The Fueling Diagram: Linking Galaxy Molecular-to-Atomic Gas Ratios to Interactions and Accretion
David V. Stark, Sheila J. Kannappan, Lisa H. Wei, Andrew J. Baker, Adam K. Leroy, Kathleen D. Eckert, Stuart N. Vogel
aa r X i v : . [ a s t r o - ph . C O ] A p r Draft version November 6, 2018
Preprint typeset using L A TEX style emulateapj v. 12/16/11
THE FUELING DIAGRAM: LINKING GALAXY MOLECULAR-TO-ATOMIC GAS RATIOS TOINTERACTIONS AND ACCRETION
David V. Stark , Sheila J. Kannappan , Lisa H. Wei , Andrew J. Baker , Adam K. Leroy , Kathleen D.Eckert , and Stuart N. Vogel Draft version November 6, 2018
ABSTRACTTo assess how external factors such as local interactions and fresh gas accretion influence the globalISM of galaxies, we analyze the relationship between recent enhancements of central star formation andtotal molecular-to-atomic (H /HI) gas ratios, using a broad sample of field galaxies spanning early-to-late type morphologies, stellar masses of 10 . − . M ⊙ , and diverse stages of evolution. We findthat galaxies occupy several loci in a “fueling diagram” that plots H /HI ratio vs. mass-correctedblue-centeredness, a metric tracing the degree to which galaxies have bluer centers than the averagegalaxy at their stellar mass. Spiral galaxies of all stellar masses show a positive correlation betweenH /HI ratio and mass-corrected blue-centeredness. When combined with previous results linkingmass-corrected blue-centeredness to external perturbations, this correlation suggests a systematic linkbetween local galaxy interactions and molecular gas inflow/replenishment. Intriguingly, E/S0 galaxiesshow a more complex picture: some follow the same correlation, some are quenched, and a distinctpopulation of blue-sequence E/S0 galaxies (with masses below key scales associated with transitions ingas richness) defines a separate loop in the fueling diagram. This population appears to be composed oflow-mass merger remnants currently in late- or post-starburst states, in which the burst first consumesthe H while the galaxy center keeps getting bluer, then exhausts the H , at which point the burstpopulation reddens as it ages. Multiple lines of evidence suggest connected evolutionary sequences inthe fueling diagram. In particular, tracking total gas-to-stellar mass ratios within the fueling diagramprovides evidence of fresh gas accretion onto low-mass E/S0s emerging from their central starburstepisodes. Drawing on a comprehensive literature search, we suggest that virtually all galaxies followthe same evolutionary patterns found in our broad sample. Keywords:
Galaxies: General — Galaxies: Interactions — Galaxies: ISM INTRODUCTION
It has been well documented that stars form in molec-ular gas (e.g., Bigiel et al. 2008). Therefore, understand-ing what drives the conversion of hydrogen between itsatomic and molecular forms is key to understanding howgalaxies evolve. The molecular-to-atomic gas mass ratio(H /HI) varies widely between galaxies, and several stud-ies have aimed to determine what properties of galaxies– or their environments – play the largest role in theevolution of H /HI.Work from the last few decades has revealed correla-tions between global H /HI and such properties as lu-minosity (or stellar mass), total gas mass, morphology,and specific star formation rate (Kenney & Young 1989;Thronson et al. 1989; Young & Knezek 1989; Braine &Combes 1993; Casoli et al. 1998; Boselli et al. 2002;Obreschkow & Rawlings 2009). Unfortunately, thesestudies have been largely focused on only certain types ofgalaxies (e.g., massive spirals) and/or star-forming/FIR- Physics and Astronomy Department, University of NorthCarolina, Chapel Hill, NC 27516 Atmospheric and Environmental Research, 131 Hartwell Av-enue, Lexington, MA 02421 Department of Physics and Astronomy, Rutgers, the StateUniversity of New Jersey, 136 Frelinghuysen Road, Piscataway,NJ 08854 National Radio Astronomy Observatory, 520 EdgemontRoad, Charlottesville, VA 22903 Department of Astronomy, University of Maryland, CollegePark, MD 20742 bright galaxies in the nearby universe, which are not rep-resentative of the galaxy population as a whole. More re-cently, the CO Legacy Database for the GALEX AreciboSDSS Survey (COLD GASS) has measured CO emissionfor a randomly selected sample of ∼
300 galaxies withstellar masses M ∗ > M ⊙ . COLD GASS finds cor-relations between H /HI and structural properties likestellar mass, global stellar mass surface density, r -bandlight concentration index, and N U V − r color, while alsofinding that there are thresholds in galaxy concentrationindex and global stellar surface mass density above whichdetections of molecular gas begin to disappear (Saintongeet al. 2011; Kauffmann et al. 2012). While the survey’sselection improves upon past work by focusing on more“normal” galaxies, a caveat is that it only includes mas-sive galaxies. Moreover, multiple physical mechanismsmay underlie the observed correlations.The question remains as to what balance of internaland external processes regulates H /HI in galaxies. Anumber of authors have aimed to explain H /HI com-pletely in terms of local physics within galaxies, set bytheir structure and dynamics. Detailed studies of atomicand molecular gas in nearby galaxies on kpc scales (Re-gan et al. 2001; Kuno et al. 2007; Walter et al. 2008;Leroy et al. 2009) have shown that H /HI is correlatedwith local internal variables such as galactocentric ra-dius, stellar and gas surface mass density, radially vary-ing velocity dispersion and rotation velocity, or combina-tions of these (Wong & Blitz 2002; Blitz & Rosolowsky Stark et al. conversion factor, X CO (Wilson 1995; Arimotoet al. 1996; Bolatto et al. 2008; Obreschkow & Rawl-ings 2009; Wolfire et al. 2010; Glover & Mac Low 2011;Leroy et al. 2011). Correlations of H /HI with inter-nal properties can be used to support models where themolecular fraction of gas is governed by the equilibriumbetween molecule formation on dust grains and destruc-tion by the FUV background (Elmegreen 1993; Blitz &Rosolowsky 2006; Krumholz et al. 2009). Alternativetheories argue that molecular cloud formation is a verynon-equilibrium process, spurred by gravitational insta-bilities, converging gas flows, and/or cloud-cloud colli-sions (Tan 2000; Mac Low & Klessen 2004; Heitsch &Hartmann 2008; Pelupessy & Papadopoulos 2009), andthat newly formed molecular clouds fail to reach equilib-rium with their environments before they are destroyedby star formation (Mac Low & Glover 2012). In this pic-ture, molecular cloud formation may be highly dependenton drivers that disrupt gas equilibrium.Consideration of global dynamical states suggests thatexternal factors lead to increases in H . At the veryleast, external perturbations and/or bars can transportgas to the central regions of galaxies where it can ex-ist at higher densities that promote the conversion ofHI to H and then stars. Barred galaxies, which may belinked to interactions (Gerin et al. 1990; Miwa & Noguchi1998), display central gas concentrations indicative ofinflows (Sakamoto et al. 1999; Sheth et al. 2005). In-teracting systems display deviations from typical H /HIand star formation rate relations, with higher averageH /HI than non-interacting galaxies (Kenney & Young1989; Braine & Combes 1993; Lisenfeld et al. 2011) andhigher star formation rate density than predicted usingthe Kennicutt-Schmidt relation defined by normal spirals(Kennicutt 1998; Bigiel et al. 2008). Moreover, Blitz &Rosolowsky (2006) find higher H /HI ratios at a givenmid-plane pressure for interacting systems compared tonon-interacting systems. Post -starburst galaxies simi-larly show excess star formation given their gas content,likely due to H heating and depletion by the starburst(Leroy et al. 2006; Robertson & Kravtsov 2008; Wei et al.2010b). Papadopoulos & Pelupessy (2010) recreate suchdeviations in simulations, linking them to quickly evolv-ing systems, particularly those that are gas rich and haveexperienced recent minor mergers or fresh gas infall. Itshould also be noted that X CO may be lower for cen-trally concentrated molecular gas, possibly making theincrease in molecular gas due to an interaction appeareven higher (Downes et al. 1993; Garcia-Burillo et al.1993; Regan 2000).The correlation of galaxy interactions with moleculargas enhancement (and/or higher CO luminosity per unitmolecular gas mass) is an established result, but an openquestion remains whether interaction-induced enhance-ments are occasional serendipitous events or the domi-nant driver of observed H /HI ratios in galaxies. Kan-nappan et al. (2004) argue that galaxy interactions ac-count for the majority of recent central star formationenhancements that produce blue central color excesses,based on the correlation of blue-centered galaxies and signs of minor mergers/encounters, a result that is con-firmed by Gonzalez-Perez et al. (2011). This correlationimplies that blue-centered galaxies experience gas inflowsto feed these star-forming events, a scenario addition-ally supported by such galaxies’ transient decreased cen-tral metallicities (Kewley et al. 2006, 2010; Rupke et al.2010). Kannappan et al. (2004) find that roughly 10% ofstar-forming galaxies show blue-centered color gradients,and most have likely experienced a blue-centered phaseat least once in their lifetimes; this percentage increaseswith decreasing luminosity. Additionally, when the sys-tematic trend towards central reddening at higher lumi-nosity is subtracted (yielding luminosity-corrected blue-centeredness), the number of galaxies identified as havingenhanced central blueness at fixed luminosity increases,and the correlation with interactions is stronger. Theseresults are interesting when combined with recent anal-yses of the rates of minor mergers and flyby encounters,which suggest that intermediate-to-high mass galaxiesexperience such frequent interactions that they can rarelybe considered truly isolated (Maller et al. 2006; Fakhouri& Ma 2008; Jogee et al. 2009; Hopkins et al. 2010; Lotzet al. 2011; Sinha & Holley-Bockelmann 2012). There-fore, interaction-induced inflows may play a key role inmolecular gas replenishment for much of the galaxy pop-ulation.To explore this idea, this paper examines the relation-ship between global H /HI and recent central star forma-tion enhancements parametrized by mass-corrected blue-centeredness (precisely defined in § /HI for nearly all spiral galaxies anda fraction of E/S0 galaxies, implying a systematic linkbetween external perturbations and global H /HI ratios.Intriguingly, our data also reveal that low-mass blue se-quence E/S0 galaxies – i.e., E/S0 galaxies that fall onthe blue-sequence in color versus stellar mass space withspirals (Kannappan et al. 2009) – define an evolutionarytrack offset from the main relation toward stronger blue-centered color gradients at a given H /HI, and trends inthese galaxies’ total gas-to-stellar mass ratios along thistrack suggest the likelihood of fresh gas accretion duringa late- to post-starburst phase. Thus we find that severalevolutionary tracks can be summarized within a “fuelingdiagram” that links the immediate fuel available for starformation, the total gas, and a metric tracing the recentinteractions that drive the fueling. DATA AND METHODS
This section describes our initial sample drawn fromthe Nearby Field Galaxy Survey and designed to be rep-resentative of intermediate mass E-Sbc galaxies, followedby the larger literature sample we use to expand our dataset and confirm our results. We also describe our newCO(1-0) and CO(2-1) observations and our methods forextracting the useful quantities of gas mass, stellar mass,blue-centeredness, and mass-corrected blue-centeredness.Finally, we discuss the cuts applied to our sample to en-sure robust results.All distances are calculated using heliocentric velocitycorrected to the Local Group frame of reference follow-ing the method of Jansen et al. (2000b) and assuming he Fueling Diagram = 70 km s − Mpc − , except in cases where a more di-rect distance indicator was available in NED. Samples
The Nearby Field Galaxy Survey
Our primary sample comes from the Nearby FieldGalaxy Survey (Jansen et al. 2000a,b; see also Jansen& Kannappan 2001), a set of ∼
200 galaxies selected tospan a broad range of B -band luminosities and mor-phologies. The data products of the original survey in-clude U BR surface photometry and optical spectroscopy(Jansen et al. 2000a,b; Kannappan & Fabricant 2001;Kannappan et al. 2002, 2009). The sample also in-cludes extensive supporting data relevant to this study.Roughly 90% of galaxies have Sloan Digital Sky Survey(SDSS) DR8 optical imaging (Aihara et al. 2011). Allhave near infrared (NIR) data from the 2 Micron All SkySurvey (2MASS; Skrutskie et al. 2006) while 55% havedeeper
Spitzer
