Molecular Gas and Star Formation in Nearby Disk Galaxies

4.2 MB·English

by  Adam K. Leroy

Accepted to the AstronomicalJournal
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
MOLECULAR GAS AND STAR FORMATION IN NEARBY DISK GALAXIES
Adam K. Leroy1, Fabian Walter2, Karin Sandstrom2, Andreas Schruba3, Juan-Carlos Munoz-Mateos1, Frank
Bigiel4, Alberto Bolatto 6, Elias Brinks7, W.J.G. de Blok8,9, Sharon Meidt2, Hans-Walter Rix2, Erik
Rosolowsky10, Eva Schinnerer2, Karl-Friedrich Schuster11, Antonio Usero5,
Accepted tothe Astronomical Journal
ABSTRACT
3 We compare moleculargas tracedby 12CO(2-1)maps from the HERACLESsurvey,with tracersof
1 therecentstarformationrate(SFR)across30nearbydiskgalaxies. Wedemonstrateafirst-orderlinear
0
correspondence between Σ and Σ but also find important second-order systematic variations
2 in the apparentmoleculargmaosldepletiSoFnRtime, τmol =Σ /Σ . At the 1 kpc commonresolutionof
dep mol SFR
n HERACLES,COemissioncorrelatescloselywithmanytracersoftherecentSFR.Weightingeachline
a of sight equally, using a fixed alpha equivalent to the Milky Way value, our data yield a molecular
CO
J gas depletion time, τmol = Σ /Σ 2.2 Gyr with 0.3 dex 1σ scatter, in very good agreement
0 withrecentliteratureddeapta. WmeoalpplSyFRaf≈orward-modelingapproachto constrainthe power-lawindex,
1 N, thatrelates the SFR surface density andthe moleculargassurface density,Σ ΣN . We find
SFR ∝ mol
N = 1 0.15 for our full data set with some scatter from galaxy to galaxy. This also agrees with
] ±
O recentwork,butwecautionthatapowerlawtreatmentoversimplifiesthetopicgiventhatweobserve
correlationsbetweenτmol andotherlocalandglobalquantities. Thestrongestoftheseareadecreased
C dep
τmolinlow-mass,low-metallicitygalaxiesandacorrelationofthekpc-scaleτmolwithdust-to-gasratio,
. dep dep
h D/G. These correlations can be explained by a CO-to-H conversion factor (α ) that depends on
2 CO
p dust shielding, and thus D/G, in the theoretically expected way. This is not a unique interpretation,
- but external evidence of conversionfactor variations makes this the most conservative explanation of
o
the strongest observed τmol trends. After applying a D/G-dependent α , some weak correlations
r dep CO
st between τdmeopl and local conditions persist. In particular, we observe lower τdmeopl and enhanced CO
a excitation associated with nuclear gas concentrations in a subset of our targets. These appear to
[
reflect real enhancements in the rate of star formation per unit gas and although the distribution of
1 τdepdoesnotappearbimodalingalaxycenters,τdepdoesappearmultivaluedatfixedΣmol,supporting
v the the idea of “disk” and “starburst” modes driven by other environmental parameters.
8 Subject headings: galaxies: evolution — galaxies: ISM — radio lines: galaxies — stars: formation
2
3
2 1. INTRODUCTION a key input to galaxy simulations and scaling relations
. measured for whole galaxies provide important bench-
1 The relationship between gas and star formation
marksfortheoutputofthesesimulations. Measurements
0 in galaxies plays a key role in many areas of astro-
of gas and star formation at large scales give context
3 physics. Its (non)evolution over cosmic time informs
for studies focusing on parts of the Milky Way (e.g.,
1 our understanding of galaxy evolution at high redshift
Lada et al. 2010; Heiderman et al. 2010) and the near-
: (Daddi et al. 2010; Tacconi et al. 2010; Genzel et al.
v estgalaxies(e.g.,Schruba et al.2010; Chen et al.2010).
2010). The small-scale efficiency of star formation is
i Ultimately,aquantitativeunderstandingofthegas-stars
X
1NationalRadioAstronomyObservtory,520EdgemontRoad, cycleis neededto understandgalaxyevolution,with im-
r
a Charlottesville,VA22903, USA plications for the galaxy luminosity function, the galaxy
2MaxPlanckInstitutefu¨rAstronomie,K¨onigstuhl17,69117, color-magnitude diagram, the structure of stellar disks,
Heidelberg,Germany
and chemical enrichment among other key topics.
3CaliforniaInstitute forTechnology, 1200 E CaliforniaBlvd,
Recentmultiwavelengthsurveysmakeitpossibletoes-
Pasadena, CA91125
4Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120, timatethesurfacedensitiesofgasandrecentstarforma-
Heidelberg,Germany tionindozensofnearbygalaxies. Thishasleadtoseveral
5Observatorio Astron´omico Nacional, C/ Alfonso XII, 3,
studies of the relationship between gas and stars. Many
28014, Madrid,Spain
6Department of Astronomy, Universityof Maryland, College of these focus on a single galaxy (e.g., Heyer et al. 2004;
Park,MD,USA Kennicutt et al. 2007; Blanc et al. 2009; Verley et al.
7Centre for Astrophysics Research, University of Hertford- 2010; Rahman et al. 2011) or a small sample (e.g.,
shire,HatfieldAL109AB,UnitedKingdom
8ASTRON, Netherlands Foundation for Radio Astronomy, Wilson et al. 2009; Warren et al. 2010). Restricted by
Postbus 2,7990AADwingeloo,TheNetherlands the availability of complete molecular gas maps, stud-
9Astrophysics, Cosmology and Gravity Centre, Department ies of large sets of galaxies (e.g., Young et al. 1996;
of Astronomy, University of Cape Town, Private Bag X3, Ron- Kennicutt 1998b; Rownd & Young 1999; Murgia et al.
debosch7701, SouthAfrica
10University of British Columbia, Okanagan Campus, 2002;Leroy et al.2005;Saintonge et al.2011)mostlyuse
Kelowna,BCCanada integrated measurements or a few low-resolution point-
11IRAM, 300 rue de la Piscine, 38406 St. Martin d’H`eres, ings per galaxy.
France
2 Leroy et al.
From 2007-2010, the HERA CO-Line Extragalactic SFR tracer, the CO transition studied, the processing
Survey (HERACLES, first maps in Leroy et al. 2009) of SFR maps, or the adopted conversion factor (Section
used the IRAM 30-m telescope12 to construct maps 3.2). UsinganexpandedversionoftheMonteCarlomod-
of CO emission from 48 nearby galaxies. The com- elingapproachofBlanc et al.(2009),wecarryoutpower
mon spatial resolution of the survey is 1 kpc, suf- law fits to our data, avoiding some of the systematic
ficient to place many resolution elements∼across a typ- biases present in previous work (Section 3.3). Finally,
ical disk galaxy. Because the targets overlap surveys we compare our results to a wide collection of literature
by Spitzer (mostly SINGS and LVL, Kennicutt et al. data, demonstrating an emerging consensus with regard
2003a; Dale et al. 2009) and GALEX (mostly the NGS, to the regionofparameterspaceoccupiedby ΣSFR-Σmol
Gil de Paz et al. 2007), a wide variety of multiwave- data,ifnottheinterpretation(Section3.4). Weconclude
lengthdata areavailableformosttargets. Inthis paper, that in the disks of normal, massive star-forming galax-
we take advantage of these data to compare tracers of ies,tofirstordertherelationshipbetweenΣSFRandΣmol
molecular gas and recent star formationat 1 kpc resolu- canbe describedby asingledepletiontime witha factor
tion across a large sample of 30 galaxies. of two scatter. This expands and reinforces the results
This paper builds on workby Leroy et al.(2008, here- of L08, B08, and Schruba et al. (2011).
