . ± . CONGC 4697 -4.5 2-1 . ± . ± (M) 8 . ± . CONGC 4736 2.3 1-0 . ± . ± (K) 6 . ± . stars FP outlierNGC 4826 2.2 1-0 . ± . ± (D) 6 . ± . stars FP outlierNGC 5005 4.0 1-0 . ± . ± (D) 8 . ± . ionised gasNGC 5055 4.0 1-0 . ± . ± (D) 8 . ± . ionised gas 𝑀 BH − 𝜎 ∗ outlier; omittedNGC 5248 4.0 1-0 . ± . ± (D) 6 . ± . ionised gasNGC 6861 -2.7 2-1 . ± . ± (D) 9 . ± . starsNGC 7052 -4.9 2-1 . ± . ± (M) 9 . ± . ionised gasNGC 7331 3.9 1-0 . ± . ± (B) 8 . ± . ionised gas Notes:
Column 1 lists the name of each galaxy contained in the final sample of spatially-resolved galaxies. The morphological classification onthe numerical Hubble scale from HyperLEDA is listed in Column 2. Spatially-resolved observations of the CO transition listed in Column 3 wereintegrated within a mask to obtain a spectrum. Column 4 lists the (line-of-sight projected) line width and associated uncertainty measured from aGaussian double peak line profile fit to this spectrum. Column 5 lists the inclination of the CO disc and in parentheses the method used to measureit (D - dust morphology, M - molecular gas morphology/kinematics, B - B -band apparent flattening, K - other kinematics). Column 6 lists thedynamically-measured SMBH mass using the tracer cited in Column 7. Column 8 contains other notes about certain galaxies. Footnotes in column3 indicate the source of the CO observations, and those in columns 6 and 7 the source of the measurement, as follows. References: (1) Zschaechneret al. (2016), (2) Curran et al. (1998), (3) Greenhill et al. (2003), (4) North et al. (2019), (5) Smith et al. (2019), (6) Cappellari et al. (2006),(7) Barth et al. (2016a), (8) Barth et al. (2016b), (9) Zabel et al. (2019), (10) this work, from a
HST
WFPC2 F606W image, (11) Braatz et al. (1997),(12) Ramakrishnan et al. (2019), (13) Beifiori et al. (2012), (14) ADS/JAO.ALMA
HST
WFPC2 F814W image, (22) Gültekin et al. (2009a), (23) Helfer et al. (2003), (24) Casasola et al. (2011), (25) Saglia et al. (2016),(26) Onishi et al. (2017), (27) HyperLEDA, (28) Herrnstein et al. (2005), (29) Sun et al. (2018), (30) Schinnerer et al. (2002), (31) Pastoriniet al. (2007), (32) Alatalo et al. (2013), (33) Davis et al. (2018a), (34) Davis & McDermid (2017), (35) Young et al. (2008), (36) Sarzi et al.(2001), (37) Davis et al. (2013b), (38) Davis et al. (2017a), (39) Bosma et al. (1977), (40) Kormendy et al. (2011), (41) Blais-Ouellette et al.(2004), (42) Rusli et al. (2013) and (43) Smith et al. (2020). log (cid:18) 𝑀 BH M (cid:12) (cid:19) = ( . ± . ) (cid:20) log (cid:18) 𝑊 sin 𝑖 km s − (cid:19) − . (cid:21) + ( . ± . ) , (6)with a total scatter in the log 𝑀 BH direction of 0 . . . ± .
5, in agreement withthe results of Davis et al. (2019b) from H i and invoking the disc-halo conspiracy. The sample of unresolved LTGs do not adequatelyconstrain the relation’s slope, and exhibit a much higher total (andintrinsic) scatter. We discuss this deviation further in Section 4.1. Δ 𝑉 CO − 𝜎 ∗ correlation Figure 4 shows the Δ 𝑉 CO − 𝜎 ∗ correlation using our data and thestellar velocity dispersions compiled by van den Bosch (2016). Thesevelocity dispersions are those available in the literature that mostclosely approximate the dispersion within 1 𝑅 e .We find that the dispersions are consistent with a linear relationshipbetween CO line width and 𝜎 ∗ for all sub-samples. The best-fitting re-lation, from the sample of spatially-resolved observations of galaxiesof all morphologies, islog (cid:18) 𝜎 ∗ km s − (cid:19) = ( . ± . ) (cid:20) log (cid:18) 𝑊 sin 𝑖 km s − (cid:19) − . (cid:21) +( . ± . ) . (7) MNRAS , 1–18 (2020)
ISDOM: The Δ 𝑉 CO − 𝑀 BH relation Table 4.
CO data, best-fitting line widths and host galaxy properties for our spatially-unresolved galaxies. All galaxies listed have well-determined CO linewidths, but a few are excluded from the final correlations. These omissions are justified in Section 4.3.Name T-type CO transition 𝑊 Inclination log ( 𝑀 BH / M (cid:12) ) SMBH method Notes(km s − ) ( ° )(1) (2) (3) (4) (5) (6) (7) (8)3C120 -1.7 1-0 . ± . ± (B) 7 . ± . reverberationArk 120 -5.0 1-0 . ± . ± (D) 8 . ± . reverberationMrk 590 1.0 1-0 . ± . ± (B) 7 . ± . reverberationNGC 383 -2.9 1-0 . ± . ± (M) 9 . ± . CONGC 524 -1.2 1-0 . ± . ± (D) 8 . ± . CONGC 541 -3.6 2-1 . ± . ± (D) 8 . ± . ionised gas OmittedNGC 1068 3.0 1-0 . ± . ± (B) 6 . ± . masersNGC 1497 -2.0 1-0 . ± . ± (M) 8 . ± . ionised gasNGC 1667 5.0 1-0 . ± . ± (B) 8 . ± . ionised gasNGC 1961 4.2 1-0 . ± . ± (B) 8 . ± . ionised gasNGC 2273 0.9 1-0 . ± . ± (B) 6 . ± . masersNGC 2911 -2.0 1-0 . ± . ± (B) 9 . ± . ionised gasNGC 3384 -2.6 2-1 . ± . ± (K) 7 . ± . stars OmittedNGC 3665 -2.1 1-0 . ± . ± (M) 8 . ± . CONGC 3862 -4.8 1-0 . ± . ± (D) 8 . ± . ionised gas OmittedNGC 4388 2.8 1-0 . ± . (B) 6 . ± . masersNGC 4429 -0.8 1-0 . ± . . ± . (M) 8 . ± . CONGC 4459 -1.6 1-0 . ± . ± (D) 7 . ± . ionised gasNGC 4486 -4.3 1-0 . ± . ± (K) 9 . ± . ionised gasNGC 4526 -1.9 1-0 . ± . ± (M) 8 . ± . CONGC 4593 3.0 1-0 . ± . ± (B) 6 . ± . reverberationNGC 5548 0.4 1-0 . ± . ± (B) 7 . ± . reverberationNGC 7052 -4.9 1-0 . ± . ± (M) 9 . ± . COUGC 3789 1.6 1-0 . ± . ± (B) 6 . ± . masers Notes:
Column 1 lists the name of each galaxy contained in the final sample of spatially-unresolved galaxies. The morphological classification on thenumerical Hubble scale from HyperLEDA is listed in Column 2. Column 3 indicates the CO transition observed. Column 4 lists the (line-of-sightprojected) line width and associated uncertainty measured from a Gaussian double peak line profile fit to this spectrum. Column 5 lists the inclinationof the CO disc and in parentheses the method used to measure it (D - dust morphology, M - molecular gas morphology/kinematics, B - B -band apparentflattening, K - other kinematics). Column 6 lists the dynamically-measured SMBH mass using the tracer (or via a Virial estimate for reverberationmapping) listed in Column 7. Column 8 contains other notes about certain galaxies. Footnotes in column 3 indicate the source of the CO observations,and those in columns 6 and 7 the source of the measurement, as follows. References: (1) Evans et al. (2005), (2) HyperLEDA, (3) Kollatschny et al.(2014), (4) this work, IRAM project 191-18, (5) this work, from a
HST
ACS/HRC F550M image, (6) Doroshenko et al. (2008), (7) Bertram et al. (2007),(8) Peterson et al. (2004), (9) Ocaña Flaquer et al. (2010), (10) North et al. (2019), (11) Young et al. (2011), (12) Cappellari et al. (2006), (13) Smithet al. (2019), (14) this work, from a
HST
WFPC2 F814W image, (15) Beifiori et al. (2012), (16) Maiolino et al. (1997), (17) Lodato & Bertin (2003),(18) Davis et al. (2016), (19) Heckman et al. (1989), (20) Kuo et al. (2011), (21) Welch & Sage (2003), (22) Cappellari et al. (2013), (23) Schulze &Gebhardt (2011), (24) Onishi et al. (2017), (25) this work, from a
HST
WFPC2 F606W image, (26) Davis et al. (2018a), (27) Combes et al. (2007),(28) Sarzi et al. (2001), (29) Ford et al. (1994), (30) Walsh et al. (2013), (31) Davis et al. (2013b), (32) Barth et al. (2013), (33) Kovačević et al. (2014),(34) Smith et al. (2020) and (35) this work, OSO 20-m project 2018-04a.
There is a systematic trend of the intrinsic scatter with morphology,ETGs having an intrinsic scatter of 0 . ± .
