THE IMPACT OF INTERACTIONS, BARS, BULGES, AND ACTIVE GALACTIC NUCLEI ON STAR FORMATION EFFICIENCY IN LOCAL MASSIVE GALAXIES

2.1.1. The Full Sample

The COLD GASS sample is shown in Figure 1 in the SFR–M_* plane. Since the sample is purely mass selected, it includes both star-forming and passive galaxies. In order to quantify gas scaling relations across the entire galaxy population, the sample selected for gas observations (both HI and CO) is constructed to have a flat M_* distribution (Catinella et al. 2010; Saintonge et al. 2011a). Additionally, in order to fully explore the SFR–M_* plane, we have targeted objects with high SFRs per unit mass. In this study, we refer to the 365 galaxies with CO measurements as the full sample (at the moment, HI data are available for 320 of these galaxies). The full sample is meant to sample uniformly the entire SFR–M_* plane and as such has an excess of high-mass galaxies and of galaxies with high specific star formation rates (sSFRs) compared to a purely volume-limited sample.

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2.1.2. The Representative Sample

2.1.3. The Control Samples

To correct the CO fluxes measured in the 22'' beam of the IRAM telescope to the total flux, we derive an aperture correction for each galaxy. In the first COLD GASS data release, we used a small sample of nearby galaxies with resolved CO maps to derive a mean relation for the aperture correction as a function of D₂₅, the SDSS g-band optical diameter. This method has the advantage of showing the range of aperture corrections that are possible at any given disk size D₂₅, given the real variation in radial molecular gas profiles within the reference sample. However, it does not take into account the specific properties of each galaxy, including its disk inclination and light profile.

In this paper, we therefore use a new prescription to correct fluxes, similar in spirit to the method used by Lisenfeld et al. (2011). For each galaxy with a CO measurement, we create a model galaxy having an exponential molecular gas distribution with a "half-light" radius corresponding to r_{50, SFR}, the radius encompassing 50% of the star formation as measured in the SDSS/GALEX photometry. This choice is based on the observation that CO and SFR distributions trace each other well in nearby star-forming galaxies (Leroy et al. 2009), even in the HI-dominated outer disk regions (Schruba et al. 2011). The model is then inclined as the real galaxy, and we simulate an observation with the 22'' IRAM beam. The ratio between this simulated observation and the total flux of the model galaxy is adopted as the aperture correction. For the more face-on systems, these values are perfectly consistent with the previous estimates. Only in the most inclined systems do we find aperture corrections on average 15% smaller.

The largest source of uncertainty in this process is the assumption that the gas profiles are exponential. Resolved maps of CO in nearby galaxies indicate that this assumption is generally valid: molecular gas profiles are observed to be exponential, with the CO and SFR scale lengths equivalent, both of which being proportional to the stellar scale lengths (Young et al. 1995; Nishiyama et al. 2001; Leroy et al. 2008), albeit with some scatter especially at small radii (Regan et al. 2001; Bigiel & Blitz 2012). At fixed disk inclination, we observe differences of at most 15%–20% in the values of $M_{{\rm H_2}}$ obtained with aperture corrections derived from the method described above and aperture corrections measured from the azimuthally averaged observed SFR profile of each galaxy. Lisenfeld et al. (2011) estimate a 30% uncertainty on their aperture corrections obtained from a similar disk modeling technique (see their Figure 3). Based on our tests and this independent estimate, we adopt a general uncertainty of 20% on the aperture corrections. Accounting also for the uncertainties in the measurement of the CO line fluxes, in the flux calibration at the telescope, and in the conversion factor α_CO (see Section 2.3), we estimate a global error of ∼0.3 dex on our values of $M_{{\rm H_2}}$, with the error budget largely dominated by the systematic uncertainty on α_CO (Saintonge et al. 2011a).

The other difference with the procedure described in Saintonge et al. (2011a) is the choice of the CO-to-H₂ conversion factor, α_CO. We have previously adopted a Galactic value of 3.2 M_☉ (K km s⁻¹ pc²)⁻¹ for all the galaxies in our sample, which did not take into account the contribution of helium. We now include this correction and therefore use α_CO =4.35 M_☉ (K km s⁻¹ pc²) for normal star-forming galaxies. Among the full sample used in this study, there are, however, galaxies undergoing major mergers. In such cases, it has been suggested that a value of 1.0 M_☉ (K km s⁻¹ pc²)⁻¹ is more appropriate (Solomon et al. 1997), and we follow this convention.