Infrared Array Camera (IRAC; Fazio etal. 2004) imaging, mainly from Sheth et al. (2010), Mof-fett et al. (2012) and Kannappan et al. (2013, submitted,hereafter K13s). In addition, all galaxies have single dish21cm data (Wei et al. 2010a, K13s).For this study, we analyze the 35 out of 39 NFGS galax-ies with CO data that pass the useability cuts applied toour final sample (see § . − . M ⊙ , morpholo-gies ranging from E to Sbc, and diverse states of starformation (e.g., starbursting, post-starburst, quiescent).Most of the CO data for this sample came from newobservations, and unlike many previous investigations ofmolecular gas in galaxies, our NFGS CO observationswere not in general designed to emphasize CO-brightgalaxies, but were instead designed to reach strong, sci-entifically useful upper limits in the case of CO non-detections. Literature Sample
To strengthen our results, we supplement our samplewith galaxies from the literature with available CO, HI,and multi-band imaging data.Our literature sample includes galaxies from threelarge surveys: the Spitzer Near Infrared Galaxy Sur-vey (SINGS; Kennicutt et al. 2003), ATLAS-3D (Younget al. 2011), and COLD GASS (Saintonge et al. 2011).These surveys are dominated by high mass galaxies, soto supplement the low mass end of our data set, we addgalaxies from Barone et al. (2000), Garland et al. (2005),Leroy et al. (2005) , Taylor et al. (1998), and Kannap-pan et al. (2009). Most of these references are themselvesthe sources of the CO data, although some CO data forgalaxies in SINGS and Kannappan et al. (2009) comefrom Leroy et al. (2009), Albrecht et al. (2007), Sageet al. (2007), Zhu et al. (1999), or our own observations( § BV RI photometry (Mu˜noz-Mateos et al. 2009). NIRimaging data is available for all galaxies from 2MASS.Combined, these data sources bring our full sample(only considering galaxies that have all necessary data)to 627 galaxies. However, our total decreases to 323galaxies after we institute a number of useability cuts(see § New Molecular Gas Data
CO(1-0) data, which we use to estimate molecular gasmasses, already existed for a handful of our NFGS galax-ies prior to this study (Sage et al. 1992; Wei et al. 2010b).The rest of the NFGS sample was observed with the Insti-tut de Radioastronomie Millim´etrique (IRAM) 30m andArizona Radio Observatory (ARO) 12m single dish tele-scopes. Total integration times were set by how long ittook to reach reasonable integrated signal-to-noise ratios(S/N >
5) or strong upper limits (yielding H /HI < ∼ − and ∼ − at these two frequencies. Fur-ther observations were taken in Fall/Winter 2009/2010with the newly commissioned EMIR receiver in conjunc-tion with the WILMA backend, which supplied 2 MHzresolution and a total bandwidth of 3.7 GHz. For allobservations, wobbler switching was used with a throwof 2 ′ and individual scans of 6 minutes. The data werecalibrated via observations of an ambient temperatureload. The absolute calibration is accurate to 15–20%.The half-power beam widths are 22 ′′ and 12 ′′ at 115 GHzand 230 GHz respectively.The ARO 12m observations took place between De-cember 2010 and April 2011. We used the ALMA 3mmreceiver in conjunction with both 2 MHz filterbanks (onefor each polarization), which provided a total bandwidthof 512 MHz. We simultaneously used the MillimeterAuto Correlator (MAC), with a resolution of 781.2 kHzand a total bandwidth of 800 MHz. Observations werecarried out in beam switching mode with typical throwsof 2 ′ –4 ′ , and individual scans of 6 minutes. The data werecalibrated using measurements of a noise diode betweenscans, and galaxies with previous observations were usedto check the calibration. Some of our ARO time was usedto obtain CO data for five extra galaxies in our literaturesample.The data were reduced using CLASS . Scans were aver-aged together and any bad channels flagged. The spectrawere Hanning smoothed to a resolution of 10.4 km s − .Baselines were then fit to emission free regions of thespectrum, with polynomials of order < ∗ A scale to Janskys using Jy/K= 6.12 and 6.3 for the EMIR and ABCD receivers mea-sured at 115 GHz, and Jy/K = 7.86 and 7.5 for the We do not include marginal detections due to the authors’predictions of a high false positive rate.
Stark et al.
EMIR and ABCD receivers measured at 230 GHz (seeIRAM 30m documentation ). The ARO data are ini-tially recorded in the T ∗ R scale, which we then convert toJanskys using Jy/K = 38.3 (see the ARO 12m documen-tation ).Fluxes were determined by summing the channelswithin the line profile. The specific integration rangesare given in Tables 1 and 2 and were judged by eye foreach case. If the profile edges were unclear, we madethe velocity ranges large enough to ensure all flux wasincluded without any doubt and also yield a more con-servative error estimate. The uncertainty in the totalflux measurement is given by σ f = σ rms ∆ V p N chan (1)Here, σ rms is the rms noise of the spectrum in Jy asmeasured from line-free channels, ∆ V is the velocity res-olution in km s − , and N chan is the number of channels inthe integration. For non-detections, we take upper lim-its to be 3 σ f , measured over a velocity range defined bythe larger of the HI line width or an equivalent linewidthfrom an H α or stellar rotation curve (see K13s).CO linewidths (W ) are determined by finding wherethe data are greater than 0.5 times the peak flux minusthe rms noise for 3 consecutive channels, starting fromthe outside of the emission line and working inwards. Thefinal left and right edges for width determination are lin-ear interpolations to get the fractional channels wherethe data cross the line height. Heliocentric velocities aredefined to be midway between the two edges found bythe above algorithm. Following the examples of Schnei-der et al. (1986) and Fouque et al. (1990), we estimateline width uncertainties by generating a series of artificialobservations over a model grid with varying line steep-ness and peak signal-to-noise ratios. At our resolution of10.4 km s − , the standard deviation of the linewidth mea-surements at each grid point is approximately describedby σ W = 6 . P . (S / N) . (2)where P is the steepness parameter (defined as P =( W − W ) /
2) and S/N is the peak signal-to-noise ra-tio. We stress that linewidths for profiles with peakS/N < Methods
Optical and NIR Photometry
Optical/NIR photometry is needed to estimate stellarmasses and track recent central star formation enhance-ments. For our analysis, we do not use products of theSDSS pipeline since it is prone to shredding extendedsources and does not make use of the most recent back-ground subtraction algorithm (Blanton et al. 2011). Weinstead recalculate total magnitudes using our own cus-tom pipeline, described in greater detail by Eckert et al. http://aro.as.arizona.edu/12 obs manual/chapter 3.htm (in prep.). After the downloaded images are co-added,bright stars and interloping galaxies are masked. Themasking process is automated with the aid of SExtrac-tor (Bertin & Arnouts 1996), but each mask is inspectedby eye and adjusted when there is clear over- or under-masking using the automatic routine. The ELLIPSE taskin IRAF is used to extract surface brightness profiles ofconstant center, PA, and ellipticity, and to sum up theflux within each isophote. For the NFGS sample, weadopt the same PAs and ellipticities used for the U BR photometry (Jansen et al. 2000b). For our literaturesample, we adopt the method of Eckert et al. (in prep.),who use ELLIPSE to determine the best PA and ellip-ticity from the low surface brightness outer disk of eachgalaxy using the coadded gri images. Models of eachgalaxy are created with the resulting surface brightnessprofiles, and are used to fill in masked regions to correctthe total flux.Total magnitudes are calculated two ways. First, weadopt a curve of growth technique very similar to theone outlined in Mu˜noz-Mateos et al. (2009), where theouter disk values of the enclosed magnitude and its radialgradient are fit with a linear function. The y -intercept ofthis line (i.e., where the enclosed magnitude is no longerincreasing) is the total magnitude. Total magnitudes arealso calculated by fitting the outer disk of the surfacebrightness profile with an exponential function, similar tothe method in Jansen et al. (2000b), except that outlierpoints are rejected from the fit. The total flux is summedup to the last isophote used in the fit, after which the fititself is used to estimate the remaining outer flux.To estimate systematic uncertainties in our total mag-nitudes, we perform each of these total magnitude ex-trapolations using slightly differently defined fit ranges(between 1 and 8 times the sky noise, between 3 and 10times the sky noise, within a 1 mag arcsec − range end-ing at 1 or 3 times the sky noise, and finally using thelast 5 data points above 1.5 times the sky noise) and thenaverage the results (ignoring > σ outliers) to obtain ourfinal magnitude. We take the difference of the maximumand minimum magnitude estimates divided by two (alsoignoring outliers) as our official systematic uncertainty.This uncertainty is added in quadrature with the Poissonstatistical uncertainty.The ellipses used for total magnitude calculation bestmatch the shape of the far outer disk or halo, and aretherefore not ideal for calculating galaxy inclinations. Toestimate photometric inclinations, ELLIPSE is run a sec-ond time where ellipticity is allowed to vary while PA iskept fixed to the previously used value. The ellipticityat a surface brightness of 22.5 mag arcsec − in the coad-ded gri images usually reliably traces the higher surfacebrightness inner disk and provides accurate inclinations,which are estimated usingcos i = s ( b/a ) − q − q (3)Here, q is the intrinsic disk thickness (assumed to be q = 0 . b/a is the minor-to-major axis ratio de-rived from the ellipticity. For the NFGS sample, we usethe same inclinations as K13s for consistency, which arebased on the same equation, but not using the b/a mea- he Fueling Diagram JHK magnitudes are also recalculated using the2MASS imaging data. Here, we redo the backgroundsubtraction for the 2MASS images using a method simi-lar to that used in the original 2MASS pipeline (Jarrettet al. 2000), where the sky was fit by 3rd order polyno-mials. However, we fit the background of each relevantframe only in the region local to the galaxy of interest(within ∼ × R ), with the galaxy itself and any starsor background galaxies masked. We impose the param-eters from our first set of optical surface brightness pro-files (center, PA, and ellipticity) to extract NIR surfacebrightness profiles.The two methods for calculating total optical magni-tudes described above are again used to calculate the to-tal NIR magnitudes. However, tests comparing the out-put of these two methods against magnitudes calculatedfrom much deeper Spitzer
IRAC 3.6 µ m imaging revealthat the exponential fit method performs systematicallyworse than the curve of growth method when applied tothe relatively shallow 2MASS data. The fits also performthe best when using a fit range between 3 and 10 timesthe sky noise. We thus solely use the curve-of-growthderived total magnitudes determined using this fit rangeas our final estimates, although we still rely on the dif-ference between the curve-of-growth and exponential fitderived magnitudes to estimate the systematic error formost galaxies. For any galaxy for which our differentmagnitude estimation techniques yield very different re-sults (disagreement of more than 0.5 mags), we resortto taking an aperture magnitude of the galaxy, and theninfer the total magnitude by multiplying by the total-to-aperture flux ratio of a higher S/N passband (anotherNIR band like J if possible, otherwise i band).All optical and NIR magnitudes are corrected for fore-ground extinction using the dust maps of Schlegel et al.(1998) and the extinction curve of O’Donnell (1994). Stellar Masses
Stellar masses are calculated with an improved versionof the method described by Kannappan et al. (2009).Taking as inputs a combination of
U BR , ugriz , JHK ,and 3.6 µ m photometry, along with global optical spec-tra (or any subset of these inputs that are available;see K13s and references therein), the stellar mass esti-mation code fits mixed young + old stellar populationsbuilt from pairs of simple stellar population (SSP) mod-els from Bruzual & Charlot (2003) assuming a SalpeterIMF. Output stellar masses are scaled by 0.7 to matcha “diet” Salpeter IMF containing fewer low mass stars(Bell et al. 2003). The only significant change comparedto Kannappan et al. (2009) is the addition of a very youngSSP with age 5 Myr to the suite of models. Note alsothat model SSP pairs can include a “middle-aged” youngSSP, as long as its age is younger than the old SSP, whichwas also true for the Kannappan et al. (2009) model grid.In addition, the U BR zero points have been adjusted forconsistency (see K13s). The final stellar mass estimate isdefined by the median and 68% confidence interval of thelikelihood weighted mass distribution over the full modelgrid.Stellar masses for our literature sample are calculatedusing only SDSS and 2MASS photometry. To determinewhether the lack of spectroscopy leads to any system- *lit /M O • )-0.2-0.10.00.10.2 l og ( M * be s t / M O • ) - l og ( M * li t / M O • ) Figure 1.