02 dex in the log 𝜎 ∗ direction, whereas LTGs have 0 . ± .
04 dex.The most recent works investigating Δ 𝑉 H i − 𝜎 ∗ have also foundmorphologically-varying results. In ETGs, Serra et al. (2016) founda linear relation with total scatter of 12%, whereas in late-typespirals Davis et al. (2019b) excluded a linear relation, obtaining 𝜎 ∗ ∝ Δ 𝑉 . ± .
25H i . This accords with the early work of Ho (2007a),that indicated that Δ 𝑉 / 𝜎 ∗ varies systematically with Hubble-type,albeit with less compelling data. The literature on the Δ 𝑉 CO − 𝜎 ∗ hasnot considered a potential morphological variation systematically.We, however, find no significant deviation from a linear relationfor either early- or late-type galaxies. This is perhaps surprising, asusing the disc-halo conspiracy for LTGs to equate Δ 𝑉 CO = Δ 𝑉 H i , theresults of Davis et al. (2019b) would predict otherwise. The smallintrinsic scatter for ETGs agrees with the results from JAM modellingof Cappellari et al. (2013), that indicate a tight correlation betweenthe rotation curve at these scales and 𝜎 ∗ . In this section we first discuss the benefits of using spatially-resolvedrather than unresolved observations. We then evaluate the biasesassociated with our sample, account for the galaxies excluded in ourfits, and finally discuss the utility of our correlations for estimatingSMBH masses.
In Section 2 we outlined the advantages of using spatially-resolvedobservations of the CO emission instead of single-dish observations.These advantages are clear in our results.First, the spatially-resolved observations have much higher sensi-tivities. Since the uncertainties on our line width measurements arederived from Monte Carlo fits to simulated data with noise char-acteristic of the real spectra, these improved sensitivities lead tosmaller line width uncertainties (of order 1 −
10 km s − rather than10 −
50 km s − ), that are also smaller fractions of the channel widths. MNRAS , 1–18 (2020) Mark D. Smith et al.
Table 5.
Best-fitting correlations, based on
HYPER-FIT fits of Equation 5.Dataset Count 𝑎 𝑏
Total Intrinsicscatter scatter(1) (2) (3) (4) (5) (6)SMBH mass ( 𝑦 ≡ log [ 𝑀 BH / M (cid:12) ] ; Figure 3):Resolved data 25 8 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . 𝑦 ≡ log [ 𝜎 ∗ / km s − ] ; Figure 4):Resolved data 25 1 . ± . . ± .
02 0.09 0 . ± . . ± . . ± .
02 0.09 0 . ± . . ± . . ± .
02 0.10 0 . ± . . ± . . ± .
03 0.08 0 . ± . . ± . . ± .
04 0.06 0 . ± . . ± . . ± .
03 0.08 0 . ± . . ± . . ± .
05 0.11 0 . ± . . ± . . ± .
04 0.11 0 . ± . . ± . . ± .
04 0.12 0 . ± . Notes:
Column 1 lists each sample of galaxies, Column 2 the number of galaxies in that sample. Columns 3 and 4 list the parameters 𝑎 and 𝑏 , respectively,measured by fitting Equation 5 to the data of that sample with HYPER-FIT . Column 5 lists the total scatter, defined as the root-mean-square deviationalong the 𝑦 -axis between the data and the best-fitting relation, of that sample. Column 6 lists the intrinsic scatter, projected along the 𝑦 -axis, of thatsample.
200 400 600 800 W /sin( i ) (km s )10 M B H ( M ) Circinus NGC1386NGC5055NGC0541NGC3862NGC3384 NGC4736NGC4826NGC3504Resolved ETGsResolved LTGsUnresolved ETGsUnresolved LTGs
Figure 3.
Correlation between deprojected line width ( 𝑊 / sin 𝑖 ) and SMBHmass ( 𝑀 BH ) for our sample galaxies. Colours indicate whether a galaxyis classified as early- (red) or late-type (blue), while the markers indicatewhether it belongs to our spatially-resolved ( × ) or unresolved (+) sample.Some galaxies appear in both samples, and hence appear twice on this plot atthe same 𝑀 BH . Labelled galaxies are discussed in Section 4.3. The tightestcorrelation determined from the resolved sample is indicated by the dark greysolid line, with the 1 𝜎 intrinsic scatter indicated by the dashed dark greylines. Error bars are shown in pale grey. Faded galaxies are excluded from thecorrelation fits. This in turn leads to best-fitting correlations with systematicallysmaller uncertainties. While present, the effect on the total scatters(dominated by the intrinsic scatters) is less significant.Second, spatially-resolved kinematics enable improved sample se-lection, ensuring that galaxies with disturbed kinematics can be omit-ted more robustly. This reduces the measured intrinsic scatters in our Δ 𝑉 CO − 𝑀 BH and Δ 𝑉 CO − 𝜎 ∗ correlations when only resolved obser-vations are used.Third, the relatively small primary beams of large single-dish ob-servations (e.g. 22 for the IRAM 30-m telescope at CO(1-0))mean that observations may not reach the flat parts of the rotationcurves of nearby galaxies. In spatially-resolved observations, not onlydo we benefit from the larger primary beams of the smaller individ-ual antennae (e.g. 55 for ALMA’s 12-m dishes at CO(1-0)), butpointing errors can also be straightforwardly diagnosed.We briefly note that, in addition to the primary beam, anotherspatial scale generally relevant for interferometric observations isthe maximum resolvable scale, i.e. the largest spatial structure towhich an array configuration is sensitive, set by the shortest baselineof the array. However, CO emission is generally patchy, and thus mostof it generally remains detectable even when only an extended arrayconfiguration is used. In addition, as the emission of a rotating discextends only over a small spatial scale in any given channel (typicallyof the order of the disc minor axis along one direction only), we arelikely to recover (most of) it all the way to the flat part of the rotationcurve, provided the emission extends that far.We have also argued that a sharp-edged double-horned line profilearises from an emitting exponential disc that reaches the flat part ofthe rotation curve. However, such a profile can also occur if the discis sharply truncated, whether the flat part is reached or not. If such
MNRAS , 1–18 (2020)
ISDOM: The Δ 𝑉 CO − 𝑀 BH relation
200 400 600 800 W /sin( i )(kms )100200300 ( k m s ) Circinus NGC1386NGC5055NGC0541NGC3862NGC3384 NGC4736NGC4826Wu (2007)Resolved ETGsResolved LTGsUnresolved ETGsUnresolved LTGs
Figure 4.
Correlation between deprojected line width ( 𝑊 / sin 𝑖 ) and stellarvelocity dispersion ( 𝜎 ∗ ) for our sample galaxies. Colours indicate whethera galaxy is classified as early- (red) or late-type (blue), while the markersindicate whether it belongs to our spatially-resolved ( × ) or unresolved (+)sample. Some galaxies appear in both samples, and hence appear twice onthis plot at the same 𝜎 ∗ . Labelled galaxies are discussed in Section 4.3. Thebest-fitting correlation found by Wu (2007) amongst local Seyfert galaxies isindicated by the solid dark grey line, with the 1 𝜎 intrinsic scatter indicated bythe dashed dark grey lines. Error bars are shown in pale grey. Faded galaxiesare excluded from the correlation fits. a disc is truncated before the flat part, the measured line width willbe strictly narrower than would be found if the disc extended further.Similarly, if the primary beam is too compact to reach the flat part,the measured line width will be artificially narrowed.In each spatially-resolved sample galaxy, we can easily assesswhether the CO emission reaches the flat part of the rotation curveby examining the kinematic major-axis position velocity diagram,and thus straightforwardly determine whether the primary beam istoo small to recover all of the emission. For each of our spatially-unresolved sample galaxies, we assess this issue as follows. As low- J CO emission generally follows dust, the extent of the dust disc in
HST optical images can be assumed to be the same as that of theCO emission. Although some of these galaxies have dust extendingto larger radii than would be reached by the primary beams of oursingle-dish telescopes, we have verified that these galaxies do notexhibit systematically narrower line profiles. However, the galaxieswith the smallest dust extents ( . . 𝑅 , where 𝑅 is the radiusof the 25 mag arcsec − 𝐵 -band isophote listed in HyperLEDA) arebiased to narrower line widths. We therefore exclude them from thissample.Notwithstanding the concerns described above, we do not finda statistically-significant difference between the correlations deter-mined from the spatially-resolved and unresolved samples, and Fig-ure 3 further indicates that the unresolved ETGs follow the relationof all resolved galaxies closely; the significant outliers are all suf-ficiently explained in Section 4.3 as resulting from observations ofCO emission that may not reach the flat part of the rotation curve.The only substantial discrepancy is found for the Δ 𝑉 CO − 𝑀 BH re-lation using unresolved LTGs, with a much greater uncertainty inthe slope (and to a lesser extent in the zero point) and significantlylarger intrinsic scatter than those of all resolved data and ETGs. Thesegalaxies are likely to be preferentially affected by the aforementionedissues, as they are systematically nearer and have more slowly ris-ing rotation curves. It is therefore unsurprising that we find greateruncertainties in their best-fitting parameters and a larger intrinsic scatter. Interestingly, the spatially-resolved LTG sample, for whichwe can exclude galaxies with disturbed kinematics, actually exhibitsa slightly smaller intrinsic scatter.For all the reasons discussed above, we conclude that spatially-resolved observations are to be preferred when calibrating (and us-ing) the Δ 𝑉 CO − 𝑀 BH correlation. We further suggest that the im-provements offered by the use of spatially-resolved observations havewider applicability, particularly when calibrating the CO TFR. In-terferometric observations in the ALMA era will therefore allowsample selections significantly more robust than was previously pos-sible, with associated improvements of the accuracy of the slopes,zero-points and intrinsic scatters of the determined relations. Our sample was selected from galaxies with dynamically-measuredSMBH masses in the literature and CO observations, and thus can-not be considered a statistically-representative sample of galaxies.Shankar et