after L08) and Bigiel et al. (2008, hereafter B08). They In Section 4, we show important second-order devia-
combined the first HERACLES maps with data from tionsfromthissimplepicture,whichcaneasilybemissed
The HI NearbyGalaxiesSurvey(THINGS Walter et al. by comparing only ΣSFR and Σmol. We find systematic
2008), SINGS, and the GALEX NGS data to com- variations in the molecular gas depletion time, τmol as
dep
pare HI, CO, and tracers of recent star formation in a function of global galaxy properties (Section 4.1) and
a sample of nearby galaxies. In the disks of large spi- localconditions (Section 4.2). This analysisincludes the
ral galaxies, they found little or no dependence of the first resolved comparison of τmol to the local dust-to-
dep
star formation rate per unit molecular gas on environ-
gas ratio, which is expected to play a key role in setting
ment. The fraction of interstellar gas in the molecular
the CO-to-H conversionfactor, α and we discuss the
phase, on the other hand, varies strongly within and possibility th2at α drives someCoOf the observed τH2
among galaxies, exhibiting correlations with interstel- CO dep
variations. We explicitly consider the central regions of
lar pressure, stellar surface density, and total gas sur-
our targets (Section 4.4) and show strong evidence for
facedensityamongotherquantities(Wong & Blitz2002;
lower τmol, i.e., more efficient star formation, in galaxy
Blitz & Rosolowsky 2006, L08). They advocated a sce- dep
nario for star formation in disk galaxies in which star centers compared to galaxy disks - a phenomenon that
formation in isolated giant molecular clouds is a fairly we discuss in context of recent proposals for “disk” and
universalprocesswhilethe formationofthesecloudsout “starburst” modes of star formation (Daddi et al. 2010;
of the atomic gas reservoir depends sensitively on envi- Genzel et al. 2010). In our best-resolved targets we ex-
ronment (see also, Wong 2009; Ostriker et al. 2010). amine how the scatter in τmol depends on spatial scale
dep
The full HERACLES sample spans a wider range of (Section 4.3). The relationship appears much shallower
masses, morphologies, metallicities, and star formation than one would expect for uncorrelated averaging in a
rates (SFRs) than the spirals studied in L08 and B08. disk. This suggests either a high degree of large-scale
Schruba et al. (2011) and Bigiel et al. (2011) used these synchronization in the star formation process or, more
to extend the findings of L08 and B08. Using stacking likely, widespread systematic, but subtle, variations in
techniques,Schruba et al.(2011)demonstratedthatcor- τmol due to still-undiagnosed drivers.
dep
relationsbetweenstarformationtracersandCOemission
Thus our conclusions may be abstracted to: molecu-
extend into the regime where atomic gas dominates the
lar gas and star formation exhibit a first order one-to-
ISM, Σ > Σ . This provides the strongest evidence
HI mol one scaling but we observe important second order vari-
yetthatstarformationindisk galaxiescanbe separated
ations about this scaling. Theseinclude likelyconversion
into star formation from molecular gas and the balance
factor effects, efficient nuclear starbursts, and weak sys-
betweenatomicandmoleculargas,ahypothesisthathas tematic variationsinτmol thatemergeconsideringscale-
a long history (e.g., Young & Scoville 1991, and refer- dep
dependent scatter or global galaxy properties. The re-
ences therein). Bigiel et al. (2011) demonstrated that a
mainderofthis sectionpresentsa briefbackground,Sec-
fixedratioofCO torecentstarformationrateremainsa
tion2describesourdataandphysicalparameterestima-
reasonable description of the ensemble of 30 galaxies.
tion, Sections 3 and 4 motivate these conclusions, and
In this paper we expand on L08, B08, Bigiel et al.
Section 5 synthesizes these results and identifies several
(2011), and Schruba et al. (2011) and examine the gen-
key future directions.
eral relationship between molecular gas and SFR in
nearby disk galaxies. We divide the analysis into two
main parts. In Section 3, we consider the scaling rela-
tion linking Σ to Σ , the molecular analog to the
SFR mol 1.1. Background
“Kennicutt-Schmidt law” or “star formation law.” We
show the distribution of data in Σ -Σ parameter Following Schmidt (1959, 1963), astronomers have
SFR mol
space using different weightings (Section 3.1) and ex- studied the relationship between gas and the SFR for
amine how this distribution changes with different ap- morethan50years. MostrecentworkfollowsKennicutt
proaches to physical parameter — varying the choice of (1989,1998b)andcomparesthesurfacedensitiesofSFR,
Σ ,andneutral(HI+H )gasmass,Σ . Recentwork
SFR 2 gas
12IRAMissupportedbyCNRS/INSU(France),theMPG(Ger- focuses heavily on the power law relationship between
many)andtheIGN(Spain). these surface densities (the “Schmidt-Kennicutt law” or
Molecular Gas and Star Formation in Nearby Disk Galaxies 3
the “star formation law”): tence of disk galaxies with τmol only slightly lower than
dep
those in local disk galaxiesbut H surface density, Σ ,
Σ =A Σ N . (1) 2 mol
SFR gas as high as that found in starbursts in the local universe
×
An alternative approach treats the ratio of gas and (Daddi et al. 2010; Tacconi et al. 2010). Merger-driven
SFRasthequantityofinterest(Young et al.1986,1996, starbursts with similar Σmol can have much lower τdmeopl,
L08). This ratio can be phrased as a gas depletion time suggestingtherelevanceofanotherparametertosetτmol.
dep
(Σ /Σ ) or its inverse, a star formation efficiency
mol SFR Density andthe dynamicaltimescale arebothgoodcan-
(Σ /Σ ). These share the same physical meaning,
SFR mol didates (Daddi et al. 2010; Genzel et al. 2010).
whichistheSFRperunitgas. Bothconvolveatimescale
Meanwhile, investigations of the Milky Way and the
withatrueefficiency,forexamplethelifetimeofamolec-
nearest galaxies have attempted to connect observed
ularcloudwiththefractionofgasconvertedtostarsover
scaling relations to the properties of individual star-
this time. We focus exclusively on molecular gas in this
forming regions. These are able to recover the galaxy-
paper and phrase this ratio as the molecular gas deple-
scalerelationsatlargescalebutfindenormousscatterin
tion time,
theratiosofSFRtracerstomoleculargasonsmallscales
(Schruba et al. 2010; Chen et al. 2010; Onodera et al.
Σ
τmol = mol , (2) 2010). Detailed studies of Milky Way and LMC clouds
dep ΣSFR suggest the time-evolution of individual star-forming re-
which is the time for star formationto consume the cur- gions as a likely source of this scatter (Murray 2010;
rent molecular gas supply. Kawamuraet al. 2009), with the volume density of in-
The state of the field is roughly the following. dividualclouds a key parameter (Heiderman et al. 2010;
Kennicutt (1998b) demonstrated a tight, non-linear Lada et al. 2010).
(N = 1.4 0.15) scaling between galaxy-averagedΣ For additional background we refer the reader to the
SFR
and Σ ±spanning from normal disk galaxies to star- recent review by Kennicutt & Evans (2012).
gas
bursts. Including HI improved the agreement between 2. DATA
disksandstarbursts,butmostofthe dynamicrangeand
2.1. Data Sets
the nonlinear slope was driven by the contrast between
the disks and merger-induced starbursts, especially the We use HERACLES CO(2-1) maps to infer the distri-
localultraluminousinfraredgalaxy(ULIRG)population. bution of H and GALEX far-ultraviolet(FUV), Spitzer
2
Theadoptionofasingleconversionfactorforallsystems infrared(IR),andliteratureHαdatatotracerecentstar
also had significant impact; adopting the “ULIRG” con- formation. We supplement these with HI data used to
version factor suggested by Downes & Solomon (1998) mask the CO, derive kinematics, and measure the dust-
for the Kennicutt (1998b) starburst data drives the im- to-gas ratio and with near-IR data used to estimate the
plied slope to N 1.7. Subsequent studies resolved stellar surface density, Σ∗.