To avoid biasing the results of this study, it is preferable not to tie the choice between the Galactic and "merger" α_CO to a visual classification. Instead, we wish to use a quantitative measure of the properties of the ISM to make this choice. While infrared luminosity is directly connected to merging activity in the most extreme cases (ultraluminous infrared galaxies (ULIRGs) and submillimeter galaxies; e.g., Solomon et al. 1997; Veilleux et al. 2002; Engel et al. 2010), there is no one-to-one correlation between a high infrared luminosity (L_FIR > 10¹¹ L_☉) and the need for a low value of α_CO, nor between morphological signs of merging and enhanced star formation activity (e.g., Bushouse et al. 1988; Alonso-Herrero et al. 2006; Dasyra et al. 2006; Cox et al. 2008). However, the high densities found in mergers may lead to both elevated dust temperatures and lower values of α_CO (Narayanan et al. 2011). We therefore choose dust temperature, as parameterized by the S_60 μm/S_100 μm IRAS flux ratio, to guide our choice between Galactic and "merger" α_CO. Based on a sample of galaxies for which independent measures of α_CO are available (Boselli et al. 2002), we choose a value of S_60 μm/S_100 μm = 0.5 as the threshold to determine α_CO (J. Gracia-Carpio et al. 2012, in preparation). We therefore apply a conversion factor of α_CO =1.0 M_☉ (K km s⁻¹ pc²)⁻¹ to all galaxies with log L_FIR/L_☉ > 11.0 and S_60 μm/S_100 μm > 0.5, and the Galactic value of α_CO =4.35 M_☉ (K km s⁻¹ pc²)⁻¹ otherwise. Of the 365 galaxies in the sample, 11 match this criteria and use the lower value of α_CO. We note that within our survey volume, IRAS was sensitive to galaxies with log L_FIR/L_☉ > 10.7; therefore, this convention to assign α_CO does not bias against part of the sample, even though only 15% of the COLD GASS galaxies have good-quality flux measurements at both 60 and 100 μm. In Appendix B, we show that key results of this study are robust against this specific choice of α_CO.

We have already reported variations in both molecular gas mass fraction ($f_{{\rm H_2}}$ ≡ $M_{{\rm H_2}}$/M_*) and depletion time (t_dep(H₂) ≡ $M_{{\rm H_2}}$/SFR) across the COLD GASS sample in the mass range 10.0 < log M_*/M_☉ < 11.5 (Saintonge et al. 2011a, 2011b). These observations are summarized in Figure 2. We, however, improve here on our previous results by using stacking to calculate mean values of t_dep(H₂) and $f_{{\rm H_2}}$, allowing us to include both CO detections and non-detections in the analysis. We compute these mean values in six bins of offset from the star formation main sequence, calculated as

$$\begin{equation} \Delta {\rm (MS)}=\log {\rm (SFR)}-0.9(0.1\log M_{\ast }-1.0), \end{equation} \tag{ 2 }$$

adopting the main-sequence definition of Peng et al. (2010). The different Δ(MS) bins are defined at fixed intervals and illustrated in Figure 1. Since the M_*–SFR relation is almost linear, Δ(MS) is almost equivalent to variations in sSFR.

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To measure the mean depletion time of a given subsample, the stacking is done directly in "depletion time units." That is, all multiplicative factors required to convert an observed CO line flux into a t_dep(H₂) value were applied to each spectrum prior to stacking. This includes all the standard factors from the Solomon et al. (1997) prescription (their Equation (2)), but also the appropriate value of α_CO (see Section 2.3), SFR⁻¹, and a weight to correct for the flat stellar mass distribution of our sample (the methodology for this is described in Saintonge et al. 2011a). After stacking these scaled spectra, the mean depletion time is obtained by integrating over the resulting line profile, selecting by hand the spectral window over which the flux is integrated to reflect the effective line width in the stacked spectrum. This effective line width is seen to increase from ∼300 to ∼500 km s⁻¹ going from low to high μ_* or C, as these quantities correlate with M_*, which in turn correlates with circular velocity.

Similarly, we obtain mean values of $f_{{\rm H_2}}$ by stacking in "mass fraction units" (i.e., using an M_*⁻¹ scaling instead of SFR⁻¹). This is the same technique used by Fabello et al. (2011a) to derive mean gas fractions from stacking, and further details can be found in that reference. The only difference in methodology is that we do not weigh the spectra by their rms noise prior to stacking. Applying such weights would cause severe biases as the rms noise in the individual IRAM spectra is correlated with the underlying properties of the galaxies as a result of our survey strategy. Since we integrate until either a galaxy is detected in CO at S/N > 5 or a sensitivity to a gas mass fraction $f_{{\rm H_2}}$ = 0.015 is reached, gas-rich galaxies and those at the smaller distances have spectra with higher rms than gas-poor and more distant objects. Applying a weight derived from this rms noise would therefore heavily bias against gas-rich objects.

Figure 2(a) shows that the mean value of both t_dep(H₂) and $f_{{\rm H_2}}$ varies as a function of Δ(MS). Passive and weakly star-forming galaxies have low gas contents and long depletion times, while the most actively star-forming galaxies have higher gas contents and shorter depletion times. This is consistent, for example, with the conclusion of Combes et al. (1994) that the increased SFR in interacting galaxies is due to both increased molecular gas mass and increased star formation efficiency. The COLD GASS sample shows over a much broader range of galaxy types that changes in the molecular gas mass fraction cannot alone account for the full amplitude of sSFR variations; compare the black dashed line and the solid gray line in Figure 2(a). The mean star formation efficiency must also vary, and the stacking analysis indeed reveals that it increases by a factor of ∼6 in the mean between passive galaxies in the red cloud and actively star-forming galaxies above the main sequence (see the magenta line in Figure 2(a)).

What causes t_dep(H₂) to vary between galaxies above, on, and under the star formation main sequence? In Appendix B, we argue that these changes are not caused by our choice of the CO-to-H₂ conversion factor. Studies of large optical data sets at both low and high redshifts, however, indicate that other important physical parameters vary smoothly as a function of distance from the star formation sequence (e.g., Schiminovich et al. 2007; Wuyts et al. 2011) and suggest that structural parameters quantifying bulge prominence are critical in setting the star formation properties of galaxies, or lack thereof. We confirm in Figures 2(b) and (c) that indeed our measures of "bulginess," the concentration index C, and the stellar mass surface density μ_* do vary with Δ(MS), and in the next sections we investigate the link between these structural parameters and star formation efficiency variations.