al. (2016) discussed the biased population of galaxieswith dynamical SMBH mass measurements, due to the need to re-solve the scales on which the SMBH dominates the potential. Ad-ditionally, the SMBH mass measurements and CO observations arehighly heterogenous, being derived using different dynamical trac-ers and resolving different physical scales for the former, and withdifferent primary beams, spectral resolutions and sensitivities for thelatter.The heterogenous CO observations have all been homogenisedfollowing the prescriptions discussed in Sections 2.1 and 2.2. Theseprocedures do not bias our conclusions regarding the correlations,but the selection of only sharp-edged double-horned profiles arguablylimits the applicability of the correlations to similar CO spectra only.The SMBH masses used in this paper are drawn from the largevariety of measurements available in the literature. Due to the dif-fering selection criteria, very few SMBH mass measurements havebeen cross-checked with multiple tracers and/or methods, and thosethat have suggest mass measurements can vary by factors of 2–4(e.g. Kormendy & Ho 2013). Figure 5 shows the variety of massmeasurement methods used. Maser dynamics are, in principle, themost precise method as masers probe the spatial scales closest to theSMBHs, while the uncertainty in the scaling factor used in reverbera-tion mapping ( 𝑓 ; meant to account for the broad-line region geometryand line-of-sight velocity dispersion anisotropy) implies these mea-surements are generally the least reliable (e.g. Pancoast et al. 2014;Mejía-Restrepo et al. 2018; Campitiello et al. 2019). The associatedSMBH mass uncertainties are taken into account by the HYPER-FIT routine, so that lower-quality measurements do not bias our results.Although it would be preferable to use homogeneously-measuredSMBH masses, to impose this requirement would excessively reducethe sample size.The 𝑀 BH − 𝜎 ∗ relation is the tightest known correlation betweenSMBH mass and host property, and it is customarily interpretedas indicating the primary co-evolutionary path for SMBH growth.Galaxies that are outliers on the 𝑀 BH − 𝜎 ∗ plane are therefore likelyto have had unusual evolutionary pathways, and it is unlikely they willfollow other host–SMBH correlations. Since we argued in Section1.2 that the CO line width of a galaxy traces the same baryonic matteras 𝜎 ∗ , any galaxy that genuinely deviates from the 𝑀 BH − 𝜎 ∗ relationis also likely to deviate from the Δ 𝑉 CO − 𝑀 BH relation. Galaxiesconsistent with only one of these relations may be genuine outliers,or may indicate one of the quantities has been incorrectly measured.Figure 6 shows the 𝑀 BH − 𝜎 ∗ relation for our sample galaxies. Afew galaxies are clearly outliers and are discussed in Section 4.3. The MNRAS , 1–18 (2020) Mark D. Smith et al.
Stellar dynamics Ionised-gas dynamics Maser dynamics Molecular-gas dynamics Reverberation mappingSMBH mass measurement method024681012 N u m b e r o f g a l a x i e s Resolved ETGsResolved LTGsUnresolved ETGsUnresolved LTGs
Figure 5.
SMBH mass measurement methods of our sample galaxies. Early-type galaxies are shown in red, late-type galaxies in blue. The spatially-resolved sample is shown in solid colour, the unresolved sample as hatchedareas. Galaxies appear in both resolved and unresolved samples for a givenmethod where both interferometric and single-dish observations exist.
100 200 300(kms )10 M B H ( M ) Circinus NGC1386NGC5055 NGC3862NGC3384NGC4736NGC4826Resolved ETGsResolved LTGsUnresolved ETGsUnresolved LTGs
Figure 6.
Correlation between stellar velocity dispersion ( 𝜎 ∗ ) and SMBHmass ( 𝑀 BH ) for our sample galaxies. Colours indicate whether a galaxy isclassified as early- (red) or late-type (blue), while the markers indicate whetherit belongs to our spatially-resolved ( × ) or unresolved (+) sample. Some galax-ies appear in both samples, and hence are indicated with both symbols super-imposed. The 𝑀 BH − 𝜎 ∗ relation found by van den Bosch (2016) is indicatedby the solid black line, with the 1 𝜎 intrinsic scatter indicated by the dasheddark grey lines. Labelled galaxies are discussed in Section 4.3. Error bars areshown in pale grey. Faded galaxies are excluded from the correlation fits. remainder of the sample galaxies all follow the empirical 𝑀 BH − 𝜎 ∗ relation and are not significantly biased in their distribution in the 𝑀 BH − 𝜎 ∗ plane. We do not, however, sample the significant popula-tion of galaxies with 𝜎 ∗ <
100 km s − , for which very few SMBHmasses are available, and that appear to deviate from the 𝑀 BH − 𝜎 ∗ relation (e.g. van den Bosch 2016).Our samples are necessarily biased towards CO-bright galaxies.The CO content of a galaxy varies with morphology, the latest rep-resentative surveys finding that only about 20 −
30% of ETGs hostdetectable molecular gas reservoirs (Combes et al. 2007; Younget al. 2011). However, this detection rate is independent of mass,
E S0 Sa Sb Sc Sd8 6 4 2 0 2 4 6 8 10Morphological type (T)02468101214 N u m b e r o f g a l a x i e s Resolved ETGsResolved LTGsUnresolved ETGsUnresolved LTGs
Figure 7.
Morphological type distribution of our sample galaxies, accordingto the numerical Hubble type listed in HyperLEDA, with 𝑇 ≤ 𝑇 > size and environment, suggesting that CO-rich ETGs are ‘normal’ETGs (Davis et al. 2019a). CO emission is also detected in ≈ Δ 𝑉 CO − 𝑀 BH correlation as a function of morphology,but do caution that this issue requires further study going beyond thecoarse classification used here. We have excluded a few galaxies from our fits even though they havewell-resolved and sharp-edged CO lines and dynamically-measuredSMBH masses. Each of these is indicated in Tables 3 and 4 and isdiscussed below.Three galaxies in our samples are known to be outliers in the 𝑀 BH − 𝜎 ∗ relation: Circinus, NGC 1386 and NGC 5055. The formertwo galaxies have SMBH measurements too small for their associatedvelocity dispersions by about an order of magnitude. However, theyare consistent with our Δ 𝑉 CO − 𝑀 BH relation, their positions on the Δ 𝑉 CO − 𝜎 ∗ relation (Figure 4) compensating. For Circinus, Davis et al.(2019b) find a similar behaviour using Δ 𝑉 H i , and suggest its centralstellar velocity dispersion may be anomalous. We therefore elect toinclude both galaxies in our fits.NGC 5055 has a SMBH mass measurement too large by aroundtwo orders of magnitude compared to that predicted from eitherthe 𝑀 BH − 𝜎 ∗ relation or our Δ 𝑉 CO − 𝑀 BH correlation. This massis based on Fabry-Perot spectroscopy taken at the Canada-France-Hawaii Telescope (Blais-Ouellette et al. 2004), in which the central300 pc exhibits dual velocity components, one consistent with theoverall galactic rotation, the other with a counter-rotating disc (fromwhich the SMBH mass is derived) or a bipolar outflow. As this SMBH MNRAS , 1–18 (2020)
ISDOM: The Δ 𝑉 CO − 𝑀 BH relation mass is suspect (see Graham 2008), we exclude this object from ourfits.We also omit the dwarf galaxy NGC 3504, which is an outlierfrom the Δ 𝑉 CO − 𝑀 BH relation. As the only dwarf galaxy in the sam-ple it would otherwise have a disproportionate effect on the deter-mined slope and scatter, and dwarfs do not appear to follow the otherSMBH–host galaxy property correlations (see e.g. Figure 1 of vanden Bosch 2016).In the unresolved sample, we omit NGC 541, NGC 3384 andNGC 3862. NGC 541 has the most compact dust disc of the galaxiesobserved, extending to only 0 . 𝑅 , and a narrow line width consis-tent with our discussion in Section 4.1. There is no dust disc visiblein NGC 3384, but the CO line width is very narrow. NGC 3862 hasa dust disc of only 0 . 𝑅 that is also nearly face-on, implying thatthe inclination uncertainties are very large.NGC 4736 and NGC 4826 are both outliers from the fundamentalplane and were therefore excluded from previous fundamental planeparameter – SMBH mass correlations (van den Bosch 2016). How-ever, they appear consistent with both correlations investigated in thispaper, and with the 𝑀 BH − 𝜎 ∗ relation, so they are included in thiswork.Finally Mrk 590, NGC 524 and NGC 4303 all have inclinationsbelow 30 ° . Studies of the Tully-Fisher relation exclude galaxies atsuch low inclinations (e.g. Tully & Fisher 1977; Pierce & Tully1988; Davis et al. 2011; Tiley et al. 2016; Topal et al. 2018). Thisis because customary approaches to measuring inclination, such asfitting ellipses to features assumed to be intrinsically circular, respondonly weakly to varying inclinations at 𝑖 ≈ ° , but the line-of-sightprojected velocity responds strongly ( 𝑣 los ∝ sin 𝑖 ). In our work, weallow these galaxies to remain (and omit to label them in Figures 3,4, and 6) as the large uncertainties have been propagated through,and thus these galaxies have low statistical weights. The best-fitting correlations for our samples (Table 5) can be com-pared to the extensive literature on other correlations. Correlationsbetween Δ 𝑉 H i at halo scales and either 𝑀 BH or 𝜎 ∗ have already beendiscussed in Sections 3.3 and 3.4, so we only briefly summarise thesefindings here before considering other correlations.We find a close correlation between Δ 𝑉 CO and 𝑀 BH , as wouldbe expected from the simple arguments presented in Section 1.2.We find a steeper slope for LTGs than for ETGs; the LTG resultis in agreement with the slope and intrinsic scatter found using H iline widths (Davis et al. 2019b). When computing a single relationfor galaxies of all morphologies, we obtain an intrinsic scatter of0 . ± . Δ 𝑉 CO − 𝜎 ∗ correlation regardless of galaxy mor-phology. For ETGs, this agrees with the H i results of Serra et al.(2016), even though we cannot assume a baryon-halo conspiracyholds. However, contrary to us, Davis et al. (2019b) exclude a linearrelation in LTGs. Wu (2007) fit a linear relation to local Seyferts,leading to larger uncertainties in the coefficients, but did not estimatethe scatter. We fit the line widths measured by Wu (2007), that are alsoFWHM but are not based on profile fits, with Equation 5, yielding thebest-fitting parameters 𝑎 = . ± .
