connection between galaxy structure and quenching efficiency | Monthly Notices of the Royal Astronomical Society

Abstract

Using data from the Sloan Digital Sky Survey (SDSS)-DR7, including structural measurements from 2D surface brightness fits with gim2d, we show how the fraction of quiescent galaxies depends on galaxy stellar mass M_*, effective radius R_e, fraction of r-band light in the bulge, B/T, and their status as a central or satellite galaxy at 0.01 < z < 0.2. For central galaxies we confirm that the quiescent fraction depends not only on stellar mass, but also on R_e. The dependence is particularly strong as a function of |$M_*/R_{\rm e}^\alpha$|⁠, with α ∼ 1.5. This appears to be driven by a simple dependence on B/T over the mass range 9 < log (M_*/M_⊙) < 11.5, and is qualitatively similar even if galaxies with B/T > 0.3 are excluded. For satellite galaxies, the quiescent fraction is always larger than that of central galaxies, for any combination of M_*, R_e and B/T. The quenching efficiency is not constant, but reaches a maximum of ∼0.7 for galaxies with 9 < log (M_*/M_⊙) < 9.5 and R_e < 1 kpc. This is the same region of parameter space in which the satellite fraction itself reaches its maximum value, suggesting that the transformation from an active central galaxy to a quiescent satellite is associated with a reduction in R_e due to an increase in dominance of a bulge component.

galaxies: evolution, galaxies: structure

1 INTRODUCTION

It is now well known that galaxies in the local Universe can generally be separated into two broad classifications: blue, star-forming, disc galaxies and red, elliptical and lenticular galaxies with little or no recent star formation (e.g. Strateva et al. 2001; Kauffmann et al. 2003; Baldry et al. 2004; Balogh et al. 2004). The star formation rate (SFR) of blue galaxies is well correlated with their stellar mass (M_*), forming the ‘main sequence’ or ‘star-forming sequence’ in the SFR-M_* plane (Brinchmann et al. 2004; Salim et al. 2007; Gilbank et al. 2010; McGee et al. 2011). Surveys show that the star-forming sequence has persisted out to z = 1 (Bell et al. 2004; Willmer et al. 2006; Noeske et al. 2007) and possibly z = 2 and further (Brammer et al. 2009; Taylor et al. 2009). Most tellingly, the number density of red, passive galaxies has roughly doubled since z = 1, while the number of blue galaxies has remained nearly constant (Bell et al. 2004; Faber et al. 2007; Brown et al. 2007; Gonçalves et al. 2012; Muzzin et al. 2013). This motivates the search for processes that cause blue, star-forming galaxies to transition to red, non-star-forming ones. This transition has become known as ‘quenching’.

It has also been established that the galaxy population varies with environment, in the sense that low-density environments are dominated by less massive, blue star-forming galaxies while denser groups and clusters tend to host massive red elliptical and lenticular galaxies (e.g. Oemler 1974; Davis & Geller 1976; Dressler 1980; Baldry et al. 2006; Pasquali et al. 2010). Interestingly, the star-forming sequence itself appears to be largely independent of environment, while the fraction of star-forming galaxies decreases dramatically with increasing local density (e.g. Carter et al. 2001; Balogh et al. 2004; Wolf et al. 2009; Poggianti et al. 2008; Peng et al. 2010).

There is some evidence to show that galaxy properties depend on the mass of their host, dark matter halo, with distinctly different behaviour for the most massive galaxies in the halo (known as centrals, since they are generally expected to lie near the centre of the halo) and the smaller, satellite galaxies that orbit around them (Hogg et al. 2003; Berlind et al. 2005; Pasquali et al. 2010). Some (van den Bosch et al. 2008; Peng et al. 2012; Woo et al. 2013) suggest that the correlations with environment are due to transformations that take place when a galaxy first becomes a satellite. This is natural, as such galaxies are expected to experience diminished cosmological gas accretion (Balogh, Navarro & Morris 2000; Kawata & Mulchaey 2008), ram-pressure with the intrahalo gas (Gunn & Gott 1972; Grebel, Gallagher & Harbeck 2003), and a different type of interaction with neighbouring galaxies (Moore et al. 1996; Moore, Lake & Katz 1998) and the tidal field (Read et al. 2006).

The fraction of quiescent galaxies clearly correlates with galaxy stellar mass and this, combined with the apparent ease with which stellar masses can be computed from photometric data, has motivated modellers and observers to consider stellar mass as the fundamental parameter that determines a galaxy's properties (e.g. Peng et al. 2010; Woo et al. 2013). However, various authors (e.g. Brinchmann et al. 2004; Kauffmann et al. 2006; Franx et al. 2008) found that galaxy surface density is more predictive of the specific SFR (sSFR) than stellar mass. Others have shown the correlation is best with velocity dispersion, either as measured directly from dynamics (e.g. Smith, Lucey & Hudson 2009; Wake, Franx & van Dokkum 2012a; Wake, van Dokkum & Franx 2012b), or inferred from the virial relations between mass and size (Franx et al. 2008). There are good indications that the trends are driven by conditions in the centre of galaxies, either as inferred from Sérsic indices derived from single-profile fits to the surface brightness (Blanton et al. 2003b; Driver et al. 2006; Allen et al. 2006; Schiminovich et al. 2007; Bell 2008; D'Onofrio et al. 2011), central surface density (e.g. Cheung et al. 2012; Fang et al. 2013), or presence of a central bulge (Martig et al. 2009; Cappellari 2013). While it remains controversial which of these characterisations is most fundamental, it seems clear that galaxy structure, and not just stellar mass, is relevant (e.g. Poggianti et al. 2013).

If galaxy properties are primarily determined by some aspect of their structure, rather than their stellar mass alone, it reopens the question of how (or if) galaxies of a given structure depend on their environment. The first purpose of this paper is to quantify the quenching efficiency of satellite galaxies as a function of their structure. This leads us to take a more general approach than some of the studies listed above, and consider how the quiescent fraction of central galaxies depends on galaxy stellar mass and radius in the local Universe sampled by the Sloan Digital Sky Survey (SDSS; York et al. 2000).

All calculations use the Λcold dark matter (ΛCDM) cosmology consistent with the nine year data release from the WMAP mission, with parameters h = 0.693, Ω_M = 0.286, and |$\Omega _\Lambda =0.714$| (Bennett et al. 2013).

2 THE DATA

2.1 The sample

We draw our sample from the seventh data release of the SDSS. The redshift range is limited to 0.01 < z < 0.2. We extract data from catalogues made by Blanton et al. (2005), Brinchmann et al. (2004), Simard et al. (2011), and Yang et al. (2012). All catalogues were position matched to the closest galaxy within an arcsec and redshift matched to within 0.0005. The resulting sample size after matching is 581 990, but this is reduced to 471 554 after making the completeness cuts described in Section 2.3. This matched catalogue, with all quantities relevant to reproduce the results in this paper, is made available online; with sample entries shown in Table 1. We use the DR7 group catalogue from Yang et al. (2012), which was generated by grouping galaxies with SDSS redshifts using the same friends-of-friends algorithm as their original DR4 catalogue (Yang et al. 2007). We define the most luminous galaxy in each group to be the central galaxy and other members to be satellites; however the changes to our results are insignificant if we define the most massive galaxy to be the central. Isolated galaxies (those not linked to any group) are also defined as centrals. Using this definition, we obtain 376 028 centrals and 95 526 satellites following the cuts described in Section 2.3.

