The JCMT Nearby Galaxies Legacy Survey IV. Velocity Dispersions in the Molecular Interstellar Medium in Spiral Galaxies
C. D. Wilson, B. E. Warren, J. Irwin, J. H. Knapen, F. P. Israel, S. Serjeant, D. Attewell, G. J. Bendo, E. Brinks, H. M. Butner, D. L. Clements, J. Leech, H. E. Matthews, S. Muehle, A. M. J. Mortier, T. J. Parkin, G. Petitpas, B. K. Tan, R. P. J. Tilanus, A. Usero, M. Vaccari, P. van der Werf, T. Wiegert, M. Zhu
aa r X i v : . [ a s t r o - ph . C O ] S e p Mon. Not. R. Astron. Soc. , 1–16 (2010) Printed 22 October 2018 (MN L A TEX style file v2.2)
The JCMT Nearby Galaxies Legacy Survey IV. VelocityDispersions in the Molecular Interstellar Medium in SpiralGalaxies
C. D. Wilson , B. E. Warren , , J. Irwin , J. H. Knapen , , F. P. Israel ,S. Serjeant , D. Attewell , G. J. Bendo , E. Brinks , H. M. Butner , D. L. Clements ,J. Leech , H. E. Matthews , S. M¨uhle , A. M. J. Mortier , T. J. Parkin ,G. Petitpas , B. K. Tan , R. P. J. Tilanus , , A. Usero , M. Vaccari ,P. van der Werf , T. Wiegert , M. Zhu Department of Physics & Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada Currently at the International Centre for Radio Astronomy Research, University of Western Australia Department of Physics, Engineering Physics and Astronomy, Queen’s University, Kingston, Ontario K7L 3N6, Canada Instituto de Astrof´ısica de Canarias, E-38200 La Laguna, Tenerife, Spain Departamento de Astrof´ısica, Universidad de La Laguna, E-38205 La Laguna, Tenerife, Spain Sterrewacht Leiden, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands Department of Physics & Astronomy, The Open University, Milton Keynes MK7 6AA, United Kingdom Astrophysics Group, Imperial College, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, United Kingdom Centre for Astrophysics Research, University of Hertfordshire, College Lane, Hatfield AL10 9AB, United Kingdom Department of Physics and Astronomy, James Madison University, MSC 4502 - 901 Carrier Drive, Harrisonburg, VA 22807, U.S.A. Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, United Kingdom National Research Council Canada, Herzberg Institute of Astrophysics, DRAO, P.O. Box 248, White Lake Road, Penticton,British Columbia V2A 69J, Canada Joint Institute for VLBI in Europe, Postbus 2, 7990 AA Dwingeloo, The Netherlands Scottish Universities Physics Alliance, Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill,Edinburgh, EH9 3HJ, UK Harvard-Smithsonian Center for Astrophysics, 60 Garden St., MS-78, Cambridge, MA 02138, USA Joint Astronomy Centre, 660 N. A’ohoku Pl., University Park, Hilo, HI 96720, USA Netherlands Organisation for Scientific Research, Laan van Nieuw Oost-Indie 300, NL-2509 AC The Hague, The Netherlands Observatorio de Madrid, OAN, Alfonso XII, 3, E-28014 Madrid, Spain Dipartimento di Astronomia, Universit´a di Padova, Vicolo dell’Osservatorio 5, 35122 Padua, Italy Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, China
11 June 2010
ABSTRACT
An analysis of large-area CO J =3-2 maps from the James Clerk Maxwell Telescope for12 nearby spiral galaxies reveals low velocity dispersions in the molecular componentof the interstellar medium. The three lowest luminosity galaxies show a relatively flatvelocity dispersion as a function of radius while the remaining nine galaxies showa central peak with a radial fall-off within 0 . − . r . Correcting for the averagecontribution due to the internal velocity dispersions of a population of giant molecularclouds, the average cloud-cloud velocity dispersion across the galactic disks is 6 . ± . − (standard deviation 2.9 km s − ), in reasonable agreement with previousmeasurements for the Galaxy and M33. The cloud-cloud velocity dispersion derivedfrom the CO data is on average two times smaller than the HI velocity dispersionmeasured in the same galaxies. The low cloud-cloud velocity dispersion implies thatthe molecular gas is the critical component determining the stability of the galacticdisk against gravitational collapse, especially in those regions of the disk which are H dominated. The cloud-cloud velocity dispersion shows a significant positive correlationwith both the far-infrared luminosity, which traces the star formation activity, and theK-band absolute magnitude, which traces the total stellar mass. For three galaxies inthe Virgo cluster, smoothing the data to a resolution of 4.5 kpc (to match the typicalresolution of high redshift CO observations) increases the measured velocity dispersionby roughly a factor of two, comparable to the dispersion measured recently in a normalgalaxy at z = 1. This comparison suggests that the mass and star formation ratesurface densities may be similar in galaxies from z = 0 − z = 1 may be partly due to the presence of physically largermolecular gas disks. Key words: galaxies: ISM — galaxies: individual(NGC 628, NGC 2403, NGC 3184,NGC 3938, NGC 4254, NGC 4303, NGC 4321, NGC 4501, NGC 4535, NGC 4736,NGC 4826, NGC 5055) – galaxies: kinematics and dynamics — galaxies: spiral – ISM:molecules – stars: formation c (cid:13) C. D. Wilson et al.
The vertical structure of the interstellar medium is de-termined by a delicate balance between gravity and pres-sure. The concentration of mass in the stellar disk dragsthe gas into a thin disk whose vertical scale height is con-trolled by the velocity dispersion. The velocity dispersionof the gas is also an important parameter for star for-mation laws based on the Toomre Q criterion (Toomre1964; Kennicutt 1989). The atomic phase of the interstel-lar medium (ISM) has been well studied and interpreted,most recently by Tamburro et al. (2009, see below). How-ever, the velocity dispersion of the star forming molecu-lar gas is much less well understood, although the avail-able data are consistent with a significantly thinner anddynamically colder molecular disk (Stark & Brand 1989;Wilson & Scoville 1990; Combes & Becquaert 1997).Determining the velocity dispersion of the moleculargas in the Galaxy is complicated by our location within theplane of the disk and the difficulty in removing the effectsof streaming motions associated with spiral arms. Nearby,relatively face-on galaxies are better targets, provided suffi-cient sensitivity and spectral and spatial resolution can beachieved. However, an additional complicating factor in anyanalysis is the fact that the observed velocity dispersions arenot significantly larger than the internal velocity dispersionof an individual giant molecular cloud (GMC). For example,Solomon et al. (1987) measure internal velocity dispersionsranging from 1 to 8 km s − and a relation between internalvelocity dispersion and cloud mass that goes as M = 2000 σ v .Certainly the net effect of the internal velocity dispersion ofa population of giant molecular clouds in the beam needsto be considered in an analysis of the cloud-cloud velocitydispersion of nearby, near face-on galaxies.For our own Galaxy, Clemens (1985) obtained a one-dimensional cloud-cloud velocity dispersion of 3.0 km s − ,significantly smaller than the value of 7-9 km s − obtainedby Stark (1984). Stark & Brand (1989) argue that the ve-locity dispersion measured by Clemens (1985) is actuallythe internal velocity dispersion of individual clouds and ob-tain a cloud-cloud velocity dispersion of 7 . ± . − for clouds within 3 kpc of the Sun. Although this mea-surement includes small-scale streaming motions, they arguethat the true value is only 20% smaller when the streamingmotions are removed (Stark & Brand 1989). More recentlyStark & Lee (2005, 2006) have re-derived the scale height ofthe molecular gas to be 35 pc for clouds less massive than2 × M ⊙ and only 20 pc for clouds more massive than thislimit. This scale height of 20 pc implies a one-dimensionalcloud-cloud velocity dispersion of just 4 km s − for themore massive molecular clouds. Combes & Becquaert (1997)point out that, given the observed scale heights of HI andCO in the Galaxy and a velocity dispersion of 9 km s − in the atomic gas, we would expect a cloud-cloud velocitydispersion of only 2.4 km s − in the molecular gas, a valuewhich is significantly smaller than any of the measurements.There are relatively few measurements of the ve-locity dispersion of the molecular gas in other galax-ies. Wilson & Scoville (1990) used a combination of in-terferometric observations of individual giant molecularclouds with single dish observations of M33 to mea-sure a cloud-cloud velocity dispersion of 5 ± − . Combes & Becquaert (1997) observed NGC 628 and NGC3938 using the CO J =1-0 and J =2-1 lines and observed ve-locity dispersions of 6 km s − and 8.5 km s − , respectively.They used gaussian fits to the observed line widths andcorrected for saturation effects (Garc´ıa-Burillo et al. 1993).Walsh et al. (2002) made CO J =1-0 and J =3-2 observationsof NGC 6946 and measured velocity dispersions from secondmoment maps of 8 . ± . − and 6 . ± . − in thetwo lines. Neither of these two studies (Combes & Becquaert1997; Walsh et al. 2002) attempted to correct for the