CENTRAL STELLAR MASS DEFICITS IN THE BULGES OF LOCAL LENTICULAR GALAXIES, AND THE CONNECTION WITH COMPACT z ∼ 1.5 GALAXIES

It is now widely believed that all massive elliptical galaxies, and massive bulges in disk galaxies, house a supermassive black hole (SMBH) at their center (Magorrian et al. 1998; Richstone et al. 1998; Ferrarese & Ford 2005). In the standard cosmological formation paradigm of the universe, galaxies grow hierarchically, such that smaller systems merge to build larger ones (e.g., White & Rees 1978; Khochfar & Burkert 2001). As galaxies containing SMBHs collide, their black holes (BHs) will migrate to the center of the merger remnant through dynamical friction, and form a bound binary (Komossa et al. 2003; Rodriguez et al. 2009; Fabbiano et al. 2011; Paggi et al. 2013). The subsequent hardening of the BH binary, following the dissipation of orbital energy and angular momentum to the nearby stars, impacts on the central stellar distribution of the newly merged galaxy. The gravitational slingshot ejection of these stars (from the binary's loss cone) via three-body interactions involving the binary is thought to be responsible for the physical origin of the partially depleted nuclear regions in luminous "core-Sérsic" galaxies which experienced "dry," i.e., gas-poor, merger events (Begelman et al. 1980; Ebisuzaki et al. 1991; Faber et al. 1997; Milosavljević & Merritt 2001; Merritt 2006; Sesana 2010; Gualandris & Merritt 2012).

Given the above scenario, the sizes and mass deficits of partially depleted cores are thought to reflect the amount of galactic merging and the ensuing extent of damage caused by binary SMBHs (after having eroded any preexisting nuclear star clusters; Bekki & Graham 2010). Accurate measurements of the central stellar mass deficits in "core-Sérsic" galaxies can therefore provide useful constraints on models of galaxy formation and evolution. A key concept is that such core formation is by and large a cumulative process in which the ejected mass from SMBH binaries scales both with the final SMBH mass and the number of mergers (e.g., Milosavljević & Merritt 2001; Merritt 2006). Some recent studies have additionally postulated enhanced core depletions as a result of recursive core passages of recoiled SMBHs (Gualandris & Merritt 2008), or due to the actions of multiple SMBHs from merging galaxies (Kulkarni & Loeb 2012).

To date, several quantitative studies of the central stellar mass deficit have focused on elliptical galaxies (e.g., Graham 2004; Trujillo et al. 2004; Merritt 2006; Kormendy & Bender 2009; Dullo & Graham 2012). Violent, major dry merger events are commonly, or at least traditionally, thought to produce these elliptical galaxies (Toomre & Toomre 1972; Barnes & Hernquist 1992; Kauffmann & Haehnelt 2000). Furthermore, as noted above, dry merger events involving SMBHs are also typically thought to be responsible for producing elliptical galaxies with partially depleted cores. Therefore, some ambiguity exists regarding the mechanisms for the formation of the lenticular (S0) disk galaxies having depleted cores.

In 1936 Hubble introduced lenticular galaxies into the tuning fork diagram (Jeans 1928; Hubble 1929); they were added as a hypothetical transition type between elliptical and spiral galaxies. Later observation of the populations of lenticular and spiral galaxies in clusters revealed the dominance of lenticular galaxies (spiral galaxies) in local (in distant) clusters (e.g., Dressler 1980; Dressler et al. 1997; Couch et al. 1998; Fasano et al. 2000; Desai et al. 2007; Poggianti et al. 2009; Sil'chenko et al. 2010). This suggested an evolutionary transformation of S0 galaxies from spiral galaxies, where mechanisms such as ram pressure stripping (Gunn & Gott 1972; Quilis et al. 2000), galaxy–galaxy harassment (Moore et al. 1996), strangulation (Larson et al. 1980; Bekki et al. 2002; Kawata & Mulchaey 2008), and gas starvation by active galactic nucleus (AGN; van den bergh 2009) were forwarded to account for the removal of disk gas and the subsequent quenching of star formation, thereby passively fading the spiral galaxies and erasing their spiral arms. These formation scenarios, however, do not in themselves explain the central stellar depletions observed in some S0 galaxies.

The theoretical work of Steinmetz & Navarro (2002) has suggested that a galaxy's morphology is a transient phenomenon. In this hierarchical picture, classic elliptical galaxies are built through major mergers (of disk galaxies) and may progressively regrow stellar disks, by gas accretion, which remain intact only until the next significant merger (see Okamoto & Nagashima 2001; Governato et al. 2009; Pichon et al. 2011; Sales et al. 2012; Conselice et al. 2013 for supporting arguments). The number of such cycles may however be low (i.e., 1) rather than several (3–5). Likewise, Arnold et al. (2011) and Forbes et al. (2011) recently pointed out that S0s might form through a two-phase inside-out assembly with the inner regions built early via a violent major merger, and "wet" minor mergers subsequently contributing to the outer parts.

This assembly scenario is consistent with the observed presence of partially depleted cores in luminous S0 galaxies. It also suggests that their bulges, most of which we know are old (e.g., MacArthur et al. 2009, and references therein), were already around at z ≈ 1.5–2. Graham (2013, his Figure 1) revealed that the compact galaxies at z = 1.5–2 have masses and structural properties consistent with those of the brighter bulges in local disk galaxies. Rather than being the precursors of elliptical galaxies prior to significant size evolution, Graham (2013) advocated that some of these compact high-z galaxies may therefore be associated with the bulges of modern disk galaxies. Furthermore, in this scenario in which compact galaxies evolve into disk galaxies with compact bulges, the (high velocity)-end of the galaxy "velocity dispersion function" would not be expected to evolve from z ∼ 1.5 to 0, just as observed (Bezanson et al. 2012).