Table 1.

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A sample of entries in our catalogue, available in the online version. These data are simply matched entries from the published catalogues of Blanton et al. (2005), Brinchmann et al. (2004), Simard et al. (2011), and Yang et al. (2012). Columns 1–3 provide the ID for simple matching with Blanton et al. (2005), Yang et al. (2012) and Simard et al. (2011), respectively. All catalogues were matched on RA, Dec. and redshift (Columns 4–6). Column 7 is the circularized half-light radius from the Simard et al. (2011) bulge/disc decomposition model, with free index n for the bulge component; Column 8 is the corresponding fraction of light in the bulge. Columns 9 and 10 are the stellar mass and SFR from Brinchmann et al. (2004), and Column 11 is the r-band petrosian magnitude from the original SDSS catalogue. Column 12 is a flag that indicates whether (1) or not (2) a galaxy is the most luminous in its halo according to the Yang et al. (2012) catalogue; galaxies with a flag of 1 are considered a ‘central’ in our analysis. Finally, Column 12 is the spatial completeness from Blanton et al. (2005), and Column 13 is the selection volume that we compute, based on the absolute magnitude and R_e of the galaxy. Additional columns that may be useful, including some that we make use of in the Appendix, are provided in the online table.

VAGC	Yang	Simard	RA	Dec.	z	R_e	B/T	M_*	SFR	m_r	Central	C	V_max
ID	ID	Rec. no.	(J2000)			(kpc)		(10¹⁰ M_⊙)	(M_⊙ yr⁻¹)	(mag)	flag		(10⁶ Mpc³)
234667	1129345	432305	161.86430	13.889750	0.010	1.00	0.23	0.02	0.04	16.34	1	0.93	0.315
204290	958798	1095350	173.42712	50.449570	0.010	1.47	0.36	0.05	0.06	15.73	1	0.88	0.761
114459	431764	897676	151.88120	57.729069	0.010	1.83	0.01	0.006	0.04	16.95	1	0.89	0.098
256139	1219961	975660	178.49693	12.198710	0.010	1.87	0.17	0.08	0.15	15.08	1	0.86	1.875

VAGC	Yang	Simard	RA	Dec.	z	R_e	B/T	M_*	SFR	m_r	Central	C	V_max
ID	ID	Rec. no.	(J2000)			(kpc)		(10¹⁰ M_⊙)	(M_⊙ yr⁻¹)	(mag)	flag		(10⁶ Mpc³)
234667	1129345	432305	161.86430	13.889750	0.010	1.00	0.23	0.02	0.04	16.34	1	0.93	0.315
204290	958798	1095350	173.42712	50.449570	0.010	1.47	0.36	0.05	0.06	15.73	1	0.88	0.761
114459	431764	897676	151.88120	57.729069	0.010	1.83	0.01	0.006	0.04	16.95	1	0.89	0.098
256139	1219961	975660	178.49693	12.198710	0.010	1.87	0.17	0.08	0.15	15.08	1	0.86	1.875

Table 1.

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VAGC	Yang	Simard	RA	Dec.	z	R_e	B/T	M_*	SFR	m_r	Central	C	V_max
ID	ID	Rec. no.	(J2000)			(kpc)		(10¹⁰ M_⊙)	(M_⊙ yr⁻¹)	(mag)	flag		(10⁶ Mpc³)
234667	1129345	432305	161.86430	13.889750	0.010	1.00	0.23	0.02	0.04	16.34	1	0.93	0.315
204290	958798	1095350	173.42712	50.449570	0.010	1.47	0.36	0.05	0.06	15.73	1	0.88	0.761
114459	431764	897676	151.88120	57.729069	0.010	1.83	0.01	0.006	0.04	16.95	1	0.89	0.098
256139	1219961	975660	178.49693	12.198710	0.010	1.87	0.17	0.08	0.15	15.08	1	0.86	1.875

VAGC	Yang	Simard	RA	Dec.	z	R_e	B/T	M_*	SFR	m_r	Central	C	V_max
ID	ID	Rec. no.	(J2000)			(kpc)		(10¹⁰ M_⊙)	(M_⊙ yr⁻¹)	(mag)	flag		(10⁶ Mpc³)
234667	1129345	432305	161.86430	13.889750	0.010	1.00	0.23	0.02	0.04	16.34	1	0.93	0.315
204290	958798	1095350	173.42712	50.449570	0.010	1.47	0.36	0.05	0.06	15.73	1	0.88	0.761
114459	431764	897676	151.88120	57.729069	0.010	1.83	0.01	0.006	0.04	16.95	1	0.89	0.098
256139	1219961	975660	178.49693	12.198710	0.010	1.87	0.17	0.08	0.15	15.08	1	0.86	1.875

2.2 Galaxy properties

We adopt the Petrosian r magnitudes, m_r for all galaxies (Abazajian et al. 2009), and calculate the absolute magnitudes from these as

\begin{equation} M_r = m_r - DM(z) - k_{0.1}(z)+1.62(z-0.1), \end{equation}

(1)

where DM(z) is the distance modulus, 1.62(z − 0.1) is the evolution term from Blanton et al. (2003c), and k_0.1(z) is an approximation of the k-correction to z = 0.1 (Blanton et al. 2003a; Blanton & Roweis 2007; Yang, Mo & van den Bosch 2009), given by

\begin{equation} k_{0.1}(z) = 2.5\log \left({\frac{z+0.9}{1.1}}\right). \end{equation}

(2)

We convert these absolute magnitudes to luminosities using M_⊙ = 4.64.

Measurements of stellar mass (M_*) and SFR are taken from the online catalogue provided by Brinchmann et al. (http://www.mpa-garching.mpg.de/SDSS/DR7/). These measurements are based on the procedure described by Brinchmann et al. (2004), and assume a Kroupa (2001) initial mass function. The SFR within the fibre is determined directly from the Hα and Hβ line emission in star-forming galaxies, and from the D4000 break for galaxies with weak emission or evidence for AGN. Outside the fibre, using a method similar to Salim et al. (2007), models of stellar populations are fit to the observed photometry. The SFRs from the fibre were added to the SFRs from the photometry fits to give an estimate of the total. The uncertainty of these SFRs is estimated to be around 0.2 dex for star forming galaxies, and 0.7 dex or more (in fact, best treated as upper limits) for quiescent galaxies (Woo et al. 2013). Stellar masses are measured with a spectral energy distribution fitting method similar to the one used by Salim et al. (2007) to measure SFR.