inter-nal velocity dispersion of individual GMCs, and so thesemeasurements are upper limits to the cloud-cloud velocitydispersion.There have been a number of theoretical attempts tomodel the cloud-cloud velocity dispersion in the Galaxy.Jog & Ostriker (1988) propose that cloud-cloud gravita-tional scattering in a differentially rotating galactic disk actsto increase the random kinetic energy of the cloud pop-ulation. In this model, inelastic collisions between cloudsact as an energy sink, resulting in an equilibrium valuefor the one-dimensional velocity dispersion of 5-7 km s − .Gammie, Ostriker & Jog (1991) extended this work usingboth analytical and numerical analyses and obtain a valueof 5 km s − for the two-dimensional velocity dispersion inthe plane of the disk. Thomasson et al. (1991) performedN body simulations of clouds and stars which include in-elastic cloud collisions but not close 2-body gravitationalencounters. They find typical velocity dispersions of 3 kms − which increase in galaxies with stronger spiral structure.More recently, Tasker & Tan (2009) have developed a threedimensional model including ISM cooling to 300 K with aresolution of 8 pc and find typical velocity dispersions of 10km s − for a model of the Milky Way.Although there have been relatively few measurementsof the velocity dispersion in the molecular gas in galaxies,the velocity dispersion of the atomic gas has been well stud-ied (see Tamburro et al. 2009, and references therein). Mostrecently, the THINGS survey (Walter et al. 2008) has pro-duced high-resolution HI maps of 34 spiral and irregulargalaxies with distances less than 11 Mpc. The typical ve-locity dispersion in the atomic gas at radii between r / r is 11 ± − for galaxies with inclinations lessthan 60 o (Leroy et al. 2008). Tamburro et al. (2009) find anHI line width that falls off systematically with radius whichthey link to the energy provided by supernovae linked torecent star formation. They also find a characteristic HI ve-locity dispersion of 10 ± − at r , which often marksthe extent of significant star formation in the disk.In this paper, we present measurements of the velocitydispersion for the molecular component of the interstellarmedium using data from the JCMT Nearby Galaxies LegacySurvey (NGLS) as well as a follow-up program on HI-richspiral galaxies in the Virgo Cluster. We use new, wide-areaobservations of the CO J =3-2 emission for 12 large spiralgalaxies with inclinations < o and distances <
17 Mpc. Wediscuss the observations, data reduction, and analysis meth-ods used in §
2. A more detailed comparison with the resultsof Combes & Becquaert (1997) is given in Appendix A. In §
3, we discuss the observed values of the velocity dispersionof the CO J =3-2 transition and the correction factor nec-essary due to the non-trivial internal velocity dispersion ofindividual giant molecular clouds. The potential need to cor- c (cid:13) , 1–16 he JCMT Nearby Galaxies Legacy Survey IV. Velocity Dispersions in the Molecular Gas rect for a non-isotropic velocity dispersion in galaxies withinclinations larger than about 30 o is discussed in AppendixB. In §
4, we compare our results with recent observationsof the velocity dispersion of the atomic gas component fromthe THINGS survey (Walter et al. 2008), investigate corre-lations of the velocity dispersion of the molecular gas withglobal galaxy properties such as mass and star formationrate, discuss the implications for understanding disk stabil-ity in galaxies, and compare our data with recent observa-tions of spiral galaxies at z = 1. We give our conclusions in § J =3-2 data The CO J =3-2 observations were obtained as part of theJCMT Nearby Galaxies Legacy Survey (NGLS) a , which isobserving an HI flux limited sample of 155 galaxies within25 Mpc (Wilson et al. 2009). The angular resolution of theJCMT at this frequency is 14.5 ′′ , which corresponds to alinear resolution ranging from 0.2 to 1.2 kpc for the galax-ies in our sample. From the large ( D > ′ ) spiral galaxiesobserved by the NGLS, we selected 9 galaxies with inclina-tions smaller than 60 o to study the velocity dispersion. Eightadditional large galaxies from the NGLS with low inclina-tions (IC 2574, UGC 04305, NGC 3031, NGC 3351, NGC4450, NGC 4579, and NGC 4725) did not have sufficientlystrong or extended detections in CO J=3-2 to be useful forthis analysis. To this sample we added three spiral galax-ies in the Virgo Cluster (NGC 4303, NGC 4501, and NGC4535) which are not part of the NGLS survey but which havebeen observed in a similar manner. (A fourth Virgo Clustergalaxy, NGC 4548, did not have a strong enough detectionto be useful here.) These galaxies were observed as part of afollow-up program to the NGLS (JCMT proposal M09AC05,PI C. Wilson) to obtain CO J=3-2 observations to completethe sample of Virgo spiral galaxies with HI fluxes > . − . The data for these three galaxies were obtainedbetween 2009 February 14 and 2009 May 26.Relevant properties of the 12 galaxies are given in Ta-ble 1. All 12 galaxies were observed in raster mapping modeto cover a rectangular area corresponding to D / ∗ A ) at a spec-tral resolution of 20 km s − . We used the 16 pixel arrayreceiver HARP-B (Buckle et al. 2009) with the ACSIS cor-relator configured to have a bandwidth of 1 GHz and a reso-lution of 0.488 MHz (0.43 km s − at the frequency of the CO J =3-2 transition). The combination of uniquely high veloc-ity resolution and large mapping area is critical for accuratemeasurements of the velocity dispersion in the molecular in-terstellar medium.Details of the reduction of the CO J =3-2 data are givenin Wilson et al. (2009) and Warren et al. (2010) and so wediscuss here only the most important processing steps andthose steps that differed from the previous analysis. The in-dividual raw data files were flagged to remove data fromany of the 16 individual receptors with bad baselines andthen the scans were combined into a data cube using a a sinc( πx )sinc( kπx ) kernel as the weighting function to deter-mine the contribution of individual receptors to each pixel inthe final map. The pixel size in the maps is 7.276 ′′ . A maskwas created to identify line-free regions of the data cubeand a first-order baseline was fit to those line-free regionsand subtracted from the cube.We then used the clumpfind algorithm (Williams et al.1994) implemented as part of the CUPID b (Berry et al.2007) task findclumps to identify regions with emission withsignal-to-noise greater than 2.5 in a data cube that had beenboxcar smoothed by 3x3 spatial pixels and 25 velocity chan-nels. Moment maps were created from the original data cubeafter applying the mask created by findclumps. The momentmaps which are the focus of this paper are the moment 2maps, which measure the velocity dispersion, σ v , for eachpixel in the image using σ v = p Σ T i ( v i − v ) / Σ T i where v i and T i are the velocity and temperature of a givenvelocity channel and v is the intensity weighted mean ve-locity of that pixel. This method of calculating the velocitydispersion differs from that used by Combes & Becquaert(1997), who fit gaussian profiles to the CO lines. How-ever, in the limit of gaussian lines with a high signal-to-noise ratio, the values from the moment 2 maps shouldagree with the results from fitting a gaussian directly tothe line profiles. A more detailed comparison of our datawith Combes & Becquaert (1997) is given in Appendix A.Moment 2 maps are often used to determine the velocitydispersion in the atomic gas, although this method is mostreliable for simple line shapes, as warped disks and HI atlarge scale heights can distort the line profiles (de Blok et al.2008).Because we were using a relatively low signal-to-noisethreshold in creating our masks, the final moment 2 mapssometimes appeared to contain spuriously high values typi-cally in the outer portions of the map. These regions appearwhite in Figures 1 and 2. These values would bias the dis-persions upward if they were included in our averages. For5 galaxies in our sample, (NGC 4321, NGC 628, NGC 2403,NGC 3184, and NGC 4826), we applied an upper thresholdto remove pixels with values that were higher than the high-est value seen in the central part of the galaxy. The thresh-olding values used were 15 km s − for NGC 628, 25 km s − for NGC 2403 and NGC 3184, 52 km s − for NGC 4321, and85 km s − for NGC 4826. We also applied a threshold cutof 65 km s − to NGC 4501 but very high values persistedin the north-western portion of the map (see below); the ve-locity dispersions in Table 1 are measured in the south-eastportion of the map only. For NGC 5055, we used a targetedthreshold to remove the block of high values seen in thenorth-east portion of the map. For the 6 galaxies (NGC 628, NGC 2403, NGC 3184, NGC4736, NGC 4826, and NGC 5055) that are in common be- b CUPID is part of the Starlink (Currie et al. 2008)software package, which is available for download fromhttp://starlink.jach.hawaii.educ (cid:13) , 1–16