12 and 𝑏 = . ± .
02, with a totalscatter of 2 . . ± .
02 dex.The total scatter is dominated by the large uncertainties of the samplestellar velocity dispersions. Our intrinsic scatters are similarly small,although we do not have a Seyfert galaxy sample to directly compare.The tightest correlations between SMBH masses and host proper- ties have intrinsic scatters comparable to ours. The careful analysis ofKormendy & Ho (2013) showed that for classical bulges and ellipti-cals, the 𝑀 BH − 𝜎 ∗ relation has an intrinsic scatter of 0 .
29 dex. Usinga less rigorously selected and larger sample of galaxies, Beifiori et al.(2012) determined a total scatter of 0 . ± .
06 dex, dominated bythe intrinsic scatter of 0 . ± .
07 dex. Our tightest correlation is forspatially-resolved galaxies, with a total scatter of 0 . . . ± .
11 dex and 0 . ± .
07 dex, respectively, while Kormendy & Ho(2013) found 0 . .
28 dex, respectively. Our results are thuscomparably tight to the bulge correlations.Looser 𝑀 BH –host property correlations, including those with Sér-sic index (Graham & Driver 2007; Davis et al. 2017b), spiral armpitch angle (Seigar et al. 2008; Davis et al. 2017b) and total galaxylight or mass (Jahnke et al. 2009; Bennert et al. 2010; Merloni et al.2010; Davis et al. 2018b), have also been proposed and investigatedover the last two decades. Beifiori et al. (2012) investigated severalof these, finding typical intrinsic scatters of 0 . − . 𝑀 BH − Δ 𝑉 CO correlation is not so tight as tooutperform those commonly used to estimate SMBH masses. In theabsence of a measurement of 𝜎 ∗ , and where a bulge decompositionis either too difficult or too laborious, use of the CO line width isthus a competitive estimator of a galaxy’s SMBH mass. To illustrate the use of CO line widths as SMBH mass estimators,we construct a SMBH mass function (see review by Kelly & Mer-loni 2012) from the Tiley et al. (2016) sample of 207 CO(1-0) linewidths, that were measured in a manner identical to that in this work.These observations were originally obtained as part of the COLDGASS survey (Saintonge et al. 2011), with the IRAM 30-m tele-scope. The sample is purely mass-selected to be representative ofgalaxies in the local universe with log ( 𝑀 ∗ / M (cid:12) ) >
10, that corre-sponds to 𝑀 BH & . M (cid:12) using the correlation of Beifiori et al.(2012). The Tiley et al. (2016) sample also contains some galaxiesbelow 10 M (cid:12) , that were later published in the extended COLDGASS survey (xCOLDGASS; Saintonge et al. 2017), but are notnecessarily statistically-representative of these galaxies. Removingthe galaxies with stellar masses less than 10 M (cid:12) makes only amarginal change to the derived SMBH mass function (and this onlyat 𝑀 BH < . M (cid:12) ), even though it makes a substantial change tothe expected distribution of galaxies in a volume-limited sample.The parent COLD GASS sample was selected to be flat in log ( 𝑀 ∗ ) ,although the need for robust double-horned profiles implies that thesample of Tiley et al. (2016) does not exactly match this criterion(see the top panel of Figure 8). Nevertheless, we need to weight thesample to match a representative galaxy stellar mass function. Weadopt the approach described by Catinella et al. (2018), wherebywe assume the local galaxy stellar mass function of Baldry et al.(2012), predict the number of galaxies in a volume-limited sample ofequal size in 0 . MNRAS , 1–18 (2020) Mark D. Smith et al. luminosity function assuming a fixed radiative efficiency 𝜂 = . 𝐿 bol / 𝐿 Edd = .
45. Sig-nificant deviations occur at SMBH masses greater than 10 M (cid:12) , butwe note that each populated bin at 𝑀 BH > M (cid:12) , in addition tothe 10 . − . M (cid:12) bin that lies substantially below the Shankaret al. (2009) results, is based on only a single galaxy and thereforehas a large associated uncertainty. In addition, the SMBH massesin the sample used for our Δ 𝑉 CO − 𝑀 BH correlation poorly sam-ple these most massive SMBHs (see e.g. Figure 3). Furthermore,for 𝑀 BH > M (cid:12) , the 𝑀 BH − 𝜎 ∗ relation appears to saturate (e.g.Gültekin et al. 2009b; McConnell & Ma 2013; Krajnović et al. 2018).We have no SMBH in this regime in our sample, and so cannot de-termine whether our correlation continues to hold or not at thesemasses.Naturally, estimating a SMBH mass function requires a very care-ful analysis of potential biases in the underlying sample; that is be-yond the scope of this paper. We highlight the morphological biasesin the CO detection fraction, and the integration limit of the COLDGASS sample of 𝑀 H / 𝑀 ∗ = . CO line emission has previously been used as a tracer of the centralparts of galaxy rotation curves, including for the Tully-Fisher rela-tion. The CO discs typically do not extend to halo-dominated radii,and thus in any given galaxy the width of the CO line probes thestellar potential, analogously to the central stellar velocity disper-sion 𝜎 ∗ . Although in a LTG one might suppose that the ‘disc-haloconspiracy’ implies that the CO line width measures a flat rotationvelocity equivalent to that measured with neutral gas, the same hasnot been shown for ETGs. The CO line width has however previouslybeen used as a proxy for the stellar velocity dispersion, that is oftenhard to measure and is strongly affected by both dust extinction andfinite apertures.In this paper, we proposed a correlation between SMBH massesand CO line widths. We investigated this correlation using two sam-ples of galaxies with CO line emission. The first is comprised ofgalaxies with synthesised spectra from spatially-resolved observa-tions, with generally very high signal-to-noise ratios (SNRs). Thesespectra were constructed by summing emission within a mask de-fined from a smoothed version of the original data cube. The secondsample is comprised of galaxies with single-dish observations, eitherfrom the literature or from new observations conducted at the IRAM30-m and OSO 20-m telescopes. All the galaxies used have robustdynamical SMBH mass measurements.Each CO line width was measured as the FWHM of a profilefit using a Gaussian double peak profile, that has been previouslyshown to recover well the intrinsic widths of noisy double-hornedspectra arising from rotating discs. The line width uncertainties wereestimated by Monte Carlo sampling from the determined parameteruncertainties.We find a good correlation of the CO line widths with both SMBHmasses and the central stellar velocity dispersions. There is some ev-idence that the SMBH mass correlation is steeper for LTGs, withoutincreased scatter. However, the stellar velocity dispersion correlationexhibits a higher intrinsic scatter for LTGs than for ETGs. Usingonly the spatially-resolved sample yields tighter correlations, and we M star (M )0510152025303540 N u m b e r o f g a l a x i e s Tiley et al. 2016Volume-limited10 M BH (M )10 ( l o g M B H / M ) ( M p c d e x ) This workShankar et al. 2009
Figure 8. Top panel:
Galaxy stellar mass function of the Tiley et al. (2016)sample drawn from COLD GASS (green histogram), and of a purely volume-limited sample of equal size following the galaxy stellar mass function ofBaldry et al. (2012) (black histogram).