∼
galaxy disks — often as radial profiles — and usu- HERACLES CO: The HERA CO Line Extragalactic
ally revealed distinct relationships between Σ , Σ , Survey(HERACLES)usedthe HeterodyneReceiverAr-
SFR HI
and Σ with shallower indices N for H than HI ray(HERA,Schuster et al.2004)ontheIRAM30mtele-
mol 2
(Wong & Blitz 2002; Heyer et al. 2004; Kennicutt et al. scope to map CO(2-1) emission from 48 nearby galax-
2007;Schruba et al.2011, B08,L08). This suggeststhat ies, of which we use 30 in this paper (see Section 2.3).
the immediate link is between SFR and H . A more HERACLEScombinesanIRAMLargeProgramandsev-
2
aggressive conclusion, motivated by the steep, relatively eral single-semester projects that spanned from 2007 to
weak relation between Σ and Σ is that star for- 2010. Leroy et al. (2009) presented the first maps (see
SFR HI
mation in galaxy disks may be broken into two parts: alsoSchuster et al.2007). Theadditionaldataherewere
(1) the formation of stars in molecular clouds and (2) observed and reduced in a similar manner. The largest
the balance between H and HI (Wong & Blitz 2002; changeis a revisedestimate of the mainbeam efficiency,
2
Blitz & Rosolowsky 2006, L08, B08). loweringobservedintensitiesby 10%. Thispropagates
≈
The fraction of dense molecular gas also appears to toarevisedCO(2-1)/(1-0)lineratioestimate,sooures-
be a key parameter. Gao & Solomon (2004) found a timates of Σ are largely unaffected compared to B08
mol
roughly fixed ratio of SFR to HCN emission, a dense and L08. The HERACLES cubes cover out to radii of
gas tracer, extending from spiral galaxies to starbursts. r withangularresolution13′′andtypical1σsensitivity
25
Over the same range, the ratio of SFR to total H , 20 mK per 5 km s−1 channel.
2
traced by CO emission, varies significantly (though the We integrate each cube along the velocity axis to pro-
two relate roughly linearly in their normal galaxy sam- duce maps of the integrated intensity along each line of
ple). Galactic studies also highlight the impact of sight. We wish to avoid including unnecessary noise in
density on the SFR on cloud scales (Wu et al. 2005; thisintegralandsorestrictthevelocityrangeoverwhich
Heiderman et al.2010;Lada et al.2010). Itremainsun- we integrate to be as small as possible while still con-
clear how the dense gas fraction varies inside galaxy taining the CO line, i.e., we “mask” the cubes. To be
disks,butmerger-inducedstarburstsdoshowhighHCN- included in the mask a pixel must meet one of two con-
to-COratios(Gao & Solomon2004;Garc´ıa-Burillo et al. ditions: 1) lie within 25 km s−1 of the local mean HI
±
2012). velocity(derivedfromTHINGS,Walter et al.2008,sup-
SFR tracers and CO can both be observed at high plemented by new and archival HI) or 2) lie in part of
redshift. Genzel et al. (2010) demonstrated broad con- the spectrum near either two consecutive channels with
sistency between local H -SFR relations and those at SNR above 4 or three consecutive channels with SNR
2
z 1 3. One key difference at high-z is the exis- above 3. Condition (2) corresponds to traditional ra-
∼ −
4 Leroy et al.
Volume Legacy survey (LVL, Dale et al. 2009). We de-
TABLE 1 scribetheprocessingofthesemapsinLeroy et al.(2012,
Sample
hereafter L12).
SINGS, LVL, and Literature Hα: Both SINGS and
Galaxy D res. i PA r25 r25 Multi-
[Mpc] [kpc] [◦] [◦] [′] [kpc] scale LVL published continuum-subtracted Hα images for
(1) (2) (3) (4) (5) (6) (7) (8) mostofoursample. Wesupplementthesewithliterature
maps, particularly from the GoldMine and Palomar-Las
NGC0337 19.3K 1.24a 51 90 1.5 10.6 ···
NGC0628 7.2K 0.46 7 20 4.9 10.4 X Campanas surveys. L12 describe our approach to these
NGC0925 9.1K 0.59 66 287 5.4 14.3 ··· maps(masking,NIIcorrection,fluxscaling,background
NGC2403 3.2W 0.21 63 124 7.9 7.4 X subtraction) and list the source of the Hα data for each
NGC2841 14.1K 0.91 74 153 3.5 14.2 ··· galaxy.
NGC2903 8.9W 0.57 65 204 5.9 15.2 X GALEX UV: For 24 galaxies, we use NUV and
NGC2976 3.6K 0.23 65 335 3.6 3.8 ··· FUV maps from the Nearby Galaxy Survey (NGS,
NGC3049 19.2K 1.24a 58 28 1.0 2.7 ··· Gil de Paz et al. 2007). For one galaxy, we use a map
NGC3184 11.8K 0.76 16 179 3.7 ···
from the Medium Imaging Survey (MIS) and we take
NGC3198 14.1K 0.91 72 215 3.2 13.0 ···
maps for five targets from the All-sky Imaging Survey
NGC3351 9.3K 0.60 41 192 3.6 10.6 ···
NGC3521 11.2K 0.72 73 340 4.2 12.9 ··· (AIS). L12 describe our processing.
NGC3627 9.4K 0.61 62 173 5.1 13.8 X BIMA+12-m and NRO 45-m CO (1-0) Maps: A sub-
NGC3938 17.9K 1.15a 14 15 1.8 6.3 ··· set of our targets have also been observed by the BIMA
NGC4214 2.9W 0.19 44 65 3.4 2.9 ··· SONG(Helfer et al.2003)ortheNobeyamaCOAtlasof
NGC4254 14.4K 0.93 32 55 2.5 14.6 ··· Nearby Spiral Galaxies (Kuno et al. 2007). Where these
NGC4321 14.3K 0.92 30 153 3.0 12.5 ··· data are available, we apply our HERACLES masks to
NGC4536 14.5K 0.94 59 299 3.5 14.9 ···
thesemapsandmeasureCO(1-0)intensity. Weonlyuse
NGC4559 7.0K 0.45 65 328 5.2 10.7 ···
BIMASONGmapsthatincludeshort-spacingdatafrom
NGC4569 9.86K 0.64 66 23 4.6 26.5 ···
NGC4579 16.4K 1.06a 39 100 2.5 15.0 ··· the Kitt Peak 12-m.
NGC4625 9.3K 0.60 47 330 0.7 1.9 ··· THINGSandSupplementalHi: WeassembleHImaps
NGC4725 11.9K 0.77 54 36 4.9 13.2 X foralltargets,whichweusetomasktheCO,estimatethe
NGC4736 4.7K 0.30 41 296 3.9 5.3 X dust-to-gas ratio, explore 24µm cirrus corrections, and
NGC5055 7.9K 0.51 59 102 5.9 17.3 ··· derive approximate rotation curves. These come from
NGC5194 7.9W 0.52 20 172 3.9 9.0 X THINGS(Walter et al.2008)andacollectionofnewand
NGC5457 6.7K 0.43 18 39 12.0 25.8 X archivalVLAdata(programsAL731andAL735). These
NGC5713 21.4K 1.38a 48 11 1.2 9.5 ··· supplemental HI are C+D configuration maps with res-
NNGGCC76393416 164..85KK 00..9444 7363 126483 45..67 199..85 ·X·· olutions 13′′–25′′. We reduced and imaged these in a
standard way using the CASA package.