C. D. Wilson et al.
Figure 1. CO J =3-2 velocity dispersion for six galaxies which are not members of the Virgo cluster. (a) NGC 628. Contour levels are2.5, 5, 10 km s − and the colour scale peak is 15 km s − . (b) NGC 3184. Contour levels are 5, 10, 15 km s − and the colour scale peakis 25 km s − . (c) NGC 3938. Contour levels and colour scale are the same as for NGC 3184. (d) NGC 4736. Contour levels are 10, 20,... 60 km s − and the colour scale peak is 85 km s − . (e) NGC 4826. Contour levels and colour scale are the same as for NGC 4736. (f)NGC 5055. Contour levels and colour scale are the same as for NGC 4736. c (cid:13) , 1–16 he JCMT Nearby Galaxies Legacy Survey IV. Velocity Dispersions in the Molecular Gas Figure 2. CO J =3-2 velocity dispersion for five galaxies which are members of the Virgo cluster and NGC 2403, which is the closestgalaxy in our sample. Colour scale runs from 0 (black) to 50 km s − (white) and contour levels are 10, 20, 30, 40, 50 km s − unlessotherwise noted. (a) NGC 4254. (b) NGC 4303. (c) NGC 4321. (d) NGC 4501. Contour levels are 10, 20, ... 60 km s − and the colourscale peak is 65 km s − . (e) NGC 4535. (f) NGC 2403. Contour levels are 5, 10, 15 km s − and the colour scale peak is 25 km s − .c (cid:13) , 1–16 C. D. Wilson et al.
Table 1.
Galaxy Properties and Velocity DispersionsGalaxy V hel Type a D a i a P A b K ( tot ) c log L F IRd
Distance e σ obsf σ c − cg σ HIh (km s − ) ( ′ ) ( o ) ( o ) (mag) (L ⊙ ) ( Mpc ) (km s − ) (km s − ) (km s − )NGC 628 648 SA(s)c 10.5 7 20 6.84 9.55 7.3 4 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . i NGC 4254 2412 Sa(s)c 5.4 29 56 6.93 10.62 16.7 9 . ± . . ± . . ± . . ± . ±
11 11 . ± . ±
15 20 ± . ± . . ± . ± . ± . ±
11 13 ± . ± . . ± . a Buta et al. (2007) b Position angle used for radial averages. NGC 628, NGC 3184: Tamburro et al. (2008); NGC 2403, NGC 4736, NGC 4826,NGC 5055: de Blok et al. (2008); NGC 3938: Paturel et al. (2000); NGC 4254, NGC 4303, NGC 4501, NGC 4535:(Cayatte et al. 1990); NGC 4321: Knapen et al. (1993). c K-band total apparent magnitude from Jarrett et al. (2003). d From Sanders et al. (2003) adjusted for the distances adopted here. e NGC 628: Karachentsev et al. (2004); NGC 2403: Freedman et al. (2001); NGC3184: Leonard et al. (2002); NGC 3938,NGC 5055: distance calculated using Hubble flow distance with velocity corrected for Virgo infall (Mould et al. 2000) and H o = 73 km s − Mpc − ; Virgo Cluster: Mei et al. (2007); NGC 4736, NGC 4826: Tonry et al. (2001). f Observed CO J =3-2 velocity dispersion and standard deviation. Regions of high velocity dispersion in the outer portionsof the disk were masked before calculating the velocity dispersion (see text). Excludes a 5.3 kpc diameter region in the centre of eachVirgo galaxy (9 pixels), NGC 3938 (11 pixels) and NGC 5055 (19 pixels). All pixels are included for NGC 628, NGC2403,and NGC 3184. For NGC 4736 and NGC 4826, a 9 pixel region is excluded to give an upper limit to the outer disk velocity dispersion(see text). Note that the uncertainty in the mean for σ obs is the same as for σ c − c . g Mean cloud-cloud velocity dispersion and the uncertainty in the mean corrected for the contribution from the internalvelocity dispersion of individual giant molecular clouds (see text). Note that the uncertainty in the mean is calculated from thestandard deviation given in the previous column by dividing by √ N , where N is the number of measurements for a given galaxy. h HI velocity dispersion measured from naturally weighted maps from Walter et al. (2008) over same area as the COmeasurement. i From van der Kruit & Shostak (1982). tween our sample and the THINGS sample (Walter et al.2008), we can compare the velocity dispersions in the atomicand molecular gas directly. The moment 2 maps for theTHINGS sample were produced using a slightly differentmasking technique (Walter et al. 2008) than the one weadopted for our CO analysis. In the THINGS processing, thedata are first smoothed to a resolution of 30 ′′ . A mask is thenmade keeping only those pixels and velocity channels (widtheither 2.6 or 5.2 km s − ) where the emission exceeds 2 σ in3 adjacent velocity channels. We used the natural weightedmaps of the HI velocity dispersion and measure the disper-sion over the same region in which the CO dispersions havebeen measured. These velocity dispersions are also given inTable 1. Note that these HI dispersions are somewhat largerthan the typical value of 11 ± − given in Leroy et al.(2008) because they are measured in the inner rather thanthe outer disks of the galaxies. The observed CO velocity dispersion maps are shown in Fig-ures 1 and 2. Figures 3 and 4 show the observed velocitydispersion as a function of radius for the 12 galaxies in our sample. Beam smearing is expected to have an effect onlyon the measured velocity dispersions for the central pixel ineach plot. Three of the galaxies (NGC 628, NGC 2403, andNGC 3184) show very flat profiles as a function of radius.These late type spirals are also the least luminous and sopresumably are also the least massive galaxies in our sam-ple. The remaining 9 galaxies show a central peak in thevelocity dispersion extending to 0 . − . r . We attributepart of this increase to the effects of a steeply rising rotationcurve at our relatively low (0.2-1.2 kpc) spatial resolution inthese galaxies. Thus, for these galaxies, we measure the aver-age velocity dispersion in the outer disk excluding a centralcircular region. The exclusion aperture was chosen by ex-amining the individual velocity dispersion maps to identifythe smallest aperture that would exclude the region of mostobviously enhanced dispersion. We found that a diameter of5.3 kpc (9 pixels or 65 ′′ at the distance of Virgo) worked wellfor all five galaxies in the Virgo cluster and that a similarphysical region was appropriate for the other galaxies in oursample. However, the maps of NGC 4736 and NGC 4826contain no data at larger radii, and so for these two galaxieswe quote disk velocity dispersions excluding only a central 9pixel diameter region. The disk velocity dispersions of thesetwo galaxies are likely biased to be somewhat higher thanthose of the other galaxies in our sample and thus we do not c (cid:13) , 1–16 he JCMT Nearby Galaxies Legacy Survey IV. Velocity Dispersions in the Molecular Gas Figure 3.