Difference between the highest quality stellar masses forthe NFGS (log M best ∗ , calculated from UBR , SDSS, 2MASS, andIRAC photometry plus integrated spectroscopy) and stellar massesfor the same galaxies estimated with data available for our litera-ture sample (Log M lit ∗ , calculated using only our custom SDSS and2MASS photometry), testing the quality of stellar masses for ourliterature sample. The solid horizontal line represents 1:1 agree-ment, while the dashed line shows the ordinary least-squares fitwith outlier rejection, which is not different at a statistically sig-nificant level. The scatter has negligible effect on our results. atic differences in our stellar mass estimates, we comparethe high quality stellar masses from the NFGS against asecond set calculated using only our custom SDSS and2MASS photometry. As shown in Figure 1, the twomethods of estimation are in good agreement. Thereis no statistical significance in the weak linear trend be-tween the two mass estimates as function of stellar mass,and the 1 σ scatter between the two estimates is 0.04dex, much less than the typical uncertainty of ∼ Blue-Centeredness
To track enhancements in recent central star forma-tion, we rely on a simple measure of the color gradi-ent referred to as blue-centeredness (∆ C ), defined as theouter disk color from the half-light radius ( r ) to the75% light radius ( r ) minus the color from the centerto r (Jansen et al. 2000b). For future reference, gen-eral discussion of blue-centeredness will use the notation,∆ C , while specific discussion involving a particular colorwill note that color explicitly, e.g. ∆( g − r ). The radii inthis definition reliably separate bulge/disk colors with-out being sensitive to variations in bulge-to-disk ratio(Kannappan et al. 2004). The half-light radius is a natu-ral separator of inner/outer galaxy growth; for example,Peletier & Balcells (1996) note shifts in colors and ages atapproximately this radius. We also stress that this sim-ple measure appears robust to variations in the dividingradii. For example, using the 40% and 90% enclosed lightradii returns approximately the same results.Before blue-centeredness is used to measure enhance-ments in recent central star formation, we accountfor other galaxy properties that may affect the colorgradients. Kannappan et al. (2004) find that blue-centeredness correlates with galaxy luminosity, likely due Whenever we have reprocessed SDSS images, blue-centeredness is calculated using the second set of ellipse fits, i.e.,the ones that are used to estimate inclinations, since they besttrack the star-forming inner disks (see § Stark et al. to the fact that both metallicity and stellar popula-tion age can influence galaxy color gradients, reddeninggalaxy centers with increasing luminosity. These authorsremove the luminosity trend by subtracting off the fittedrelation between ∆( B − R ) and luminosity. We follow thesame approach, performing an ordinary least-squares fit(Isobe et al. 1990) of ∆ C against stellar mass (Figure 2).We derive the following relations:∆( u − r ) = ( − . ± . M ∗ + (0 . ± . u − g ) = ( − . ± . M ∗ + (0 . ± . g − r ) = ( − . ± . M ∗ + (0 . ± . y vs. x iscrucial, since in order to remove any trend with stellarmass, we must minimize the scatter in ∆ C relative tostellar mass. Following Kannappan et al. (2004), we cal-ibrate this mass correction using the NFGS sample (notjust our subset with CO data) since it is our most repre-sentative data set and has the most robust stellar massestimates. The fit is limited to star-forming disk galaxies,identified as galaxies with morphology S0 or later and ei-ther detected H α emission extending beyond the nucleusor U − K <
4, which helps exclude quenched galaxies(Kannappan & Wei 2008, K13s). We reject galaxies withknown strong AGN and restrict the fit to M ∗ > . M ⊙ ,avoiding the low M ∗ tail of the NFGS where all blue-centeredness states may not be evenly represented. Intotal, 135 NFGS galaxies were used to derive these rela-tions. The residuals of this fit give mass-corrected blue-centeredness (denoted by ∆ C m ). In simple terms, ∆ C m is a measure of the color difference between the inner andouter regions of a galaxy, relative to the typical color dif-ference for galaxies at a given stellar mass, where highervalues imply bluer centers. More physically, this param-eter tracks recent central star formation relative to thetypical star-forming galaxy at a given stellar mass.We find that galaxies with and without strong pecu-liarities (i.e., signs of recent interactions) as defined byKannappan et al. (2004) have different underlying dis-tributions of ∆( g − r ) m at a 99% confidence level, soour definition of mass-corrected blue-centeredness suc-cessfully recreates the correlation found by these au-thors using luminosity-corrected blue-centeredness (theirFig. 8). However, we stress that while our mass correc-tion is physically motivated, it is modest, and the distri-butions of uncorrected ∆( g − r ) for peculiar/non-peculiargalaxies differ at confidence level comparable to that fordistributions using ∆( g − r ) m . Our general results pre-sented in § § C m in-cludes contributions from the measurement error of ∆ C ,as well as additional uncertainties due to the error in r and r , the error in the stellar mass, and the uncertaintyin the fitted relation between ∆ C and stellar mass. Inthe majority of cases, the Poisson error is dominant.We note that optical color gradients have advantagesover direct star formation rate tracers (e.g., FUV+24 µm )for the purposes of our study. A practical advantage isthat the data needed to compute color gradients are read-ily available for most galaxies. In addition, the longertimescales over which optical indicators remain sensitive * /M O • -0.3-0.2-0.10.00.10.20.3 ∆ ( g -r) Figure 2. ∆( g − r ) versus log (M ∗ / M ⊙ ), illustrating the correla-tion between blue-centeredness (∆ C ) and stellar mass. To isolatethe effect of recent central star formation enhancements, we re-move the stellar mass trend using an ordinary least-squares fit,minimizing scatter in blue-centeredness relative to stellar mass. The residuals of this fit give mass-corrected blue-centeredness (∆ C m ), which measures outer minus inner color relative to thetypical value for a galaxy at a given stellar mass, allowing us totrace recent central star formation enhancements above the norm. to enhanced star formation are more useful for study-ing the extended evolution of galaxies. They enable usto analyze the stellar populations beyond the timescaleof the star formation and gas consumption itself, allow-ing us to note the longer term consequences of recentstar formation episodes. We defer a detailed analysis ofthe timescales of these optical indicators to future work,but Figure 11 of Kannappan et al. (2004) shows a sim-ple model wherein the blue-centeredness fades on the or-der of 0.5–2 Gyr after the central star formation episodeends. It should be noted that this model represents a sin-gle case, and the evolution of blue-centeredness may varydepending on the duration and size of the burst as wellas the composition of the preexisting stellar populationsin the bulge and disk.For consistency and since the vast majority of ourgalaxies have SDSS data, we always quote ∆ C m usingSDSS-equivalent colors. A handful of galaxies from ourNFGS sample do not have SDSS data, but do have U BR photometry. We derive the following conversions be-tween the NFGS
U BR and ugriz systems using colorsmeasured within the B band 25 mag arcsec − isophotefor 183 NFGS galaxies: g − r = 0 . B − R ) − . σ = 0 .
04 (7) u − g = 1 . U − B ) + 1 . σ = 0 .
16 (8) u − r = 0 . U − R ) + 0 . σ = 0 .