The effective radii R_e we use are the r-band circular half-light radii from Simard et al. (2011). The parameters are derived using the gim2d software (Simard et al. 2002) to fit the surface brightness profiles with parametric models. These fits were performed simultaneously on g and r images, using a simple disc or bulge + disc model, with particular care given to subtraction of the background, which can be a large source of systematic uncertainty. Three model fits are provided: an n_b = 4 (de Vaucouleurs) bulge + disc decomposition, a free n_b bulge + disc decomposition, and a single-component Sérsic model. We take our parameters from the free n_b bulge + disc decomposition, except where otherwise noted,¹ and we justify this decision in Appendix A.

In this paper, we will consider correlations with galaxy stellar mass, ‘inferred velocity dispersion’²M_*/R_e, and surface density³|$M_*/R_{\rm e}^2$|⁠. In Appendix B we present several figures which illustrate how the sample is distributed amongst these parameters. While not directly related to the results in the rest of the paper, they can be helpful for interpreting some of the trends we discuss.

2.3 Completeness corrections

2.3.1 Magnitude limit

The SDSS legacy survey targets objects with m_r < 17.77, which means the stellar mass limit of the sample is redshift dependent. First, we calculate a conservative absolute magnitude limit,

\begin{equation} M_{r,{\rm lim}}=17.77-DM(z)-k_{0.1}(z)+1.62(z-0.1)-0.1, \end{equation}

(3)

where the extra −0.1 factor is brought into account for the scatter in k-correction (Yang et al. 2009). The few galaxies with M_r fainter than this limit are removed from the sample. For the remaining galaxies, we calculate the maximum redshift for which the galaxy would be brighter than m_r = 17.77, and calculate the corresponding selection volume, V_max, as

\begin{equation} V_{\rm max}=0.1947\times \frac{4}{3}{\pi }\frac{d_{\rm C}(z)^3 - d_{\rm C}(z=0.01)^3}{(1+z)^3}, \end{equation}

(4)

where the factor 0.1947 represents the fraction of sky covered by the SDSS (Simard et al. 2011), and d_C is the comoving distance.

2.3.2 Angular resolution

Fig. 1 shows the distribution of R_e as a function of redshift for all galaxies in our initial sample. The apparent correlation is driven primarily by the fact that the limited spatial resolution of the SDSS means that physically small galaxies will appear as point sources and will not be selected for spectroscopy in the main galaxy sample (Strauss et al. 2002). The average angular resolution of SDSS is ∼1.2 arcsec (Shin et al. 2008), but we take a conservative minimum of 1.5 arcsec for this calculation. The actual galaxy selection criteria are more complicated than this (Scranton et al. 2002; Taylor et al. 2010), but our conservative approach admits a simpler analysis. The red line in Fig. 1 shows the value of R_e corresponding to an angular size of 1.5 arcsec, as a function of redshift. To make a well-defined sample, we exclude galaxies below this line from the rest of the analysis. The selection volume of the remaining galaxies may be limited by the distance at which they would drop below this line, rather than by their luminosity. Specifically, for each galaxy we calculate the redshift at which the angular size of its effective radius is 1.5 arcsec, and calculate the corresponding volume correction from equation (4).

Figure 1.

The effective radii of galaxies in our initial SDSS sample are shown as a function of their redshift. Instead of showing individual points, we use logarithmically spaced contours to represent the density of points in this space. The red line indicates the radius corresponding to an angular size of 1.5 arcsec as a function of redshift. Galaxies below this limit are removed from the sample to define a clean selection limit.

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2.3.3 Weights

The selection volume of each galaxy is taken to be the smaller of the two volumes described above. In addition, we weight galaxies by the spatially-dependent spectroscopic completeness factor, C, available from the NYU-VAGC (Blanton et al. 2005). Thus, each galaxy in our sample is given a weight of

\begin{equation} w_i=\frac{1}{V_{\rm max}C}, \end{equation}

(5)

which represents the number of such galaxies per unit volume in a complete sample.

2.4 Separating active and quiescent galaxies

We base our separation of star-forming (active) and non-star-forming (quiescent) galaxies on the sSFR of each galaxy. Fig. 2 shows the correlation of sSFR and stellar mass, where the contours indicate the weighted density of the population. The main sequence of star-forming galaxies is readily apparent, and clearly separated from the rest of the galaxy population (recall that SFR is not accurately measured at low values, where it is best treated as an upper limit). This bimodality motivates dividing the population into two and, since the main sequence shows a small mass-dependence, our division must also be mass dependent. We divide the population at sSFR_o(M_*), where

\begin{equation} \log {(\mathrm{sSFR}_o)} = -0.24\log {(M_*/\mathrm{M}_{\odot })} - 8.50. \end{equation}

(6)

Any galaxy with sSFR < sSFR_o is considered quiescent. This division is shown in Fig. 2 as the red line.

Figure 2.

The sSFR is shown as a function of stellar mass, with contours representing the weighted number density of points in this plane. The red line represents our division into quiescent and active galaxies.

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2.5 Stellar mass and effective radius distribution

We now present the distribution of the quiescent and active galaxy populations as a function of both their stellar mass and effective radius. Fig. 3 shows the raw distribution of active and quiescent central galaxies in this plane, where the contours indicate the number of galaxies in the sample. There is a well-defined correlation between these quantities, with a slope that is clearly steeper for quiescent galaxies than it is for star-forming galaxies. For reference, we show lines of constant surface mass density (⁠|$M_*/R_{\rm e}^2$|⁠, dashed lines) and constant inferred velocity dispersion (M_*/R_e, dotted lines).

Figure 3.

Contours show the raw (unweighted) number density of central galaxies as a function of stellar mass M_* and effective radii R_e, for active (top) and quiescent (bottom) galaxies. Contours are logarithmically spaced with 1.5 contours per dex. The dashed lines represent surface densities of 10⁸, 10⁹, and 10¹⁰ M_⊙ kpc⁻² from left to right, while the dotted lines represent inferred velocity dispersions of 10⁹, 10¹⁰, and 10¹¹ M_⊙ kpc⁻¹, for reference.

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Fig. 3 is useful to see where the data actually lie. However, because the galaxy selection is biased against low-luminosity and low-R_e galaxies at higher redshift, the physical distribution is obtained by weighting the galaxies as given in equation (5): this weighted distribution is shown in Fig. 4. This naturally has a large effect on the distribution. It is still evident that the M_* − R_e relation is fundamentally different for the active and quiescent populations, as is well-known (e.g. Kormendy 1985; Poggianti et al. 2013). Star-forming galaxies show a scaling which is approximately M_* ∝ |$R_{\rm e}^2$| (dashed lines), representing constant surface mass density. The massive, quiescent galaxies show a considerably steeper relation, that lies somewhere between lines of constant mass density and constant inferred velocity dispersion (the latter indicated by dotted lines). At lower masses, M_* < 10¹⁰ M_⊙ or so, the volume density of central, quiescent galaxies drops off rapidly, in agreement with Geha et al. (2012). Moreover at these masses the correlation becomes flatter, with R_e nearly independent of mass.

Figure 4.

As Fig. 3, but where the contours represent the weighted density; equivalently, the physical volume density of central galaxies. Contours are again logarithmically spaced, with 1.5 contours per dex.