Regarding the analysis of surface brightness profiles, Trujillo et al. (2004) avoided the inclusion of S0 galaxies in their sample of well-resolved local galaxies because it was felt that the introduction of an eight-parameter model (five or seven core-Sérsic parameters for the bulge plus two for the exponential disk) might be considered excessive at that time. Ferrarese et al. (2006) also avoided introducing two additional disk parameters in their modeling of well-resolved early-type galaxies in the Virgo cluster; however, because their sample included disk galaxies, their core-Sérsic parameters do not correspond to the bulge component.¹ Although Kormendy et al. (2009) did fit a Sérsic bulge plus an exponential disk to their S0 galaxies, they marked the core region by eye rather than objectively fitting a core-Sérsic bulge plus exponential disk model. Depending on the sharpness of the (inner core)-to-(outer Sérsic) transition region, this practice may substantially overestimate the formal "break radius"—which is not to be confused with the inner or outer edge of the transition region.

Here, we endeavor to provide the most accurate measurements to date of the centrally depleted stellar mass in lenticular disk galaxies. This is achieved by simultaneously fitting both a core-Sérsic model to the bulge and an exponential model to the disk.

This paper is organized as follows. Our initial sample of six suspected lenticular galaxies with depleted cores, plus the data reduction, and the light profile extraction technique are discussed in Section 2. In Dullo & Graham (2012), we did not have a sufficient radial extent of these six galaxies' light profiles to include a disk component. Here, we are able to test if this may have slightly biased some of our previous measurements of the bulge parameters. Section 3 introduces the analytical models used to describe the light profiles of "core-Sérsic" lenticular galaxies, and Section 4 details our fitting analysis while in Section 5 we describe the method for measuring the mass deficits of the core-Sérsic lenticular galaxies. Our interpretations of the central stellar mass deficits in the context of core-Sérsic lenticular galaxy formation scenarios are discussed in Section 6. In Section 6.1, we discuss the formation of core-Sérsic lenticular galaxies, and in Section 6.2 we compare the physical properties of their bulges with those of compact galaxies at z = 1.5–2. In Section 6.3, we discuss the role of galaxy environment. Section 7 summarizes our main conclusions. At the end of this paper are two appendices. The first provides notes on the six individual galaxies studied in this paper and the second provides a response to the criticism of Dullo & Graham (2012) by Lauer (2012) regarding the identification of partially depleted cores.

2.1. Sample Selection

2.2. Imaging Data

High-resolution Hubble Space Telescope (HST) optical images of these galaxies were retrieved from the public HST data archive. We only used images from broadband filters. While the HST Advanced Camera for Survey (ACS; Ford et al. 1998) Wide Field Channel (WFC) F475W and F850LP images, from the Virgo Cluster Survey GO-9401 program (PI: P. Côté), are available for NGC 4382, for the remaining five galaxies (NGC 507, NGC 2300, NGC 3607, NGC 3706, and NGC 6849) we used the Wide Field Planetary Camera 2 (WFPC2; Holtzman et al. 1995) F555W images taken from the following programs: NGC 507, NGC 3706, and NGC 6849 from the GO-6587 program (PI: D. Richstone); NGC 2300 from the GO-6099 program (PI: S. Faber); and NGC 3607 from the GO-5999 program (PI: A. Phillips). For NGC 3607, we also used the near-infrared NICMOS/NIC2 F160W image observed in the GO-11219 program (PI: A. Capetti) to enable us to better avoid this galaxy's inner dusty spiral structure. Global properties and observation details of all the sample galaxies are listed in Table 1.

The WFPC2 consists of three wide field cameras (WF2, WF3, and WF4) and a high-resolution planetary camera (PC1); each has a CCD detector with 800 × 800 pixels. The three wide field cameras have a 01 per pixel spatial sampling. The smaller, high-resolution planetary camera (PC1), where each galaxy's center had been placed, has a plate scale of 0046 and a square 36'' × 36'' field of view (FOV).

Having two CCD cameras with 2048 × 4096 pixels, the ACS WFC has a 0049 pixel scale and covers a 202'' × 202'' rhomboidal area.

Combining the constituent CCDs of each camera, the light profiles from the WFPC2 and ACS observations probe a large range in radius, R ≳ 80''. For comparison, Lauer et al. (2005, and references therein) deconvolved all six sample galaxy images with the point-spread function (PSF) and provided profiles out to a maximum of 10''. The greater radial extent that we now have, from high-quality CCD imaging, enables us to better sample and measure the disk light.

While our WFPC2/F555W (roughly Jonson–Cousins V-band) images match Lauer et al.'s. (2005) V-band images, for NGC 4382 the ACS/F475W (roughly SDSS g) and ACS/F850LP (roughly SDSS z) data are transformed to the V band using

$$\begin{equation} g-V=0.98 (g-z)-1.43, \end{equation} \tag{ 1 }$$

which is acquired here from the least-squares fit to the (g − V) and (g−z) data shown in Figure 1; see also Sirianni et al. (2005) and Kormendy et al. (2009). The zero points in the Vega magnitude systems, which are adopted here to calibrate the WFPC2 (Holtzman et al. 1995) and ACS (Sirianni et al. 2005) profiles, were taken from the STScI Web site.³

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2.3. Data Reduction

2.4. Surface Photometry

The galaxy light profiles were extracted using the IRAF/STSDAS task ellipse (Jedrzejewski 1987). We used the ellipse task to construct the best-fitting concentric elliptical isophotes to the galaxy image starting from an initial elliptical isophote defined by the first guess values of the isophote center (X, Y), ellipticity (), and position angle (P.A.). We used median filtering, logarithmic spacing, and 3σ clipping for flagging deviant sample points at each isophote. To extract the major-axis light profiles, for all galaxies, the isophote center (X, Y), , and P.A. were set free to vary. For each galaxy, we found that the isophote center was stable, i.e., within the small quoted error box.