21 (9)These relations are useful only for the NFGS due tothe possibly different
U BR zeropoints used in the NFGSrelative to other photometric studies (see K13s). Therelations have been corrected for foreground extinction, he Fueling Diagram differences , both fore-ground extinction corrections and k-corrections cancel.Where these conversions are used, their uncertainties areincorporated into the final error on ∆ C m . Internal Extinction Effects
Since we make use of optical color gradients, internaldust extinction is a concern. A systematic effect fromdust may manifest itself as a dependence on inclination,since higher inclination galaxies show more dust alongthe line of sight. To determine whether internal extinc-tion is systematically biasing our results, we run Spear-man rank tests on all star-forming disk galaxies in theNFGS with measured inclinations > ◦ after excludingAGN. We find no significant correlation between incli-nation and ∆ C m . Shown in Figure 3, the same ranktest for galaxies with stellar masses above ∼ . M ⊙ –roughly equivalent to the 120 km s − rotation velocitythreshold above which dust lanes become more promi-nent in galaxies (Dalcanton et al. 2004; see also K13s) –implies somewhat significant correlations (3%, 5%, and4% chance of being random for ∆( u − r ) m , ∆( u − g ) m ,and ∆( g − r ) m respectively). Though weak correlationsmay exist, these trends are much smaller than the scat-ter (Fig. 3). Thus we conclude that systematic internalextinction effects should have a minimal effect on ourresults.We should note that while we find only small system-atic effects due to inclination, dust within galaxies willinevitably alter our color gradients if it is present. Thereare galaxies in our sample for which visual inspectionhas revealed significant dust features. These galaxies andtheir impact on our results are discussed in § § Gas Masses
To ensure that our data are as uniform as possible, werecalculate all gas masses using the same formulae. TheHI mass is calculated as (Haynes & Giovanelli 1984): M HI = 2 . × D F (10)Here, F is the measured 21cm flux in Jy km s − and D is the distance to the galaxy in Mpc. The moleculargas mass is estimated as (Sanders et al. 1991): M H = 1 . × (cid:18) X CO × (cid:19) D F CO (11)Here, F CO is the measured CO flux in Jy km s − . Weassume a constant X CO of 2 × cm − (K km s − ) − (Strong & Mattox 1996; Dame et al. 2001); see § CO may affect ourresults. In further analysis, we multiply all gas massesby a factor of 1.4 to account for helium. Beam Corrections
The majority of our CO flux measurements come fromsingle dish telescopes with single pointings at galaxy cen-ters. Unlike 21cm beams, which are typically severaltimes the size of our galaxies, the CO beams are oftencomparable to or smaller than our galaxies. However,since CO scale lengths are typically smaller than opticalscale lengths, this size mismatch is not always a major issue when trying to estimate total H mass. By mod-eling the beam pattern of the telescope and assuminga CO flux distribution, one can estimate the additionalflux not detected by a single pointing. We apply beamcorrections to our single-dish CO data following the samemethod as Lisenfeld et al. (2011). The aperture correc-tion is defined as the ratio of the total-to-observed COintensity, f = I CO , total /I CO , observed (12)We assume that the CO distribution I CO follows anexponential disk, I CO ( r ) = I e − r/h CO (13)where h CO is the scale length of the CO emission. Thetotal CO intensity is simply the integral of this CO dis-tribution to infinity: I CO , total = Z ∞ πI re − r/h CO dr = 2 πI h (14)The observed CO intensity is the integral of the COdistribution convolved with the beam pattern. Assuminga Gaussian beam with HPBW, Θ, this is written: I CO , observed = 4 I CO Z ∞ Z ∞ exp − p x + y h CO ! × exp − ln 2 "(cid:18) x Θ (cid:19) + (cid:18) y cos i Θ (cid:19) dxdy A major uncertainty in this calculation is the valueof h CO . Studies of star-forming late-type galaxies haveshown h CO ∼ (0 . ± . R , where R is the B -band25 mag arcsec − isophotal radius (Young et al. 1995;Leroy et al. 2008; Schruba et al. 2011). We assume thisrelation holds for all late type galaxies in our sample.Whether the same is true for E/S0 galaxies is uncertain,as their CO scale lengths have not been as thoroughlystudied in the literature. We examine the CO profilesof Wei (2010; see also Wei et al. 2010b), who mappedthe CO(1-0) distribution in a sample of E/S0 galaxiesusing the CARMA array. We find an average value of h CO = 0 . R with a standard deviation of 0.05 R . Weadopt this scale length for all E/S0 galaxies in our sam-ple. It should be noted that these radial profiles areprimarily for blue-sequence E/S0s, not the more com-mon red-sequence E/S0s, simply because CO is more of-ten detected in the former. The two red-sequence E/S0galaxies in the Wei (2010) sample have CO scale lengthsclose to 0.05 R , but two data points are not enough towarrant separate definitions of h CO for red- and blue-sequence E/S0s.We assume uncertainties in h CO of 0.05 R for bothspiral and E/S0 galaxies. The additional uncertaintythat propagates into the beam-corrected H mass de-pends on the size of the galaxy relative to the beam.Within our final sample (see § Stark et al. -0.5 0.0 0.5 ∆ (u-r) m i n c li na t i on -0.6 -0.4 -0.2 -0.0 0.2 0.4 0.6 ∆ (u-g) m -0.2 -0.1 0.0 0.1 0.2 0.3 ∆ (g-r) m Figure 3.
Inclination versus ∆ C m for star-forming disk galaxies with i > ◦ from the NFGS. The full sample shows no correlation betweenthese two variables, implying no systematic effect of inclination (and associated dust extinction) on our results. Red crosses mark galaxieswith stellar masses above 10 . M ⊙ , which show a weak correlations between inclination and ∆ C m (3%, 5%, and 4% chance of beingrandom for ∆( u − r ), ∆( u − g ), and ∆( g − r ) respectively). The dotted lines show the inverse least-squares fits (i.e., minimizing the scatterin the x -direction) to just the more massive galaxies. Any systematic effects due to inclination appear minor. However, irregular duststructures, not probed with this test, will inevitably alter color gradients (see § § fluxes from the single dish observations and beam-correctthese fluxes using the measured scale-lengths from theCO maps. Useability Criteria
After identifying from our NFGS+literature compila-tion all galaxies with the necessary optical/NIR imagingas well as 21cm and CO(1-0) flux measurements (627galaxies), we institute a number of usability criteria thatgalaxies must pass before they are included in our fi-nal sample. These are: (1) SDSS r -band half-light radiilarger than 5” to ensure blue-centeredness calculationsare not compromised by variations in the PSF betweenthe different SDSS passbands; (2) minimal beam correc-tions to detected CO fluxes, so that the corrected COfluxes are no larger than 1.5 times the measured fluxes(equivalent to a change in H / HI < . masses are minimally dependent on theassumed model of the CO distribution; (3) strong upperlimits on total H masses, i.e. where CO detections aremissing but HI detections are not, H /HI must be < . § mass; these are discussedin § physical size thanks to the wide variety of distances within oursample. The distributions of physical sizes of our galax-ies before and after we institute our useability criteriaare not significantly different, as confirmed by a K-S test.Our final sample includes some galaxies taken from theNFGS, which were in fact originally chosen to be repre-sentative of the galaxy population (see § u − r color versus stellarmass plane in Figure 4. This sample includes some galax-ies with M ∗ < . M ⊙ , although the blue-centerednessmass-correction was calibrated with only galaxies abovethis mass. These lower mass galaxies do not show un-usual behavior within our results, and are therefore keptin our final sample (see § RESULTS
In this section, we describe our findings on the rela-tionship between global H /HI and mass-corrected blue-centeredness. These variables are plotted in Figure 5,which we hereafter refer to as the “fueling diagram,”since it links the fraction of gas available as direct fuelfor star formation and a tracer of recent interactions that he Fueling Diagram * /M sun ( u -r) i Sa-SdSa-Sd, no gas detectedE-S0/aE-S0/a, no gas detectedPeculiar/Interacting
Figure 4.
Our final NFGS+literature sample plotted in ( u − r ) i versus stellar mass space. The dashed line represents the red/bluesequence divider, which is based on the analysis of Moffett etal. (2013, in prep.), which identifies the midpoint between the twosequence peaks at each stellar mass. Our red/blue sequence divideris shifted redder than this midpoint by +0.1 mag. The superscript i indicates that an internal extinction correction has been appliedfollowing Moffett et al. drive the fueling.In § /HI and ∆ C m , consistentwith the idea that molecular gas content is systematicallylinked to galaxy interactions as traced by mass-correctedblue-centeredness. The right and bottom branches arewell-defined loci that deviate from this expected trend,showing first increasing then decreasing mass-correctedblue-centeredness as H /HI decreases.In § § § The Distribution of Galaxies in the FuelingDiagram
The Three Branches
The fueling diagram is shown in Figure 5, plotted usingmass-corrected blue-centeredness based on u − r , u − g ,and g − r colors, all of which recreate the same basicstructure. The regions of parameter space roughly defin-ing the left, right, and bottom branches are overlaid onthe ∆( g − r ) m data in Figure 6.The majority of our sample falls on the left branch, which shows a positive correlation between H /HI andmass-corrected blue-centeredness. There is considerablescatter which appears to increase above H /HI ∼ C m . Weattribute at least some of this scatter to centrally con-centrated dust. Visual inspection has shown several ofthe galaxies that scatter to the left of the main trendhave distinct dust features (e.g., M82, which lies at∆( g − r ) m = − .
14 and H /HI=3.6). Galaxies in the“dusty zone” do not have preferentially high inclination( § § g − r ) m ∼ . − .
1, is far less populatedbut still well defined. It shows a relationship opposite tothe left branch, where mass-corrected blue-centerednessincreases while H /HI decreases. The bottom branch,which encompasses galaxies below H /HI ∼ /HI and mass-correctedblue-centeredness.Among the galaxies in our sample with gas detectionsand reliable ∆ C m measurements, ∼
75% are on the leftbranch, ∼
5% are on the right branch, and ∼
20% are onthe bottom branch. However, these percentages are verycrude since the branches connect with each other andtheir definitions are not exact. We also stress that oursample is not statistically representative of the galaxypopulation, largely because of the lack of CO measure-ments for low-mass galaxies. Thus, the fractions of galax-ies falling on the left, right, and bottom branches inFig. 5 cannot be used to infer the true frequency withwhich galaxies fall on these parts of the fueling diagram.If instead we limit ourselves to the more representativeNFGS subsample, the fractions of galaxies on the left,right, and bottom branches are roughly 65%, 10%, and25%. But again, this subsample is only approximatelyrepresentative.Between these three branches exists a region whereno data points lie. This hole is clearest in the ver-sion of the fueling diagram using ∆( g − r ) m because theright/bottom branches are most evenly populated. Forthis reason, we default to using the ∆( g − r ) m version ofplot to show further results. Is the hole real?
The structure seen in the fueling diagram – particularlythe unoccupied region between the three branches – doesnot appear to be artificially created by our sample restric-tions. As described in § § Stark et al. -0.5 0.0 0.50.0 ∆ (u-r) m -2 -1 H / H I -0.4 0.0 0.40.0 ∆ (u-g) m -0.2 0.0 0.20.0 ∆ (g-r) m Figure 5.
Relationship between H /HI and mass-corrected blue-centeredness shown using three different color gradients. Grey pointsdenote lower and upper limits in H /HI. To the left of the y -axis are dots representing H /HI values for galaxies with peculiar morphologies,many clearly interacting. Due to their disturbed state, we cannot measure ∆ C m . Below each x -axis are dots showing the measured ∆ C m for quenched galaxies. All three panels show distinct loci and an empty region between them. -0.3 -0.2 -0.1 -0.0 0.1 0.2 0.3 ∆ (g-r) m -2 -1 H / H I Left Branch RightBranchBottom Branch
Figure 6.