Note. —Sampleusedinthispaper. Columnsgive(1)galaxy
name;(2)adopted distanceinMpc;(3)FWHMspatialresolu-
tion of HERACLES data at that distance, in kiloparsecs; (4) 2.2. Physical Parameter Estimates
adopted inclination and (5) position angle indegrees; adopted
Following standard practice in this field, we estimate
radiusofthetheB-band25th magnitudeisophote,usedtonor-
physical parameters from observables. Despite the in-
malize the radius in (6) arcminutes and (7) kiloparsecs. Most
analysis in this paper considers data inside 0.75 r25. Column trinsic uncertainty involved in this process, these esti-
(8)indicatesifthegalaxyiscloseandlargeenoughforthemul- mates play a fundamental role in enhancing our under-
tiscaleanalysisinSection4.3. standing of the physics of galaxy and star formation,
a Toodistanttoconvolveto1kpcresolution. Includedinanal-
as demonstrated from the earliest works in this subfield
ysisatnativeresolution.
K,W Distance adopted from K: Kennicuttetal. (2011) or W: (Young & Knezek 1989; Kennicutt 1989). We adopt an
Walteretal.(2008). approachlargelyorientedtophysicalquantities,butdis-
cuss the impact of our assumptions throughout.
CO Intensity to H : We convertCO (2-1) intensity to
dio masking(e.g.,Helfer et al.2003; Walter et al.2008). 2
H mass via
Condition (1) is less conventional, but important to our 2
analysis. Integrating over the HI line, which is detected
throughoutourtargets,guaranteesthatwehaveaninte- 0.7 α1−0
grated intensity measurement along each line of sight, Σmol[M⊙pc−2]=6.3 CO ICO [Kkms−1],
(cid:18)R (cid:19) (cid:18)4.35(cid:19)
even lines of sight that lack bright CO emission (see 21
(3)
Schruba et al. 2011, for detailed discussion of this ap-
where R is the CO(2-1)-to-CO(1-0) line ratio and
proach). This avoids a traditional weakness of masking, 21
α is the CO(1-0)-to-H conversion factor. By de-
that nondetections are difficult to deal with quantita- CO 2
fault, we adopt a Galactic conversion factor, α1−0 =
tively. We calculate maps of the statistical uncertainty CO
in the integrated CO intensity from the combination of 4.35 M⊙ pc−2 (Kkms−1)−1 equivalent to XCO =
the mask and estimates of the noise derivedfromsignal- 2 1020cm−2(Kkms−1)−1 (Strong & Mattox 1996;
×
free regions. The result is an integrated intensity and Dame et al. 2001) and a line ratio of R = 0.7. This
21
associateduncertainty for each line of sight in the HER- line ratio is slightly lower than the R =0.8 derived by
21
ACLES mask. Leroy et al. (2009), reflecting the revised efficiency used
SINGS and LVL IR:We usemapsofIRemissionfrom in the reduction. The appendix motivates this value us-
3.6–160µm from the Spitzer Infrared Nearby Galaxies ing integrated flux ratios and follow-up spectroscopy of
Survey (SINGS, Kennicutt et al. 2003a) and the Local HERACLES targets. Equation 3 and all “Σ ” in this
mol
Molecular Gas and Star Formation in Nearby Disk Galaxies 5
paper include a factorof1.36to accountfor helium. Be- Bolatto et al. 2008; Narayananet al. 2012). Over the
cause we consider only molecular gas, any results that range of D/G′ that we consider, this prescription rea-
we derive using a fixed α can be straightforwardlyre- sonably resembles the shallow power law dependences
CO
stated in terms of CO intensity. of α on metallicity calculated from simulations by
CO
We adoptthis“Galactic”α1−0 tofacilitate cleancom- Feldmann et al.(2012)andNarayananet al.(2012),who
parison to previous work, butCOimproved estimates exist both suggest αCO Z−0.7. “ ΣGMC = 50 M⊙ pc−2”
∼ h i
for HERACLES.Sandstrom et al. (2012) solveddirectly yields a steeper dependence of α on metallicity over
CO
for the CO-to-H conversion factor across the HERA- our range of interest but we will see in Sections 4.1 and
2
CLES sample using dust as an independent tracer of 4.2that it offers a simple way to accountfor mostof the
the gas mass. They find a somewhat lower average dependence of τH2 on dust-to-gas ratios in our observa-
dep
α1−0 3.1. We quote this as a CO (1-0) conversion tions. LowsurfacedensityGMCsorsignificantcontribu-
CO ≈
factor, though Sandstrom et al. (2012) directly solve for tion of “translucent” (A 1–2 mag) gas to the overall
V
∼
the CO (2-1) conversion factor. They find a CO(2-1) CO emissionare supported by observationsof the Milky
ccoomnvpearsrieodntfoacotuorr o“fGαa2Cla−Oc1ti≈c”4C.4OM(2⊙-1p)cc−o2n(vKerksimons−fa1)c−to1r, WseravyaHtioeynesrbeyt aHl.u(g2h0e0s9e)taanld. L(2is0z1t0)e;tWal.o(n2g01e0t)a,lL.M(2C01o1b)-,
α2C−O1 = 6.3 M⊙ pc−2 (Kkms−1)−1. Sandstrom et al. apnrodpMria3t1ef(oSrchmrourbeaaecttivael.lyisntaprr-efopr.)mibnugtsmysatyemnso(tHbueghapes-
(2012) find 0.4 dex point-to-point scatter, of which
≈ et al., submitted). We return to this issue in Section 4.
0.3maybeintrinsicwiththeremaindersolutionuncer-
≈ We calculate α (D/G′) using D/G′ derivedfor fixed
tainties. Because Sandstrom et al. (2012) solve directly CO
α . Given observations of Σ , I , Σ , and a pre-
for a CO (2-1) conversion factor using the same HERA- CO HI CO dust
scription for α (D/G′), one can simultaneously solve
CLES data employed in this paper, these values should CO
for α and D/G′. The solution is often multivalued
be borne in mind when reading our results. Our results CO
andunstable,thoughnotintractable. However,afterex-
remainpinnedtoaGalacticCO(1-0)conversionfactorof
α1C−O0 =4.35 M⊙ pc−2 (Kkms−1)−1 that may be ≈30% pHeerrismchenelt-abtaiosendarnedsuclotsmpofarSisaonndswtritohmtehteasl.elf(-2c0o1n2s)is,tewnet
too high, on average. As a result, a systematic bias of
foundthatthe processdoes notclearlyimproveouresti-
30%inΣ appearsplausible withfactor oftwovari-
≈ mol mates. Inthe interestsofclarityandsimplicity, wework
ations in the conversionfactor point-to-point.
with only D/G calculated using fixed α throughout
In addition to a fixed conversionα , we consider the CO
CO the paper. This simplification biases our α estimate
effects ofvariationsinα due to decreaseddustshield- CO
CO high by 8% (“Σ = 100”) and 15% (“Σ = 50”).
ing at low metallicity and variations in the linewidth, ≈ ≈
With improved Σ estimates, we expect that the self-
optical depth, and temperature of CO in galaxy cen- dust
consistent treatment will become necessary.
ters. Our “variable” α builds on the work of
CO The third term, c , accounts for depressed val-
Sandstrom et al. (2012), who compare HI, CO(2-1), center
ues of α in the centers of galaxies. Sandstrom et al.