The deviations of isophotes from perfect ellipses can be characterized well by higher order coefficients of the Fourier series expansion of the intensity (Jedrzejewski 1987). In particular, the coefficient of the cos 4θ term, B₄, is found to be of great importance in describing these deviations. Negative B₄ values imply that the isophotes are "boxy," but, if B₄ is positive, the isophote will be identified as "disky." Disky isophotes are frequently due to the presence of embedded disks in less massive, fast rotating, dissipative (gas rich) galaxies (e.g., Carter 1978, 1987; Davies et al. 1983; Bender et al. 1988; Peletier et al. 1990; Jaffe et al. 1994; Faber et al. 1997). In contrast, dissipationless violent relaxation of stars is often invoked to explain the boxy isophotes of triaxial, pressure-supported massive galaxies (Nieto & Bender 1989), which usually also contain hot X-ray-emitting gas (e.g., Cattaneo et al. 2009).

Faber et al. (1997) reported a trend between the isophotal shape, kinematics and the central structure of early-type galaxies. Galaxies which were identified as having cores by the Nuker model (e.g., Lauer et al. 1995) were found to be slowly rotating, boxy systems while those which lack cores according to this model (which are labeled as "power-law" galaxies) were shown to be fast rotating and disky (see also Lauer 2012; although Emsellem et al. 2007 and Glass et al. 2011 highlighted the absence of a one-to-one correspondence between these galaxies' central structure and kinematics). This is further discussed in Section 4.1.

In Figure 2, we show the results of the ellipse fitting. As noted in Rest et al. (2001), the isophotal parameters derived from the ellipse fits tend to be more uncertain in the very inner regions (R ≲ 03); this feature is mainly due to the PSF and some contributions from the discrete sampling and subpixel interpolation of the IRAF fitting routine (Ravindranath et al. 2001). We note that while the disky/boxy isophotal deviations vary with radius in all of the six galaxies, NGC 507 and NGC 4382 have core regions which appear preferentially boxy within 1'' (Figure 2). Nieto & Bender (1989) reported that the S0 galaxy NGC 2300 has boxy inner (1'' < R ≲ 20'') isophotes and disky "pointed" outer (20'' < R < 50'') isophotes, in agreement with our result (Figure 2).

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In constructing "composite" light profiles for each galaxy, we combine the very inner (R ≲ 1'') Lauer et al. (2005) PSF-deconvolved, high-resolution V-band light profile with our photometrically calibrated (V-band) profile of the PSF-unaffected region beyond ∼1''. For all six galaxies in our sample, we find an excellent agreement (an overlap) between our light profiles and those published by Lauer et al. (2005) over the 1''–5'' radial range.

Given the two-component (bulge/disk) nature of lenticular galaxies, we apply a bulge-to-disk (B/D) photometric decomposition to the one-dimensional, major-axis surface brightness profiles of all the galaxies in our sample. When needed, a bar component is also included.

The radial intensity distribution of our lenticular galaxies' disk component is modeled with an exponential function given by

$$\begin{equation} I_{{\rm disk}}(R)=I_{0d} \exp [-R/h], \end{equation} \tag{ 2 }$$

where I_0d and h are the central intensity and scale length of the disk, respectively.

We adopt the Ferrers (1877) function to describe the radial intensity distribution of the bar component, given by

$$\begin{eqnarray} I_{{\rm bar}}(R) &=& I_{0{\rm bar}}[1-(R/a_{{\rm bar}})^{2}]^{n_{{\rm bar}}+0.5},\quad R< a_{{\rm bar}},\nonumber\\ I_{{\rm bar}}(R) &=& 0,\quad R> a_{{\rm bar}}, \end{eqnarray} \tag{ 3 }$$

where I_0bar, a_bar, and n_bar are the central intensity, major-axis length, and shape parameter of the bar, respectively (cf. Laurikainen et al. 2010).

Since the work by Caon et al. (1993) and Andredakis et al. (1995), several studies have revealed that, in general, the Sérsic (1963) model describes the underlying light distributions of both elliptical galaxies and the bulges of disk galaxies exceedingly well over a large radial range. This model can be written as

$$\begin{equation} I(R) = I_{0} \exp \left[ - b_{n} \left(\frac{R}{R_{e}}\right)^{1/n}\right], \end{equation} \tag{ 4 }$$

where I₀ = I(R = 0) is the central intensity. The quantity b_n ≈ 2n − 1/3, for 1 ≲ n ≲ 10 (e.g., Caon et al. 1993; Graham 2001), is a function of the Sérsic index n, and is defined in such a way to ensure that the half-light radius, R_e, encloses half of the total luminosity. Reviewed in Graham & Driver (2005), the total luminosity of the Sérsic model within any radius R is given by

$$\begin{equation} L_{T,{\rm Ser}}({<}R) = I_{e} R^{2}_{e} 2 \pi n \frac{e^{b_{n}}}{(b_{n})^{2n}} \gamma (2n,x), \end{equation} \tag{ 5 }$$

where γ(2n, x) is the incomplete gamma function and x = b_n(R/R_e)^1/n.

Systematic downward departures of the inner light profile relative to the inward extrapolation of the outer Sérsic model are known to exist in luminous galaxy/bulge light profiles. These are not exactly the same objects as "core" galaxies identified with the Nuker model (Lauer et al. 1995; Byun et al. 1996) or the double power-law model of Ferrarese et al. (1994). "Core-Sérsic" galaxies have partially depleted cores relative to their outer Sérsic profile whereas "core" galaxies need not have any deficit but instead simply an inner power-law slope γ < 0.3. As detailed in Dullo & Graham (2012), the core-Sérsic model (Graham et al. 2003), a combination of an inner power-law and an outer Sérsic function, provides a good representation of the brightness profiles of bulges in disk galaxies with depleted cores. The model is defined as

$$\begin{equation} I(R) =I^{\prime } \left[1+\left(\frac{R_{b}}{R}\right)^{\alpha }\right]^{\gamma /\alpha } \exp \left[-b_{n}\left(\frac{R^{\alpha }+R^{\alpha }_{b}}{R_{e}^{\alpha }} \right)^{1/(\alpha n)}\right], \end{equation} \tag{ 6 }$$

with

$$\begin{equation} I^{\prime } = I_{b}2^{-\gamma /\alpha } \exp \left[b_{n} (2^{1/\alpha } R_{b}/R_{e})^{1/n}\right]. \end{equation} \tag{ 7 }$$

The term I_b denotes the intensity at the core's break radius R_b, γ is the slope of the inner power law, and α controls the sharpness of the transition between the inner power law and the outer Sérsic profile. Both R_e and b_n have the same general meaning as in the Sérsic model.