Empirically defined branches in H /HI vs. ∆ C m space.These data points are the same as in Figure 5c. gion. These galaxies lack reliable ∆ C measurements, sowe do not plot them within the fueling diagram. How-ever, we mark their measured H /HI to the left of the y -axis in Figure 5. Their H /HI values do not exclusivelycluster in the range spanned by the hole, although somehave the proper values to fall within it. We conclude thatif galaxies like those represented in our sample ever fallin the empty region, they must do so only briefly dur-ing a phase of rapid evolution. The specific reasons whygalaxies rarely settle in this region of parameter space arenot immediately apparent. Detailed modeling of galaxiesmay be necessary to explain this phenomenon and willbe the focus of future work. X CO Effects
The structure of galaxies in the fueling diagram ap-pears robust against possible variations of X CO due toits dependence on metallicity. To test this, we use O/Hto estimate X CO for each galaxy, employing the calibra-tion from Obreschkow & Rawlings (2009). Estimates ofO/H from optical line ratios are only available for ourNFGS (Kewley et al. 2005) and SINGS (Moustakas et al.2010) samples and the studies of Barone et al. (2000) andTaylor et al. (1998). To be able to carry out this anal-ysis for our full sample, we also estimate X CO for eachgalaxy from B band luminosity, again using the calibra-tion of Obreschkow & Rawlings (2009), who find it to bethe next most reliable estimator of X CO after metallicity.The values of 12+log O/H in our sample (where known)range from 7.9–9.2, yielding X CO estimates between 0.4and 10 times the Milky Way value. The calibration using B -band luminosity yields a similar range of X CO .Figure 7 shows the effect that variable X CO due tometallicity has on the fueling diagram. Even with thevariation in X CO , the right/bottom branches remain dis-tinct from the left branch and the hole remains intact,although some of the upper limits on the bottom branchshow significant increases in H /HI due to their estimatesof X CO being several times the Milky Way value. Thesegalaxies are mainly dwarfs with stellar masses . a few × M ⊙ , where this sort of deviation might be expected.In general however, the structure of the fueling diagramremains unchanged.The above analysis ignores other physics that may al-ter X CO . Most relevant to our study is the possible de-crease in X CO in very high gas surface density regimeswhere the the ISM turns almost entirely molecular. Sucha situation could occur as the result of inflows that drivelarge amounts of gas to the centers of galaxies, and hasbeen observed in many systems from ULIRGs to ordi-nary spirals (Downes et al. 1993; Regan 2000). The gasin these extremely high surface density regions is ex-pected to have increased temperature relative to molec-ular clouds in less dense environments (Narayanan et al. he Fueling Diagram -0.2 -0.1 0.0 0.1 0.2 0.3 ∆ (g-r) m H / H I -0.2 -0.1 0.0 0.1 0.2 0.3 ∆ (g-r) m Figure 7.
The possible effect of variations in X CO on our data, with X CO estimated separately for each galaxy using B -band luminosity(left) and log(O/H) derived from nebular emission lines (right). Lighter arrows denote galaxies with H /HI upper or lower limits, and X’sdenote galaxies where log(O/H) is unavailable. Some upper limits show significant adjustments, but X CO variations do not change theoverall appearance of three distinct branches. F CO(2 − /F CO(1 − ratio. Where available, we compare F CO(2 − /F CO(1 − (both beam corrected as in § /HI, butwe find no correlations. Any evidence of increased cen-tral gas temperature is likely being washed out in ourglobal CO measurements. Even if some of the increasein H /HI with ∆ C m along the left branch is the resultof overestimated X CO , this is still consistent with ourphysical interpretation that the left branch of the fuelingdiagram is the result of galaxy interactions and inflows(see § § CO . Distribution of Galaxy Properties Within theFueling Diagram
Having established the basic structure of the fuelingdiagram and its reliability, we now explore how galaxyproperties – specifically morphology, the presence of abar, stellar mass, blue versus red sequence, and gas con-tent – distribute themselves throughout the fueling di-agram. Doing so may provide an understanding of thephysical processes that drive the observed trends. Thegalaxy properties discussed in this section are overlaid onthe fueling diagram in Figure 8 and briefly summarizedin § Morphology
Figure 8a displays galaxy morphologies within the fuel-ing diagram. All galaxies are classified by eye using SDSS g -band images, but we check our classifications againstpreviously published types when available. Galaxies areseparated into two categories: E/S0s (including S0a) andspirals (Sa–Sd). Using the distinction between S0a andSa as the separation between early- and late-type galax-ies may be somewhat sensitive to classification error, but this division is useful since the presence or absence of ex-tended spiral arms represents a basic transition in struc-ture likely strongly linked to star formation history.We find a clear bimodality in the distribution of E/S0and spiral morphologies. Spiral galaxies almost exclu-sively fall on the left branch, and in fact, a Spearmanrank test on all spiral galaxies with H /HI > /HI and ∆ C m , with ∼ σ confidence (for u − r , u − g , and g − r , the probabilities of the distribu-tions being random are 5 × − , 8 × − , and 1 × − respectively). E/S0s show a much more diverse distri-bution throughout the fueling diagram: some occupythe left branch with spirals, but also and more notice-ably the rest almost completely define the right branchand much of the bottom branch. Several of the E/S0son the right/bottom branches are also centrally concen-trated Blue Compact Dwarf galaxies (BCDs), which arelumped with traditional E/S0s in our simplified morpho-logical classification scheme. Towards the left end of thebottom branch, there is a strong shift in morphology fromE/S0 to spiral.Barred galaxies are also shown in Figure 8a. Exceptfor galaxies that have existing bar classifications fromthe NFGS or Nair & Abraham (2010), bar classifica-tions were done by eye using SDSS i -band imaging, sincebars are best identified in bands that trace the stellarlight (Eskridge et al. 2000). Bars are noticeably ab-sent from all galaxies above ∆( g − r ) m ∼ .
15, whichincludes most of the right branch, as well as sections ofthe left and bottom branches. Within the left branchalone, a Spearman Rank test does not suggest a smoothcorrelation of bar fraction with ∆ C m or with H /HI. Al-though our full sample is not statistically representativeof the galaxy population, we speculate that the sameprocesses that produce extreme blue-centeredness maydestroy bars, while milder processes associated with evo-lution along the left branch do not. If we limit our ex-amination of bars to only the more representative NFGS2 Stark et al. -0.2 -0.1 0.0 0.1 0.2 0.310 -2 -1
1 10 H / H I ∆ (g-r) m BarredE/S0-S0/aSa-Sd -0.2 -0.1 0.0 0.1 0.2 0.310 -2 -1
1 10 H / H I ∆ (g-r) m M * > M b M t 1 10 H / H I ∆ (g-r) m Red Seq.Blue Seq. -0.2 -0.1 0.0 0.1 0.2 0.310 -2 -1 1 10 H / H I ∆ (g-r) m log(M HI+H2+He /M * ) -1 0 1 a bc d Figure 8. ( a ) Distribution of early (E/S0 - S0a) and late (Sa-Sd) morphologies and bars. ( b ) Distribution of stellar masses in threefundamental mass regimes: stellar mass above M b , between M t and M b , and below M t , where M b is the bimodality mass (10 . M ⊙ )and M t is the gas-richness threshold mass (10 . M ⊙ ). Also marked are galaxies that fall below the range of our blue-centeredness mass-correction. See § c ) Distribution of red and blue sequence galaxies ( d ) Distribution of M HI+H +He /M ∗ . subsample, we still see no significant trend between ∆ C m and bar fraction within the left branch. Bars are impor-tant galactic structures to put into the context of ourstudy, since like galaxy interactions, they are thoughtto enable inflows of gas to the centers of galaxies. Wediscuss bars and interpret their role in § Stellar Mass Figure 8b displays the distribution of stellar masseswithin the fueling diagram. Instead of examiningthe continuous distribution of stellar masses, we di-vide the data into three characteristic mass regimes:(1) M ∗ > M b = 3 × M ⊙ , where M b is the bi-modality mass, a stellar mass scale above which thepopulation of galaxies goes from being typically star- forming with disk-like morphology to typically non-star-forming with spheroidal morphology (Kauffmann et al.2003), (2) M ∗ < M t = 5 × M ⊙ , where M t is thegas-richness threshold mass, below which there is a sig-nificant increase in gas-dominated galaxies (Kannappanet al. 2009, K13s), and (3) M t < M ∗ < M b , wherebulged spirals with intermediate mass content are thenorm (K13s). Galaxies with M ∗ < . M ⊙ are also de-noted with an extra “+” symbol in this figure. Thesegalaxies technically fall outside the stellar mass rangeused to calibrate the blue-centeredness mass-correction( § he Fueling Diagram t . Among these galaxies, the mostextreme blue-centeredness is found for NGC 3738, with∆( g − r ) m = 0 . 19. This galaxy is a centrally concentratedBCD, making it completely consistent with its neighbor-ing galaxies in the fueling diagram.The different stellar mass regimes display patternswithin the fueling diagram. While galaxies in all threeregimes span the full range of H /HI, we find almost nogalaxies above M b on the right/bottom branches. In-stead, most of the galaxies on these branches fall below M t . There is also a tendency for galaxies below M t tocluster in the lower-left corner of the fueling diagram(many having H /HI upper limits), but elsewhere alongthe rising branch they appear to spread roughly evenly,as do galaxies in the higher stellar mass regimes. Wenote that with our low number statistics, the apparenttendency of galaxies on the upper right branch to havestellar masses between M t and M b is not significant andshould not be over-interpreted given that the range be-tween M t and M b is very narrow, and stellar mass esti-mation involves typical errors of ∼ § C m . To determine how depen-dent our results are on this mass correction, we plot thefueling diagram using the uncorrected ∆( g − r ), ratherthan ∆( g − r ) m , in Figure 9. The general structure of thefueling diagram remains intact, specifically the presenceof three branches with a hole between them. The distri-bution of different mass regimes illustrates the tendencyof high-mass galaxies to have more red-centered colorgradients, which originally motivated our mass correc-tion. Red and Blue Sequences Figure 8c shows the distribution of red and blue-sequence E/S0s and spirals in the fueling diagram, whichare classified based on their positions within the u − r versus stellar mass plane shown in Figure 4. The leftbranch is composed of a mix of red and blue sequencegalaxies. Intriguingly, the right and bottom branches arealmost completely dominated by blue sequence galaxies,despite the common assumption that E/S0 galaxies al-ways fall on the red sequence. High-mass, red-sequenceE/S0 galaxies in our sample are often quenched, i.e., haveno detected CO or HI emission and total gas-to-stellarmass ratio upper limits less than 0.04M ⊙ . These systemsare shown below the x -axis in Figures 5, 8, 9, and 10. Gas Content Figure 8d shows the distribution of total gas-to-stellarmass ratio (total gas = HI+H with a 1.4 × mass correc-tion for He) within the fueling diagram. Broadly speak-ing, HI-to-stellar mass ratios and total gas-to-stellar We note that the quenched population does not center around∆ C m ∼ 0, but rather around ∆( g − r ) m ∼ . 