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We show the same distributions for satellite galaxies, in Fig. 5. Interestingly, the population of active satellite galaxies shows a very similar correlation between M_* and R_e to the one that is observed for central galaxies. However, the distribution of quiescent galaxies is markedly different. In particular, the relative number of low-mass (M_* < 10^9.5 M_⊙), quiescent galaxies is larger for satellite galaxies, compared with centrals; this is most easily seen as a steeper stellar mass function for quiescent satellites (see Fig. B2). These low-mass galaxies do not follow the tight correlation between M_* and R_e exhibited by more massive galaxies, but have approximately uniform sizes of R_e ∼ 1 kpc.

Figure 5.

As Fig. 4, but for satellite galaxies.

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The minimum observable effective radius in the data is R_min = 0.3 kpc, corresponding to 1.5 arcsec at the lowest redshift of our sample, z = 0.01. Fig. 4 shows that the distribution of both populations approaches this limit. In particular, our sample of star-forming galaxies may be incomplete for M_* < 10⁸ M_⊙, where the size distribution indicates that a substantial fraction of galaxies likely lie below our resolution limit. The quiescent galaxies appear to reach a minimum radius of ∼0.5 kpc, for galaxies with masses M_* < 10¹⁰ M_⊙. This is, perhaps, uncomfortably close to the selection limit of R_min = 0.3 kpc. However, this distribution is in agreement with results shown by Kormendy et al. (2009), using higher resolution data. They demonstrate (see their fig. 38) that the lower surface brightness distribution of spheroidal galaxies indeed reaches a minimum of ∼0.4 kpc. Their data do indicate that the high surface-brightness, elliptical galaxy sequence may extend to smaller radii; extrapolating the relation we observe in Fig. 4 shows this limit would be reached for galaxies with M_* < 10⁹ M_⊙. However, the mass function of these elliptical galaxies peaks well above this point. An Hubble Space Telescope study of the Coma Cluster by Hoyos et al. (2011) also demonstrates that there are few, if any, galaxies with R_e < R_min. Thus, formally we expect our sample is only fully complete for M_* > 10⁹ M_⊙, although significant incompleteness is unlikely to be an issue for up to an order of magnitude below that limit.

Fig. 6 shows the fraction of all galaxies that are satellites, as a function of M_* and R_e. Satellites show a different distribution in both mass and radius than central galaxies; they are generally smaller and less massive. Their relative abundance peaks at ∼50 per cent, around M_* = 10^9.2 M_⊙ and R_e = 1 kpc. In this figure, and similar figures that follow, we indicate the region where the galaxy density exceeds 100 per bin by the white, solid contours. Within this region, uncertainties on all fractions should be significantly less than the spacing between contour levels representing the quantity of interest. The dashed line shows a lower density of 20 per bin; regions outside the dashed line are of low statistical significance. We confirm that the mass-dependence of the satellite fraction is in good agreement with that given by Wetzel et al. (2013), as expected since we are using the same sample and definition. It is clear by comparing with Figs 4 and 5 that this maximum in satellite fraction is due to the population of high-surface brightness, quiescent galaxies that is largely absent among central galaxies.

$The satellite fraction as a function of stellar mass M* and effective radii Re. Differences between coloured contour levels are statistically significant within the solid white contours, which indicate the region where the number density of galaxies contributing to the calculation is greater than 100 per bin. The dashed, white contours indicate a lower number density of 20 per bin; correlations outside this region are of low statistical significance.$

Figure 6.

The satellite fraction as a function of stellar mass M_* and effective radii R_e. Differences between coloured contour levels are statistically significant within the solid white contours, which indicate the region where the number density of galaxies contributing to the calculation is greater than 100 per bin. The dashed, white contours indicate a lower number density of 20 per bin; correlations outside this region are of low statistical significance.

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3 RESULTS

3.1 Quenching and quenching efficiency

We start by showing the fraction of central and satellite galaxies that are quiescent, as functions of stellar mass, inferred velocity dispersion, and surface density, in Fig. 7. The 1σ uncertainties displayed are calculated assuming the relative uncertainty of the weighted fraction is the same as that calculated on the unweighted distribution determined from the beta distribution of Cameron (2011). As previously shown by others (e.g. Kauffmann et al. 2006; Cheung et al. 2012; Wake et al. 2012a,b), we find that the quiescent fraction increases less sharply with stellar mass than with either inferred velocity dispersion or surface density. To quantify this, we note that the quenched fraction of central galaxies increases from 0.2 to 0.8 over 1.4 dex in M_*, compared with only ∼0.7 dex in the other two quantities.

$The quiescent fraction of galaxies in our sample is shown as a function of stellar mass (left), inferred velocity dispersion (middle), and surface density (right). Central galaxies are shown as black circles, while satellites are represented by red triangles. Error bars represent the 1σ statistical uncertainty.$

Figure 7.

The quiescent fraction of galaxies in our sample is shown as a function of stellar mass (left), inferred velocity dispersion (middle), and surface density (right). Central galaxies are shown as black circles, while satellites are represented by red triangles. Error bars represent the 1σ statistical uncertainty.

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The red points in Fig. 7 show that the quiescent fraction of satellite galaxies is always larger than it is for centrals of the same stellar mass, surface density, or inferred velocity dispersion. In general, the quiescent fraction of satellites both has a higher normalization and is a weaker function of these variables than it is for central galaxies. This means the difference between the satellite and central populations tends to decrease as these measures increase.

Baldry et al. (2006), Peng et al. (2010) and others have shown that the trend of increasing quiescent fraction with increasing local density is largely independent of stellar mass. It is also fundamental in the hierarchical CDM model that satellite galaxies were once centrals in their own halo. These motivate us, following van den Bosch et al. (2008) and Peng et al. (2010), to consider the efficiency with which star formation is quenched in galaxies following their transformation from central to satellite. Physically, this is the fraction of satellites that were active when they became satellites and were subsequently quenched by the satellite-exclusive process (van den Bosch et al. 2008). Operationally, if we assume that the progenitors of the satellite population are identical to the local population of central galaxies, and if the associated quenching process does not significantly change the stellar mass of the galaxy, then we can measure this efficiency from the quiescent fraction of satellite (QF_sat) and central (QF_cent) galaxies as

\begin{equation} QE=\frac{QF_{{\rm sat}}-QF_{\rm cent}}{1-QF_{\rm cent}}. \end{equation}

(7)

This quantity is presented in Fig. 8, as a function of all three parameters under consideration here. In all three cases, this efficiency is approximately constant at ∼0.4, at least above some threshold value. This reflects the fact that high stellar mass (or high surface density, etc.) galaxies are more likely to be quiescent as a result of their ‘intrinsic’ properties, regardless of whether or not they are satellites. The relatively small difference in quenched fraction between satellites and centrals at these high values is thus still indicative of a highly efficient process.

Figure 8.