Figure 3 displays the best model fits to the major-axis surface brightness profiles of the six galaxies listed in Table 1. We follow the iterative fitting technique of Dullo & Graham (2012), minimizing the rms residuals to determine the best-fit parameters that match the data. It is important to note that these profiles now cover a large range in radius (out to R ≳ 80''), giving both the core-Sérsic and the exponential models enough radial expanse to both quantify the curvature in the bulge profile (i.e., the Sérsic index) and define the disk scale length. Table 2 lists the fit parameters obtained from the adopted core-Sérsic plus exponential bulge + disk models.

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Apparent from Figure 3 is that the global light distribution of all the sample galaxies, except for NGC 3706 (E not S0) and NGC 6849 (barred), can be accurately represented by the core-Sérsic + exponential model with small rms residuals ≲ 0.05 mag arcsec⁻². If a single core-Sérsic model is fit to the light profile of a disk galaxy (i.e., a two-component system comprised of a flattened disk and a triaxial bulge), this would result in parameters that do not describe the triaxial bulge component of the galaxy, effecting in particular the Sérsic index, and ultimately the mass deficit measurement as happened in Ferrarese et al. (2006, see also Meert et al. 2012). Although NGC 3706 is classified as a lenticular galaxy in the RC3, we find that its light profile is best fitted by a single core-Sérsic model, without an exponential disk component. This suggests that the galaxy may be an elliptical galaxy misclassified as an S0 in the RC3, consistent with the conclusion of Laurikainen et al. (2010). As for NGC 6849, the three-component bulge–bar–disk light profile is well described by the core-Sérsic bulge + Ferrers bar + exponential disk decomposition model (see Figure 3 and Appendix A.1.6).

While the V-band surface brightness profile of NGC 3607 is well described by the core-Sérsic bulge + exponential disk model, the 131 core radius of this fit is suspiciously larger than the 022 core radius reported by Richings et al. (2011) from their H-band profile analysis. The explanation is that a dusty nuclear spiral has caused a reduction to the inner V-band light profile. Our analysis of the PSF-affected H-band light profile (Figure 3) gives a core radius of 011, which is in fair agreement with the result found by Richings et al. (2011) but does not support a large core in this galaxy. Given that the core size we find with the PSF-affected H-band data is comparable to the seeing, coupled with the dusty spiral structure, we are unable to conclude if there is indeed any partially depleted core in this galaxy, and as such we exclude it from our final analysis.

We have found that the bulge model parameters (Table 2) generally agree well with those from Dullo & Graham (2012). For NGC 2300, the contribution of the disk light to the inner 15'' profile which we modeled in Dullo & Graham (2012) did however result in a break radius R_b = 098 which is slightly larger than the one from this work (R_b = 053). With the exception of this galaxy, the agreement between the break radii from these two studies is good, constrained to less than a 20% discrepancy. For each galaxy, we find that the V-band surface brightness at the break radius (μ_{b, V}) given in Table 2 agrees with those presented in Dullo & Graham (2012) to within the range of error bar: there is ∼5% discrepancy, which is well within the Dullo & Graham (2012) ∼10% uncertainty range. We have also compared the inner power-law slopes (γ) from the two studies. We find that the new γ values (Table 2) are consistent with those reported in Dullo & Graham (2012).

The five core-Sérsic lenticular galaxies (Table 2) have bulge Sérsic indices n ∼ 3, while typically for core-Sérsic elliptical galaxies n is greater than 3. This may be because, for a given magnitude, the bulges of disk galaxies appear to have lower Sérsic indices than elliptical galaxies of the same magnitude (Graham 2001, his Figure 14). It may also be that the elliptical core-Sérsic galaxies from Dullo & Graham (2012) are brighter.

4.1. Kinematics and Central Structure of Core-Sérsic Lenticular Galaxies

The central stellar mass deficit (M_def) of "core-Sérsic" galaxies is predicted to be generated mainly via the three-body encounters of the core stars with the inspiraling BHs in a merger remnant (e.g., Ebisuzaki et al. 1991; Milosavljević & Merritt 2001; Merritt 2006). Graham (2004) measured this stellar mass deficit from the luminosity difference L_def between the inward extrapolation of the outer Sérsic model and the (sharp-transition⁵) core-Sérsic model. This approach was adopted in subsequent works by Ferrarese et al. (2006), Merritt (2006), and Hyde et al. (2008). We adopt a slightly different methodology to those studies by using a finite value for α in Equation (6) and thus a smoother transition region between the inner power-law and the outer Sérsic profile of the core-Sérsic model. The total core-Sérsic model luminosity (Trujillo et al. 2004; their Equation (A19)) is given by

$$\begin{eqnarray} L_{T,cS} &=& 2\pi I^{\prime }n(R_{e}/b^{n})^{2}\int _{b(R_{b}/R_{e})^{1/n}}^{+\infty }e^{-x}x^{n(\gamma +\alpha)-1}\nonumber\\ &&\times[x^{n\alpha }-(b^{n}R_{b}/R_{e})^{\alpha }]^{(2-\gamma -\alpha)/\alpha }dx, \end{eqnarray} \tag{ 8 }$$

where all the parameters have the same meaning as in Equation (6). The difference in luminosity between the outer Sérsic model (Equation (5)) and the core-Sérsic model (Equation (8)) is of course the central stellar flux deficit.