Bottom panel:
Local SMBH massfunction derived from the Tiley et al. (2016) sample and our Δ 𝑉 CO − 𝑀 BH correlation (green histogram) and that determined by Shankar et al. (2009)from the local AGN luminosity function (solid black line). Error bars aregiven by the square-root of the sum of the squared weights. The verticaldashed line indicates the SMBH mass corresponding to the 10 M (cid:12) stellarmass limit of the COLD GASS sample, assuming the correlation of Beifioriet al. (2012), below which we expect our sample to be incomplete. suggest that the lower SNRs and less robust selection of unresolvedobservations account for this.The tightest correlation is found from our spatially-resolved sampleaslog (cid:18) 𝑀 BH M (cid:12) (cid:19) = ( . ± . ) (cid:20) log (cid:18) 𝑊 sin 𝑖 km s − (cid:19) − . (cid:21) + ( . ± . ) , (8)with a total scatter of 0 . 𝑀 BH direction, dominatedby the intrinsic scatter of 0 . . 𝑀 BH − 𝜎 ∗ relation.We applied our adopted correlation to the CO line widths mea- MNRAS , 1–18 (2020)
ISDOM: The Δ 𝑉 CO − 𝑀 BH relation sured in the COLD GASS survey as part of previous CO Tully-Fisherrelation studies, thereby estimating the galaxies’ SMBH masses, andconstructed a local SMBH mass function, correcting for the origi-nal sample’s bias in stellar mass. We showed that our SMBH massfunction thus derived is consistent with that estimated from the localAGN luminosity function.We suggest that our correlation has significant value to estimateSMBH masses where the conventional proxies are unavailable. TheCO observations required are simple to make and avoid the need forcomplicated bulge-disc decompositions. We have further shown thatthe use of resolved CO observations to generate synthesised spectradramatically improves the line width measurements. We also suggestthat substantial improvements could be made in the CO Tully-Fisherrelation by using (low-resolution) interferometric observations, suchas those available with the Atacama Compact Array, as these obser-vations allow more robust sample selection and the high SNRs yieldsignificantly smaller line width measurement uncertainties. ACKNOWLEDGEMENTS
The authors would like to thank Henrik Olofsson at the Onsala SpaceObservatory for carrying out observations and Alfred Tiley for pro-viding the COLD GASS Gaussian double peak profile fits used inSection 4.5. We would also like to thank our referee for helpfulsuggestions.MDS acknowledges support from a Science and Technology Facil-ities Council (STFC) DPhil studentship under grant ST/N504233/1.MB was supported by STFC consolidated grant ‘Astrophysics at Ox-ford’ ST/H002456/1 and ST/K00106X/1. TAD acknowledges sup-port from STFC through grant ST/S00033X/1. MC acknowledgessupport from a Royal Society University Research Fellowship.This paper makes use of the following ALMA data:ADS/JAO.ALMA
DATA AVAILABILITY
The data underlying this article are available in Zenodo, athttps://dx.doi.org/10.5281/zenodo.4067034.
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APPENDIX A: NEW SINGLE-DISH OBSERVATIONSA1 IRAM 30-m telescope observations
We carried out new observations of 51 galaxies using the IRAM 30-m telescope on Pico Veleta, Spain, in programme 191-18, between26th and 31st December 2018. Twenty-two of these galaxies weredetected.The observations used the wobbler to switch between the sourceand two off-source positions azimuthally-separated from the sourceby ± , significantly larger than the expected sizes of the sourcesobserved. If there had been emission at these off-source positions, thespectra would exhibit negative features, but there is no such feature.The heterodyne Eight Mixer Receiver (EMIR; Carter et al. 2012)was used to simultaneously observe the CO(1-0) and CO(2-1)transitions. The receiver was tuned to frequencies allowing severalsources at similar redshifts to be observed sequentially without re-tuning, and the spectra were subsequently corrected to remove theresulting frequency and velocity offsets. Although four sidebandsare available at each frequency, only some were recorded due tolimitations in the manner backends can be connected.Strong, compact, continuum sources were observed as pointingand focusing calibrators. At the beginning of each observing shift,at 2-3 hour intervals, after long slews, and after sunrise and sunset,both pointing and focusing calibrations were performed. Additionalpointing calibrations were performed before observing each sciencetarget, unless consecutive science targets were close by on the sky,using calibrators near the targets. Pointing calibrations were thusperformed typically every hour. The calibrations adopted were themeans of those required at 115 and 230 GHz, except when the cal-ibrations were not well-determined for one of these (typically at230 GHz), when typical offsets from the other frequency (typically115 GHz) were adopted. For these calibrations, we used the BroadBand Continuum (BBC) backend, that covers the entire EMIR band.Each science source was observed using multiple sets of 12 × 𝑇 ∗ A units was less than 3 mK. Thislimit corresponds to 𝑀 H ≈ M (cid:12) in a galaxy at the distance of theVirgo cluster, assuming a typical line-of-sight projected line widthof 400 km s − .Two backends were used for science observations: the FourierTransform Spectrograph (FTS; Klein et al. 2012) and the Wide-band Line Multiple Autocorrelator (WILMA ). FTS was used in the‘wide’ mode, with eight units each with a bandwidth of ≈ ≈
200 kHz, corresponding to total bandwidthsof ≈
10 400 and ≈ − , and channel widths of ≈ . ≈ .
25 km s − , at 115 and 230 GHz, respectively. Four FTS unitswere attached to the CO(1-0) sideband and two to the CO(2-1)sideband. The remaining two FTS units were attached to the upperouter sideband on the 230 GHz receiver, as required by the connectorbox, although no emission line was expected within this sideband. Each pair of FTS units measured the horizontal and vertical polar-isations of the band separately, and these were averaged together.WILMA served as a backup with a 16 GHz bandwidth and a 2 MHzchannel width.Data reduction was performed off-line using the
Continuumand Line Analysis Single-dish Software (CLASS) fromthe
Grenoble Image and Line Data Analysis Software(GILDAS) suite . Every 6-minute scan was manually checkedfor bad data. The frequency axis was transformed from that usedto tune the receiver for groups of multiple targets to the truerest-frequencies of the CO transitions and then to velocitiesusing the optical convention. FTS operates on three sections ofeach spectrum, which can lead to ‘platforming’ errors, i.e. absoluteflux offsets between the sections. This effect was removed forevery 6-minute scan by masking detected lines and subtracting afirst-order fit to the remaining baseline in each section. We thenaveraged together all polarisations and (good) scans for each sciencesource and binned to 30 km s − channels. We performed anotherfit to the baseline to remove any remaining offset arising from thebackground, again masking regions where the CO line was detected.Additionally, as many of these galaxies are sufficiently local thatthe CO(1-0) line lies close to the 118 GHz atmospheric oxygenline, the high-frequency channels were also masked where theyexhibited increased noise. Although the bandpass never containedthe emission line itself, it often included its broad wings.Many of our sources were observed at relatively low elevations,of 20-30 ° . In addition to the increased airmass at low elevations, andhence the longer integrations required to reach the same sensitivity,the 30-m telescope exhibits an elevation-dependent gain due to smallsurface deformations (see e.g. Greve et al. 1998). For a point source,the peak gain is found at 50 ° elevation, whereas at 20 ° it has droppedto 92% at 145 GHz and 80% at 210 GHz. For an extended source,and at lower frequencies, this correction is expected to be less sig-nificant. We therefore assume that we can neglect this correction forall sources. Nevertheless, the fluxes adopted may be underestimatedby up to ≈
20% for a compact source at CO(2-1).We do not know a priori the extent of the CO emission in anysource. However, since the telescope does not have a uniform sensi-tivity across the beam, and our targets are expected to be extended,we should in principle correct for the coupling between the sourceemission distribution and the telescope’s beam, as expressed throughthe 𝐾 -factor (Baars 1973). For a circular Gaussian source as extendedas the beam, the correction can be as large as a factor of 2, whereasfor a point-source, no correction is required. For simplicity, and hav-ing noted the danger of assuming any particular source shape, weneglect this 𝐾 -factor here, implicitly assuming that all sources arepoint-like. This decision is intended to maximise the utility of ourdata to the community, rather than imposing our choice of assump-tions. As noted in the main text, none of these corrections wouldaffect our measured line widths.Table A1 describes the spectra obtained for each galaxy. The de-tected lines are shown in Figure A1. For the same reasons as above,the associated quantities listed are in main beam temperature units,without 𝐾 -factor correction. The fluxes listed are thus formally lowerlimits, but they are likely only slightly underestimated. We convert tomain beam temperatures using the 30-m telescope efficiencies listedin Table 2.Integrated line fluxes are measured as the integral over the velocity , 1–18 (2020) Mark D. Smith et al. range listed in Table A1 and indicated by shading in Figure A1, i.e. 𝐼 = ∫ 𝑣 𝑣 𝑇 mb ( 𝑣 ) 𝑑𝑣 , (A1)where 𝑇 mb ( 𝑣 ) is the flux in each velocity channel (of width 𝑑𝑣 )expressed as a main beam temperature, and the integral is taken overthe velocity range 𝑣 to 𝑣 .We adopt the standard estimate of the uncertainty in the integratedflux (e.g. Sage et al. 2007; Young et al. 2011), 𝜎 = 𝜎 rms Δ 𝑣 √︄ 𝑁 line (cid:18) + 𝑁 line 𝑁 noise (cid:19) , (A2)where 𝜎 rms is the noise per channel (measured in line-free channels), Δ 𝑣 the velocity width of each channel, 𝑁 line the number of channelsintegrated over, and 𝑁 noise the number of channels used to estimatethe noise, that we assume is approximately the number of chan-nels in the bandpass. The line ratios are thus 𝐼 ( − ) / 𝐼 ( − ) in mainbeam temperature units. Molecular gas masses for detected lines areestimated adopting 𝑋 CO = × mol cm − (K km s − ) − , andthe quoted uncertainties include the uncertainties in the distancesadopted from van den Bosch (2016). For each undetected galaxy, weestimate an upper limit on the molecular gas mass by assuming theline width predicted from the CO Tully-Fisher Relation (Tiley et al.2016), calculating the sensitivity using Equation A2, and hence theH mass that would be (marginally) detected at 1 𝜎 sensitivity usingEquation A1. A2 Onsala Space Observatory 20-m observations