The importance of structural parameters (or morphology) in setting the gas properties of galaxies has previously been recognized. For example, there are thresholds in C and μ_* above which the detection rate of both HI and CO drops significantly (Catinella et al. 2012; Saintonge et al. 2011a). As also shown in Kauffmann et al. (2012), the C −μ_* plane is particularly efficient at separating the quenched population from the gas-rich, star-forming galaxies. For this reason, we refer to the critical values of C = 2.6 and μ_* = 10^8.7 M_☉ kpc⁻² as "quenching thresholds." These critical values, determined from the gas properties of the galaxies, agree well with similar thresholds in stellar population or morphological indicators. For example, a concentration index of 2.6 corresponds to the transition between the late- and early-type galaxy populations, as reported by studies that compared this indicator to traditional visual morphologies, quantitative bulge/disk decompositions, and stellar population indicators (e.g., Strateva et al. 2001; Shimasaku et al. 2001; Nakamura et al. 2003; Weinmann et al. 2009; Kauffmann et al. 2003b). Similarly, a stellar mass surface density of 3 × 10⁸ M_☉ kpc⁻² was identified by Kauffmann et al. (2003b) as marking the transition between galaxies dominated by young and old stellar populations. In comparison, stellar mass is a poor quantity to separate the gas-rich from the gas-poor populations (Catinella et al. 2010; Saintonge et al. 2011a).

In Figure 3, galaxies with cold gas mass fractions above the sensitivity limits of our surveys (f_gas = 1.5%) are color-coded according to their t_dep(H₂) (panel (a)) or their t_dep(HI) (panel (b)). This shows clearly that the galaxies with the longest values of t_dep(H₂) and t_dep(HI) have high concentration indices and high stellar mass surface densities. It therefore appears that bulge-dominated, high stellar mass density galaxies either (1) have very little cold gas, either atomic or molecular, or else (2) tend to be inefficient at converting into stars the molecular gas they do have.

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Care must be taken in interpreting this last observation. Since at high μ_* and C the detection rate of CO and HI is low, the galaxies we are detecting will tend to be the most gas-rich at fixed SFRs and therefore those having the longest depletion times. While it can be unambiguously concluded from Figure 3 that the longest values of t_dep(H₂) and t_dep(HI) are only found in bulge-dominated galaxies, this "Malmquist bias" means that we cannot conclude from Figure 3 alone that the mean depletion time is longer in bulge-dominated galaxies. To circumvent this issue, we can use stacking over representative samples of galaxies with CO and HI spectra in order to include both detections and non-detections in the analysis.

The mean values of t_dep(H₂) and t_dep(HI) are shown as a function of C and μ_* in Figure 4. The stacking analysis confirms that both H₂ and HI depletion times are longer in galaxies with high C and μ_*, even when including the CO and HI non-detections. The specific behavior of t_dep(H₂) and t_dep(HI) as a function of C and μ_* is, however, different. The molecular gas depletion time increases steadily with C and μ_* in the regime of disk-dominated galaxies located on or around the star formation main sequence (|Δ(MS)| < 0.5; see Figures 4(c) and (d)) and reaches a maximum value in the mean when reaching values of C and μ_* characteristic of bulge-dominated galaxies. In contrast, t_dep(HI) increases more slowly at C < 2.6 and log μ_* < 8.7 but then suddenly reaches a value close to a Hubble time for the bulge-dominated galaxies, located well below the star formation main sequence. An interpretation of these trends is presented below in Section 4.3.

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It is already established that in systems well above the main sequence of star-forming galaxies in the SFR–M_* plane, t_dep(H₂) is reduced by an order of magnitude compared to the normal star-forming population (e.g., Gao & Solomon 2004; Bothwell et al. 2010; Genzel et al. 2010; Daddi et al. 2010). In the local universe, these are the ULIRGs, most of which (if not all) are major mergers (Sanders & Mirabel 1996; Veilleux et al. 2002). For this reason, we speculated in Saintonge et al. (2011b) that milder dynamical effects, such as minor mergers and bar instabilities, could lead to more modest yet measurable variations in the global t_dep(H₂). We have now also established that t_dep(H₂) is longer in bulge-dominated galaxies than in star-forming disks, which may be interpreted in this same framework by an increased stability against star formation. In this section, we address the question of the impact of interactions and bars on star formation efficiency, and we come back to the role of bulges in Section 4.3.

Whereas major mergers with mass ratios close to unity are very rare in the local universe, the COLD GASS sample includes a fair number of objects undergoing milder dynamical perturbations that may be affecting their star formation efficiency. The analysis here focuses on galaxies with bars and on those displaying signs of interactions or morphological irregularities. We use the classification of Wang et al. (2012) to identify galaxies with strong bars, defined as having ellipticity e_bar > 0.5. Not only is the identification of such bars robust, but these are the kinds of bars that are linked to nuclear starbursts (see Wang et al. 2012 for the full details).