To convert the luminosity deficits into mass deficits, individual stellar mass-to-light ratios (M/Ls) were derived for each galaxy. To determine these ratios, we have made use of the available (preferentially nuclear) colors of the galaxies as well as the color–age–metallicity–(M/L) diagram from Graham & Spitler (2009, their Figure A1). As in Graham (2004), we have assumed that the inner regions of these galaxies have an evolved (old) single population of stars.

For NGC 2300, NGC 3607, and NGC 4382, the nuclear V − I colors of 1.33, 1.36, and 1.11, taken from Lauer et al. (2005), correspond to stellar M/L_V ratios of 5.0, 5.7, and 2.6, respectively. Using the HyperLeda database, NGC 507 and NGC 3706 have V − I colors of 1.40 and 1.34, respectively, while NGC 6849 has V − I = 1.03. From this, we obtain M/L_V ratios of 5.5, 5.2, and 2.4 for NGC 507, NGC 3706, and NGC 6849, respectively (see Table 3). These M/Ls were used to convert the stellar flux deficits into stellar mass deficits. These have been plotted in Figure 4 against each galaxy's expected BH mass as derived from the M–σ relation (Graham et al. 2011; the lower half of their Table 2) based on the σ-values in Table 1.

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As noted above, high-accuracy N-body simulations by Merritt (2006) revealed that the effect of multiple dissipationless mergers on core formation is cumulative; thus, the extent of core evacuation could reflect the amount of merging. He found that the total mass deficit after N "dry" major mergers is ≈0.5NM_BH, where M_BH is the final BH mass. This result hinges on a key assumption that the central BH would tidally disrupt infalling high-density satellites, thereby protecting any preexisting core (Faber et al. 1997; Boylan-Kolchin & Ma 2007).

Figure 4 shows that the mass deficits for the "core-Sérsic" lenticular galaxies (plus one elliptical galaxy) listed in Table 2 are M_def ∼ 0.5–2 M_BH, which translates to a few (1–4) "dry" major merger events. For reference, measurements of close galaxy pairs in real data (i.e., not simulations) suggest that massive galaxies (>10^10.5 M_☉) have experienced 0.5–2 major mergers since z ∼ 0.7–1 (e.g., Bell et al. 2004, 2006; Bluck et al. 2012; Man et al. 2012; Xu et al. 2012). Our figure is double this value, but it has no upper redshift constraint associated with it. The mean elliptical galaxy M_def/M_BH mass ratio from Graham (2004) is 2.1 ± 1.1, while the mean ratio from Ferrarese et al. (2006) is 2.4 ± 0.8 after excluding the S0 galaxy NGC 4382 from their sample (as they did at the end of their Section 5.2). We used the M_BH–σ relation presented in Graham et al. (2011; the lower half of their Table 2) for estimating the SMBH masses of the five core-Sérsic galaxies shown in Table 3. While this M_BH–σ relation was constructed by combining core-Sérsic and Sérsic galaxies, Graham & Scott (2013, their Table 3) have recently shown that core-Sérsic and Sérsic galaxies follow similar M_BH–σ relations. They additionally reported an M_BH–σ relation for their combined (core-Sérsic + Sérsic) galaxies which is consistent with the relation found by Graham et al. (2011). We find that, for all our core-Sérsic galaxies, the SMBH masses predicted using the Graham & Scott (2013) M_BH–σ relations which are defined by the core-Sérsic, Sérsic or core-Sérsic + Sérsic galaxies agree with those used in this study (Table 3) within the range of error bars. We make use of Equation (4) from Graham et al. (2011) and the σ-values in Table 1 and assume a 10% uncertainty on σ to estimate the 1σ uncertainty on each galaxy's SMBH mass (Table 3).

For NGC 4382, Kormendy & Bender (2009) reported a mass deficit of M_def ∼ 1.3 × 10⁹ M_☉ ≈ 13 M_BH when using M_BH = 1 × 10⁸ M_☉, while Gültekin et al. (2011) used Nuker model parameters and found a mass deficit of M_def ∼ 5.9 × 10⁸ M_☉ ≈ 45.6 M_BH when they assumed a very small BH mass of 1.3 × 10⁷ M_☉. Ferrarese et al. (2006, see their Figure 20) noted that the large-scale stellar disk of NGC 4382, which was incorporated into their single Sérsic fit to this galaxy, might have biased their ∼10 M_BH mass deficit measurement. Indeed, their galaxy Sérsic index was ≈6–7, while we have found that the bulge Sérsic index is less than 3. Our analysis of this bulge's central stellar mass deficit yields M_def ∼ 1.2 × 10⁸ M_☉ ≈ 1.3 M_BH (using M_BH = 9.55 × 10⁷ M_☉), smaller than the results of Ferrarese et al. (2006), Kormendy et al. (2009), and Gültekin et al. (2011).

Previously, Milosavljević & Merritt (2001), Milosavljević et al. (2002), Ravindranath et al. (2002), and Lauer et al. (2007a) had used the Nuker model to measure mass deficits that are up to an order of magnitude larger than those obtained here. As detailed in Trujillo et al. (2004) and Dullo & Graham (2012), this discrepancy arises in part from the differences in the estimated core sizes from the two models. While the Nuker model break radii are up to three times larger than the core-Sérsic model break radii, due to the Nuker model fitting a power law to each galaxy's outer curved Sérsic profile (Graham et al. 2003), the core-Sérsic break radii agree with model-independent core sizes where the negative logarithmic slope of the light profile equals 0.5 (Dullo & Graham 2012).