Observed CO J =3-2 velocity dispersion as a function of radius normalized by r . These velocity dispersions have not beencorrected for any contribution from the internal velocity dispersion of individual giant molecular clouds (see text). Where appropriate,the central region excluded from calculating the disk-averaged velocity dispersion is indicated by the dashed line. Figure 4.
Observed CO J =3-2 velocity dispersion as a function of radius normalized by r , showing nine galaxies on a single plot.Data points with r < .
65 kpc are not plotted for the 6 galaxies with central peaks in the velocity dispersion.c (cid:13) , 1–16
C. D. Wilson et al. include them in calculating the average outer disk velocitydispersion.The average observed velocity dispersions in the molec-ular gas measured for the 12 galaxies in our sample are givenin Table 1. These velocity dispersions are consistent withprevious measurements for the Milky Way (Stark & Brand1989), M33, (Wilson & Scoville 1990) and other nearbygalaxies (Combes & Becquaert 1997; Walsh et al. 2002).The observed velocity dispersion in the molecular gas diskranges from a low of 4.1 km s − in NGC 628 to a high of20.1 km s − in NGC 4501. We exclude NGC 4736 and NGC4826 from our averages because we can only trace the veloc-ity dispersions in the inner region where the profile is stillrising steeply. We further exclude NGC 4501 because its veryhigh velocity dispersion and evidence for double peaked lineprofiles in the north-west portion of the disk suggest thatthe molecular gas has been affected by the same ram pres-sure effects seen in HI (Vollmer et al. 2008). The averageobserved value for the remaining 9 galaxies is 7 . ± . − (standard deviation 2.6 km s − ), 50% smaller than theaverage of 11 ± − measured for the atomic gas inthe outer disks of spiral galaxies (Leroy et al. 2008). If wecompare the atomic and molecular velocity dispersions inthe same region of the disk (Table 1), the observed veloc-ity dispersion in the molecular gas is on average ∼ The low values measured for the velocity dispersion, par-ticularly for NGC 628 and NGC 3938, lead us to considerthe effect of internal velocity dispersions of individual giantmolecular clouds on the observed velocity dispersion. A sec-ond complicating effect, that of an anisotropy between thevertical and in-plane motions of the GMCs, would be ex-pected to produce a correlation of velocity dispersion withinclination, which is not seen in our data (Figure B1). Nev-ertheless, we discuss the potential magnitude of this effectin Appendix B.Individual giant molecular clouds have internal velocitydispersions that are substantially larger than the thermalline-widths expected for gas with physical temperatures of10-30 K. In the study of Solomon et al. (1987), individualGMCs show internal velocity dispersions ranging from 1-8 km s − . These internal velocity dispersions are obtainedfrom an intensity-weighted measure of the dispersion in ra-dial velocity within a single cloud and thus are directly com-parable (in technique) to the intensity-weighted dispersionsaveraged over the galactic disk presented here. What weneed is an estimate of the contribution of the internal ve-locity dispersions of an ensemble of GMCs with a range ofmasses to the observed velocity dispersion in the disk. Withthis value, it is easy to show that the observed velocity dis-persion, σ v , is given by σ v = σ c − c + σ int where σ int is themass-weighted average internal velocity dispersion for ourensemble of clouds and σ c − c is the value we are interestedin measuring, that is, the cloud-cloud velocity dispersion.It is well known that the cloud internal velocity dis-persion, σ int , relates to the cloud mass as M ∝ σ int , asfirst proposed by Henriksen & Turner (1984). Observation-ally, Solomon et al. (1987) find that the internal velocity dispersion σ int (in km s − ) relates to the cloud mass M (inM ⊙ ) as M = 2000 σ int . If we assume a cloud mass function dN/dm ∝ m − α , then we can estimate the mass-weighted av-erage internal velocity dispersion for an ensemble of cloudsbetween M low and M high . Since column density is propor-tional to intensity for the CO lines (Strong et al. 1988), amass-weighted average is also equivalent to an intensity-weighted average. The mass-weighted square of the internalvelocity dispersion is then R mσ int dN/ R mdN which, usingthe relation between σ int and M given by Solomon et al.(1987) and assuming α = 2, reduces to σ int = 144 . − α . − α M . − αhigh − M . − αlow M − αhigh − M − αlow For α = 1 . M high = 10 M ⊙ and M low = 10 M ⊙ (e.g., Solomon et al. 1987), σ int = 3 . − . The exact result clearly depends on the details of themodel.Interestingly, this estimate of the average cloud internalvelocity dispersion is comparable to the value of 4.1 km s − observed in the disk of NGC 628. The average CO J =3-2intensity in NGC 628 of 0.8 K km s − is the lowest inten-sity in our sample and translates into an average mass perJCMT beam of only 4 × M ⊙ . For a GMC mass func-tion with slope α = 1 .