A few of the most extended targets were observed using the OnsalaSpace Observatory (OSO) 20-m telescope in service mode, largelythrough an automated script. The observations were carried out intwo observing sessions 20th-23rd November 2018 and 27th Febru-rary - 6th March 2019, using the 3 mm receiver (Belitsky et al. 2015)to cover the CO(1-0) line. This yields a 4 GHz bandpass, that isfully-sampled by the Omnisys A (OSA) backends with a 76 kHzraw channel width. At 115 GHz, this is equivalent to a bandpass of ≈
10 000 km s − and a channel width of ≈ . − . The two back-end units cover the horizontal and vertical polarisations simultane-ously, that are then co-added to improve the SNR. The observationswere carried out in dual beam-switching mode, whereby the source ismoved between the signal beam and the reference beam, and the twospectra are subtracted from each other. This beam-switching modehas a fixed 11 throw.For each source, individual scans of 4 minutes each were manuallyinspected, and those with bad baselines removed. This issue signifi-cantly affected the observations of NGC 4335, for which around halfthe scans had to be eliminated. Using CLASS , the remaining scanswere then averaged for each source and binned to 30 km s − channels.The detected emission lines and the region of increased noise closeto the 118 GHz atmospheric oxygen line were then masked, and alinear baseline fit carried out and subtracted. Four of the 9 sourcesobserved were detected in CO(1-0).The native 𝑇 ∗ A units were converted to 𝑇 mb using the main beamefficiencies calculated for each scan. The spectra were then inte-grated over the line to calculate the integrated flux and correspondingmolecular gas mass, following the prescription given in Section A1(Equations A1 and A2). The results are listed in Table A2 and thespectra of the detected sources are shown in Figure A2.The conversion factor from temperature to flux units is not avail-able for 115 GHz, but we rescaled the value given at 86 GHz, assum-ing that the product of the conversion factor and main beam efficiency is constant, as suggested by OSO staff. Thus, 𝑆 ( Jy ) = . − 𝜂 mb 𝑇 ∗ A , (A3)where we have assumed a point source. This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS , 1–18 (2020)
ISDOM: The Δ 𝑉 CO − 𝑀 BH relation Table A1.
New observations using the IRAM 30-m telescope.Galaxy T-type rms (1-0) rms (2-1) Velocity range 𝐼 ( − ) 𝐼 ( − ) 𝐼 ( − ) 𝐼 ( − ) log (cid:16) 𝑀 H2 M (cid:12) (cid:17) Notes(mK) (mK) (km s − ) (K km s − ) (K km s − )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)3C382 -5.0 1.8 2.9 < . < . − . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . < . − . ± . . ± . . ± . < . < . < . − . ± . . ± . . ± . < . − . ± . . ± . . ± . < . − . ± . . ± . . ± . < . < . − . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . < . − . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . < . < . 𝑣 = − < . 𝑣 =
500 km s − NGC 4350 -1.8 2.4 3.0 < . < . < . < . < . < . < . < . < . < . < . − . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . < . < . − . ± . . ± . . ± . < . − . ± . . ± . . ± . < . − . ± . . ± . . ± . −
10 600 2 . ± . . ± . . ± . < . Notes:
Column 1 lists the name of each target galaxy, as listed in Table 2 of van den Bosch (2016). The morphological classification on the numerical Hubblescale from HyperLEDA is listed in Column 2. Columns 3 and 4 indicate the rms noise achieved in the sideband containing the CO(1-0) and CO(2-1) line,respectively. For detected galaxies, columns 5-8 list the velocity range used in Equation A1, the integrated CO(1-0) and CO(2-1) flux, and the associated lineratio, respectively. All fluxes are expressed as main beam temperatures ( 𝑇 mb ). Column 9 contains the estimated total molecular gas mass or upper-limit, calculatedas described in the text. Finally, Column 10 contains notes on specific galaxies as follows. (1) This source was strongly detected in both lines before the intendedsensitivity was reached, so the noise exceeds 3 mK in at least one line. (2) NGC4335 was initially not detected at the 4631 km s − systemic velocity listed in theNASA/IPAC Extragalactic Database. This was surprising due to the prominent dust disc visible in HST images. The Sloan Digital Sky Survey lists a velocity of −
111 km s − , so we obtained a second spectrum centred on the corresponding frequency. The galaxy remained undetected. The velocities given in the table arethe centres of the band for each of these two spectra. MNRAS , 1–18 (2020) Mark D. Smith et al. )5051015 T m b ( m K ) )50510152025 T m b ( m K ) (a) ARK 120 Figure A1.
One of the 22 galaxies detected in our CO observations using the IRAM 30-m telescope (programme 191-18). For each galaxy, the left panel showsthe extent of the 30-m beam at CO(1-0) (red solid circle) and CO(2-1) (red dashed circle), overlaid on an image of the galaxy from DSS. Also overlaidare the areas enclosed by one effective radius (from van den Bosch 2016; green solid ellipse) and 𝐷 (from HyperLEDA; green dashed ellipse), adoptingthe inclination and position angle listed in HyperLEDA and the distance from van den Bosch (2016). The central and right panels show the spectrum of the CO(1-0) and CO(2-1) emission line, respectively. The velocity range used to determine the integrated flux is shaded. All 22 detected galaxies are shown inFigure A3 in the supplemental material.
Table A2.
New observations using the Onsala Space Observatory 20-m telescope.Galaxy T-type rms (1-0) Velocity range 𝐼 ( − ) log (cid:16) 𝑀 H2 M (cid:12) (cid:17) Notes(mK) (km s − ) (K km s − )(1) (2) (3) (4) (5) (6) (7)Mrk 279 -2.0 1 . − . ± . . ± . . − . ± . . ± . . < . . < . . − ± . ± . . < . . < . . < . . − . ± . . ± . Notes:
Column 1 lists the name of each target galaxy, as listed in Table 2 of van den Bosch (2016). The morphological classification on the numerical Hubblescale from HyperLEDA is listed in Column 2. Column 3 indicates the rms noise achieved in the bandpass containing the CO(1-0) line. For detected galaxies,Columns 4 and 5 list the velocity range used in Equation A1, and the integrated CO(1-0) flux respectively. All fluxes are expressed as main beam temperatures( 𝑇 mb ). Column 6 contains the estimated total molecular gas mass or upper-limit, calculated as described in the text. Finally, Column 7 contains notes onspecific galaxies as follows. (1) CO(1-0) emission was strongly detected in NGC 3079 before the anticipated sensitivity was reached, so the rms noise appearscomparatively high. (2) Bad baselines in many of the scans of NGC 4335 yielded a noise higher than requested. )05 T m b ( m K ) (a) Mrk 279 Figure A2.
One of the four galaxies detected in our CO observations using the OSO 20-m telescope (programme 2018-04a). For each galaxy, the left panelshows the extent of the 20-m beam at CO(1-0) (red solid circle), overlaid on an image of the galaxy from DSS. Also overlaid are the areas enclosed by oneeffective radius (from van den Bosch 2016; green solid ellipse) and 𝐷 (from HyperLEDA; green dashed ellipse), adopting the inclination and position anglelisted in HyperLEDA and the distance from van den Bosch (2016). The right panel shows the spectrum of the CO(1-0) emission line. The velocity range usedto determine the integrated flux is shaded. All four detections are shown in Figure A4 in the supplementary material.MNRAS , 1–18 (2020)
ISDOM: The Δ 𝑉 CO − 𝑀 BH relation - Supplemental Material WISDOM project - VI. Exploring the relation between supermassiveblack hole mass and galaxy rotation with molecular gas -Supplemental Material © a r X i v : . [ a s t r o - ph . GA ] O c t Mark D. Smith et al.
200 300 400 500 600 700Velocity (kms )024681012 F l u x ( J y ) (a) Circinus; ALMA; CO(1-0) )0.000.050.100.150.200.250.300.35 F l u x ( J y ) (b) NGC 383; ALMA; CO(2-1) )0.050.000.050.100.150.20 F l u x ( J y ) (c) NGC 524; ALMA; CO(2-1)
800 1000 1200 1400 1600 1800 2000 2200Velocity (kms )0.000.010.020.030.040.050.06 F l u x ( J y ) (d) NGC 1332; ALMA; CO(2-1)
500 600 700 800 900 1000 1100 1200Velocity (kms )0.000.050.100.150.200.250.300.350.40 F l u x ( J y ) (e) NGC 1386; ALMA; CO(1-0) )0.000.050.100.150.200.250.300.35 F l u x ( J y ) (f) NGC 3081; ALMA; CO(2-1)
Figure 9.