The quenching efficiencies (equation 7) of galaxies as a function of stellar mass (left), inferred velocity dispersion (middle), and surface density (right). Results for all galaxies are shown as black circles, and results for galaxies with M_* > 10 are shown as blue triangles.

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We note that galaxy samples that are stellar mass limited, including our own, may not be complete in M_*/R_e or |$M_*/R_{\rm e}^2$|⁠, as is apparent from Figs 4 and 5. A selection limit in R_e further complicates this, and the level of completeness depends on how the mass–size relation extrapolates to arbitrarily low masses. Our sample is limited to M_* ≳ 10^7.5 M_⊙ and, assuming there is not a large population of galaxies with sizes below our resolution limit of ∼0.3 kpc, Fig. 4 shows that we are also likely complete for M_*/R_e > 10⁸ M_⊙/kpc. However, as the M_*–R_e relation for star-forming galaxies is approximately parallel to lines of constant |$M_*/R_{\rm e}^2$|⁠, this quantity is potentially incomplete for all values. We show the effect of imposing a higher stellar mass limit by comparing, as blue triangles in Fig. 8, the results for a sample restricted to M_* > 10¹⁰ M_⊙. This significantly changes the shape of the dependence on structural variables, with QE only remaining unchanged at the highest values of M_*/R_e. This highlights the difficulty in interpreting 1D projections such as those shown in Fig. 7, and this partially motivates a more general approach.

While physically motivated, the combinations of M_*/R_e and |$M_*/R_{\rm e}^2$| are somewhat arbitrary, and we now consider the quiescent fraction in a more general way, as a function of log (M_*/ M_⊙) and log (R_e) independently. Fig. 9 shows contours of constant quiescent fraction in this plane. For central galaxies, we observe the remarkable fact that the contour lines are closely spaced and nearly linear in this space, following an approximate relation M_* ∝ |$R_{\rm e}^{1.5}$|⁠, shown by the dashed line. It is quite evident from this representation that, at least for masses M_* ≲ 10^10.5 M_⊙, the quiescent fraction does not depend on stellar mass alone.

$The central (left) and satellite (right) galaxy quiescent fraction as a function of stellar mass M* and effective radius Re. Contours are spaced every 0.1 in quiescent fraction. The dashed line indicates constant M*/$R_{\rm e}^{1.5}$. Solid and dashed, white contours indicate the region where the number density of galaxies contributing to the calculation is greater than 100 per bin, and 20 per bin, respectively. This representation demonstrates that the quiescent fraction does not depend only on stellar mass, but also on galaxy structure.$

Figure 9.

The central (left) and satellite (right) galaxy quiescent fraction as a function of stellar mass M_* and effective radius R_e. Contours are spaced every 0.1 in quiescent fraction. The dashed line indicates constant M_*/|$R_{\rm e}^{1.5}$|⁠. Solid and dashed, white contours indicate the region where the number density of galaxies contributing to the calculation is greater than 100 per bin, and 20 per bin, respectively. This representation demonstrates that the quiescent fraction does not depend only on stellar mass, but also on galaxy structure.

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The right panel of Fig. 9 shows the quiescent fraction of satellite galaxies. Here the contours show more structure and are generally flatter; the quiescent fraction depends almost entirely on R_e at 8.5 < log (M_*/M_⊙) < 9.5 and increasingly more on mass at higher stellar masses. To quantitatively compare these two populations, we show the difference in quenched fraction between satellites and centrals in Fig. 10. At almost all locations within this plane the difference is positive, indicating that satellites are more likely to be quenched than central galaxies of the same mass and size. The difference ranges from 0 to ∼0.5, with a broad maximum near M_* = 10^9.2 M_⊙ and R_e < 2 kpc.

$The quenched fraction difference as a function of stellar mass M* and effective radius Re.$

Figure 10.

The quenched fraction difference as a function of stellar mass M_* and effective radius R_e.

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To isolate the influence of environment from internal mechanisms, we now consider the quenching efficiency as a function of M_* and R_e, in Fig. 11. The contours here show quite a simple structure, with a localized peak at M_* = 10^9.4 M_⊙ and R_e = 1 kpc. It is remarkable that this peak in efficiency is in the same location as the peak in satellite fraction, shown in Fig. 6. This does not appear to be a trivial coincidence; we examine it further in Section 4.3.

Figure 11.

The quenching efficiency as a function of stellar mass M_* and effective radius R_e. The lowest contour includes everything below −0.1.

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For most central galaxies [with 9 < log (M_*/M_⊙) < 11], the shape of the quiescent fraction contours in Fig. 9 indicates that M_*/|$R_{\rm e}^{1.5}$| should be a more discerning parameter than either inferred velocity dispersion or surface density. To show this explicitly, we plot the quiescent fraction as a function of M_*/|$R_{\rm e}^{1.5}$| in Fig. 12. This should be compared directly with analogous plots as a function of M_*, M_*/R_e and |$M_*/R_{\rm e}^2$| from Fig. 7. The fraction of quenched central galaxies increases very steeply, from 0.2 to 0.8 over a range of only ∼0.5 dex in M_*/|$R_{\rm e}^{1.5}$|⁠; recall that the same increase occurs over ∼0.7 dex as a function of surface density and inferred velocity dispersion. This intermediate dependence has appeared in the work of other authors who have considered related properties of galaxies (e.g. Franx et al. 2008; Barro et al. 2013; Cappellari et al. 2013).

$The quiescent fraction of satellite and central galaxies as a function of M*/$R_{\rm e}^{1.5}$. Central galaxies are shown in black and satellite galaxies are in red.$

Figure 12.

The quiescent fraction of satellite and central galaxies as a function of M_*/|$R_{\rm e}^{1.5}$|⁠. Central galaxies are shown in black and satellite galaxies are in red.

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Fig. 12 also shows that the quenched fraction of satellite galaxies increases gradually as a function of M_*/|$R_{\rm e}^{1.5}$|⁠; it does not show the sharp threshold that is observed for central galaxies. The corresponding quenching efficiency as a function of M_*/|$R_{\rm e}^{1.5}$| is shown in Fig. 13. This also shows the same qualitative behaviour as it does as a function of the other quantities (cf. Fig. 8), remaining relatively constant at ∼0.4, above a certain threshold in each parameter. This reflects the fact that no one-dimensional quantity captures the complex dependence seen in Fig. 11.

$The quenching efficiency as a function of M*/$R_{\rm e}^{1.5}$. All galaxies are shown as black circles, while the subsample restricted to galaxies with M* > 10 are shown as blue triangles.$

Figure 13.

The quenching efficiency as a function of M_*/|$R_{\rm e}^{1.5}$|⁠. All galaxies are shown as black circles, while the subsample restricted to galaxies with M_* > 10 are shown as blue triangles.

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4 DISCUSSION

4.1 Quiescent central galaxies

Comparing the two panels of Fig. 4, it is evident that the observed trends in quiescent fraction are driven by the fact that the M_*–R_e relation is different for star-forming and quiescent galaxies. In fact, the central quiescent population shows two well-known sequences itself: a high-surface brightness population commonly identified with elliptical galaxies, and a lower-surface brightness population of ‘spheroidal galaxies’ that is much more prominent among satellite galaxies. The lack of evolution in the star-forming mass function, and corresponding growth in the quiescent galaxy mass function, makes it inevitable that galaxies must be migrating from the active population into the quiescent. How, then, do these different structural relationships arise? There are two general possibilities that we will explore in turn.