Two different approaches are then used to identify interacting or otherwise disturbed galaxies. First, we use a set of quantitative morphological parameters measured by Wang et al. (2011) for the GASS sample, following the technique of Lotz et al. (2004). Second, we performed a visual inspection of all COLD GASS galaxies and classified them as either being normal, showing signs of interaction and/or morphological disturbances, or finally appearing to undergo a major merger. All galaxies identified as major mergers are IRAS detected, with significant infrared luminosities (L_IR > 10¹¹ L_☉). In what follows we use the visual classification, but in Appendix A we show that not only is there a significant overlap between the subsamples identified by the two methods but the results of the analysis are not affected by the classification technique.

3.3.1. Interacting Galaxies

In Figure 5, the distribution of t_dep(H₂) for the COLD GASS galaxies with reliable CO and SFR measurements is shown, for both the representative and full samples. In the top panels, the populations of interacting/morphologically disturbed and barred galaxies are highlighted. In the bottom panel of Figure 5, we show that a simple stellar mass surface density cut at log μ_* = 8.7 is also efficient in separating the short and long depletion time populations in both the full and representative samples. The mean values of t_dep(H₂) for the low and high μ_* samples and the statistical significance of the difference between the distributions are summarized in Table 1. A KS test indicates that in both samples, low and high μ_* systems have t_dep(H₂) distributions that have a probability <0.001 of being equivalent. Since most of the morphologically disturbed galaxies have low stellar mass surface densities, to reliably assess the impact of interactions and bars on depletion time we define control samples of galaxies matched in μ_* and NUV−r color but showing no signs of disturbance.

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Table 1. Mean Molecular Gas Depletion Timescales^a in Selected COLD GASS Subsamples

Sample	Bulges			Bars			Interactions
	Low μ*	High μ*	KSprob	Bars	Control	KSprob	Interact	Control	KSprob
Full	0.96 ± 0.44	1.9 ± 0.9	<0.001	0.88 ± 0.35	1.3 ± 0.8	0.26	0.63 ± 0.41	1.1 ± 0.6	0.005
Representative	1.2 ± 0.5	2.0 ± 0.9	<0.001	0.87 ± 0.24	1.2 ± 0.6	0.24	0.95 ± 0.44	1.1 ± 0.5	0.49

Note. ^aThe mean depletion times are in units of 10⁹ yr, and the errors quoted are the standard deviations around that mean value in any given subsample.

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As seen in Figure 5 and Table 1, morphologically disturbed galaxies in the full sample have significantly shorter depletion times than objects in the control sample (KS probability of 0.005 that their depletion times are drawn from the same distribution). Combes et al. (1994) similarly observed the depletion time to be a factor of two shorter in galaxy pairs. In Section 4, we argue that the short t_dep(H₂) values in interacting/disturbed galaxies come from a change in the fraction of the gas that is found in the densest phase, due to the pressure increase. In the representative sample, however, the depletion times of disturbed galaxies and their control are equivalent. This is consistent with previous findings that mergers cannot all be identically associated with episodes of active star formation (e.g., Di Matteo et al. 2007), either because some interactions may not drive gas inward and compress it or else because there is a delay between the occurrence of the signposts of morphological perturbations and starburst events.

3.3.2. Barred Galaxies

3.3.3. The Global Star Formation Law

To assess whether the t_dep(H₂) variations are caused by systematic changes in the global surface density of the molecular gas, the COLD GASS sample is shown in the Kennicutt-Schmidt plane in Figure 6. Surface densities are computed assuming that star formation and molecular gas are distributed similarly (Leroy et al. 2008), with a "half-light" radius, r_{50, SFR}, measured for each galaxy as part of our standard photometry pipeline (Wang et al. 2010). Results are shown for both the full and representative samples. With the full sample one can assess the distribution of different galaxy types in the KS plane, while the representative sample allows the determination of an unbiased global star formation relation for local massive galaxies (M_* >10¹⁰ M_☉). This relation is

$$\begin{equation} \log \Sigma _{{\rm SFR}} = \Bigg \lbrace \begin{array}{@{}l}(0.86\pm 0.21)(\log \Sigma _{{\rm H2}})-(2.94\pm 0.26) \\ \ms (1.18\pm 0.24)(\log \Sigma _{{\rm H2}})-(3.30\pm 0.28), \end{array} \end{equation} \tag{ 3 }$$

where the errors given for the slope and intercept are 3σ formal fit errors, which approximate the total error including systematic effects and calibration uncertainties (Genzel et al. 2010). As different authors use different fitting strategies, we present for comparison purposes the results of an ordinary least-squares regression of y on x (top equation) and of a bisector fit (bottom equation, and our preferred method). In both cases, the scatter of the residuals around the relation is σ_KS = 0.28, and the slope is consistent with linear. These values are in agreement with other derivations of the star formation law at the kpc scale (Leroy et al. 2008; Blanc et al. 2009; Bigiel et al. 2011; Rahman et al. 2012) and at high redshift (Genzel et al. 2010; Daddi et al. 2010).

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The t_dep(H₂) variations observed across the COLD GASS sample do not come from a star formation law with significantly steeper slope than in other recent work, nor from systematic trends between $\Sigma _{{\rm H_2}}$ and, e.g., μ_* or interaction state. Rather, the t_dep(H₂) variations manifest themselves as structure within the scatter around a ∼linear KS relation, where specific populations, for example, galaxies with high/low μ_*, are preferentially located below/above the mean KS relation (Figure 6). As expected from previous studies, the galaxies undergoing major mergers have short depletion times and mark the upper envelope of the distribution in the KS plane (Figure 6). Mildly interacting/disturbed galaxies, having low stellar mass surface densities, then fall systematically above the mean KS relation.