An extended version of Figure 1. Gaussian double peak profile fit (green) to CO spectra synthesised from interferometric observations (blue). Themean noise estimate ( ± 𝜎 ) is shown in the top-left corner. The red vertical lines are at 𝑣 (solid) and bound 𝑊 (dashed), defined in Equation 3. The greybands indicate the 67% confidence interval in 𝑊 . ISDOM: The Δ 𝑉 CO − 𝑀 BH relation - Supplemental Material )0.000.050.100.150.200.250.300.35 F l u x ( J y ) (g) NGC 3245; ALMA; CO(2-1) )0.000.020.040.060.08 F l u x ( J y ) (h) NGC 3258; ALMA; CO(2-1) )0.00.51.01.52.02.53.03.54.0 F l u x ( J y ) (i) NGC 3504; ALMA; CO(2-1) )05101520 F l u x ( m J y ) (j) NGC 3557; ALMA; CO(2-1)
800 900 1000 1100 1200 1300 1400 1500 1600Velocity (kms )0.00.10.20.30.40.5 F l u x ( J y ) (k) NGC 3607; ALMA; CO(2-1)
500 600 700 800 900Velocity (kms )0246810 F l u x ( J y ) (l) NGC 3627; BIMA; CO(1-0)
Figure 9 – continued An extended version of Figure 1. Gaussian double peak profile fit (green) to CO spectra synthesised from interferometric observations(blue). The mean noise estimate ( ± 𝜎 ) is shown in the top-left corner. The red vertical lines are at 𝑣 (solid) and bound 𝑊 (dashed), defined in Equation 3.The grey bands indicate the 67% confidence interval in 𝑊 . Mark D. Smith et al.
100 200 300 400 500 600 700 800Velocity (kms )0.00.51.01.52.02.53.03.5 F l u x ( J y ) (m) NGC 4258; BIMA; CO(1-0) )02468 F l u x ( J y ) (n) NGC 4303; ALMA; CO(2-1)
700 800 900 1000 1100 1200 1300 1400Velocity (kms )0.050.000.050.100.150.200.25 F l u x ( J y ) (o) NGC 4429; CARMA; CO(1-0)
800 900 1000 1100 1200 1300 1400 1500 1600Velocity (kms )0.00.10.20.30.40.5 F l u x ( J y ) (p) NGC 4459; CARMA; CO(1-0)
200 300 400 500 600 700 800 900 1000Velocity (kms )0.00.20.40.60.8 F l u x ( J y ) (q) NGC 4526; CARMA; CO(2-1) )0.000.020.040.060.08 F l u x ( J y ) (r) NGC 4697; ALMA; CO(2-1)
Figure 9 – continued An extended version of Figure 1. Gaussian double peak profile fit (green) to CO spectra synthesised from interferometric observations(blue). The mean noise estimate ( ± 𝜎 ) is shown in the top-left corner. The red vertical lines are at 𝑣 (solid) and bound 𝑊 (dashed), defined in Equation 3.The grey bands indicate the 67% confidence interval in 𝑊 . ISDOM: The Δ 𝑉 CO − 𝑀 BH relation - Supplemental Material
150 200 250 300 350 400 450Velocity (kms )0246810 F l u x ( J y ) (s) NGC 4736; BIMA; CO(1-0)
200 300 400 500 600Velocity (kms )012345678 F l u x ( J y ) (t) NGC 4826; BIMA; CO(1-0)
600 700 800 900 1000 1100 1200 1300Velocity (kms )0.00.51.01.52.02.5 F l u x ( J y ) (u) NGC 5005; BIMA; CO(1-0)
300 350 400 450 500 550 600 650 700Velocity (kms )01234567 F l u x ( J y ) (v) NGC 5055; BIMA; CO(1-0)
950 1000 1050 1100 1150 1200 1250 1300 1350Velocity (kms )0.00.51.01.52.02.53.03.54.0 F l u x ( J y ) (w) NGC 5248; BIMA; CO(1-0) )0.00.10.20.30.40.5 F l u x ( J y ) (x) NGC 6861; ALMA; CO(2-1)
Figure 9 – continued An extended version of Figure 1. Gaussian double peak profile fit (green) to CO spectra synthesised from interferometric observations(blue). The mean noise estimate ( ± 𝜎 ) is shown in the top-left corner. The red vertical lines are at 𝑣 (solid) and bound 𝑊 (dashed), defined in Equation 3.The grey bands indicate the 67% confidence interval in 𝑊 . Mark D. Smith et al. )0.000.020.040.060.08 F l u x ( J y ) (y) NGC 7052; ACA; CO(2-1)
500 600 700 800 900 1000 1100Velocity (kms )01234567 F l u x ( J y ) (z) NGC 7331; BIMA; CO(1-0)
Figure 9 – continued An extended version of Figure 1. Gaussian double peak profile fit (green) to CO spectra synthesised from interferometric observations(blue). The mean noise estimate ( ± 𝜎 ) is shown in the top-left corner. The red vertical lines are at 𝑣 (solid) and bound 𝑊 (dashed), defined in Equation 3.The grey bands indicate the 67% confidence interval in 𝑊 .
600 400 200 0 200 400 600Velocity (kms )0.020.000.020.040.060.08 F l u x ( J y ) (a) 3C120; NRAO 12-m; CO(1-0) )0.020.000.020.040.06 F l u x ( J y ) (b) ARK 120; IRAM 30-m; CO(1-0)
Figure 10.
An extended version of Figure 2. Gaussian double peak profile fit (green) to CO spectra synthesised from interferometric observations (blue). Themean noise estimate ( ± 𝜎 ) is shown in the top-left corner. The red vertical lines are at 𝑣 (solid) and bound 𝑊 (dashed), defined in Equation 3. The greybands indicate the 67% confidence interval in 𝑊 . ISDOM: The Δ 𝑉 CO − 𝑀 BH relation - Supplemental Material )0.020.000.020.040.060.080.100.12 F l u x ( J y ) (c) MRK 590; IRAM 30-m; CO(1-0)
400 300 200 100 0 100 200 300 400Velocity (kms )0.020.000.020.040.06 F l u x ( J y ) (d) NGC 383; IRAM 30-m; CO(1-0) )0.020.000.020.040.06 F l u x ( J y ) (e) NGC 524; IRAM 30-m; CO(1-0)
200 100 0 100 200Velocity (kms )5051015202530 F l u x ( m J y ) (f) NGC 541; IRAM 30-m; CO(2-1)
800 900 1000 1100 1200 1300 1400 1500Velocity (kms )024681012 F l u x ( J y ) (g) NGC 1068; NRAO 12-m; CO(1-0) )0.020.010.000.010.020.030.04 F l u x ( J y ) (h) NGC 1497; IRAM 30-m; CO(1-0)
Figure 10 – continued An extended version of Figure 2. Gaussian double peak profile fit (green) to CO spectra from single dish observations (blue). The meannoise estimate ( ± 𝜎 ) is shown in the top-left corner. The red vertical lines are at 𝑣 (solid) and bound 𝑊 (dashed), defined in Equation 3. The grey bandsindicate the 67% confidence interval in 𝑊 . Mark D. Smith et al. )0.00.20.40.60.81.0 F l u x ( J y ) (i) NGC 1667; NRAO 12-m; CO(1-0) )0.00.20.40.60.81.01.2 F l u x ( J y ) (j) NGC 1961; IRAM 30-m; CO(1-0) )0.20.00.20.40.6 F l u x ( J y ) (k) NGC 2273; NRAO 12-m; CO(1-0) )0.030.020.010.000.010.020.030.040.05 F l u x ( J y ) (l) NGC 2911; IRAM 30-m; CO(1-0)
500 600 700 800 900 1000Velocity (kms )0.040.020.000.020.040.06 F l u x ( J y ) (m) NGC 3384; IRAM 30-m; CO(2-1) )0.050.000.050.100.15 F l u x ( J y ) (n) NGC 3665 IRAM 30-m; CO(1-0)
Figure 10 – continued An extended version of Figure 2. Gaussian double peak profile fit (green) to CO spectra from single dish observations (blue). The meannoise estimate ( ± 𝜎 ) is shown in the top-left corner. The red vertical lines are at 𝑣 (solid) and bound 𝑊 (dashed), defined in Equation 3. The grey bandsindicate the 67% confidence interval in 𝑊 . ISDOM: The Δ 𝑉 CO − 𝑀 BH relation - Supplemental Material
200 150 100 50 0 50 100 150 200 250Velocity (kms )0.0100.0050.0000.0050.0100.0150.020 F l u x ( J y ) (o) NGC 3862; IRAM 30-m; CO(1-0) )0.20.00.20.40.60.81.0 F l u x ( J y ) (p) NGC 4388; NRAO 12-m; CO(1-0)
600 800 1000 1200 1400 1600Velocity (kms )0.020.000.020.040.060.08 F l u x ( J y ) (q) NGC 4429; IRAM 30-m; CO(1-0)
700 800 900 1000 1100 1200 1300 1400 1500 1600Velocity (kms )0.000.050.100.150.200.25 F l u x ( J y ) (r) NGC 4459; IRAM 30-m; CO(1-0)
600 500 400 300 200 100 0 100Velocity (kms )0.010.000.010.020.030.040.05 F l u x ( J y ) (s) NGC 4486; IRAM 30-m; CO(1-0) )0.050.000.050.100.150.200.25 F l u x ( J y ) (t) NGC 4526; IRAM 30-m; CO(1-0)
Figure 10 – continued An extended version of Figure 2. Gaussian double peak profile fit (green) to CO spectra from single dish observations (blue). The meannoise estimate ( ± 𝜎 ) is shown in the top-left corner. The red vertical lines are at 𝑣 (solid) and bound 𝑊 (dashed), defined in Equation 3. The grey bandsindicate the 67% confidence interval in 𝑊 . Mark D. Smith et al. )0.10.00.10.20.3 F l u x ( J y ) (u) NGC 4593; IRAM 30-m; CO(1-0) )0.10.00.10.20.3 F l u x ( J y ) (v) NGC 5548; NRAO 12-m; CO(1-0)
600 400 200 0 200 400Velocity (kms )0.0040.0020.0000.0020.0040.0060.0080.010 F l u x ( J y ) (w) NGC 7052; IRAM 30-m; CO(1-0) )1000100200300 F l u x ( J y ) (x) UGC 3789; OSO 20-m; CO(1-0)
Figure 10 – continued An extended version of Figure 2. Gaussian double peak profile fit (green) to CO spectra from single dish observations (blue). The meannoise estimate ( ± 𝜎 ) is shown in the top-left corner. The red vertical lines are at 𝑣 (solid) and bound 𝑊 (dashed), defined in Equation 3. The grey bandsindicate the 67% confidence interval in 𝑊 . ISDOM: The Δ 𝑉 CO − 𝑀 BH relation - Supplemental Material )5051015 T m b ( m K ) )50510152025 T m b ( m K ) (a) ARK 120 )1510505101520 T m b ( m K ) )1050510152025 T m b ( m K ) (b) ESO558-009 )1050510 T m b ( m K ) )50510152025 T m b ( m K ) (c) H0507+164; No reliable 𝑅 e or 𝐷 measurements are available for this galaxy due to the proximity of the foreground star shown. )5051015202530 T m b ( m K ) )105051015202530354045505560 T m b ( m K ) (d) IC 1481 Figure A3.