and Σ in 22 HERACLES galaxies and Wolfire et al. CO
Dust (2012) find such depressions in the centers of many
(2010), who consider the effects of dust shielding on the
systems (see also Israel 2009a,b). These likely re-
“CO-dark” layer of molecular clouds, where most H is
flect the same line-broadening and temperature effects
H . The α prescription combines three terms
2 CO that drive the commonly invoked “ULIRG conversion
factor” (Downes & Solomon 1998), though the depres-
αCO =α0CO cCO−dark(D/G) ccenter(rgal) . (4) sion observed by Sandstrom et al. (2012) have lower
CHOere(2α-0C1O) c=on6v.e3rsMion⊙ fpacc−to2r(Kinktmhes−d1i)s−k1oifs aougralfiadxuyciaatl mDoawgnnietsud&eStohlaonmotnhe(1fa9c9t8o)r. ofS5anddesptrroemssioetnaflo.u(n2d01b2y)
solar metallicity (Equation 3). The term cCO−dark rep- could not identify a unique observational driver for
resents a correction to the H mass to reflect the H these depressions, though they correlate well with stel-
2 2
in a CO-dark layer not directly traced by CO emission. lar surface density. Instead, they appear to be present
We calculate this factor following Wolfire et al. (2010), with varying magnitudes in the centers of most systems
assuming that all GMCs share a fixed surface density, with bright central CO emission. Following their rec-
ΣGMC and adopting a linear scaling between the dust- ommendation, we apply this correction where rgal <
hto-gas riatio and metallicity (see also Glover & Mac Low 0.1r25 in systems that have such central CO concentra-
2011). In this case tions. Wheneveravailable,weadoptccenter directlyfrom
Sandstrom et al. (2012), taking the factor by which the
central α falls below the mean for the disk of that
0.4 CO
cCO−dark(D/G′)≈0.65exp(cid:18)D/G′ Σ100(cid:19) . (5) gnaoltaxiny.thFeorsasymstpelme sofwSitahndcsetnrtormaleCtOalc.o(n2c0e1n2t)r,awtioenaspbpulyt
a factor of two depression, again following their recom-
Here D/G′ is normalized to our adopted “Galac-
mendations. The appendix presents additional details.
tic” value of 0.01, with the normalization constructed
SFR from Hα, UV, and 24µm Emission: L12 com-
to yield α = α0 for D/G′ = 1. Σ =
CO CO 100 bined UV, Hα, and IR emission to estimate the recent
ΣGMC /100 M⊙ pc−2. The appendix presents this cal- star formation rate surface density, Σ , at 1 kpc res-
h i SFR
culation in detail.
olution (the limiting common physical resolution of the
We consider two cases: ΣGMC = 100 M⊙ pc−2 HERACLES survey) for our sample. We adopt their es-
(“Σ = 100”) and ΣGMC =h50 M⊙i pc−2 (“Σ = 50”). timates and refer the reader to that work for detailed
h i
“Σ = 100” reflects a typical surface density that is of- discussion. Briefly, our baseline estimate of Σ com-
SFR
ten assumed and observedfor extragalactic GMCs (e.g.,
6 Leroy et al.
bines Hα and infrared emission at 24µm via on comparison to Zibetti et al. (2009), we use
ΣSFR M⊙ yr−1 kpc−2 =634 IHα erg s sr−1 + (6) Σ∗(cid:2)M⊙ pc−2(cid:3)=200 I3.6 (cid:2)MJy sr−1(cid:3) , (8)
(cid:2) (cid:3) 0.00325 I(cid:2)24 µm MJ(cid:3)y sr−1(7) wbyhich5i0s%∼. 30% lower than L08. This value is uncertain
(cid:2) (cid:3) ∼
where IHα and I24µm refer to the line-integrated Hα in- We estimate the stellar surface density, Σ∗, for each
tensity and intensity at 24µm. kpc-sizedelementfromthecontaminant-corrected3.6µm
The Hα emission captures direct emission from HII mapsofMeidt et al.(2012). Startingfromareprocessing
regions powered by massive young stars while the 24µm oftheSINGSdata(aspartoftheS4GsurveySheth et al.
emission accounts for recent star formation obscured by 2010), they used independent component analysis to re-
dust. BeforeestimatingΣ ,wecorrectour24µmmaps move contamination by young stars and hot dust from
SFR
for the effects of heating of dust by a weak, pervasive the overall maps. These contaminants make a minor
radiation field (i.e., a “cirrus”) with magnitude derived contribution to the overall 3.6µm flux but may be im-
from modeling the infrared spectral energy distribution. portant locally. We convert the contaminant-corrected
The cirrus removed corresponds to the expected emis- 3.6µm maps to Σ∗ estimates using Equation 8.
sionfrom the local dust mass illuminated by a quiescent Rotation Velocities: Following L08 and Boissier et al.
radiation field, typically 0.6 times the Solar neigh- (2003) we work with a simple two-parameter fit to the
borhood interstellar radiat∼ion field (see L12 for details). rotation curve of each galaxy
Wederivetheappropriateweightingforthecombination
r
of Hα and 24µm emission based on comparing our pro- gal
v (r )=v 1 exp − (9)
rot gal flat
cessed Hα and 24µm maps to literature estimates of Hα (cid:20) − (cid:18) l (cid:19)(cid:21)
flat
extinction. The resulting linear combination resembles
withv andl freeparameters. Wederivethesefrom
that of Kennicutt et al. (2007) but places slightly more flat flat
fits to the rotation curves of de Blok et al. (2008) wher-
weight on the 24µm term. For comparison, we also esti-
ever they are available. Where these are not available,
mateΣ fromcombiningFUVand24µmemissionand
SFR wecarryoutour owntilted ringfits to the combinedHI
taking Hα alone while assuming a typical 1 magnitude
and CO first moment maps. We use these fits to calcu-
of extinction.
late the orbital time τ = 2πr /v for each line of
L12 estimate a substantial uncertainty in the absolute orb gal rot
sight.
calibration of “hybrid” UV+IR or Hα+IR tracers, with
magnitude 50%. Inadditiontothisoveralluncertainty
≈ 2.3. Sample and Galaxy Properties
in the calibration, they derive a point-to-point uncer-
tainty in Σ of 0.15 dex based on intercomparison Wepresentmeasurementsforgalaxiesmeetingthe fol-
SFR
≈
of different estimates. lowing criteria: 1) a HERACLES CO map containing a
Dust Properties: In order to measure dust properties, clear CO detection (S/N> 5 over a significant area and
we convolve the Spitzer 24, 70, and 160µm data and the multiple channels), 2) Spitzer data at 24µm, and 3) in-
CO andHI maps to the resolutionof the Spitzer 160µm clination . 75◦. The first condition excludes low mass
data. At this resolution, we build radial profiles of each galaxies without CO detections (these are discussed in
bandandthenfitthe dustmodels ofDraine & Li(2007) Schruba et al. 2012). The second removes a few targets
to these profiles. These fits, presented in L12, provide withsaturatedorincompleteSpitzercoverage. Thethird
us with radial estimates of the dust-to-gas ratio, D/G, removes a handful of edge-on galaxies. We are left with
and are used to help account for “cirrus” contamination the 30 disk galaxies listed in Table 1.
when estimating Σ . Note that the 40′′ resolution For each target, Table 1 gives the distance, phys-
SFR
∼
of the 160µm data used to measure these dust proper- ical resolution of the HERACLES maps at that dis-
tiesissignificantlycoarserthanthe1kpcresolutionused tance, inclination, position angle, and optical radius.
for the rest of our data. Where possible, we have com- The Table notes note the subset of galaxies that that
paredourSpitzer-baseddustmassestomassesestimated are close and large enough for us to carry out the
using the improved SED coverage offered by Herschel multi-resolution analysis in Section 4.3. We adopt
(e.g., Aniano et al. 2012); above Σdust 0.05 M⊙ pc−2 distances from Kennicutt et al. (2011) where possible
≈
themedianoffsetbetweentheHerschelandSpitzerbased and from Walter et al. (2008) elsewhere. We take ori-
dust masses is only 10%; howeverthe dust masses de- entations from Walter et al. (2008) and from LEDA
≈
rived for individual rings using only Spitzer do scatter (Prugniel & Heraudeau 1998) and NED elsewhere.
by 0.3 dex (a factor of two) compared to Herschel- Table 2 reports integratedand disk-averageproperties
≈
baseddustmassesandshowweaksystematictrendswith foroursample. Wereportourintegratedstellarmasses-
the sense that Spitzer underestimates the mass of cooler timate, galaxy morphology, metallicity and dust-to-gas
( 15 K) dust in the outskirts of galaxies (both consis- ratio at 0.4 r , average gas mass and star forma-
25
∼ ≈
tent with the analysis of Draine et al. 2007). We expect tion rate surface density inside 0.75 r , our parameter-
25
that once Herschel images become available, they will ized rotation curve fit, and the orbital time at 0.4 r .