More recently, Kormendy et al. (2009) fit Sérsic models to core-Sérsic galaxy light profiles and tried to quantify the core from a visual inspection, rather than using the core-Sésic model in an objective analysis. They report large break radii and mass deficits M_def ∼ 10–20 M_BH. In an effort to reconcile these large deficits, they speculated that they may be due to recoiled BHs, which might enhance the core depletion following their repetitive core passages (Boylan-Kolchin et al. 2004; Gualandris & Merritt 2008); cf. also Postman et al. (2012) for a similar reasoning. If this mechanism always occurred, then the lower M_def/M_BH ratios in Dullo & Graham (2012) for elliptical galaxies would suggest that the effective number of major mergers is less than one, i.e., only a minor merger is required. However, given the near-linear relation between BH mass and host spheroid mass, and luminosity, for core-Sérsic galaxies (Graham 2012; Graham & Scott 2013) this scenario is unlikely. At least for the elliptical core-Sérsic galaxies, which are the dominant population among the known core-Sérsic galaxies, this linear BH–galaxy mass scaling relation readily arises from the self-addition of comparable mass systems, not minor mergers.

6.1. Formation of Core-Sérsic Lenticular Galaxies

6.2. Bulges of Today's S0s versus Compact High-redshift Galaxies

Recent observations have revealed that the sizes of compact massive galaxies at redshift of z ∼ 1.5–2 (having effective radii R_e ≲ 2 kpc) are up to a factor of ∼5 smaller than the present-day elliptical galaxies of comparable stellar mass (Daddi et al. 2005; Trujillo et al. 2006; Cimatti et al. 2008; Damjanov et al. 2009; Saracco et al. 2011; Szomoru et al. 2012, and references therein). Numerous recent papers have explored the evolutionary fate of the compact massive galaxies observed at z ∼ 1.5 (e.g., Cimatti et al. 2012; Carollo et al. 2013). While today's elliptical galaxies are widely regarded as the descendants of these compact high-redshift galaxies (e.g., Hopkins et al. 2009), Graham (2013, his Figure 1) showed that massive local disk galaxies can also be alternative candidates given the high stellar density and compactness of their bulges. Comparing the properties of our massive present-day bulges with compact high-redshift galaxies, we plot the size–mass (Figure 5(a)) and size–(Sérsic index) (Figure 5(b)) diagrams for a sample of 106 galaxies. One hundred and one of these objects are compact massive quiescent galaxies at redshift z = 0.2–2.7 taken from Damjanov et al. (2011, selected from their Table 2), while five are the bulges from local S0s (Tables 2 and 3). This figure clearly shows that the location of the bulges of our five core-Sérsic S0s coincides with that of the high-redshift compact galaxies in both the R_e–M_* and R_e–n diagrams.

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This overlap suggests that the compact high-redshift galaxies are the progenitors of (the bulges of) massive present-day S0s (e.g., Dutton et al. 2013; Graham 2013). Indeed, the inside-out growth mechanism described at the end of Section 6.1, which could drive the buildup of the core-Sérsic S0s (Section 6.3), would also eliminate the difficulties encountered in trying to explain the size evolution of these compact high-redshift galaxies into much larger, modern-day elliptical galaxies. Large elliptical galaxies already exist at z ≈ 1.5–2 (e.g., Bruce et al. 2012). We further note that van der Wel et al. (2011, see also Chevance et al. 2012) wrote that the majority of compact high-redshift galaxies have small undeveloped disks. In addition, Poggianti et al. (2013) found that 4.4% of their total low-redshift galaxy population had sizes and mass densities comparable to the compact, massive high-redshift galaxies, with 70% of these compact low-redshift galaxies found to be S0s. Given the results in Graham (2013, his Figure 1), a comparison of local S0 galaxy "bulge" sizes and densities, rather than the entire "galaxy" sizes and densities, should yield a higher percentage match. It seems plausible that minor mergers and cold gas accretion (e.g., Conselice et al. 2013), in a preferred plane due to known cosmological streaming/feeding paths, may transform some of the compact high-redshift galaxies into modern S0s by the creation of a younger surrounding disk. This process eliminates the difficulties that arise when trying to evolve the compact high-z galaxies into local elliptical galaxies, such as the shortage of satellites required to produce the necessary expansion via many minor mergers (Trujillo 2012). It is also consistent with cosmological models (e.g., Steinmetz & Navarro 2002), and explains many properties of early-type galaxies.

6.3. The Role of Galaxy Environment

Several studies have highlighted that environment plays a major role in the formation of S0 galaxies (e.g., Dressler 1980; Dressler et al. 1997; Couch et al. 1998; Fasano et al. 2000; Poggianti et al. 2009; Wilman et al. 2009; Just et al. 2010; Bekki & Couch 2011). Three of our five S0 galaxies (NGC 507, NGC 2300, and NGC 3607) reside in X-ray bright galaxy groups, while NGC 6849 is an isolated galaxy, and NGC 4382 is a member of the Virgo cluster.

NGC 6849, the isolated core-Sérsic lenticular galaxy, may have had its bulge built through an early violent "dry" major merger, while subsequent late accretion of gas and stars built up its disk—the picture in Graham (2013); see also Conselice et al. (2013). This hierarchical inside-out growth scenario is supported by its radial color profile plotted in Figure 6. The B − R color gradient reveals that the galaxy becomes progressively bluer toward larger radii (≳ 10'') where the disk dominates. Arnold et al. (2011) proposed such a two-phase assembly mechanism to explain the isolated field galaxy NGC 3115 (except for its dwarf companion) based on their analysis of its kinematics and metallicity. Reda et al. (2004) also found that mergers are a dominant formation path to forming some isolated early-type galaxies. In passing we note that van den Bergh (2009) alternatively suggested that disk gas ejection by AGN might be a dominant process that transforms isolated spiral galaxies into S0s. While by itself this process does not appear capable of generating a depleted stellar core in galaxies, it may have transformed some spiral galaxies into lenticular galaxies.