Additionally, galaxies with the highest stellar mass surface densities and concentration indices (i.e., the bulge-dominated galaxies) are found systematically below the mean KS relation, with long global molecular gas depletion times ranging between 1 and 5 Gyr. A similar observation was made by Crocker et al. (2012) for a small sample of nearby early-type galaxies with detailed observations of multiple molecular gas lines. In Figure 6(a), there are a few galaxies deviating from the rest of the population, having high stellar mass surface densities yet short depletion times. These are, however, all merging systems, which may be in a transition phase and will ultimately lie below the mean KS relation after the starburst phase, as suggested by simulations (Bournaud et al. 2011). We come back to this discussion in Section 4.3.

The main conclusions to be drawn from Figure 6 are that (1) in the representative sample, the "merger branch" of the KS relation mostly disappears, confirming that very efficiently star-forming major mergers are rare events that do not contribute significantly to the star formation budget in the local universe; (2) the global surface density of H₂ (estimated form our CO(1–0) line fluxes) is not the only parameter driving the star formation efficiency of galaxies, as we observe structure within the scatter about the mean KS relation; and (3) the bulge-dominated galaxies, which have the longest molecular gas depletion times, are inefficient star formers despite have $\Sigma _{{\rm H_2}}$ values as high as spiral galaxies (see also Young et al. 2008; Shapiro et al. 2010).

As explained in Section 1, most studies suggest that quenching is not strongly linked with stellar mass, but rather with a measure of "bulginess." Given the well-established correlation between supermassive black holes and bulges (e.g., Häring & Rix 2004; Magorrian et al. 1998; Merloni et al. 2010; Beifiori et al. 2012), AGN feedback as an important quenching mechanism is appealing (e.g., Somerville et al. 2008), as it would explain why few galaxies without central mass concentration are quenched, while a very large fraction of the bulge-dominated systems are (e.g., Bell 2008).

In this light, there has been work done to investigate the link between the presence of AGNs and the gas content of galaxies, which should be most directly affected by the feedback. However, Ho et al. (2008) and Fabello et al. (2011b) report no difference in the atomic gas properties of active and inactive galaxies, in large representative nearby samples. This would seem to argue against the AGN feedback scenario presented above, although both studies point out that molecular gas, which is generally significantly more centrally concentrated than HI, may be a more sensitive tracer. Here, we use our IRAM CO observations to investigate whether the presence of an active nucleus influences the molecular gas contents of galaxies, in order to address the question of why bulge-dominated galaxies have on average longer t_dep(H₂). As detailed below, we find that while AGNs may affect the amount of molecular gas in their host galaxies, the SFR is also reduced, leaving the depletion time unchanged (or if anything reduced) as compared with a properly matched control sample.

We identify as active the COLD GASS galaxies located above the Kauffmann et al. (2003a) line in the BPT diagram (the line ratio diagnostic plot first presented by Baldwin et al. 1981). Of these, 6% are Seyferts, the rest being either LINERs or composite systems where part of the line emission is from star formation. In the reference sample of "non-AGNs" we include the star-forming systems identified from the BPT diagram and the inactive galaxies that have no line emission (S/N < 3 in Hα, [N ii], Hβ, and [O iii]). To compare fairly their molecular gas properties, we match subsamples of AGN hosts and reference galaxies, requiring that the two subsamples have equivalent distribution in μ_* and NUV−r color. The results presented below are unchanged if instead we control for star formation activity in the central region (i.e., using the fiber D_n(4000) instead of the global NUV−r color) or for another structural parameter such as M_* or C.

As a proxy for the Eddington ratio, we use the ratio L[O iii]/σ⁴. The luminosity in the [O iii] line, which we correct for extinction following Wild et al. (2007), can be used as a proxy for the black hole accretion rate (Kauffmann et al. 2003a), while the black hole mass is proportional to σ⁴ (Tremaine et al. 2002). We use for σ the stellar velocity dispersion measured in the SDSS fiber, corrected for aperture effects as detailed in Graves et al. (2009). Each subsample (AGN and control) is divided into three bins of L[O iii]/σ⁴, and galaxies are stacked in order to obtain the mean values of $f_{{\rm H_2}}$ and t_dep(H₂). The results are shown in Figure 7. At all values of the Eddington ratio, the mean molecular gas mass fraction is lower in the AGN subsample, but the mean depletion times are consistent or even shorter than in the control.

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Maiolino et al. (1997) conducted a similar study, comparing the molecular gas properties of Seyfert and field galaxies. They report no strong difference in the global H₂ contents but an increased star formation efficiency in Seyfert 2 hosts. Our very tentative observation of a shorter t_dep(H₂) in AGN hosts may be the extension of what these authors are finding in the more powerful Seyferts, although a direct test of this is not possible due to the lack of overlap between the types of AGNs probed by our studies and the different methodology in assigning control samples.

The most important conclusion of this section in the context of this work is that the high incidence of AGNs in bulge-dominated galaxies cannot explain why t_dep(H₂) is longer at high concentration index and μ_*. There does, however, appear to be a link between AGNs and $f_{{\rm H_2}}$, but we caution that this observation pertains only to the type of AGNs that are in our sample, typically LINERs accreting at a rate of at most ∼0.01 L_Edd.