25
significantly improve the accuracy of dust-based portion We take metallicities from Moustakas et al. (2010), av-
of this analysis. eraging their PT05 and KK04 strong-line calibrations.
Stellar Mass: To estimate the stellar mass for whole They argue that these two calibrations bracket the true
galaxies, we draw 3.6µm fluxes from Dale et al. (2007, metallicity and that the relative ordering of metallici-
2009), convert to a luminosity using our adopted dis- ties is robust (see also Kewley & Ellison 2008), but the
tance,andapplyafixed3.6µmmass-to-lightratio. Based uncertainty in the absolute value is considerable. For
Molecular Gas and Star Formation in Nearby Disk Galaxies 7
cases where Moustakas et al. (2010) do not present a sumptions.
metallicity, we draw one from the recent compilations Kennicutt (1998b) presented disk-averaged measure-
by Marble et al. (2010) and Calzetti et al. (2010). ments for 57 normal spiral galaxies and 15 starburst
galaxies. He used literature CO with a fixed α to
CO
2.4. Methodology estimate Σ . To estimate Σ , he used Hα in disk
mol SFR
galaxies and IR emission in starbursts.
We sampleourtargetsat1kpc resolution. This isfine
Calzetti et al.(2010)estimateddisk-averagedΣ for
enoughtoisolatemanykeyphysicalconditionsinthein- SFR
a large set of nearby galaxies. We cross-index these
terstellar medium (ISM): metallicity, coarse kinematics,
with integrated CO fluxes from Young et al. (1995),
gas and stellar surface density. At the same time, we
Helfer et al. (2003), and Leroy et al. (2009) to derive
expecttoaverageseveralstarformingregionsineachel-
ement (e.g., Schruba et al. 2010), with Mmol & 107 M⊙ Σmol assuming that CO emission covers the same area
as Hα. From the combination of these data we have
ealnedmMen∗t.&T1h0is4mMi⊙nimfoirzmesedcoonvceerrnthsealbaosutt∼ev5oMlutyironinoefaicnh- disk-averageΣSFR and Σmol estimates for 41 galaxies.
Saintonge et al. (2012), following Saintonge et al.
dividual regions,sampling the IMF, and drift of stars or
(2011), present the COLDGASS survey, which obtained
leakage of ionizing photons from their parent region.
integrated molecular gas mass and SFRs for 366 galax-
We convolve each map to have a symmetric gaussian
beam with FWHM 1 kpc. For the Spitzer 24µm maps ies with M∗ >1010 M⊙, 215 with secure CO detections.
we first convert from the MIPS PSF to a 13′′ gaussian Thislargesurveyrepresentsthebestsampleofintegrated
galaxymeasurementstodate. Toconverttosurfaceden-
beamusingakernelkindly providedbyK.Gordon,then
sities, we take the area of the star-forming disk in these
we convolve to 1 kpc. This exercise effectively places
galaxies to be 0.75 r . Saintonge et al. (2012) derive
our targets at a common distance but does not account 25
theirSFRsfromSEDmodelingthatyieldsresultscloseto
for foreshortening along the minor axis. Five galaxies
what one would obtain converting the UV+IR luminos-
are too distant to convolve to 1 kpc. We mark these in
ity directly to a SFR. This yields higher SFRs than our
Table 1 and include them in our analysis at their native
approachfor matched measurements. Comparing galax-
resolution.
ies with matched stellar mass or molecular gas content,
Wesampleeachmaptogenerateasetofintensitymea-
we find the offset to be 0.19 dex, a factor of 1.55.
surements. The sampling points are distributed on a ≈ ≈
This agrees well with what one would expect account-
hexagonal grid with points spaced by 0.5kpc, one half-
ing for our subtraction of an IR cirrus with magnitude
resolution element. At each sampling point we measure
1.2andour24µmcoefficient,whichis 1.2lowerthan
CO(2-1) intensity, Hi intensity, a suite of star formation ≈ ≈
what one would adopt to match a bolometric TIR SFR
rate tracers (described in L12), dust properties, and Σ∗. indicator (see L12 for calculations and discussion).
Weusethesetoestimatephysicalconditionsasdescribed
Leroy et al. (2005) combined new data with
above and in L12, taking into account the inclination of
measurements by Young et al. (1995), Elfhag et al.
the galaxy.
(1996), Taylor et al. (1998), B¨oker et al. (2003), and
We also identify a sample of galaxies to study the ef-
Murgia et al. (2002) to compare Σ and Σ for
fects of physical resolution. Nine galaxies, marked in SFR mol
individual 30–50′′ pointings in a wide sample of
Table 1, have both the proximity and extent to allow us ∼
nearby galaxies. They estimate Σ from the 20cm
to test the effect of physical resolution on our results. SFR
radio continuum (Condon 1992). These low-resolution
We convolvethese to a successionofphysicalresolutions
pointings typically cover several kpc, a larger area than
from 0.6 to 2.4 kpc for further analysis (Section 4.3).
our resolution elements but less than an average over a
WetreatregionswithΣSFR <10−3 M⊙ yr−1 kpc−2 or whole galaxy disk.
I <2.5 σ asupperlimitsandconsideronlypoints
CO × CO Wong & Blitz (2002), Schuster et al. (2007), and
withr <0.75r —theHERACLESmapscontainsig-
gal 25 Crosthwaite & Turner (2007) presented radial pro-
nal outside this radius (Schruba et al. 2011) but mostly
files of Σ and Σ for several nearby galaxies.
not significant emission over individual lines-of-sight. In mol SFR
Wong & Blitz (2002) targeted 7 nearby spirals, using
total we have 14,500 lines of sight with at least one
significant mea∼surement, of which 1,900 have CO upper Hα to calculate ΣSFR. Schuster et al. (2007) targeted
M51 and derived Σ from 20-cm radio continuum
limits and 1,650 have SF upper limits. Points for which SFR
to estimate Σ . We only present the Wong & Blitz
neither measurement is significant are not considered in SFR
(2002)andSchuster et al.(2007)profilesdowntoΣ
tnhael panatatleyrsnis.leaNdysqutoistovsearmsapmlinpglintghebymaapsfaicntoar hofexago5-, 5 M⊙ pc−2, below which we consider them smooml ≈e-
∼ what unreliable. Crosthwaite & Turner (2007) targeted
so that this corresponds to > 2,000 independent mea-
NGC 6946 and used IR emission to estimate Σ .
surements. The maximum (2.5σ) upper limit on Σ is SFR
mol Kennicutt et al. (2007), Blanc et al. (2009),
≈6M⊙ pc−2,themedianupperlimitis≈2.6M⊙ pc−2. Rahman et al. (2011), and Rahman et al. (2012)
targeted small regions, similar to B08 and the work
2.5. Literature Data
presented here. Kennicutt et al. (2007) focused on
WecompareourresultstorecentmeasurementsofSFR luminous regions in M51, mainly in the spirals arms.
and molecular gas. These employ a variety of sampling They infer Σ from a combination of Hα and 24µm
SFR
schemes and SFR tracers. We adjust each to match our emission. Rahman et al. (2011) explored a range of
adoptedCO-to-H2 conversionfactorandIMF.Contrast- methodologies. We focus on their most robust measure-
ing our approachwith these data illuminates the impact ments, drawn from bright regions in NGC4254 with
ofmethodologyandallowsusto explorewhetherdiverse Σ from a combination of NUV and 24µm emission.