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The "dry" major merger scenario for the bulges of bright lenticular galaxies in groups may be naturally consistent with the observed morphology density relation for the galaxy groups. Studies have shown that galaxy–galaxy interaction and merging play an important role in transforming group spirals into S0s and giving the observed S0 fractions in groups (e.g., Postman & Geller 1984; Helsdon & Ponman 2003; Just et al. 2010; Bekki & Couch 2011). Our three X-ray bright group galaxies are the brightest central galaxies from their respective groups. As pointed out by Helsdon & Ponman (2003, and references therein), these central S0 galaxies are assumed to be the by-products of an earlier merger activity in the collapsing group core plus some recent merger and accretion events. Interestingly, as shown in Figure 6, the outskirts of these galaxies (color information was not available for NGC 507) are relatively bluer than their centers. This result further strengthens the view that bulges in luminous group S0s grow by mergers while their disks are gradually built and enhanced via latter gas accretion.

For NGC 4382, our fifth lenticular galaxy and the only cluster galaxy in our sample, our analysis of its brightness profile and thus the mass deficit (Figures 3 and 4) suggests a "dry" merger event as a formation path. In contrast, processes such as ram pressure stripping (Gunn & Gott 1972; Quilis et al. 2000), galaxy harassment (Moore et al. 1996), and strangulation (Larson et al. 1980; Bekki et al. 2002) are often noted as plausible formation mechanisms for cluster lenticular galaxies, rather than galaxy mergers, due to the high cluster velocity dispersion and high intracluster medium density. We do not deny these mechanisms, only that they alone cannot account for partially depleted cores. For example, Vollmer et al. (2008a, 2008b) present wonderful observational evidence of the ram pressure stripped Virgo spiral galaxies NGC 4501 and NGC 4522, while Merluzzi et al. (2013) describe in detail the stripping process of a galaxy in A3558. The merger event in NGC 4382's past may have occurred prior to it entering the cluster. Coupling N-body simulations with a semi-analytic formation model, Okamoto & Nagashima (2001) also reported that the fractions of cluster S0 galaxies produced by major mergers are significantly smaller than the observed fractions. In contrast, Bekki (1998) proposed unequal galaxy merging between two spirals as a dominant formation origin for cluster lenticular galaxies (see also Burkert & Naab 2005; Jesseit et al. 2005). NGC 4382 is situated in the outskirts of the Virgo cluster, a location where mergers are likely to occur, and it displays stellar shells in its image (Schweizer & Seitzer 1992). These appear to suggest that NGC 4382 might have a merger related origin (although see Chung et al. 2009). The g − z = 1.95 bulge color of NGC 4382 (Figure 6) is however bluer than the typical g − z = 1.56 (AB mag) color quoted for ellipticals (Fukugita et al. 1995). If the core in NGC 4382 was formed from the inspiral of SMBHs in a relatively gas-free merger event, then the progenitor stars which make the bulge were not old, suggestive of ongoing core formation in some lenticular galaxies rather than all being formed at redshifts beyond 1.5–2 prior to the subsequent accretion of a disk.

We have used the IRAF ellipse task to derive the major-axis surface brightness profiles and isophotal parameters for six early-type galaxies observed with the high-resolution HST WFPC2 and ACS cameras. While one of these turned out to be an elliptical galaxy, which we modeled with a core-Sérsic profile, we have modeled the surface brightness profiles of the remaining five lenticular galaxies using a core-Sérsic model for the bulge plus an exponential model for the disk. This is the first time this has been done for disk galaxies with depleted cores. In our analysis, we have additionally accounted for the bar component in one of these disk galaxies by using the Ferrers (1877) function. Our primary conclusions are as follows:

• 1.  
  The core-Sérsic bulge plus exponential disk model gives an accurate description to core-Sérsic lenticular galaxy light profiles. The rms residual scatter of the fits is ≲ 0.05 mag arcsec⁻².
• 2.  
  The Sérsic index n is ∼3 for the bulges of our core-Sérsic lenticular galaxies, whereas n ≳ 3 for the brighter core-Sérsic elliptical galaxies in Dullo & Graham (2012).
• 3.  
  We have identified partially depleted cores, with sizes ranging from 24 to 102 pc, in four rapidly rotating, luminous lenticular galaxies. This contradicts the results of Lauer (2012), which reported that galaxies possessing cores rotate slowly.
• 4.  
  We have measured central stellar mass deficits in four of the luminous "core-Sérsic" lenticular galaxies, finding M_def ∼ 0.5–2M_BH, in agreement with previous core-Sérsic analysis of elliptical galaxies. (NGC 3607 was excluded because its dusty nuclear spiral compromises the recovery of its core parameters.)
• 5.  
  Our results tentatively suggest that, regardless of their environments, core-Sérsic lenticular galaxies could be assembled in two stages: an earlier violent "dry" major merger process involving massive BHs, which forms the bulge component, followed by subsequent disk formation through minor mergers and/or very gentle cold gas accretion about a preferred plane. Dry intermediate-mass ratio mergers of S0s with smaller BH-hosting ellipticals could also account for the buildup of some core-Sérsic S0s.
• 6.  
  The location of the bulges of our five S0 galaxies, including the S0 NGC 3607 possibly without a depleted core, in the mass–size and mass–(Sérsic index) diagram coincides with that of the compact early-type galaxies seen at redshift of z ∼ 0.2–2.7. This could be an indication that today's massive bulges may be descendants of the compact high-redshift early-type galaxies.

This research was supported under the Australian Research Councils funding scheme (DP110103509 and FT110100263). This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Based on observations made with the NASA/ESA Hubble Space Telescope, and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA) and the Canadian Astronomy Data Centre (CADC/NRC/CSA). We are grateful to Juan P. Madrid for his help with IRAF.