The key observations presented in this work can be summarized as follows:

• 1.  
  Both the molecular gas mass fraction ($f_{{\rm H_2}}$) and depletion time (t_dep(H₂)) vary across the SFR–M_* plane. Galaxies above the star-forming sequence have both higher $f_{{\rm H_2}}$ and shorter t_dep(H₂). Conversely, explaining the low sSFRs of galaxies below the star-forming sequence requires both $f_{{\rm H_2}}$ to decrease and t_dep(H₂) to increase.
• 2.  
  The bulge-dominated galaxies in the sample, identified by their large concentration indices or their high stellar mass surface densities (C > 2.6, μ_* >10^8.7 M_☉ kpc⁻²), either have no cold gas down to the limit of our survey or else are on average inefficient at converting into stars the molecular gas they do have. Despite the fact that molecular gas in early-type galaxies has high surface densities just like in normal star-forming disks, we find their mean t_dep(H₂) to be twice as long. The atomic gas depletion time is also longer in bulge-dominated galaxies.
• 3.  
  At fixed μ_* and color, galaxies hosting AGNs have lower molecular gas mass fractions than their control sample, at all values of the Eddington ratio probed by our sample. There is tentative evidence that the depletion timescale of the molecular gas is either unchanged or lowered in the presence of an AGN, but not increased, indicating that active nuclei are not the main agent responsible for the long depletion times in bulge-dominated galaxies.
• 4.  
  Among the gas-rich, disk-dominated population, galaxies undergoing merging events or having disturbed morphologies have the shortest depletion times, on average a factor of two shorter compared to matched control samples. Not all mergers or interactions are, however, associated with episodes of particularly efficient star formation.
• 5.  
  Global molecular gas depletion times are only mildly shorter in galaxies hosting strong stellar bars, everything else being equal. Even though resolved gas studies show that bars can lead to enhanced nuclear star formation efficiency, the effect is not strong enough to significantly affect the global depletion time.
• 6.  
  We derive the star formation law for an unbiased sample of galaxies, representative of the local population with M_* >10¹⁰ M_☉. This relation has a slope of 1.18 ± 0.24, consistent with previous studies; the t_dep(H₂) variations manifest themselves as structure within the scatter around this best-fit relation, with bulge-dominated galaxies falling systematically below the mean relation.

We now discuss these results, addressing the two main questions posed in the Introduction, and comparing them to previously published work.

Our results confirm previous observations that the transition from star-forming to quiescent galaxies is correlated with the presence of a bulge, as quantified by either stellar mass surface density, Sérsic index, velocity dispersion, or concentration index (see also Catinella et al. 2010; Saintonge et al. 2011a; Kauffmann et al. 2012). While there is still some debate as to which of these measures of "bulginess" correlates best with quiescence (for different views on this, see, e.g., Franx et al. 2008; Wuyts et al. 2011; Bell et al. 2012; Wake et al. 2012), various studies generally agree that stellar mass is a poorer diagnostic to separate star-forming from quiescent galaxies. Our results bring additional weight to these previous studies, since they are based on cold gas measurements, a direct tracer of the instantaneous potential of a galaxy to form stars, rather than on indicators such as color, which are averages over the different star formation history of each galaxy.

Structural parameters such as μ_* and C correlate not only with quiescence but also with star formation efficiency. These physical quantities are therefore at the core of this question. Only in galaxies with lower μ_* do we see the dynamical processes that can significantly increase star formation efficiency. At the other extreme, high central concentrations may lead to reduced star formation efficiency or complete quenching of the star formation.

The single quantity that may link these observations is the dense molecular gas fraction. We speculate that while t_dep(H₂) (measured from CO(1–0) line fluxes) varies across our sample, were we to measure a depletion time for the dense gas, it would show significantly less scatter. A commonly used dense gas tracer is the HCN(1–0) line, with observations showing that the HCN(1–0)/CO(1–0) ratio is increased in efficiently star-forming galaxies like LIRGs (Gao & Solomon 2004; Juneau et al. 2009; Graciá-Carpio et al. 2008; García-Burillo et al. 2012) and possibly reduced in early-type galaxies (Crocker et al. 2012). We caution, however, that although the HCN/CO ratio appears to be a signpost for the star-forming dense gas fraction, it is not a perfect tracer (e.g., Graciá-Carpio et al. 2006). Indeed, HCN is a minor species subject to the abundance of nitrogen and the details of the chemical network (e.g., Sternberg et al. 1994; Usero et al. 2004; Meijerink et al. 2007), and its (1–0) transition is sensitive to the specific physical excitation conditions, with mid-infrared pumping possibly playing a role (Aalto et al. 1995). Other possibilities to trace the dense star-forming gas would be the HCO⁺(1–0) transition or higher rotational transitions of, e.g., CO, HCN, or HCO⁺.

Theoretical and numerical work also supports this picture. Krumholz & Thompson (2007) find that a line with a high critical density like HCN(1–0) traces well the efficiently star-forming gas between galaxies with different global properties. On the other hand, they find that a lower density tracer like CO(1–0) tracks regions with various star formation properties from galaxy to galaxy. With high-resolution hydrodynamic simulations, Bournaud et al. (2011) find the probability distribution function (PDF) of the local gas density in mergers to be broader and shifted to higher densities (or perhaps to have a different functional form), compared to the mostly lognormal PDFs found in normal star-forming galaxies (Wada & Norman 2001). They conclude that these variations in the dense gas fractions at different stages of a merger cause galaxies to go from having "normal" t_dep(H₂) before the interaction begins to having short t_dep(H₂) at the peak of the merging activity (resulting in the merger sequence in the KS plane). The end products of these mergers, early-type systems with some amount of dense molecular gas left, are somewhat inefficient at forming stars and have longer than average t_dep(H₂). This scenario explains well the location of the various galaxy types on the COLD GASS KS relation (Figure 6).