5, this surface density translates intoan average of just 10 clouds with 10 < M < M ⊙ perbeam. This calculation suggests that, although the numberof massive ( > M ⊙ ) GMCs per beam may be subject tosmall number statistics in NGC 628, their effect on the veloc-ity dispersion should be observable on average if such largeclouds are present in NGC 628. This analysis suggests thatNGC 628 is likely deficient the largest molecular clouds; ifwe instead limit the maximum cloud mass to 10 M ⊙ , thenthe mass-weighted average internal velocity dispersion re-duces to σ int = 2 . − . The larger average integratedintensities and observed velocity dispersions suggests thatthe molecular cloud mass spectrum is likely to be fully pop-ulated in the remaining galaxies in our sample. Thus, incorrecting the observed velocity dispersions for the effectsof internal cloud velocity dispersions, we use a value for σ int of 2.2 km s − for NGC 628 and 3.5 km s − for the rest ofthe sample. The corrected values for the cloud-cloud velocitydispersion are given in Table 1 along with the uncertaintyin the mean cloud-cloud velocity dispersion for each galaxy.The uncertainty in the mean has been calculated assumingthat the errors are normally distributed, so that the uncer-tainty in the mean is given by the standard deviation dividedby √ N , where N is the number of measurements for a givengalaxy. Based on the discussion in the previous section, the ob-served velocity dispersion includes both a contribution fromthe internal velocity dispersion of individual giant molecularclouds as well as a contribution from the cloud-cloud velocitydispersion. It is this second quantity, the cloud-cloud veloc-ity dispersion, which is of interest for determining the molec-ular gas scale height, analysing the stability of the gas disk,etc. The small observed velocity dispersions imply that the c (cid:13) , 1–16 he JCMT Nearby Galaxies Legacy Survey IV. Velocity Dispersions in the Molecular Gas correction for the internal velocity dispersion of the cloudsis not negligible. Correcting for the average internal cloudvelocity dispersion as discussed in § − . Again excluding NGC 4501, NGC 4736, andNGC 4826, we obtain an average value of 6 . ± . − (standard deviation 2.9 km s − ). The average cloud-cloud velocity dispersion in the molecu-lar gas in this group of spiral galaxies of 6 . ± . − isslightly smaller than previous estimates for external galaxieswhich did not take the effect of internal cloud dispersion intoaccount (Combes & Becquaert 1997; Walsh et al. 2002), butis comparable to recent measurements for the cloud-clouddispersion of massive clouds in the Galaxy (Stark & Lee2006) and in M33 (Wilson & Scoville 1990). An additional possible concern in interpreting the CO data isthe high optical depth of the CO line. Since we are interestedin the cloud-cloud velocity dispersion, it is important tocheck whether the surface density of the molecular gas is suf-ficiently high that shielding of one cloud by another at a sim-ilar velocity could affect our measurements. For all but oneof the galaxies in our sample, the projected surface density N H is substantially smaller than the typical surface densityof individual giant molecular clouds ( N H = 1 . ± . × cm − , McKee 1989), and thus cloud-cloud shielding is un-likely to be a problem. Only in NGC 4736, where the surfacedensity may be as high as 3 × cm − (assuming a COJ=3-2/J=1-0 line ratio of 0.3 and a CO to H conversionfactor of 2 × cm − (K km s − ) − Strong et al. 1988), isit possible the clouds may shield one another to some degree.However, the actual surface density depends sensitively onthe value that we assume for the CO J=3-2/J=1-0 line ra-tio; if we adopt a value of 0.6 which is more appropriate forthe dense gas, rather than the value of 0.3 found in a directcomparison of CO J=3-2 and J=1-0 maps of NGLS galaxies(Wilson et al. 2009; Warren et al. 2010), then the projecteddisk-averaged column density is similar to that of individualGMCs. Thus, we conclude that we can ignore the possibilityof cloud-cloud shielding in the disks of the galaxies in thissample.
Combes & Becquaert (1997) showed that the molecular andatomic components in NGC 628 and NGC 3938 had verti-cal velocity dispersions that are similar to each other andvirtually constant with radius. As a consequence, the au-thors suggested that the two layers had similar scale heightsand that HI and H simply represent different phases of thesame dynamical component. It is clear, however, from ob-servations of our own Milky Way as well as edge-on galaxiesthat the molecular disk is significantly thinner than the HIdisk. Our observed velocity dispersions are comparable to those found by Combes & Becquaert (1997), although wehave shown that it is necessary to correct for internal ve-locity dispersion to determine the cloud-cloud velocity dis-persion that is relevant for scale height determinations. ForHI, on the other hand, we know that its stable phases occurin both hot diffuse gas as well as colder clouds (the warmneutral medium and cold neutral medium, respectively). Al-though discrete HI clouds are identifiable in our Galaxy (seeLockwood 2001; Stil et al. 2006), the clouds are smaller andwarmer than molecular clouds. Because of the admixture ofcool and warm HI components over the size scale of the beamin external galaxies, similar corrections need not be appliedto the HI velocity dispersions. Also, since the HI is a diffusecollisional medium, its velocity dispersion is assumed to beisotropic (e.g. Malhotra 1995). We have therefore comparedthe observed HI dispersion directly with our cloud-cloud ve-locity dispersion derived from the CO data. The published HI velocity dispersion map for NGC 4501(Vollmer et al. 2008) shows velocity dispersions in the rangeof 10-20 km s − across the extended disk, comparable to thecloud-cloud velocity dispersion (Table 1) over the same area.High resolution HI data have been published for NGC 4321(Knapen et al. 1993) and NGC 4254 (Phookun et al. 1993),but the velocity dispersion maps are not presented; we couldfind no published high resolution HI data for NGC 4303 andNGC 4535. An older measurement of the HI velocity disper-sion of 10 km s − for NGC 3938 (van der Kruit & Shostak1982) is roughly 3 times larger than our derived cloud-cloudvelocity dispersion.We have compared the velocity dispersions in the molec-ular and atomic gas measured over the same regions for sixgalaxies in our sample for which maps of the atomic gasvelocity dispersion are available from the THINGS sample(Walter et al. 2008). On average, the cloud-cloud velocitydispersion determined from CO data is roughly half that ofthe atomic gas. The exception to this trend is NGC 4826,for which the cloud-cloud velocity dispersion is a factor of5 times smaller than the the HI velocity dispersion. How-ever, this galaxy has quite a steep radial gradient in the ob-served velocity dispersion (Figure 3) and so the average diskvalue depends sensitively on what aperture is used. Overall,these results imply that the scale height of the moleculargas is roughly half that of the atomic gas. This estimateof the ratio of the scale heights is roughly consistent withthe estimate of the relative HI and CO scale heights in theMilky Way as discussed in Combes & Becquaert (1997). Weshould note, however, that narrow (4-5 km s − ) HI line com-ponents have been seen in a few Local Group dwarf galax-ies observed with high spatial resolution (Young & Lo 1996,1997; de Blok & Walter 2006). These narrow lines, whichmay represent atomic gas cooling to form the precursors ofGMCs, are typically superimposed on a broader underlyingline which likely represents the overall warm neutral atomicmedium. The infrared luminosity is a useful tracer of the star forma-tion activity within a galaxy (Kennicutt 1998). Enhanced c (cid:13) , 1–16 C. D. Wilson et al. star formation might be expected to increase the veloc-ity dispersion in the interstellar medium via stellar windsand supernova explosions. Indeed, Tamburro et al. (2009)find evidence that supernovae linked to recent star forma-tion are important for maintaining the velocity dispersionin the atomic gas. We find a statistically significant cor-relation (95% confidence level) of both the observed andthe cloud-cloud velocity dispersion with infrared luminosity(Sanders et al. 2003) for the 9 galaxies in our sample. Thus,like the atomic gas, there is some evidence for star forma-tion activity enhancing the velocity dispersion in the densemolecular gas. We also find a statistically significant corre-lation (95% confidence level) of both the observed and thecloud-cloud velocity dispersion with the absolute K-bandand absolute B-band magnitude (Jarrett et al. 2003). As-suming the K-band magnitude traces the total stellar mass,this correlation suggests that the cloud-cloud velocity dis-persion is enhanced in more masssive galaxies. For all thesecorrelations, however, it is important to keep in mind thatwe have compared the average velocity dispersion in thedisk (excluding the central regions) with a global luminos-ity which would include the contribution from the centralregions.There also appears to be a dependence in our sampleof the velocity dispersion on galaxy morphology. We dividedour sample into early (type ab-bc) and late (type c-cd) spi-rals and calculated the average velocity dispersion for eachsub-sample. The average observed dispersion for 6 late-typespirals is 5 . ± . − , while the value for 3 early-typespirals is 9 . ± . − . These two values differ at the 6sigma level. Of course, this dependence on morphology couldbe tracing some other variable in our sample, such as massor star formation activity. In fact, the average infrared lu-minosities differ by a factor of three between the early- andlate-type samples, while the K-band luminosity differs by afactor of four. Thus, it seems most likely that the depen-dence on morphology is driven by differences in the averagestar formation rates and masses between the early and latetype samples. The velocity dispersion of the interstellar medium is animportant parameter in understanding the stability ofgalactic disks against gravitational collapse. Jog & Solomon(1984a,b) showed that a rotating disk composed of two flu-ids with different surface densities and velocity dispersionscan be unstable to perturbations even if each fluid disk isstable on its own. They also showed that a galaxy must betreated as a two fluid system when the colder gaseous com-ponent comprises as little as 10% of the total mass of thesystem. Treating the stellar component as a collisional fluid,they found that the critical velocity dispersion required forstability in this higher dispersion system is larger in thepresence of a second cold fluid than if the stellar system istreated in isolation. Rafikov (2001) considered the case of asingle fluid and multiple collisionless (stellar) components,but found that the stability conditions were quite similar inthe two fluid case whether or not the stellar component wastreated as collisionless.Yang et al. (2007) applied the approach of Rafikov(2001) to compare the location of star forming regions in the Large Magellanic Cloud (LMC) with the disk stability cri-terion. They adopted a gas velocity dispersion of 5 km s − ,very similar to the value found in our sample of spiral galax-ies. They found that there was a much better spatial correla-tion of star forming regions with regions where the disk wasunstable when instability was evaluated using the contribu-tion of both the gas and the stars. Leroy et al. (2008) appliedthe two collisional fluid equation of Rafikov (2001) to a num-ber of galaxies in the THINGS sample (Walter et al. 2008).They adopted a gas velocity dispersion of 11 km s − frommeasurements of the HI component. Similarly to Yang et al.