05 (as one colorexample). The ∆( g − r ) m values are not due to the presence ofexcess recent central star formation, but rather the fact that themass correction applied to the color gradients was calibrated onstar-forming disk galaxies, which tend to show more red-centeredcolor gradients than do passively evolving galaxies. -0.3 -0.2 -0.1 0.0 0.1 0.2 0.310 -2 -1 1 10 H / H I ∆ (g-r) M * > M b M t The fueling diagram plotted using blue-centerednesswithout a mass correction. Without the mass correction appliedto blue-centeredness, there is a tendency for higher stellar massgalaxies to have more red-centered color gradients (motivating themass correction), but the underlying structure of the fueling dia-gram remains intact. mass ratios on the left branch are both anti-correlatedwith H /HI. However, there is significant diversity be-low H /HI ∼ /HI ∼ /HI < g − r ) m has a 1.6% chance of being ran-dom. This probability drops to 0.2% when restrictingthe test to M ∗ > . M ⊙ (i.e., the mass above whichthe blue-centeredness mass correction was calibrated). Afew red-sequence galaxies with very low gas fractions alsolie on the bottom branch, which are among the minor-ity of massive ( M ∗ > M t ) E/S0s whose gas data are notupper limits. AGN While our sample lacks uniform/complete data forAGN classification, we display known AGN in Figure 10and briefly discuss them for two reasons. First, it is im-portant to note that AGN themselves are not the causeof strongly blue-centered color gradients, as their lightcontribution is typically too small to have any signifi-cant effect on mass-corrected blue-centeredness, whichuses colors measured over large regions of galaxies. Sec-ond, we note that AGN are predominantly seen amongthe high mass galaxies in our sample (see also Fig. 8b),4 Stark et al. -0.2 -0.1 0.0 0.1 0.2 0.30.01 0.1 1 10 H / H I ∆ (g-r) m Figure 10. Known AGN (stars) within the fueling diagram. Thisclassification is not complete or uniform in our sample due to thelimited number of classifications available in the literature and in-complete nuclear spectroscopy. with 25 out of 27 AGN hosted by galaxies with M ∗ > M t .Their presence, particularly among the high mass ellipti-cal galaxies which show AGN in the quenched regime butalso among galaxies with detected gas, affects our physi-cal interpretation of the fueling diagram, and is discussedin § § Properties Summary To summarize, the main properties of each branch ofthe fueling diagram are as follows:The left branch is where spiral galaxies are primar-ily found. Many galaxies here are barred, but withoutany discernible pattern with respect to ∆ C m or H /HI.Galaxies on the left branch cover the full range of stellarmasses, along with a wide range of HI- and total gas-to-stellar mass ratios, which broadly behave inversely toH /HI.The right and bottom branches are almost entirelypopulated by unbarred E/S0 galaxies, although this typedistribution transitions into largely spirals on the left sideof the bottom branch, which is also where we begin tosee barred galaxies again. Stellar masses fall predom-inantly below the bimodality mass, and most fall be-low the threshold mass. Gas fractions are moderate tohigh, between 10% and 100% of the stellar mass, andshow a negative correlation with mass-corrected blue-centeredness along the bottom branch.We also note that the right/bottom branches are domi-nated by blue-sequence E/S0 galaxies, i.e., galaxies withspheroidal morphologies that fall on the blue sequencein color versus stellar mass space, which are thought torepresent a transitional phase (Kannappan et al. 2009).This fact, as well as the properties of galaxies within thedifferent branches of the fueling diagram, may reveal im-portant clues as to how these branches relate to differentevolutionary states, as discussed in § Do Galaxies Evolve Within the Fueling Diagram? If mass-corrected blue-centeredness and H /HI aretime-varying properties, galaxies should evolve withinthe fueling diagram. To determine whether there is anyunified direction of evolution within the fueling diagramor any one of its branches, we search for systematic off-sets between ∆( u − g ) m and ∆( g − r ) m . This comparisonis useful because u − g color reddens faster than g − r colorafter a star forming event, and therefore ∆( u − g ) m tracksrecently enhanced central star formation over shortertime scales and will return to low values faster than∆( g − r ) m . Before comparing these two measurements,we must first account for the fact that the range of val-ues for ∆( u − g ) m is larger than for ∆( g − r ) m (see Fig-ure 5). We therefore divide ∆( u − g ) m and ∆( g − r ) m by their median absolute deviations (0.102 and 0.054 re-spectively, found with the same NFGS subsample usedto derive Eqs. 4–6) to obtain normalized mass-correctedblue-centeredness values, ∆( u − g ) m ∗ and ∆( g − r ) m ∗ , forwhich the values cover a similar range while not chang-ing the position of zero (i.e., the average gradient for thepopulation).In Figure 11, arrows display the relative positions of∆( u − g ) m ∗ (head of arrow) and ∆( g − r ) m ∗ (tail of ar-row). Galaxies on the left branch are directed randomlyleft or right along it. This result suggests that galax-ies either do not evolve throughout this region of thefueling diagram, or the evolution is not necessarily in aunified direction. Given the prior association of mass-corrected blue-centeredness with interactions (Kannap-pan et al. 2004; Gonzalez-Perez et al. 2011), we supposethat galaxies may oscillate along the left branch, risingwhen inflows enhance central star formation and H /HI(with some of the apparent rise in H /HI possibly as-sociated with a decrease in X CO due to the central gasconcentration), and fall along the same locus as outerdisk gas and star formation are renewed.Conversely, the loop composed of the right and bottombranches shows some partial systematic behavior. Al-though the arrows on the right branch show no preferreddirection, the bottom branch shows an excess of galaxieswith ∆( u − g ) m ∗ lower than ∆( g − r ) m ∗ , implying thatthese galaxies are evolving leftwards towards lower mass-corrected blue-centeredness. Ignoring the bottom-left re-gion of the fueling diagram where the left and bottombranches cannot be distinguished (∆( g − r ) m < . σ confidence level, assuming theuncertainty in the number of rightward/leftward facingarrows follows Poisson statistics. The right and bottombranches are likely closely linked (discussed further in § u − g ) m ∗ and ∆( g − r ) m ∗ , which wouldexplain the lack of a unified direction of arrows for rightbranch galaxies in Figure 11. At this point, we do nothave an estimate of the timescales associated with theevolution along the the right or bottom branches, but he Fueling Diagram -4 -2 0 2 4 6 ∆ (g-r) m* ∆ (u-g) m* H / H I Figure 11. Arrows going from ∆( g − r ) m ∗ to ∆( u − g ) m ∗ . Since u − g color is more sensitive to high mass short lived stars, centralenhancements in u − g color should be shorter lived than centralenhancements in g − r color. The data at the bottom branch sup-port this expectation by showing ∆( g − r ) m ∗ more blue-centeredthan ∆( u − g ) m ∗ in most cases, indicating that these galaxies’ cen-tral star formation has ceased and the young population is fading.This color comparison suggests a uniform evolutionary direction ofgalaxies within this region of parameter space. estimating these timescales by comparing the galaxy col-ors to stellar population synthesis models will be a focusof future work. We also note that the results of Fig-ure 11 are not dependent on the stellar mass correctionapplied to blue-centeredness as the same result is foundeven without any mass correction whatsoever.Since comparing ∆( g − r ) m ∗ and ∆( u − g ) m ∗ gives aclear direction of evolution along the bottom branch, wecan tell that galaxies here shift from primarily E/S0 toprimarily spiral morphologies, as well as generally towardincreasing gas-to-stellar mass ratios. We interpret thispattern as a sign of disk rebuilding in § DISCUSSION In § /HI to recent central star formation enhancements.Having described the three-branch distribution of galax-ies within the fueling diagram, the variation of galaxyproperties along and between the branches, and the ap-parent evolution within the diagram, we now collect theseresults to provide an interpretation of the physical pro-cesses that drive it. We first discuss the role of galaxyinteractions in driving H /HI ratios, considering the im-portance of the merger mass ratio, stellar mass, andgas richness of the galaxies involved. We then explorehow trends within the fueling diagram support a sce-nario of fresh gas accretion and stellar disk rebuildingalong the bottom branch. We finish by reassessing thevalidity of the assumed link between mass-corrected blue-centeredness and galaxy interactions in light of our newresults, specifically addressing the role of bars. Mergers and Interactions in the Fueling Diagram In the following section, we describe the role that merg-ers play in driving the evolution in each branch of thefueling diagram. The Left Branch and Regions Above It The very existence of the left branch provides supportfor the idea that local galaxy interactions play a key rolein replenishment of molecular gas: since mass-correctedblue-centeredness is a signpost of recent galaxy interac-tions (Kannappan et al. 2004), and it is correlated withH /HI, galaxy interactions appear to be linked to H /HIin a systematic way. The analysis of ∆( u − g ) m ∗ and∆( g − r ) m ∗ in § /HI and ∆ C m (with a possible contributiondue to overluminous CO), then down as the molecularreservoir is consumed and the young central stellar pop-ulation fades. Total gas-to-stellar mass ratios supportthis scenario. We expect HI and total gas-to-stellar massratios to decrease at higher ∆ C m since the gas is be-ing converted into H and then stars, but we also expecta mix of gas fractions at low ∆ C m since galaxies settlehere before or after each burst event while accreting freshdisk gas. The bulk of the evolution along the left branchmust be driven by minor rather than major mergers orinteractions, since most galaxies appear to retain theirspiral morphologies. An alternate possibility is that therelation along the left branch reflects bar-driven inflows.However, bars do not show any statistically significantcorrelation with ∆ C m along the left branch. The possi-ble role of bars is explored further in § /HI on the left branch (in contrast, gas-rich, lowmass, but comparable mass ratio mergers appear to fol-low a different path; see § /HI on the left branch arelikely moving into the quenched regime, up and off theplot, as their remaining gas reservoirs have