4.1.1 Hypothesis 1: quenching probability depends on galaxy structure

First, we can consider that star-forming galaxies populate the M_*–R_e plane as shown in the top panel of Fig. 4, and that the probability of quenching is given by a function that is similar to⁴ the contour shapes of Fig. 9; in other words, it increases steadily with increasing |${\sim } M_*/R_{\rm e}^{1.5}$|⁠. If this is the case, we might hope to find some other property of the star-forming population that depends on this quantity.

For example, if the quenching process is a gradual one, we might see that amongst active galaxies, sSFR shows a similar dependence on M_* and R_e as the quiescent fraction of the whole sample. This relation is shown as contours in Fig. 14 and, indeed, the trends are qualitatively similar to the trends in quiescent fraction. Specifically, for M_* > 10¹¹ M_⊙ or so the contours are vertical, indicating the sSFR depends only on stellar mass, and is in fact quite low, representing a doubling time greater than a Hubble time. For lower masses, however, the contours show a strong and non-trivial dependence on R_e. For example, at fixed M_* ∼ 10^9.5 M_⊙, the sSFR varies with R_e by a factor of ∼3, actually reaching a maximum for R_e ∼ 3 kpc. This behaviour does not exactly match that of the quiescent fraction, but it is qualitatively consistent with what would be expected if high surface mass density galaxies are more likely to be quenched, over a finite time-scale.

$The specific SFR of active, central galaxies are shown as coloured contours, as a function of M* and Re. For M* < 1011 M⊙, the sSFR shows a dependence on both M* and Re, which is qualitatively similar to that of the quiescent fraction shown in Fig. 9.$

Figure 14.

The specific SFR of active, central galaxies are shown as coloured contours, as a function of M_* and R_e. For M_* < 10¹¹ M_⊙, the sSFR shows a dependence on both M_* and R_e, which is qualitatively similar to that of the quiescent fraction shown in Fig. 9.

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4.1.2 Hypothesis 2: structural changes associated with quenching

An alternative interpretation of the contours in Fig. 9 is that the quenching process occurs at a rate that depends only on M_*, but is accompanied by a change in structure. This could occur if the disc component fades (e.g. Weinmann et al. 2009), or is destroyed, or if the central density increases due to tidal torques inducing a central starburst, for example. To roughly quantify this, we investigated a simple model in which some mass-dependent quenching process causes a galaxy's radius, but not mass, to decrease. We attempted to recreate the observed central quiescent fraction (Fig. 9. left) by arbitrarily quenching galaxies in the existing active central population, at a rate given by the mass-quenching efficiency of Peng et al. (2010),

\begin{equation} QE_M=1-{\rm exp}(-(M_*/p_1)^{p_2}) \end{equation}

(8)

with the parameters p₁ = 10^10.88 M_⊙ and p₂ = 0.65 adjusted to provide a good fit to our data, which are based on a different definition of ‘quiescent’.

To give a reference point, we first show the naive prediction that would result if quenching did not affect R_e, in the left panel of Fig. 15. This recovers the expected result that the quiescent fraction does not depend on radius. We then reduced the radius of all quenched galaxies by 0.25 dex, and the result is shown in the middle panel. This does a reasonable job of qualitatively reproducing the data, but the contours are spaced too far apart, and are too flat at low masses, compared with the data in Fig. 9. In fact, the simplest interpretation of the quiescent fraction variation is that galaxies increase their stellar mass, as well as decrease R_e, upon quenching. This is qualitatively consistent with the merging process, which likely plays a role especially at high masses (Cappellari 2013). If, however, we retain the hypothesis that M_* is unchanged, then we are driven to a model in which the decrease in R_e is mass-dependent. Such a model is shown in the right panel of Fig. 15, where we find reasonable qualitative agreement with the observations when log (R_e) is reduced by the discontinuous function

\begin{eqnarray*} &&\!\!\!\!&&{\Delta \log {(R_{\rm e})}}\\ &&\quad = \left\lbrace \begin{array}{@{}l@{\quad }l@{}}0.25 & {\rm if\, } \log {(M_*/ \mathrm{M}_{\odot })}<9\\ 1.25-0.1\log (M_*/ \mathrm{M}_{\odot }) & {\rm if } \, 9<\log (M_*/\mathrm{M}_{\odot })<11\\ 0.1 &{\rm if\, } \log (M_*/ \mathrm{M}_{\odot })>11, \end{array}\right. \end{eqnarray*}

for R_e measured in units of kpc.

$We show predictions of the quiescent fraction as a function of stellar mass M* and effective radius Re for three simple toy models, in which active galaxies taken from the distribution in the top panel of Fig. 4 are converted to quiescent galaxies, with a mass-dependent efficiency given by equation (8). In the left panel, we assume that the quenching process results in no change in Re; thus, the contours are vertical as expected. In the middle panel, we assume that log (Re) decreases by 0.25 when galaxies are quenched. This provides a better match to the data in the left panel of Fig. 9, but the predicted contours are too flat, and too widely spaced. In the right panel, therefore, we show a model in which the amount by which Re decreases is mildly mass-dependent (smaller at higher masses; see text for details). This provides a reasonable, qualitative match to the data.$

Figure 15.

We show predictions of the quiescent fraction as a function of stellar mass M_* and effective radius R_e for three simple toy models, in which active galaxies taken from the distribution in the top panel of Fig. 4 are converted to quiescent galaxies, with a mass-dependent efficiency given by equation (8). In the left panel, we assume that the quenching process results in no change in R_e; thus, the contours are vertical as expected. In the middle panel, we assume that log (R_e) decreases by 0.25 when galaxies are quenched. This provides a better match to the data in the left panel of Fig. 9, but the predicted contours are too flat, and too widely spaced. In the right panel, therefore, we show a model in which the amount by which R_e decreases is mildly mass-dependent (smaller at higher masses; see text for details). This provides a reasonable, qualitative match to the data.

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This analysis simply illustrates that, if central galaxies are quenched at a rate that depends only on their stellar mass, this process must result in a reduction of R_e by about a factor of ∼2, and perhaps a bit less for more massive galaxies. It will be interesting to explore if more physical models, like those of Weinmann et al. (2009) based on disc-fading, for example, are consistent with these quantities.