(2007), they found that the Q values were smaller when boththe stars and the gas were included in the analysis; however,they found that the disks were globally stable against largescale perturbations.The results for the molecular velocity dispersion pre-sented here imply that the interstellar medium in spiralgalaxies is itself a multi-fluid system, with the molecular gasdisk being dynamically significantly colder than the atomicgas disk. Since previous analyses have found that the colderof the two components has the larger effect on the disk stabil-ity (Jog & Solomon 1984a), it seems likely that, if we were touse one phase of the ISM in our stability analysis, it shouldbe the dynamically coldest phase, which is the moleculargas. This would be especially true for the inner regions ofthose spiral disks where the ISM mass is predominantly H .The Toomre Q parameter for the combined system tends todecrease as the velocity dispersion of the coldest (gas) com-ponent decreases and as the gas mass fraction (Σ gas / Σ ∗ )increases (Jog & Solomon 1984b; Rafikov 2001). This effectsuggests that the Q values derived by Leroy et al. (2008) arelikely to be significantly larger than the values that would bederived if the molecular gas values for surface density andvelocity dispersion were used in the analysis, a possibilitythat was discussed in Leroy et al. (2008) as well. It wouldbe informative to repeat the stability analysis for the galax-ies in common between our sample and the THINGS sampleto see if the disks remain globally stable as judged by the Q parameter when the cloud-cloud velocity dispersion of themolecular gas is included. We plan to investigate this issuefurther in a future paper.The need to treat the ISM itself as a multi-fluid systemsuggests that we may not be able to separate the discussionof the instabilities in the atomic and molecular phases. Forexample, we might imagine that the Q value for the atomicgas governs the formation of molecular clouds from the HIdisk, while the star formation from those clouds would thenbe governed by the Q value for the molecular disk. How-ever, the two fluid analysis by Jog & Solomon (1984a) andRafikov (2001) implies that the Q value and hence the stabil-ity properties of the atomic disk are affected by the presenceof the dynamically colder molecular disk. In particular, anatomic gas disk with a stable value of Q when considered inisolation might be found to be unstable when the presenceof a relatively small quantity of molecular gas is included. Ofcourse, a complete analysis would include the properties ofthe stellar disk (perhaps multiple components, as in Rafikov2001) in addition to the two fluid components of the ISM.Such an analysis is beyond the scope of this paper. c (cid:13) , 1–16 he JCMT Nearby Galaxies Legacy Survey IV. Velocity Dispersions in the Molecular Gas The scale height of a gaseous component in hydrostatic equi-librium depends on both gravitational and pressure gradi-ents. Gravitational gradients originate in the disk as well asa dark matter halo potential. The pressure will include inter-nal thermal pressure, turbulent pressure and, if important,pressure due to cosmic rays and magnetic fields. At the ra-dius of the Sun in the Milky Way, the magnetic and cosmicray pressures supply about half of the total pressure and thethermal and turbulent pressures supply the remaining half(Hanasz & Lesch 2004). At the temperatures of the molecu-lar components, turbulent pressure dominates over thermalpressure within and between clouds (e.g. Brunt 2003). Inthe HI, thermal pressure likely dominates in the Warm Neu-tral Medium whereas both may be important for the ColdNeutral Medium (Heiles & Troland 2003). Measured veloc-ity dispersions can only probe the dynamical components(thermal and turbulent) and therefore can only predict thescale height of the gas provided that the dynamical compo-nents dominate over the magnetic and cosmic ray pressuresand provided that the disk ISM is in pressure equilibrium.Star formation activity is typically associated with heat-ing sources and sources of turbulence through supernovaeand stellar winds. Most of the galaxies in our sample showa radial decline in the CO velocity dispersion (Figure 4).The velocity dispersion in HI is also a declining functionof radius (Tamburro et al. 2009), although HI disks re-tain significant velocity dispersions outside any star formingdisk (e.g. Sellwood & Balbus 1999; Tamburro et al. 2009).Tamburro et al. (2009) found a good correlation between thekinetic energy of the HI and the star formation rate and sug-gest that supernovae are likely sufficient to maintain the HIvelocity dispersion in regions with significant star formation.The correlation of the cloud-cloud velocity dispersion withthe star formation rate as traced by the infrared luminos-ity suggests that star formation may also be the dominantsource of turbulence in the H -rich parts of spiral disks.However, some galaxies do show a lack of correla-tion between turbulence in the atomic gas and star for-mation as a function of radius. (e.g. Dickey et al. 1990;van Zee & Bryant 1999; Petric & Rupen 2007). The threelowest luminosity galaxies in our sample show a roughlyconstant cloud-cloud velocity dispersion as a function ofradius (see also Combes & Becquaert 1997) These resultssuggest that non-thermal energy input in the form of turbu-lence that is unrelated to star formation may be importantfor understanding the vertical velocity dispersions in disks.Magnetic instabilities may be the most promising sourceof turbulence. Parker instabilities (Parker 1966) are well-known, but seem to require cosmic rays from supernovae astriggers to be most effective (Hanasz & Lesch 2000). Thus,Parker instabilities cannot account for the observed disper-sions seen outside of the active star forming disk, but couldbe important for the inner molecular disks where star forma-tion is occurring. Another possibility is the Balbus-Hawley(or magneto-rotational) instability (Balbus & Hawley 1991,1998), or other instabilities related to magnetic stresses (e.g.Sellwood & Balbus 1999). Tamburro et al. (2009) suggestthat a combination of thermal broadening and magneto-rotational instabilities can account for the HI velocity dis-persion beyond r . Simulations of the magneto-rotational instability by Piontek & Ostriker (2007) for the two-phaseHI component have shown that the turbulent velocity ampli-tude varies as ∝ n − . , where n is the mean density of thecomponent. If this turbulence is dominant in both molecu-lar and atomic gas, then the difference in velocity dispersionbetween the two components may simply relate to their re-spective densities. Observations of the molecular gas content in galaxies atredshifts z = 1 − ∼
10 kpc), significantly moreso than the quasars and submillimeter galaxies (Daddi et al.2010; Tacconi et al. 2010) Given the sensitivity and widefield of view of our observations, it is interesting to examinehow our galaxies would appear if placed at a redshift of 1.We have processed a subset of our galaxies to see whatchanges are produced in an analysis of the velocity disper-sion when the spatial resolution of the data is degraded. Forthree of the brightest galaxies in the Virgo Cluster (NGC4254, NGC 4321, and NGC 4303), we convolved the baseline-subtracted data cube with a 54 ′′ gaussian to achieve an ef-fective beam of 56 ′′ or 4.5 kpc at a distance of 16.7 Mpc.We then constructed moment maps from the smoothed datacube using the methods described in §
2. A comparison of theresulting velocity dispersion maps for NGC 4254 is shownin Figure 5. Depending on how much of the central highdispersion regions is excluded from the analysis, the averagevelocity dispersion in the outer disk of the low resolutionimage is on average twice as large as the value in the highresolution image. Similar increases of about a factor of twoin the average velocity dispersion in the disk are seen forNGC 4321 and NGC 4303. The images also suggest that aplot of velocity dispersion as a function of radius would yieldhigher values at a given radius in the low resolution image.These effects of resolution will need to be taken into accountas we begin to accumulate data on the dense molecular gasproperties in galaxies at high redshift.The average values of 20-30 km s − seen at low res-olution in the disks of these three galaxies are quite simi-lar to the value of ∼
20 km s − found in EGS13035123 byTacconi et al. (2010). EGS13035123 has 10-20 times the starformation rate, H gas mass, and stellar mass comparedto NGC 4254 (Kennicutt et al. 2003; Wilson et al. 2009;Kranz et al. 2003). However, EGS13035123 is also roughlya factor of three larger in its CO radius than NGC 4254(Wilson et al. 2009), which implies that the gas surface den-sity, stellar surface density, and star formation rate surfacedensity inside the molecular disks of these two galaxies are c (cid:13) , 1–16 C. D. Wilson et al.