An extended version of Figure A1. New CO observations from the IRAM 30-m telescope from our programme 191-18. For each galaxy, theleft panel shows the extent of the 30-m beam at CO(1-0) (red, solid) and CO(2-1) (red, dashed) overlaid on an image of the galaxy from DSS. The areaenclosed by one effective radius (from van den Bosch 2016; green, solid) and 𝐷 (from HyperLEDA; green, dashed), adopting the inclination and positionangle recorded in HyperLEDA and the distance from van den Bosch (2016), is indicated. The central and right panels show the spectrum of the CO(1-0) and CO(2-1) emission lines respectively with the region used to determine the integrated flux shaded. Mark D. Smith et al. )5051015 T m b ( m K ) )5051015 T m b ( m K ) (e) J0437+2456; No 𝑅 e or 𝐷 measurements are available in van den Bosch (2016) or HyperLEDA. )505101520 T m b ( m K ) )50510152025303540455055 T m b ( m K ) (f) MRK 1029 )050100150200250300350 T m b ( m K ) )050100150200250300350400450500550600 T m b ( m K ) (g) NGC 613 )20020406080100120140160180 T m b ( m K ) )020406080100120140160180200220240260 T m b ( m K ) (h) NGC 1300 Figure A3 – continued An extended version of Figure A1. New CO observations from the IRAM 30-m telescope from our programme 191-18. For each galaxy,the left panel shows the extent of the 30-m beam at CO(1-0) (red, solid) and CO(2-1) (red, dashed) overlaid on an image of the galaxy from DSS. The areaenclosed by one effective radius (from van den Bosch 2016; green, solid) and 𝐷 (from HyperLEDA; green, dashed), adopting the inclination and positionangle recorded in HyperLEDA and the distance from van den Bosch (2016), is indicated. The central and right panels show the spectrum of the CO(1-0) and CO(2-1) emission lines respectively with the region used to determine the integrated flux shaded.
ISDOM: The Δ 𝑉 CO − 𝑀 BH relation - Supplemental Material )4202468 T m b ( m K ) )50510 T m b ( m K ) (i) NGC 1497 )020406080100120140160180200220240 T m b ( m K ) )050100150200250300350400450 T m b ( m K ) (j) NGC 1961 )105051015 T m b ( m K ) )5051015 T m b ( m K ) (k) NGC 2179 )050100150 T m b ( m K ) )050100150200 T m b ( m K ) (l) NGC 2748 Figure A3 – continued An extended version of Figure A1. New CO observations from the IRAM 30-m telescope from our programme 191-18. For each galaxy,the left panel shows the extent of the 30-m beam at CO(1-0) (red, solid) and CO(2-1) (red, dashed) overlaid on an image of the galaxy from DSS. The areaenclosed by one effective radius (from van den Bosch 2016; green, solid) and 𝐷 (from HyperLEDA; green, dashed), adopting the inclination and positionangle recorded in HyperLEDA and the distance from van den Bosch (2016), is indicated. The central and right panels show the spectrum of the CO(1-0) and CO(2-1) emission lines respectively with the region used to determine the integrated flux shaded. Mark D. Smith et al. )0510 T m b ( m K ) )5051015 T m b ( m K ) (m) NGC 2911 )50510152025 T m b ( m K ) )02040 T m b ( m K ) (n) NGC 2960 )505101520 T m b ( m K ) )50510152025 T m b ( m K ) (o) NGC 4151 )20246 T m b ( m K ) )64202468 T m b ( m K ) (p) NGC 6264 Figure A3 – continued An extended version of Figure A1. New CO observations from the IRAM 30-m telescope from our programme 191-18. For each galaxy,the left panel shows the extent of the 30-m beam at CO(1-0) (red, solid) and CO(2-1) (red, dashed) overlaid on an image of the galaxy from DSS. The areaenclosed by one effective radius (from van den Bosch 2016; green, solid) and 𝐷 (from HyperLEDA; green, dashed), adopting the inclination and positionangle recorded in HyperLEDA and the distance from van den Bosch (2016), is indicated. The central and right panels show the spectrum of the CO(1-0) and CO(2-1) emission lines respectively with the region used to determine the integrated flux shaded.
ISDOM: The Δ 𝑉 CO − 𝑀 BH relation - Supplemental Material )50510 T m b ( m K ) )5051015 T m b ( m K ) (q) NGC 6323 )1050510152025 T m b ( m K ) )5051015202530 T m b ( m K ) (r) NGC 6500 )5051015 T m b ( m K ) )1050510152025 T m b ( m K ) (s) NGC 7682 )50510 T m b ( m K ) )5051015 T m b ( m K ) (t) UGC 1214 Figure A3 – continued An extended version of Figure A1. New CO observations from the IRAM 30-m telescope from our programme 191-18. For each galaxy,the left panel shows the extent of the 30-m beam at CO(1-0) (red, solid) and CO(2-1) (red, dashed) overlaid on an image of the galaxy from DSS. The areaenclosed by one effective radius (from van den Bosch 2016; green, solid) and 𝐷 (from HyperLEDA; green, dashed), adopting the inclination and positionangle recorded in HyperLEDA and the distance from van den Bosch (2016), is indicated. The central and right panels show the spectrum of the CO(1-0) and CO(2-1) emission lines respectively with the region used to determine the integrated flux shaded. Mark D. Smith et al. )10505101520253035404550 T m b ( m K ) )10505101520253035404550556065 T m b ( m K ) (u) UGC 3789 )50510152025 T m b ( m K ) )5051015 T m b ( m K ) (v) UGC 6093 Figure A3 – continued An extended version of Figure A1. New CO observations from the IRAM 30-m telescope from our programme 191-18. For each galaxy,the left panel shows the extent of the 30-m beam at CO(1-0) (red, solid) and CO(2-1) (red, dashed) overlaid on an image of the galaxy from DSS. The areaenclosed by one effective radius (from van den Bosch 2016; green, solid) and 𝐷 (from HyperLEDA; green, dashed), adopting the inclination and positionangle recorded in HyperLEDA and the distance from van den Bosch (2016), is indicated. The central and right panels show the spectrum of the CO(1-0) and CO(2-1) emission lines respectively with the region used to determine the integrated flux shaded.
ISDOM: The Δ 𝑉 CO − 𝑀 BH relation - Supplemental Material )05 T m b ( m K ) (a) MRK 279 )105051015202530 T m b ( m K ) (b) NGC 2273 )050100150200250300 T m b ( m K ) (c) NGC 3079; The inclination of the 𝑅 e and 𝐷 contours has been artificially reduced from the90 ° recorded in HyperLEDA to make them distinguishable. )5051015202530 T m b ( m K ) (d) UGC 3789 Figure A4.
An extended version of Figure A2. New CO observations from the OSO 20-m telescope from our programme 2018-04a. For each galaxy, the leftpanel shows the extent of the 20-m beam at CO(1-0) (red, solid) overlaid on an image of the galaxy from DSS. The area enclosed by one effective radius(from van den Bosch 2016; green, solid) and 𝐷 (from HyperLEDA; green, dashed), adopting the inclination and position angle recorded in HyperLEDA andthe distance from van den Bosch (2016), is indicated. The right panel shows the spectrum of the12