4.2 The role of the bulge

The fact that the fraction of quiescent central galaxies depends strongly on surface density or inferred velocity dispersion makes it tempting to associate a quenching process with these very physical characteristics of the galaxy mass distribution. However, Fig. 9 shows that these choices are simply projections of the more general dependence on M_* and R_e, and that the best one-dimensional description of quiescent fraction based on these global quantities is actually |$M_*/R_{\rm e}^{1.5}$|⁠. It is unclear from this analysis alone whether this quantity has physical significance, or if it is a secondary outcome of a dependence on something more fundamental, such as central velocity dispersion or the presence, or mass, of a central bulge. This has been suggested by others (e.g. Martig et al. 2009; Cappellari 2013; Fang et al. 2013), and could be a natural scenario if a central, supermassive black hole is responsible for the quenching, given the observed correlation between black hole masses and bulge properties (e.g. Magorrian et al. 1998; Gebhardt et al. 2000; Ferrarese & Merritt 2000). The fact that the massive, quenched population is dominated by ‘elliptical’ galaxies that likely formed at z > 2 may also be a good reason to consider the quenching associated with bulge-dominated galaxies to differ from that which leads to the buildup of the lower mass, ‘spheroidal’ population.

The gim2d fits to the surface brightness distributions provide information on the bulge mass, size and ellipticity; naturally these results are more sensitive to the models (and limitations of the data), than what we have considered so far. For this analysis, the bulge component is identified from the two-component gim2d fits to the r-band images, with the Sérsic index fixed at n = 4. This is necessary because a free Sérsic index results in many ‘bulges’ with low-n, and it is not clear how best to treat them in this simple scenario.

We are first interested in how the quiescent fraction depends on three parameters: M_*, R_e and the fraction of r-band luminosity contained in the bulge component, B/T. We show this as contours of constant quiescent fraction as a function of M_* and B/T in Fig. 16, and as a function of B/T and R_e in Fig. 17. These figures seem to indicate that the quiescent fraction is determined primarily from M_* and B/T in a largely separable way. There are two thresholds in stellar mass. For galaxies with M_* < 10⁹ M_⊙, all galaxies are forming stars, regardless of their B/T, while for the most massive galaxies (M_* > 10^11.5 M_⊙), almost no galaxies are forming stars. But between these limits, the quiescent fraction depends mostly on B/T, varying from 0 to 0.8 as B/T varies from 0 to only 0.3. Fig. 17 shows similar behaviour when R_e is considered as a variable, with quiescent fraction depending only on B/T over the range 0.6 < R_e < 10 range that encompasses the great majority of galaxies in our sample.

$Contours show the quiescent fraction of central galaxies, as a function of stellar mass and bulge fraction. This suggests two clear thresholds in stellar mass. For M* < 109 M⊙ almost all galaxies are forming stars, whether a bulge is present or not; conversely, for M* > 1011 almost all galaxies are quiescent. Between these masses, however, the fraction of quiescent galaxies appears to correlate with B/T in a way that is only weakly dependent on mass.$

Figure 16.

Contours show the quiescent fraction of central galaxies, as a function of stellar mass and bulge fraction. This suggests two clear thresholds in stellar mass. For M_* < 10⁹ M_⊙ almost all galaxies are forming stars, whether a bulge is present or not; conversely, for M_* > 10¹¹ almost all galaxies are quiescent. Between these masses, however, the fraction of quiescent galaxies appears to correlate with B/T in a way that is only weakly dependent on mass.

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$Contours show the quiescent fraction of central galaxies, as a function of bulge fraction and Re. Interestingly, this shows that Re plays little role in establishing the quiescent fraction, independently from B/T. The fraction of star-forming galaxies decreases remarkably sharply, from >90 per cent for pure disc galaxies to <20 per cent for galaxies with as little as 40 per cent of their light in a bulge component.$

Figure 17.

Contours show the quiescent fraction of central galaxies, as a function of bulge fraction and R_e. Interestingly, this shows that R_e plays little role in establishing the quiescent fraction, independently from B/T. The fraction of star-forming galaxies decreases remarkably sharply, from >90 per cent for pure disc galaxies to <20 per cent for galaxies with as little as 40 per cent of their light in a bulge component.

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It is apparent that galaxies in this sample with a substantial bulge, B/T > 0.3 or so, are almost all quiescent. This necessarily includes most of the high mass-density galaxies that we identify with ‘ellipticals’ following Kormendy & Bender (2012), and which dominate the M_* − R_e distribution of quiescent galaxies in Fig. 4. It is interesting to consider any remaining trends in quiescent fraction if these galaxies are removed, and we show the result in Fig. 18. This is the equivalent of the left panel of Fig. 9, restricted to disc-dominated galaxies, and we observe the same strong dependence on |$M_*/R_{\rm e}^{1.5}$|⁠. Thus we interpret the trend as due, not to the varying mix of bulge-dominated and disc-dominated galaxies with M_* and R_e, but as a result of the simple correlation shown in Fig. 16 between quiescent fraction and bulge fraction amongst galaxies with both components. It may be this correlation that is responsible for the more complex dependence on |$M_*/R_{\rm e}^{1.5}$|⁠; in any case it reinforces the fact that is not correct to assume galaxy mass is the driving parameter (e.g. Peng et al. 2010). If the bulge itself does play a role, it will be of interest to investigate these correlations more carefully, with an accurate determination of the bulge mass and structure (e.g. Mendel et al. 2013).

$We show the quiescent fraction of central galaxies, as in Fig. 9, but for disc dominated (B/T < 0.3) galaxies only. The shape of the contours in this plane is similar to that of the whole central galaxy population (left panel of Fig. 9), demonstrating that the trend is not driven by bulge-dominated galaxies.$

Figure 18.

We show the quiescent fraction of central galaxies, as in Fig. 9, but for disc dominated (B/T < 0.3) galaxies only. The shape of the contours in this plane is similar to that of the whole central galaxy population (left panel of Fig. 9), demonstrating that the trend is not driven by bulge-dominated galaxies.

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4.3 Satellite quenching

Fig. 6 showed that satellite galaxies are distributed differently in M_* and R_e than central galaxies, and in Fig. 19 we show the well-known result that this difference in structure also extends to bulge fraction. Interestingly, the low-mass galaxies that dominate the satellite population are more likely to have intermediate bulge fractions, 0.3 < B/T < 0.7. Amongst central galaxies, such bulge-dominated galaxies are almost all quiescent. Thus it is interesting to revisit the question of whether galaxies with identical morphological structure still show a dependence on whether they are a central or satellite galaxy. We do this by creating a randomly matched sample of satellite galaxies that has the same abundance as central galaxies at every M_*, R_e and B/T. We then recreate the quenching efficiency plot shown in Fig. 11, but where the comparison is now made between populations that are structurally similar, in Fig. 20. The result is almost unchanged, and shows that quenching efficiency is almost always positive, and still reaches a localized maximum of ∼0.7 at the same region of parameter space.

$The fraction of satellite galaxies is shown as a function of M* and bulge fraction. Relative to central galaxies, satellites are more common at low masses, 9 < M*/M⊙ < 9.5, and intermediate bulge fractions, 0.3 < B/T < 0.7.$

Figure 19.

The fraction of satellite galaxies is shown as a function of M_* and bulge fraction. Relative to central galaxies, satellites are more common at low masses, 9 < M_*/M_⊙ < 9.5, and intermediate bulge fractions, 0.3 < B/T < 0.7.

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Figure 20.