SFR
observations yield consistent results under matched as-
8 Leroy et al.
TABLE 2
SampleProperties
Galaxy log(M∗) Morphology z D/G hΣHI+H2i hΣSFRi vflat lflat hτorbi
log10 [M⊙] T-Type [12+log[O/H]] [M⊙ pc−2] [10−3 Mk⊙pcy2r−1] [kms−1] [kpc] [108 yr]
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
NGC0337 9.9 6.7 8.51 0.004 21 14 130 2.9 2.4
NGC0628 10.0 5.2 8.69 0.012 15 4.0 200 0.8 1.3
NGC0925 9.7 7.0 8.52 0.004 7.5 1.3 140 6.9 4.4
NGC2403 9.6 6.0 8.57 0.009 10 3.3 120 0.95 1.6
NGC2841 10.7 3.0 8.88 0.037 4.6 1.4 310 2.3 1.2
NGC2903 10.4 4.0 8.90c 0.012 12 5.7 210 2.4 2.0
NGC2976 9.0 5.2 8.67 0.008 7.6 4.4 88 1.1 1.4
NGC3049 9.5 2.5 8.82 0.005 8.0 10 180 3.0 1.5
NGC3184 10.2 6.0 8.83 0.018 14 2.8 200 2.5 1.8
NGC3198 10.0 5.2 8.62 0.012 8.4 2.3 150 3.0 2.6
NGC3351 10.1 3.1 8.90 0.018 8.5 5.2 200 1.1 1.2
NGC3521 10.7 4.0 8.70 0.012 22 7.8 229 1.5 1.5
NGC3627 10.5 3.1 8.67 0.016 13 7.7 190 1.1 1.8
NGC3938 10.3 5.1 8.71c 0.018 22 7.9 140 0.73 1.6
NGC4214 8.7 9.8 8.36c 0.0038 9.2 8.4 350 11 2.0
NGC4254 10.5 5.2 8.79 0.01 47 18 170 1.4 1.6
NGC4321 10.6 4.1 8.84 0.012 30 9.0 229 1.8 1.4
NGC4536 10.2 4.3 8.61 0.005 13 6.8 180 0.7 2.0
NGC4559 9.5 6.0 8.55 0.005 10 1.8 100 2.1 2.9
NGC4569 10.2 2.4 8.88c 0.017 8.5 1.9 220 3.2 1.8
NGC4579 10.7 2.8 8.93c 0.021 13 3.8 270 1.7 1.2
NGC4625 8.9 8.8 8.70 0.011 8.5 6.6 27 0.53 2.3
NGC4725 10.5 2.2 8.73 0.03 4.5 0.75 220 1.1 1.9
NGC4736 10.2 2.4 8.66 0.008 17 10 170 0.25 0.77
NGC5055 10.5 4.0 8.77 0.02 18 4.1 200 0.71 1.7
NGC5194 10.5 4.0 8.87 0.02 53 20 210 0.58 1.0
NGC5457 10.4 6.0 8.46c 0.013 10 2.4 210 1.2 2.7
NGC5713 10.3 4.0 8.64 0.006 54 37 ··· ··· ···
NGC6946 10.5 5.9 8.73 0.007 37 21 190 1.2 1.5
NGC7331 10.8 3.9 8.68 0.01 16 4.4 260 1.9 1.9
Note. —Propertiesofsamplegalaxies. Columnsgive(1)galaxyname;(2)integratedstellarmassofwholegalaxiesbasedon
3.6µm flux of Daleetal. (2007, 2009); (3) morphology; (4) “characteristic” metallicity at 0.4 r25 from Moustakas etal. (2010),
averaging theirPT05andKK04calibrations;(5) dust-to-gas ratioat0.4r25 based onourmodelingofSpitzerdata; (6)average
HI+H2 surface density inside 0.75 r25; (7) average star formation rate surface density inside 0.75 r25; parameters for simple
rotationcurvefit,(8)vflat and(9)lflat;and(10)orbitaltimeat0.4r25 basedontherotationcurve.
c MetallicityfromcompilationofCalzetti etal.(2010)andMarbleetal.(2010)orKennicutt etal.(2003b)(NGC5457).
Rahman et al.(2012)extendedthis worktoconsiderthe panel and bottom row, blue contours show data density
fullsetofCARMASTINGgalaxies,usingonlythe24µm adopting different weightings. The top right panel gives
emission with a nonlinear calibration to infer Σ . identical weight to each line of sight, treating each kpc2
SFR
Blanc et al. (2009) studied the central 4.1 4.1kpc2 of as equal regardless of location. The bottom left panel
×
M51, deriving Σ from Hα spectroscopy corrected gives equal weight to each galaxy and so weights mea-
SFR
using the Balmer decrement. surementsfromsmallgalaxieswith little areamorethan
measurements from large galaxies. The bottom right
3. ΣSFR-ΣMOL SCALINGRELATIONS:FIRSTORDER panel treats each radial ring in each galaxy equally, and
CONSTANCYOFτMOL
DEP sogivesmoreweighttothecentralpartsofgalaxiesthan
We estimate ΣSFR and Σmol for 14,500points in 30 their outer regions. Dashed lines here and throughout
∼
nearby galaxies. In this section we analyzethese data in this paper indicate fixed τmol and a horizontal line indi-
dep
the context of a traditional “star formation law” scaling
catesthelimitofourΣ measurements. Inthetopleft
relation ( 1.1). We show the data distribution in Σ - SFR
SFR panel, dark points show measurements where one quan-
§
Σ parameter space ( 3.1) and examine how this de-
mol tity is an upper limit. Table 3 summarizes key values
§
pendsonmethodology( 3.2). UsingaMonteCarlotech-
from the plots in this section.
§
nique based on that of Blanc et al. (2009), we consider
The top rows of Figure 1 and Table 3 show the good
the best fit power-law to the ensemble data and individ-
correspondence between Σ and Σ that we have
SFR mol
ual galaxies ( 3.3). We compare our results to a broad
previously found in the HERACLES sample (B08,L08,
§
sample of literature data ( 3.4).
Schruba et al. 2011; Bigiel et al. 2011). Our dynamic
§
3.1. Combined Measurement range at 1 kpc resolution spans from ΣSFR 10−3
to 10−1 M⊙ yr−1 kpc−2 and Σmol from a∼few to
Figure 1 compares ΣSFR, estimated from Hα+24µm, 100 M⊙ pc−2. Across this range, Σmol and ΣSFR cor-
andΣmol at1 kpc resolutionforourwhole sample. Indi- relate well,exhibiting a Spearmanrankcorrelationcoef-
vidualkpc resolutionlines ofsightappearasgraypoints ficient&0.7formosttracersandweightings. Thisquan-
and the red points show the median ΣSFR and standard tifies the tight, one-to-one relationship visible by eye in
deviationafterbinningthedatabyΣ . Inthetopright
mol
Molecular Gas and Star Formation in Nearby Disk Galaxies 9
Fig.1.—Starformationratesurfacedensity, ΣSFR,estimated fromHα+24µm emission,asafunctionofmoleculargas surfacedensity,
Σmol,derivedfromCO(2-1)emissionfor30nearbydiskgalaxies. Thetopleftpanelshowsindividualpoints(darkgraypointsshowupper
limits)withtherunningmedianandstandarddeviationindicatedbyredpointsanderrorbars. Theredpointswitherrorbarsfromthefirst
panelappearinallfourpanelstoalloweasycomparison. DottedlinesindicatedfixedH2 depletiontimes;thenumberindicateslog10τDep
inyr. Thetop rightpanel shows thedensity ofthedata inthetop leftpanel. Inthe bottom panels wevarytheweighting usedtoderive
datadensity. Thebottomleftpanelgivesequalweighttoeachgalaxy. Thebottomrightpanelgivesequalweighttoeachgalaxyandeach
radialbin.