In early simulation work, Ostriker & Peebles (1973) pointed out that galaxies with significant spheroidal components are more stable against fragmentation than pure disks. Since fragmentation introduced by gravitational instabilities is a key element of star formation, the natural conclusion may be that bulges can therefore reduce star formation efficiency. This can be understood in terms of the stability parameter, Q (Toomre 1964), which in the case of gas+stars systems can be extended to include the two components (e.g., Jog & Solomon 1984; Elmegreen 1995; Romeo & Wiegert 2011), as confirmed by observations (Wong & Blitz 2002; Leroy et al. 2008; Hitschfeld et al. 2009). Specifically, a gas disk, which would be otherwise unstable, can be made stable by a significant stellar bulge. Under the framework presented above, long depletion times in bulge-dominated galaxies would therefore result from a gas density PDF shifted to lower densities than in normal star-forming galaxies. We note that the effect of a stellar component on the stability of a gas disk could, however, be reversed in galaxies with lower stellar masses than those in the COLD GASS sample, when stars are distributed in a disk without a significant central concentration. In that case, higher stellar mass surface densities could translate into a shorter depletion time, as argued, for example, by Shi et al. (2011).

As seen in Figure 6, bulge-dominated galaxies fall systematically below the mean molecular KS relation, indicating that at fixed gas surface density they are less efficient at forming stars. The observation is in line with the scenario presented above, in which massive stellar bulges can stabilize gas disks, therefore reducing the star formation efficiency. Although this mechanism is not sufficient in itself to make star-forming galaxies "red and dead," it may be efficient at keeping already-quenched galaxies on the red sequence, by preventing further star formation even in the event of late-time cold gas accretion (Martig et al. 2009). In massive galaxies, radio-mode AGN feedback may be the most important agent in keeping galaxies on the red sequence (e.g., Gabor et al. 2011; van de Voort et al. 2011); however, the contribution of the bulge in the reduction of the star formation efficiency could be an important effect in lower mass galaxies where AGNs are not prevalent.

Interestingly, we also find the longest values of t_dep(HI) in galaxies above the "quenching thresholds" (C > 2.6 and μ_* >10^8.7 M_☉ kpc⁻²; see Figure 3), although in this case the reason may be different, and the different behavior of t_dep(H₂) and t_dep(HI) as a function of μ_* hints at changes in the bottleneck of the star formation process across the local galaxy population. In high-density bulge-dominated galaxies, the atomic gas depletion time increases significantly. This suggests that these galaxies have large reservoirs of HI gas, presumably located in the outer disk, that do not participate in the star formation process. In this regime, the bottleneck for star formation is the transport of this atomic gas to regions of higher density where the atomic-to-molecular conversion (and hence star formation) takes place efficiently. At stellar mass surface densities characteristic of disk-dominated galaxies, t_dep(HI) has a mean value of ∼3 Gyr with large galaxy-to-galaxy variations (Schiminovich et al. 2010) but increases slowly with μ_* and C similarly to t_dep(H₂). On average, there is therefore no accumulation of atomic gas, the conversion to CO(1–0)-detectable molecular gas proceeding unimpeded. The t_dep(H₂) variations then come about as galaxies have different fractions of their molecular gas in efficiently star-forming dense cores. This interpretation is supported by our observation that even among galaxies with low stellar mass surface densities, the ones undergoing merging, or to some extent those hosting a strong stellar bar, have the shortest CO-based t_dep(H₂).

Since bulge-dominated galaxies preferentially host AGNs, it has been suggested that the correlation between quenching and the presence of a bulge may be a consequence of the feedback from the AGN. If this were the case, there should be differences in the gas contents of galaxies with and without AGNs, everything else being equal. Compared to a control sample matched in μ_* and color (either global NUV−r or central D_n(4000)), galaxies hosting an AGN with $-4<\log L{[{\rm O\,\mathsc{iii}}]}/\sigma ^4<-2$ have lower molecular gas mass fractions than inactive galaxies. This observation indicates a possible connection between AGN activity and the quenching of star formation, although our sample does not include the stronger AGNs that are likely to contribute most to this process. Galaxies with and without AGNs in our matched subsamples do not have statistically different mean values of t_dep(H₂), however, suggesting that the AGNs with modest accretion rates are not responsible for the long depletion times in bulge-dominated galaxies. There is very marginal evidence that t_dep(H₂) is even reduced in AGN hosts, although the difference is not statistically significant in our sample, which includes mostly LINERs. The non-result is in agreement with Juneau et al. (2009), who report no difference in the HCN/CO ratio between galaxies with and without AGNs, which in the framework of this discussion could explain why we do not observe variations in the CO-based values of t_dep(H₂) for AGN-hosting galaxies. The disconnect between nuclear properties and outer disk star formation explains why there is no correlation between AGN activity and the generally extended HI contents of the host galaxies (Ho et al. 2008; Fabello et al. 2011b; Diamond-Stanic & Rieke 2012).