The quenching efficiency is shown as a function of M_* and R_e, for a sample in which the M_*–R_e–B/T distribution is forced to be the same for the central and satellite galaxies. This still reaches a localized maximum of ∼0.7, for galaxies with log(M_*/M_⊙) ∼ 9.4 and R_e ∼ 1 kpc.

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It is remarkable that Fig. 20 shows that satellite quenching efficiency is certainly not a function of stellar mass alone. In fact, it reaches a maximum value in the same localized region where there is an excess of satellite galaxies, relative to the number of centrals (Fig. 6). It is possible that this is a coincidence, and satellite galaxies just happen to most commonly have a structure for which quenching efficiency is high. On the other hand, if we dismiss the possibility that this is a coincidence, it implies that satellite quenching must be accompanied by a change in structure; as star formation shuts down, galaxies migrate towards that region of M_*, R_e, B/T space where most satellite galaxies are found. In this case, quenching efficiency does not have the physical meaning that we ascribed to it, since satellite galaxies are not being compared with their rightful, central progenitors. For satellites more so than centrals, it may also be the case that the stellar mass changes during the quenching process; this would considerably complicate the analysis.

5 SUMMARY AND CONCLUSIONS

We have used a sample of 471 554 galaxies at 0.01 < z < 0.2 selected from the SDSS DR7, to examine how the fraction of quiescent galaxies depends upon stellar mass, effective radius, bulge fraction, and whether a galaxy is central or satellite in the group catalogue of Yang et al. (2012). We use the gim2d parametric fits of Simard et al. (2011) to determine the circular half-light radius (R_e) of all galaxies in the sample, and the specific SFRs and stellar masses of Brinchmann et al. (2004) to classify galaxies as active (on the star-forming main sequence) or quiescent. We make the following observations:

The fraction of quiescent galaxies is a steeper function of M_*/R_e and M_*/|$R_{\rm e}^2$| than it is of stellar mass alone. This confirms the findings of many other authors (e.g. Kauffmann et al. 2006; Franx et al. 2008; Cheung et al. 2012; Wake et al. 2012a,b).
The quiescent fraction of satellite galaxies is always higher than that of central galaxies, except perhaps at the highest masses where almost all galaxies are quenched centrals. Thus, a galaxy's status as satellite or central in its halo plays a role in its evolution. The quenching efficiency (Peng et al. 2010), which attempts to quantify the fraction of satellite galaxies that had their star formation quenched as a satellite, is ∼40 per cent, approximately independent of stellar mass for M_* > 10⁹ M_⊙.
We presented the quiescent fraction of central galaxies as a function of both M_* and R_e in Fig. 10. This representation makes it clear that the fraction does not depend on stellar mass alone, and that over most of the parameter space it appears to depend most strongly on |$\sim\! M_*/R_{\rm e}^{1.5}$|⁠.
We showed that the quiescent fraction of central galaxies correlates strongly with B/T in a simple way that largely accounts for the more complex dependence on R_e. Galaxies with more than 40 per cent of their light in a bulge component are almost all quiescent, and galaxies less massive than M_* = 10⁹ M_⊙ are almost all forming stars. Otherwise, the quiescent fraction increases monotonically with increasing B/T at fixed M_*.
The quenching efficiency is highest for galaxies with 10⁹ < M_* < 10¹⁰ M_⊙ and 10^−0.2 < R_e < 10^0.2 kpc (Fig. 11), but appears roughly constant above a certain threshold when taken solely as a function of M_*, M_*/R_e, or M_*/|$R_{\rm e}^2$|⁠.
There are structural differences between satellite and central galaxies, such that, at a given stellar mass, satellite galaxies tend to have smaller R_e and more light in a bulge component. The fraction of satellites is greatest (at about 50 per cent) for galaxies with 9.0 < log (M_*/M_⊙) < 10.0, and R_e < 2 kpc. Even after accounting for this difference by matching central and satellite galaxies to have the same M_*, R_e, and B/T, the quenching efficiency remains positive at all masses, and reaches a maximum of 70 per cent for galaxies with log (M_*/M_⊙) ∼ 9.4 and R_e ∼ 1 kpc.

For central galaxies, it is appealing to consider a probability of star formation activity ending that depends on their internal structure. In particular, the strong correlation between quiescent fraction and B/T points to the dominance of a central bulge component as the driving parameter. We showed that, amongst star-forming central galaxies with M_* < 10¹¹ M_⊙, the average sSFR decreases with increasing M_*/R_e, qualitatively supporting a picture in which the presence of a bulge reduces the sSFR and increases the probability of being quenched. Alternatively, the data could be explained if the probability of quenching depends only on M_*, but is accompanied by a change in structure, with R_e shrinking by a factor of ∼2 due to the increased prominence of a bulge when star formation is terminated.

For satellite galaxies, the fact that the quenching efficiency is a maximum for the same combination of M_* and R_e at which the satellite fraction itself peaks almost certainly means that their R_e, and perhaps their mass, changes upon quenching.

CMBO acknowledges support from an NSERC Undergraduate Student Research Award. MLB acknowledges support from an NSERC Discovery Grant, and NOVA and NWO grants that supported his sabbatical leave at the Sterrewacht at Leiden University, where this work was completed. MLB thanks Sean McGee, Asa Bluck, Sara Ellison and an anonymous referee for their careful reading of the manuscript, and for helpful comments which improved our interpretation of the data.

Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

Specifically, when we consider properties of the bulge component we use the models with n_b = 4.

The stellar velocity dispersion is assumed to be related to M_* and R_e through the virial relation σ² ∝ GM_*/R_e.

Surface density is actually M_*/|$\pi R^2_{\rm e}$|⁠, but we omit π for simplicity.

If the M_*–R_e distribution of active galaxies evolves with time (e.g. Trujillo et al. 2006; Bruce et al. 2012), the relevant quenching probability will not be identical to the quiescent fraction observed today. Qualitatively, however, the scenario we describe still applies.

REFERENCES

Abazajian

K. N.

, et al. ,

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2009

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543

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Article Contents

The connection between galaxy structure and quenching efficiency

Abstract

1 INTRODUCTION

2 THE DATA

2.1 The sample

2.2 Galaxy properties

2.3 Completeness corrections

2.3.1 Magnitude limit

2.3.2 Angular resolution

2.3.3 Weights

2.4 Separating active and quiescent galaxies

2.5 Stellar mass and effective radius distribution

3 RESULTS

3.1 Quenching and quenching efficiency

4 DISCUSSION

4.1 Quiescent central galaxies

4.1.1 Hypothesis 1: quenching probability depends on galaxy structure

4.1.2 Hypothesis 2: structural changes associated with quenching

4.2 The role of the bulge

4.3 Satellite quenching

5 SUMMARY AND CONCLUSIONS

REFERENCES

APPENDIX A: APPROPRIATE CHOICE OF EFFECTIVE RADIUS

APPENDIX B: STELLAR MASS, INFERRED VELOCITY DISPERSION AND SURFACE DENSITY DISTRIBUTIONS

SUPPORTING INFORMATION

Supplementary data

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