Figure 5. (a) CO J =3-2 velocity dispersion for NGC 4254 atthe native resolution of the JCMT data (14.5 ′′ or 1.15 kpc at adistance of 16.7 Mpc). Colour scale runs from 0 to 60 km s − and the contours are 10, 20, 30, 40, 50 km s − . (b) CO J =3-2velocity dispersion for NGC 4254 smoothed to a resolution of 4.5kpc (56 ′′ ) to match the resolution of observations of disk galaxiesat z ∼ quite similar. Thus, the similar velocity dispersions betweenthe two galaxies are likely related to the similar mass surfacedensities in the disk. The two galaxies also have quite sim-ilar molecular gas fractions of ∼ .
25 (Tacconi et al. 2010;Wilson et al. 2009; Kranz et al. 2003). This comparison sup-ports a picture where the high star formation rates seen at z = 1 may be at least partly due to the presence of physicallylarger molecular gas disks at this epoch. We have used large-area high velocity resolution CO J =3-2 observations of 12 nearby galaxies to study the verti-cal velocity dispersion in the dense molecular gas. Threeof the galaxies show a roughly constant velocity disper-sion as a function of radius, while the other nine galaxieshave a central peak followed by a fall-off with radius totypically 0 . − . r . Flat velocity dispersion profiles areseen only in some of the late-type spiral galaxies in oursample, and those with flat profiles have the lowest mass.The observed values of the velocity dispersion range from4.1 km s − to 20.1 km s − . These velocity dispersions arecomparable to the internal velocity dispersions of individ-ual giant molecular clouds in our own and other galax-ies (Solomon et al. 1987; Wilson & Scoville 1990). Correct-ing for these internal velocity dispersions yields an averagecloud-cloud velocity dispersion of 6 . ± . − mea-sured over 9 galaxies with good radial profiles. This cloud-cloud velocity dispersion is comparable to recent measure-ments in our own Galaxy (Stark & Lee 2005, 2006) and M33(Wilson & Scoville 1990).A direct comparison with the high resolution HI mapsfrom the THINGS survey (Walter et al. 2008) in six galaxiesshow that the cloud-cloud velocity dispersion is on averagetwice as small as the velocity dispersion of the atomic gas,which implies a much smaller scale height for the moleculargas. Theoretical analyses of the stability of multi-componentdisks suggest that the dynamically coldest component isthe most important in driving instability (Jog & Solomon1984a,b; Rafikov 2001). This analysis suggests that it is theproperties of the dense molecular gas, rather than the atomicgas, that are the most important for determining whethergalactic disks are stable against gravitational collapse, espe-cially where the mass of the ISM is H dominated.The cloud-cloud velocity dispersion is correlated at the95% confidence level with both the far-infrared luminosityand the K-band absolute magnitude. Thus, as for the atomicgas, we find evidence that star formation activity (as tracedby the infrared luminosity) tends to increase the velocitydispersion in the dense molecular gas. The correlation withK magnitude, which traces the total stellar mass, impliesthat the cloud-cloud velocity dispersion is also enhanced inmore massive galaxies.We have used our data to examine the apparent kine-matical properties of the molecular disk at a spatial reso-lution of 4.5 kpc chosen to match the best resolution forgalaxies at redshifts 1-2 (Tacconi et al. 2008). A degrada-tion of the resolution from 1.2 kpc to 4.5 kpc results in anincrease in the average velocity dispersion in the outer diskby a factor of two. The average velocity dispersion of NGC4254 viewed with 4.5 kpc resolution is quite comparable tothe velocity dispersion of 20 km s − seen in a normal galaxyat z = 1 (Tamburro et al. 2009). Both galaxies have compa-rable gas and stellar surface densities, as well as star forma-tion rate surface densities, which suggests that the higherstar formation rates seen at z = 1 may be partly attributedto the presence of physically larger molecular disks. Thisanalysis suggests that this data set can provide a valuablelocal bench mark in understanding lower spatial resolutionobservations of galaxies in the early universe. c (cid:13) , 1–16 he JCMT Nearby Galaxies Legacy Survey IV. Velocity Dispersions in the Molecular Gas ACKNOWLEDGMENTS
We thank the anonymous referee for a referee report whichspurred us to re-examine our data processing choices and re-sulted in a significant improvement in the paper. The JamesClerk Maxwell Telescope is operated by The Joint Astron-omy Centre on behalf of the Science and Technology Facil-ities Council of the United Kingdom, the Netherlands Or-ganisation for Scientific Research, and the National ResearchCouncil of Canada. The research of J.I. and C.D.W. is sup-ported by grants from NSERC (Canada). A.U. has beensupported through a Post Doctoral Research Assistantshipfrom the UK Science & Technology Facilities Council. Travelsupport for B.E.W. and T.W. was supplied by the NationalResearch Council (Canada). We acknowledge the usageof the HyperLeda database (http://leda.univ-lyon1.fr) andthank R.N. Henriksen for useful discussions. This researchhas made use of the NASA/IPAC Extragalactic Database(NED) which is operated by the Jet Propulsion Laboratory,California Institute of Technology, under contract with theNational Aeronautics and Space Administration.
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APPENDIX A: COMPARISON WITHPREVIOUS PROCESSING METHODS
There are two different methods that have been used tomeasure velocity dispersions in molecular gas in galaxies.Combes & Becquaert (1997) measured velocity dispersionsin NGC 628 and NGC 3938 by fitting gaussian profiles toindividual spectra, while Walsh et al. (2002) used moment2 maps of NGC 6946 to determine the average velocity dis-persion. While the moment 2 maps used in this paper areeasier to compute and analyse than fitting individual profilesto many hundreds of spectra, they can potentially be sub-ject to some systematic effects depending on choices made inthe processing. We investigate some of these effects here bycomparing our data and moment 2 maps for NGC 628 andNGC 3938 with the results given by Combes & Becquaert(1997) for the same galaxies.We first investigated whether the measured velocity dis-persion was affected by the angular and spectral resolution
Table A1.
Velocity dispersions measured with different spectraland spatial resolutionsData cube used a NGC 3938 NGC 628Original 3.7 3.1Binned to 2.6 km s − ′′ gaussian 6.5 4.2Convolved and binned 7.4 4.7Combes & Becquaert (1997) 9 6.5 a All values measured for the CO J=3-2 line in km s − .Velocity dispersion measured using a signal-to-noise cutoff of 3.5 σ . Table A2.