One of the main results of this work is that global structural parameters, in this case concentration index and stellar mass surface density, are critical in both establishing the bimodality between gas-rich star-forming and gas-poor quiescent galaxies and setting the efficiency of star formation. Star formation, however, is not purely a global process, as it depends strongly on small-scale physical conditions, which our integrated measurements cannot track. Significant work has, however, gone into measuring gas and star formation in nearby galaxies at the (sub-) kiloparsec scale, with results, if taken at face value, that may appear at odds with the conclusions of this study (e.g., Bigiel et al. 2011, who present evidence for a constant depletion time in nearby galaxies).

The relation we observe between t_dep(H₂) and the global stellar mass surface density may not apply at small scales, although Figure 15 of Leroy et al. (2008) indicates that the local mean depletion time in kpc-sized regions of nearby spirals increases by a factor of two over one decade in μ_* (a similar effect can be seen in Figure 2 of Rahman et al. 2012). The global values of μ_* may not track the local conditions in individual sites of star formation, but rather the probability of incidence of various dynamical processes that can influence whether star formation proceeds "normally" in virialized GMCs or rather in dense super star-forming complexes.

In a study of the resolved star formation law, Schruba et al. (2011) argue that star formation efficiency does not vary significantly within individual galaxies, with however significant galaxy-to-galaxy variations. Even though this is consistent with the observations presented here, the interpretation is fundamentally different. Indeed, Schruba et al. (2011) ascribe the t_dep(H₂) variations to a metallicity dependence of the conversion factor α_CO, while our analysis suggests that they are caused by actual changes in star formation efficiency. As detailed in Appendix B, we do not find any evidence for metallicity or extinction to be the main driver of the observed t_dep(H₂) variations. In the stellar mass range of the COLD GASS sample (>10¹⁰ M_☉), the mass–metallicity relation is flat (Tremonti et al. 2004), implying that quantities such as μ_* and C do not correlate with metallicity. However, toward the low-mass end of our sample, and even more so at M_* <10¹⁰ M_☉, the $M_{{\rm H_2}}/$SFR ratio may very well be modulated simultaneously by variations in α_CO and actual changes in star formation efficiency. Even after accounting for metallicity effects on α_CO, high star formation efficiencies have indeed been reported for several low-mass, low-μ_* local galaxies where high-resolution measurements of both gas and star formation are possible, for example, M33 (Gardan et al. 2007; Gratier et al. 2010), IC 10 (Leroy et al. 2006), and NGC 6822 (Gratier et al. 2010) (see, however, the counterargument in the case of the Small Magellanic Cloud (SMC) in Bolatto et al. 2011). Disentangling the two effects will require both large statistical samples of low-mass galaxies akin to COLD GASS and resolved gas maps of galaxies spanning a broader range of properties.

The main difference between our global results and those of studies focusing on the (sub-)kpc scale may rather be more methodology based. As pointed out correctly by Rahman et al. (2012), resolved studies measure t_dep(H₂) in regions of the galaxies where CO is detected, but studies like ours include the total gas mass and the total SFR. The resolved measurements therefore teach us about star formation in the gas-rich GMCs, and the global measurements about the total timescale for star formation, including any diffuse gas or star formation component. In particular, the global values of t_dep(H₂) include star formation coming from the outer disks, regions where CO is in general not detected in resolved maps and therefore not included in resolved studies. Since star formation is known to be very inefficient in these outer regions (t_dep(HI) >t_Hubble; Bigiel et al. 2010), the relative contributions of outer disk star formation to the total value may be responsible for some of the galaxy-to-galaxy star formation efficiency variations and the difference in absolute value of the mean depletion time reported in different studies (in general a factor of ∼2 higher in resolved studies). For example, Bolatto et al. (2011) find t_dep(H₂) ∼1.6 Gyr at the kpc scale in the SMC, but t_dep(H₂) =0.6 Gyr for the entire galaxy, in line with the values we find in galaxies with low stellar mass surface densities. There are, however, arguments against the "outer disk effect" interpretation. First, there is evidence that the molecular star formation law extends even in the HI-dominated outer regions of normal star-forming disks (e.g., Heyer et al. 2004; Schruba et al. 2011). Second, the metallicity gradients of galaxies in the stellar mass range M_* >10¹⁰ M_☉ are remarkably flat out to the optical diameter (Moran et al. 2012), such that there is no evidence that the CO measurements of COLD GASS galaxies are subject to radially dependent α_CO variations.

High-resolution mapping of CO in a broad range of galaxies will be necessary to further make the connection between local and global measurements. As the latter are most commonly available for high-redshift systems, understanding this relation is critical. Surveys like COLD GASS, offering homogeneously measured quantities over large, representative samples of galaxies, are essential to identify the key populations where star formation efficiency is modulated, allowing us to understand the physical processes that are responsible for regulating the star formation budget of the local universe. For example, while bars can lead to nuclear starbursts and the formation of bulges, they are not responsible for increasing significantly the star formation efficiency over the local galaxy population. Galaxy interactions and mergers, however, do have that effect. Now that statistically large samples are starting to be collected at high redshifts (L. Tacconi et al. 2012, in preparation), it will also be possible to track over cosmic time the relative contributions of different mechanisms such as bar instabilities, bulge stabilization, interactions/mergers, and AGN feedback in the regulation of star formation.