become al-most entirely molecular and may soon be completely de-pleted. In addition, some of the high stellar mass E/S0sat the peak of the rising branch may have previouslybeen quenched but recently experienced small gas ac-cretion events, possibly associated with satellite accre-tion (e.g., Martini et al. 2013). Some of these E/S0shost AGN, as do many of the high mass E/S0s in thequenched regime. A gas accretion event could providefuel for AGN activity coupled with a central moleculargas concentration, resulting in a high H /HI ratio withminimal change to ∆ C m (since most of the star forma-tion would be occurring very close to the AGN). Galaxiesundergoing this process would jump vertically in the fuel-ing diagram, between the quenched regime and the peakof the left branch. This path could place them in thehole of the fueling diagram, although they would likelymove through it relatively quickly.As previously noted in § Stark et al. ter above the left branch towards more red-centered colorgradients, likely caused by internal extinction. Whiledust effects may be altering the measured color gradi-ents, they usefully highlight galaxies in early stages ofstar-forming events when the young stars are still heav-ily embedded in dust clouds. We suspect galaxies in this“dusty zone” represent a stage very soon after mergers orinteractions that are mild enough not to have driven thegalaxy into the peculiar morphology region off the plot,shown on the left hand side of the fueling diagram. As thestar formation progresses, the dust is likely to clear, al-lowing these galaxies to develop the bluer-centered colorgradients expected for their H /HI ratios. The Right Branch We suggest galaxies on the right branch may be theresult of gas-rich mergers, specifically between galaxiesof comparable stellar mass. Along with their high val-ues of mass-corrected blue-centeredness (suggestive of astrong central starburst), the spheroidal morphologies ofgalaxies on the right branch are consistent with recentlyviolent histories. Most of these galaxies are classified asblue-sequence E/S0s, and several are also classified asBCDs (e.g., Haro 2, NGC 7077, UM 465). The existenceof blue sequence E/S0s and BCDs in the same regime ofthe fueling diagram argues in favor of them experiencingsimilar evolutionary processes. Previous observationaland theoretical studies of BCDs (e.g., ¨Ostlin et al. 2001;Pustilnik et al. 2001; Bekki 2008) also support mergerdriven evolution.While most of these galaxies do not show obvious out-ward signs of a recent strong interaction in their opti-cal images, such as irregular structure or tidal features(the lack of these features is actually built in to ouranalysis since we do not plot highly peculiar/interactingsystems), smooth optical morphology is not inconsistentwith a merger having recently occurred. Merger simu-lations find the strongest morphological disturbances be-fore the peak of induced star formation, which in turntypically occurs before galaxies land on the right branch,and the complete coalescence of the two merging galaxynuclei commonly happens several hundred Myr beforethe main starburst event (Lotz et al. 2008, 2010). Thediverse arrow directions in Figure 11 on the right branchsuggest these galaxies are still actively forming stars wellafter the merger remnant has settled. Signatures of re-cent mergers may be more obvious in observations of gasmorphology and kinematics. HI maps can be extremelyuseful since they trace extended structure and can re-tain signatures of interactions as long as 1 Gyr after theevents (Holwerda et al. 2011). For example, the highresolution HI map of Haro 2 (Bravo-Alfaro et al. 2004)shows the HI kinematic and optical major axes to be al-most perpendicular, consistent with a merger or recentaccretion event.Blue-sequence E/S0s are known to emerge primarilybelow M b , and become abundant below M t (Kannappanet al. 2009). As seen in Fig. 8, the blue E/S0s on theright branch are consistent with this pattern. However,the existence of the right branch cannot be driven bystellar mass alone. Low stellar mass galaxies are foundthroughout the fueling diagram, and if ∆ C m were dic-tated solely by stellar mass (i.e., equal size bursts occur-ring in higher/low mass galaxies yielding lower/higher ∆ C m ), then the hole seen in the fueling diagram shouldnot exist. A merger origin for the right branch is moreconsistent with such a large gap between the left andright branches. Furthermore, gas richness likely producesdistinct evolutionary tracks for galaxies: gas-rich merg-ers drive galaxies along the right branch, while gas-poormergers drive galaxies into the quenched regime, up andoff the plot, as discussed in § b and espe-cially M t is a simple consequence of increasing gas rich-ness below those scales (Kannappan et al. 2009, K13s). The Bottom Branch The bottom branch appears to be part of the sameevolutionary sequence as the right branch but at a laterstage. Galaxies here show many of the same propertiesas those on the right branch in terms of stellar mass, gasrichness, and prominence of blue-sequence E/S0s. How-ever, they show depressed H /HI ratios while uniformlyevolving leftwards in the fueling diagram ( § Evidence for Disk Rebuilding We have argued that relatively low mass, gas-rich, butroughly equal-mass-ratio mergers appear to be responsi-ble for the creation of blue-sequence E/S0 galaxies on theright and bottom branches of the fueling diagram. Com-bining the known direction of evolution on the bottombranch ( § § increase in the total gas-to-stellar mass ratio as ∆ C m decreases . Since galaxies here appear to be evolving left-ward on the fueling diagram, their total gas content mustbe growing as their central stellar populations fade. Inthe same direction, there is a transition from E/S0 mor-phologies to spiral morphologies. These combined trendsare consistent with a scenario of fresh outer-disk gas ac-cretion and eventual conversion into visible spiral arms,and in fact blue-sequence E/S0s have ideal stellar surfacemass densities for turning gas efficiently into stars, pro-moting stellar disk rebuilding (Kannappan et al. 2009;see also Kauffmann et al. 2006). Notwithstanding thisself consistent picture of morphological transformation,there remain a handful of blue sequence E/S0s in the bot-tom left corner. One possible explanation for their pres-ence is that spiral structure formation has been inhibited.Two examples where such inhibition may be occurringare described in Kannappan et al. (2009): NGC 7360(∆( g − r ) m =0.027, H /HI < g − r ) m =-0.002,H /HI=0.011), which is a polar ring galaxy. In both ofthese cases, peculiar kinematics may be stifling spiralarm formation.Falling below the gas-richness threshold mass M t ( § t and have not only high gas frac-tions (as is typical for blue-sequence E/S0s in general,Kannappan et al. 2009, Wei et al. 2010a), but gas frac-tions that increase as their central starbursts fade. The he Fueling Diagram t as argued by K13s. Theoretical stud-ies of gas accretion from the last decade might suggestthat M t reflects the critical mass scale for cold-modeaccretion (Birnboim & Dekel 2003; Kereˇs et al. 2005).However, Nelson et al. (2013) calls this interpretationinto question, arguing that there is no strong transitionfrom cold to hot mode accretion, and that the amountof gas accreted via the cold mode is not as large as pre-viously thought. Regardless of the mode of accretion,the high/increasing gas fractions on the bottom branchmay be explained using the halo mass dependence of gascooling times (Lu et al. 2011).Conversely, galaxies on the bottom branch that haveabnormally low gas fractions relative to the rest of thepopulation have masses above M t . One possible rea-son may be reduced accretion. Above the bimodalitymass M b in particular, both observations and theory sug-gest significantly quenched cosmic accretion onto galaxies(e.g., Gabor & Dav´e 2012, K13s). Another possible rea-son certain galaxies might fail to accrete fresh gas on thebottom branch is their environments. Galaxies in denseclusters and groups have long been observed to have de-pressed HI fractions (Giovanelli & Haynes 1985; Solaneset al. 2001; Cortese et al. 2011), and galaxies near massivecompanions are also more likely to be quenched, even inthe dwarf regime below M t (Geha et al. 2012). One likelyexample of neighbor-inhibited accretion within our sam-ple is NGC 3073, a blue-sequence E/S0 below M t thathas an abnormally low gas-to-stellar mass ratio, but liesvery close to its much larger companion, NGC 3079. Thefact that NGC 3079 has an AGN and observed outflows(Cecil et al. 2001) may also be related to the low gas frac-tion in NGC 3073. Other outliers on the bottom branch,NGC 4111 and NGC 4270, reside in dense groups. A fullenvironmental analysis has not been performed on oursample, but these anecdotal cases hint that environment,as well as stellar mass, likely determines which galaxiesare capable of regrowing disks.A final possible explanation of some outliers on the bot-tom branch may be that they never even proceeded alongthe right and bottom branches to reach their current lo-cations. As discussed in § Revisiting the Link Between Mass-CorrectedBlue-Centeredness and Galaxy Interactions vs.Bars Throughout this paper, we have made the assumptionthat mass-corrected blue-centeredness is linked to galaxyinteractions. This assumption is motivated by Kannap-pan et al. (2004), who link blue-centered galaxies to mor-phological peculiarities indicative of galaxy interactions.One possible issue with this assumption is that E/S0soften lack morphological peculiarities (partially by theirdefinition of having smooth light distributions), but maystill have blue centers. Therefore, it is not necessarily ob-vious that E/S0s have blue centers for the same reason that clearly disturbed galaxies do.Our results argue strongly in support of the assump-tion that high mass-corrected blue-centeredness impliesa recent galaxy encounter, even in cases where morpho-logical peculiarities are not obvious. In fact, the galaxiesthat have experienced the strongest encounters withoutquenching (gas-rich major mergers of low-mass galaxies)are probably the blue-sequence E/S0s on the right andbottom branches that show relatively smooth structurein their optical images. A notable exception to the linkbetween blue-centered color gradients and recent interac-tions is the existence of the galaxies in the “dusty” zoneabove the left branch, which appear to be in early, moredust-embedded stages of star formation. This impliesthat there is a window shortly after the start of inducedstar formation where mass-corrected blue-centeredness isa poor indicator of a recent interaction.Bars have been suggested as an alternate mechanismfor funneling gas to the centers of galaxies based on di-rect observations of gas kinematics (Regan et al. 1995;Laine et al. 1999; Regan et al. 1999). The relative im-portance of bars versus interactions is not well known dueto a lack of large, homogeneous samples capable of ade-quately testing both mechanisms. Recently, Ellison et al.