Velocity dispersions measured with different signal-to-noise cutoffs for maskS/N cutoff used a NGC 3938 NGC 6285 σ σ σ σ σ σ a All values measured for the CO J=3-2 line in km s − . of the data. The CO J=1-0 data from Combes & Becquaert(1997) have an angular resolution of 23 ′′ and a spectral res-olution of 2.6 km s − , while the JCMT CO J=3-2 data havean angular resolution of 14.5 ′′ and a spectral resolution of0.43 km s − . We produced three additional data cubes foreach galaxy: one binned by 6 channels in velocity, one con-volved to achieve a gaussian beam of 23 ′′ , and one that wasboth convolved and binned. From these cubes we made mo-ment 2 maps using the method described in § spatial resolu-tion may be a more important factor in increasing the mea-sured velocity dispersion than spectral resolution, as longas the spectral resolution is sufficient to resolve the lines.Interestingly, our average velocity dispersions for these twogalaxies are only slightly smaller than those measured byCombes & Becquaert (1997) when our data are smoothedspatially and spectrally to match the IRAM data.We next investigated the effect of the choice of thesignal-to-noise cutoff for the masks used in creating themoment map. For this analysis, we used the data cubesthat had been smoothed spatially to match the data fromCombes & Becquaert (1997) to give better signal-to-noisein our maps, but which had no spectral smooting applied.The results are given in Table A2. It is clear that the mea-sured velocity dispersion decreases systematically has highersignal-to-noise cutoffs are used in the mask.Finally, we performed gaussian fits to selected spectra c (cid:13) , 1–16 he JCMT Nearby Galaxies Legacy Survey IV. Velocity Dispersions in the Molecular Gas Table A3.
Comparison of velocity dispersion from gaussian fitsand second moment maps for selected positions in NGC 3938Position a Gaussian fit Moment 2 map b ( ′′ , ′′ ) (km s − ) (km s − )(0,44) 9.4 ± ± ± ± ± a All values measured for the CO J=3-2 line. The spectra have been convolvedto a 23 ′′ beam and binned to 2.6 km s − resolution. (0,0) corresponds to(11:52:49.6,44:07:17.7 J2000). b Measured from maps made using a 2.5 σ cutoff. from the data cube of NGC 3938 that had been convolvedto 23 ′′ and binned to 2.6 km s − resolution (Figure A1 andTable A3. To mimic approximately the selection of spec-tra shown in Combes & Becquaert (1997), we selected thespectrum with the highest velocity dispersion in a map madewith a 3.5 σ cutoff, and then stepped away from this spec-trum in steps of 3 pixels (21.8 ′′ ) in the north and southdirections. We obtain similar values for the velocity disper-sions from fits to the unbinned spectra; binned spectra areshown in Figure A1 for clarity. Although there is consider-able scatter in the velocity dispersions for individual spec-tra, the average value derived from gaussian fits is 1.2 timeslarger (the standard deviation 0.4) than the value derivedfrom the moment 2 map.On the basis of this analysis, we opted to use a signal-to-noise cutoff of 2.5 σ on our original data cubes, as thischoice seemed to give good agreement with the resultsfrom Combes & Becquaert (1997) when both data sets werematched in angular and frequency resolution. APPENDIX B: THE POSSIBLE EFFECT OFANISOTROPIES IN THE VELOCITYDISPERSION
There is no statistically significant correlation of velocitydispersion in the molecular gas with inclination in our data(Figure B1). The average observed velocity dispersion is 5.3km s − for the 4 galaxies with inclinations < o and 8.1km s − for the 8 galaxies with inclinations > o and thesevalues agree within 2 sigma. We have also checked for anycorrelation of the velocity dispersion normalized by each ofthe star formation rate and D with inclination and againfind no correlation.For an inclined galaxy, the observed velocity disper-sion is a combination of the in-plane ( σ r , σ θ ) and verticalvelocity ( σ z ) dispersions. We will assume that σ r = σ θ and will refer to the in-plane component of the velocitydispersion as σ r from here on for simplicity. Thus, for agalaxy with inclination i , the observed velocity dispersionis σ obs = p σ z cos i + σ r sin i . If the radial and verticalvelocity dispersions of the molecular gas were isotropic, wewould not expect any trend of velocity dispersion with incli-nation. If, however, the velocity ellipsoid of the giant molec-ular clouds (which contain most of the mass of the molec- Figure A1.
Observed CO J =3-2 emission at five positions inNGC 3938. The spectra have been convolved to a 23 ′′ beam andbinned to 2.6 km s − resolution. Spectra are spaced by 22 ′′ alongthe declination axis ordered from north (top) to south (bottom)and the central spectrum corresponds to (11:52:49.6,44:07:17.7).Gaussian fits to each spectrum are overlaid; the bar indicates theregion used to obtain the fit. ular ISM) is anisotropic, with σ r > σ z , then the observedvelocity dispersion would tend to increase with increasinginclination.Unfortunately, there is no direct information on theshape of the velocity ellipsoid for giant molecular clouds. Intheoretical models, the cloud velocity dispersion has been at-tributed to cloud-cloud scattering (Gammie, Ostriker & Jog1991) as well as to the driving effects of spiral structure(Thomasson et al. 1991). Since both these models were two-dimensional, they can give us no guidance on the relativestrength of the vertical and in-plane velocity dispersions. c (cid:13) , 1–16 C. D. Wilson et al.
Figure B1.
Observed CO J =3-2 velocity dispersion as a func-tion of galaxy inclination angle. Error bars show the standarddeviation of the observed values within an individual galaxy. In contrast, there have been a number of studies of thestellar velocity ellipsoid (Delhaye 1965; Dehnen & Binney1998; Elias et al. 2006). If the velocity ellipsoid of any starscan give us a clue to that of GMCs, it will be the youngestO and B type stars, which may be sufficiently young to stilltrace the motions of their parent clouds. The smallest valuesfor the velocity ellipsoid can be found in Delhaye (1965), whomeasured a relative velocity dispersion σ z /σ r = 0 .
75 for 35O-B5 supergiants. Dehnen & Binney (1998) measure a sig-nificantly smaller value of σ z /σ r = 0 . +0 . − . for 500 mainsequence stars with − . < B − V < .
14. However, thiscolour range extends well into the A star range where mainsequence lifetimes are larger than 100 Myr. Since this veloc-ity dispersion ratio is well known to decrease with the ageof the stellar population (Delhaye 1965; Dehnen & Binney1998), this value may not be an appropriate one to adopt forGMCs. In a recent study of OB stars using Hipparcos data,Elias et al. (2006) obtained a value of σ z /σ r = 0 . ± .
06 for800 stars with spectral types O-B6 within 1 kpc of the Sun.Dividing the sample into stars in the Gould’s Belt and theLocal Galactic Disk results in values of σ z /σ r = 0 . ± . σ z /σ r = 0 . ± .
09, respectively.Gammie, Ostriker & Jog (1991) caution that a criticaldifference between star-cloud and cloud-cloud scattering,namely the relative sizes of the epicyclic amplitude and thecloud tidal radius, prevents direct application of stellar re-sults to molecular clouds. However, this model ignores thepossible effect of spiral arms, which could conceivably intro-duce an anisotropy into the cloud motions. In estimating thepossible correction to our observed velocity dispersions forthe effects of anisotropy in the velocity ellipsoid, we adopta conservative value of σ z /σ r = 0 .
6, which is the 1 σ upperlimit obtained by Elias et al. (2006) for their entire sample.With this value, corrections for the velocity ellipsoid onlyexceed 10% for inclinations greater than 27 o . c (cid:13)000