the top row. tom left panel) reveals a significant population of low
The median τmol weighting each line of sight equally Σ , high Σ , low τmol data. This drives the median
dep mol SFR dep
is 2.2 Gyr with a scatter of 0.3 dex, a factor of two. depletiontime for the sample from 2.2Gyr, weighting
The absolute value of the median τmol, i.e., the scale by line-of-sight, to 1.3 Gyr, weig≈hting by galaxy. In
dep
of the x- and y-axes in Figure 1, depends on the cali- Section 4.1 we show≈that these low apparent τmol orig-
dep
bration of our SFR tracer and CO-to-H2 conversionfac- inate from low-mass, low-metallicity systems (see also
tor. Eachremains uncertain at the 30–50%level and we Schruba et al.2011;Krumholz et al.2011;Schruba et al.
suggest that an overall uncertainty of 60% on the ab- 2012). Because of their small size, these systems do not
solute value of τmol represents a realistic, if somewhat contribute many data comparedto large,metal-richspi-
dep
conservative, value. Our Σ and Σ estimates can rals. Therefore, they only weakly influence the overall
mol SFR
be compared internally with much better accuracy than data distribution seen in the top row. We examine τmol
dep
this(L12,Sandstrom et al.2012),sowesuggestthatthis as a function of host galaxy properties and local condi-
uncertaintybeviewedasanoverallscalingofourresults. tionsinSections4.1and4.2. Intheappendixwepresent
The bottom row in Figure 1 begins to revealthe devi- Σ Σ relationsforindividualgalaxies(seealsoTa-
SFR mol
ations from a simple one-to-one scaling that will be the ble 2)−, allowing the reader to see how Figure 1 emerges
subjectofSection4. Weightingallgalaxiesequally(bot-
10 Leroy et al.
mate each quantity (see references in Leroy et al. 2011,
TABLE 3 L12) and the recent literature includes many claims
τmol at1kpc Resolution
dep about the effect of physical parameter estimation on the
relation between Σ and Σ . In this section, we
SFR mol
Tracer Medianτdmeopl Scatter rcorr explore the effects of varying our approach to estimate
[Gyr] [1σ dex] (Σmol,ΣSFR) ΣSFR and Σmol.
Weightingasequaleach...
line-of-sight 3.2.1. Choice of SFR Tracer
... fixedαCO 2.2 0.28 0.72±0.02
... Σ=100αCO 2.6 0.26 0.75±0.01 Figure 2 and the lower part of Table 3 report the
... Σ=50αCO 3.1 0.28 0.70±0.01 results of varying our approach to trace the SFR. We
galaxy show Σ estimated from only Hα, with a fixed, typi-
... fixedαCO 1.3 0.32 0.67±0.19 calA SF=R1mag(topleft),alongwithresultscombining
... ... onlyM∗>1010 M⊙ 1.7 0.21 0.87±0.18 Hα
... ... onlyM∗<1010 M⊙ 0.4 0.29 0.53±0.37 FUV,insteadofHα,with24µmemission(topright). We
... Σ=100αCO 1.8 0.20 0.89±0.17 also show the results of varying the approach to the IR
... ... onlyM∗>1010 M⊙ 2.0 0.13 0.95±0.25 cirrus. Our best-estimate ΣSFR combines Hα or FUV
... ... onlyM∗<1010 M⊙ 1.1 0.26 0.87±0.35 with 24µm after correcting the 24µm emission for con-
... Σ=50αCO 2.4 0.26 0.90±0.19 tamination by an IR cirrus following L12. We illustrate
...... ...... oonnllyyMM∗∗<>11001100 MM⊙⊙ 22..71 00..2311 00..7984±±00..4241 the impact of this correction by plotting results for two
TracingΣSFR with... limiting cases of IR cirrus correction: no cirrus subtrac-
(weightinglines-of-sightequally) tion (bottom left) and removing double our best cirrus
Hα+24µm estimate (bottom right), which we consider a maximum
... best estimate 2.2 0.28 0.72±0.02
reasonable correction. Data density contours in Figure
... nocirrus 2.0 0.22 0.79±0.02
... doublecirrus 3.0 0.37 0.62±0.02 2 weight each point equally and the large black points
FUV+24µm indicate the original binned results from Figure 1.
... best estimate 2.2 0.27 0.72±0.02 ThetopleftpanelofFigure2andTable3showthatthe
... nocirrus 1.9 0.21 0.81±0.02
basic relationship between Σ and Σ persists even
... doublecirrus 3.2 0.39 0.58±0.02 SFR mol
Hα+1mag 2.1 0.30 0.66±0.02 when we derive ΣSFR from Hα alone. The median τdmeopl
andscatterusing only Hα resemblewhatwe find for our
Note. — Medianmolecular gas depletion time, scatter, and corre-
lation between ΣSFR and Σmo in our sample. Line-of-sight averages best estimate and the correlation between Hα and CO
treat each kpc-resolution line of sight as equal. Galaxy averages re- appearsonlymoderatelyweakerthanforthehybridSFR
fer to τdmeopl =hΣmoli/hΣSFRi inside0.75 r25 for each galaxy. Unless tracer. It also appears moderately flatter than relations
otherwise noted, we calculate Σmol using fixed αCO and ΣSFR from that incorporate IR emission as we underestimate ex-
Hα+24µm. Quotederrorbarsonτdmeoplreport1σscatter,uncertainties tinctionin the centralparts ofgalaxies( 3.3). Inasmuch
ontherankcorrelationarisefromrandomlyrepairingdata. as Hα represents an unambiguous trace§r of recent star
formation, the top left panel in Figure 2 demonstrates
from the superposition of individual systems (see also
that subtle biases in the treatment of IR emission, e.g.,
Section 3.3).
24µm emission tracing the ISM rather than recent star
Weighting radial rings equally (bottom right panel)
formation, do not drive our results.
highlights these same low τmol-low Σ galaxies and
dep mol ThetoprightpanelshowsΣ tracedbyFUV+24µm
SFR
brings out an additional low τmol population at higher emission. The distribution agrees well with what we
dep
Σ . These point emerge because the radial weighting found using Hα+24µm, as do the median and scatter
mol
emphasizes points in the central parts of galaxies rela- in τmol. The agreement of FUV+24µm and Hα with
dep
tive to their outskirts. We show in Section 4.4 that the our best estimate Hα+24µm occur partially because we
central regions of many of our targets exhibit enhanced have designed our SFR tracers to yield self-consistent
efficiency compare to their disks. As will small galaxies, results (L12). However, that procedure considered only
these central regions contribute only a tiny fraction of theoverallnormalizationanddidnotrequirethedetailed
the area in our survey and thus exert little impact on agreement we see comparing Figures 1 and 2.
the plots in the top row. In the bottom row, we vary our approach to the in-
Figure 1 thus illustrates our main conclusions: a first frared cirrus. By default, we correct the 24µm map
order simple linear correlation between ΣSFR and Σmol for infrared cirrus following L12. The bottom left panel
and real second order variations. It also illustrates showstheresultsofapplyingnocirrussubtraction,while
the limitation of considering only ΣSFR-Σmol parameter in the bottom right panel we double our cirrus subtrac-
space to elicit these second-order variations. Metallic- tion. Turning off the cirrus subtraction yields median
ity, dust-to-gas ratio, and position in a galaxy all play τmol 10%shorterthan our best estimate with notably
key roles but are not encoded in this plot, leading to dep ≈
lowerscatterandourstrongestobservedcorrelation. The
double-valued Σ at fixed Σ in some regimes. We
SFR mol tighter correlation reflects the fact that the relationship
explorethese systematic variations in τmol andmotivate
dep between 24µm and CO emission is the strongest in the
our explanations throughout the rest of the paper. data (see also Schruba et al. 2011). Σ tracers that
SFR
more heavily emphasize 24µm exhibit the strongest cor-
3.2. Relationship for Different SFR and Molecular Gas relation with Σ traced by CO.
mol
Tracers Doubling the cirrus subtraction leads to an 25%
Figure1 showsourbest-estimate Σ andΣ com- longer τmol, larger scatter, and a mildly weaker c≈orrela-
SFR mol dep
puted from fixed α . Many approaches exist to esti- tion between Σ and Σ . This partially reflects un-
CO SFR mol