(2011) used the abundance of bars and close pairs in alarge sample from the SDSS to argue that bars induce ∼ all the galaxiesare E/S0s. More likely, any existing bars were destroyedby violent mergers whose remnants populate the rightand bottom branches of the fueling diagram.Bars are found on the left branch, but the bar frac-tion shows no smooth trend with either ∆ C m or withH /HI (although bars are absent at the top-right of theleft branch), and they are even quite abundant in the8 Stark et al. bottom-left corner of the fueling diagram where galax-ies show no sign of gas inflow. This lack of a smoothcorrelation may be explained if bar lifetimes are on theorder of a few Gyr (Jogee et al. 2004; Bournaud et al.2005; Debattista et al. 2006), in which case bars maydrive gas inflow that boosts central gas concentrationsand star formation but also remain well after central gasconcentrations have been depleted and starbursts haveceased (Sheth et al. 2005; Wang et al. 2012, but see Hoet al. 1997 and Sakamoto et al. 1999 for alternate view-points). This possible longevity makes interpreting therole bars play on the left branch difficult. However, sincethere are galaxies near the top of the left branch without bars, they certainly do not seem to be required to initi-ate an inflow event. Bars may increase the strength ofinflows and induce quicker depletion, but at this point itis unclear whether barred and unbarred galaxies behavesystematically differently on the left branch. CONCLUSIONS Using mass-corrected color gradients and H /HI ra-tios for a sample of galaxies spanning a broad rangeof morphologies, stellar masses, and evolutionary states,we have analyzed the relationship between recent centralstar formation enhancements, likely to reflect galaxy in-teractions, and global H /HI ratios and total gas contentin galaxies. We summarize our main results: • The parameter space of global H /HI and recentlyenhanced central blueness, which we refer to asthe “fueling diagram,” shows a complex relation-ship composed of three main branches – the leftbranch, the right branch, and the bottom branch– with most of our galaxies falling on the leftbranch. Galaxies in specific evolutionary statestend to concentrate in certain regions of the dia-gram (e.g., dusty, early-stage starbursts), or canbe represented on one axis of the diagram (e.g.,quenched systems). Since our sample is not statis-tically representative of the galaxy population, wecannot estimate the frequency with which galaxiesfall on each branch. • The left branch is composed primarily of star-forming spiral galaxies with a wide range of stel-lar masses and gas fractions. It follows a positivecorrelation between global H /HI and recently en-hanced central star formation. We interpret thiscorrelation as evidence that H /HI ratios are sys-tematically linked to local encounters with othergalaxies that drive inflows and replenish molecu-lar gas reservoirs. Additionally, apparent enhance-ment of H /HI ratio measurements may be causedby decreased X CO in the high surface density gasoften found in the centers of galaxies that expe-rience inflow events. Galaxies on the left branchlikely evolve in both directions along it before andafter inflow events. • The right and bottom branches are composed al-most exclusively of gas-rich blue-sequence E/S0galaxies with stellar masses below the bimodalityscale M b and typically also below the gas-richnessthreshold scale M t . Several lines of evidence sug-gest these two branches are part of a continuous evolutionary sequence of galaxies formed by gas-rich mergers of galaxies with roughly equal masses,which results in E/S0 galaxies that are experienc-ing strong central starbursts, depleting their molec-ular gas, and then fading back towards the leftbranch. • The population of galaxies on the bottom branchevolving back towards the left branch shows a gen-eral increase in total gas content and displays aclear transition from primarily E/S0 to primarilyspiral morphologies. These results strongly sug-gest fresh cosmic gas accretion and post-mergerdisk rebuilding in the low mass regime. Our cur-rent analysis does not constrain the timescale ofthis regrowth, but this question will be a topic offollow-up research. • E/S0s above M t and especially M b do not obviouslymove along the branches and may instead movevertically in the plot, due to minor accretion eventsassociated with nuclear fueling of star formation orAGN. • Barred galaxies are common on the left branch,although the presence of a bar shows no clear cor-relation with mass-corrected blue-centeredness orH /HI. It is unclear whether bars are involved inthe small inflow events that drive the evolution onthe left branch, but bars are likely destroyed in themergers that create the right/bottom branches andtherefore play little role in these galaxies’ evolution.The fueling diagram presented in this study links theamounts of atomic and molecular gas fuel in a galaxywith a metric for the events that drive central fueling andHI-to-H conversion, providing a useful framework forunderstanding how interactions, inflows, and gas accre-tion drive the continued growth and evolution of galax-ies. The movement of galaxies through the intercon-nected sequences of the fueling diagram highlights theirdynamic evolution. The left branch of the fueling di-agram holds the “normal” star-forming galaxies, whichappear to progress up and down along the left branchduring and after inflow events, with star formation al-ternately concentrated in the center vs. outer disk. Theright and bottom branches of the fueling diagram holdthe more dramatically transforming galaxies that havelikely experienced recent gas-rich mergers and centralstarbursts. These typically low mass spheroids proceedalong the right and bottom branches until reconnectingwith the left branch, potentially re-forming disk galax-ies along the way. Some galaxies may proceed throughthe branches of the fueling diagram multiple times un-til quenching mergers drive them off the plot. Thus theinterplay of bulge building and disk regrowth is a funda-mental process revealed in varying degrees by the distinctevolutionary tracks in the fueling diagram.We would like to thank Lisa Young for kindly providingthe CO(1-0) spectrum for NGC 5173. We would also liketo thank Amanda Moffett for useful discussions relatingto IRAC reduction and photometry. We thank G. Cecil,C. Clemens, F. Heitsch, M. Krumholz, M. Mac Low, M. he Fueling Diagram Spitzer Space Telescope Aguerri, J. A. 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Table 1 New IRAM 30m CO(1-0) and CO(2-1) Measurements CO(1-0) CO(2-1) Name Flux cz W 50 a rms Range b Flux cz W 50 a rms Range b R Log M H c Log M H , corr c,d Jy km s − km s − km s − mJy km s − Jy km s − km s − km s − mJy km s − ′′ M ⊙ M ⊙ UGC439 38.81 ± ± ± ± ± ± ± ± 20 11.40 7596–7937 21.46 ± ± ± ± ± ± ± ± 7] 37.37 3113–3295 20.1 8.26 ± ± ± ± ± ± 19 33.67 1886–2084 31.7 8.27 ± ± ± ± 22 25.75 1300–1720 29.51 ± ± 14] 30.92 1321–1658 54.9 8.31 ± ± < · · · · · · < · · · · · · < < ± ± ± ± ± ± ± ± 13 15.32 3993–4310 26.49 ± ± ± ± ± ± ± ± 41] 32.77 1231–1560 36.5 7.74 ± ± ± ± 36] 18.92 6479–6899 · · · · · · · · · · · · · · · ± ± ± ± · · · · · · · · · · · · · · · ± ± < · · · · · · < · · · · · · < < ± ± ± ± 11 49.66 2406–2831 41.6 9.15 ± ± ± ± < · · · · · · < < ± ± 18 12.77 2504–2816 24.05 ± ± ± ± ± ± ± ± ± ± ± ± 45] 10.35 1732–1964 4.00 ± ± 6] 10.05 1795–1936 27.0 7.45 ± ± ± ± ± ± 18] 29.70 1059–1224 20.3 7.56 ± ± ± ± 29] 17.99 4861–5091 4.46 ± ± 6] 40.81 4924–5025 43.7 8.56 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 2] 25.00 2302–2531 · · · · · · · · · · · · · · · ± ± ± ± ± ± ± ± < · · · · · · < · · · · · · < < < · · · · · · < · · · · · · < < ± ± 17] 19.61 1144–1368 8.62 ± ± 47] 39.18 1105–1388 27.5 7.39 ± ± e < · · · · · · ± ± 4] 47.12 1262–1292 · · · · · · · · · UGC9562SW f < · · · · · · ± ± 2] 39.59 1035–1060 · · · · · · · · · IC1066 11.18 ± ± 14 18.32 1488–1704 9.43 ± ± 14] 21.18 1505–1652 46.0 7.99 ± ± ± ± ± ± 20] 18.94 2990–3383 64.4 8.48 ± ± ± ± 17 28.06 2656–3014 46.68 ± ± 16 25.84 2675–3000 62.5 8.98 ± ± < · · · · · · < · · · · · · < < ± ± 27] 17.15 5435–5832 · · · · · · · · · · · · · · · ± ± ± ± ± ± ± ± ± ± 20 32.05 2500–2847 40.80 ± ± 7] 39.36 2538–2834 68.3 8.77 ± ± Note . — a Brackets denote galaxies with S/N < b Range of velocities used inintegration. c Masses include factor of 1.4 to account for Helium. d Beam-corrected H mass (see § e Offset from center of UGC9562 by +9 ′′ ,+11 . ′′ to observepolar ring. Upper limit integration on CO(1-0) flux based on integration range for CO(2-1) detection. CO(2-1) measurements done at a resolution of 2.6 km s − due toextremely small linewidth. f Offset from center of UGC9562 by − ′′ , − . ′′ to observe polar ring. Upper limit integration on CO(1-0) flux based on integration range forCO(2-1) detection. CO(2-1) measurements done at a resolution of 2.6 km s − due to extremely small linewidth. he Fueling Diagram Table 2 New ARO 12m CO(1-0) MeasurementsName Flux cz W 50 a rms Range b R Log M H c Log M H , corr c,d Jy km s − km s − km s − mJy km s − ′′ M ⊙ M ⊙ UGC439 32.37 ± ± ± ± ± ± 7] 81.05 7632–7932 24.2 9.79 ± ± < · · · · · · < < ± ± 5] 70.20 1760–2109 31.7 8.64 ± ± ± ± 18] 93.91 1600–1667 40.2 7.83 ± ± ± ± 5] 258.50 1474–1642 60.0 8.90 ± ± ± ± 19 124.77 1072–1368 26.6 8.71 ± ± ± ± 18] 88.97 3270–3431 22.8 9.10 ± ± ± ± 34] 91.01 2884–3164 36.9 9.05 ± ± ± ± 12] 44.79 5741–5925 19.1 8.87 ± ± ± ± ± ± ± ± 26] 104.81 2564–2701 46.3 8.81 ± ± ± ± 7] 77.30 1504–1651 35.4 8.21 ± ± ± ± 9] 79.92 961–1043 35.1 7.05 ± ± ± ± 13] 62.56 712–782 31.2 7.27 ± ± ± ± 33] 85.13 1071–1204 20.3 7.79 ± ± ± ± 11] 93.26 1450–1650 33.8 8.44 ± ± ± ± 24] 154.42 822–1027 41.9 8.43 ± ± < · · · · · · < < ± ± 29] 89.07 751–896 56.1 7.44 ± ± < · · · · · · < < ± ± 55] 134.02 2592–2984 62.5 9.29 ± ± e ± ± 8] 154.74 2843–3008 · · · · · · · · · NGC7328W f ± ± 9] 112.62 2641–2924 · · · · · · · · · UGC12265N 21.33 ± ± 8] 53.57 5570–5862 16.8 9.21 ± ± ± ± 11] 136.14 3080–3313 44.8 9.19 ± ± ± ± 51] 118.60 2543–2833 68.3 8.93 ± ± Note . — a Brackets denote galaxies with S/N < b Range of velocities used in integration. c Mass includes factor of 1.4 to account for Helium. d Beam-corrected H mass (see § e Offset from center of NGC7328 by +28 . ′′ ,+1 . ′′ . f Offset from centerof NGC7328 by − ′′ , − . ′′ . ∗ Non-NFGS galaxy. Stark et al. Table 3 Fueling Diagram Catalog DescriptionColumn Description1 Object name2 Right Ascension3 Declination4 Assumed distance to galaxy5 Inclination (see § u − r color7 Stellar mass8 Uncertainty in stellar mass9 Reference for HI mass10 Reference for uncorrected H mass11 H upper limit flag12 H mass after beam correction13 Uncertainty in H mass after beam correction14 X CO derived from B band luminosity15 X CO derived from O/H16 u − r blue-centeredness17 Uncertainty in u − r blue-centeredness18 Stellar mass-corrected u − r blue-centeredness19 Uncertainty in stellar mass-corrected u − r blue-centeredness20 u − g blue-centeredness21 Uncertainty in u − g blue-centeredness22 Stellar mass-corrected u − g blue-centeredness23 Uncertainty in stellar mass-corrected u − g blue-centeredness24 g − r blue-centeredness25 Uncertainty in g − r blue-centeredness26 Stellar mass-corrected g − r blue-centeredness27 Uncertainty in stellar mass-corrected g − r blue-centeredness28 Morphology (see § §§