A.1. Notes on Individual Galaxies

A.2. Comments on Dullo & Graham (2012)

Commenting on Dullo & Graham (2012), Lauer (2012) presented Sérsic model fits to the outer regions of composite light profiles (using the inner 10'' HST profiles from Lauer et al. 2005 combined with ground-based profiles out to ∼100'' taken from the literature) for three galaxies which Dullo & Graham (2012), and others, had shown not to possess depleted cores: NGC 1374, NGC 4473 and NGC 5576. Lauer's (2012) fits suggested the presence of depleted cores relative to his outer Sérsic model. He therefore claimed that Dullo & Graham (2012) had misclassified these three galaxies as coreless Sérsic galaxies due to an incorrect application of the Sérsic model to radially limited 10'' light profiles taken from Lauer et al. (2005). However, there were already ∼100'' high-resolution HST profiles published for these galaxies that had been well fit using Sérsic models with no central light deficit (Turner et al. 2012, NGC 1374; Ferrarese et al. 2006 and Kormendy et al. 2009, NGC 4473; Trujillo et al. 2004, NGC 5576). Figure 7 shows that the light profiles for these galaxies, covering a large radial extent, are described by the sum of two Sérsic profiles without any partially depleted core. The reason for these two-component models is detailed below. Basically, taking into account additional information, such as the presence of tidal material and/or kinematic substructure can help to identify the required components of a fit. In general, we recommend showing the residuals about one's fitted model, as they can reveal if the large-scale curvature in the radial light distribution is well matched, and we advise against subjectively restricting the fitted radial range.

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A.2.1. NGC 1374

Turner et al. (2012) fit a PSF-convolved Sérsic model to this galaxy, with no evidence for a depleted core. In Dullo & Graham (2012), we revealed that there is actually an additional component at the center of this galaxy. In Figure 7(a), we show our (PSF convolved) nuclear disk + Sérsic model fit to the light profile of NGC 1374 taken from Turner et al. (2012); see also the fit presented in Dullo & Graham (2012) to the inner ∼10''. Some small (in amplitude), large-scale residual is present in Figure 7(a). The rotation curve in Graham et al. (1998, see also Longo et al. 1994) revealed that this galaxy rotates out to 40'', suggesting the presence of an additional component which may be the cause of some of the residual structure about our exponential (for the nuclear disk) plus n = 4.3 Sérsic (for the underlying host galaxy light) model.

A.2.2. NGC 4473

Ferrarese et al. (2006) fit a PSF-convolved Sérsic model to NGC 4473, with no depleted core. Kormendy et al. (2009) actually identified a central light excess in this galaxy, above their adopted Sérsic (n ≈ 4) fit, and they remarked that the extra light is due to a known counter-rotating embedded stellar disk (Emsellem et al. 2004; Cappellari & McDermid 2005; Cappellari et al. 2007). Figure 7(b) plots our convolved exponential + Sérsic model fit to this galaxy's light profile taken from Ferrarese et al. (2006). We fit an exponential n = 1 function to the counter-rotating disk and find a Sérsic n ∼ 3 model fits the underlying galaxy light. Furthermore, Pinkney et al. (2003) remarked that this galaxy has unusual parameters from their Nuker model fit. They found that it has (1) the smallest α value of their sample (i.e., a broad transition region between the inner and outer Nuker model power-law profiles) and (2) a very steep β value (the steepest from all the galaxies modeled by Byun et al. 1996). As warned in Graham et al. (2003), this is what one expects when fitting the Nuker model to what is actually a Sérsic profile with a low value of n and no depleted core. Pinkney et al. (2003) additionally remarked that the absolute magnitude of this galaxy is consistent with the "power-law" galaxies, i.e., those without depleted cores.

A.2.3. NGC 5576

Trujillo et al. (2004) modeled the deconvolved 100'' light profile of NGC 5576 with the Sérsic model, finding no depleted core. Kim et al. (2012, their Figure 5) showed that NGC 5576 and the barred S0 NGC 5574 are an interacting pair (see also Tal et al. 2009) having a long tidal tail, which extends out to 60 kpc in their 3.6 μm image. They showed the presence of tidal disturbances in the outskirts (from 1' to 2') of NGC 5576 because of this interaction. In Figure 7(c), we therefore fit a double Sérsic model to the light profile of NGC 5576 presented in Lauer (2012).⁶ We find that the central galaxy light distribution is well fit with an inner n ∼ 3.5 Sérsic model, and the extra light, which is likely to be due to the re-distribution of material from the minor to the major axis as a result of the tidal interaction, is described by an outer n ∼ 1.2 Sérsic model. Kim et al. (2012) also fit a double Sérsic model (an inner n = 3.45 Sérsic model plus an outer n = 1.48 Sérsic model) to their light profile which is sampled from R = 118 to 2475. In general agreement with this and the inner n ∼ 4.5 Sérsic model fit presented in Trujillo et al. (2004), our n ∼ 3.5 Sérsic fit to this galaxy's inner light distribution (Figure 7(c)) not only shows the absence of a central luminosity deficit in this galaxy, but is also consistent with its magnitude M_V = −21.11 mag and velocity dispersion σ = 171 km s⁻¹ (see Graham et al. 2001, their Figure 13; Dullo & Graham 2012, their Figure 14). This is in contrast to the single-component n ∼ 8 Sérsic fit by Lauer (2012, their Figure 1).

We also note that, contrary to the claim by Lauer (2012), Dullo & Graham (2012, their Section 4) explicitly noted that the spurious downward departure in the inner light profile of NGC 4486B (relative to the inward extrapolation of its outer Sérsic profile) is due to the presence of a double optical nucleus, rather than a typical depleted core. Coupled with NGC 4458, NGC 4478, and NGC 7213, we therefore have that seven of the 39 galaxies (i.e., ∼18%) classified as "core" galaxies according to the Nuker model analysis by Lauer et al. (2005) do not have central stellar deficits relative to their outer Sérsic profiles and are therefore not identified as "core-Sérsic" galaxies. Such "mismatches" will be most prevalent among galaxy samples fainter than M_B ≈ −20.5 mag that contain spheroids with low Sérsic indices and thus have relatively flat inner cores that are not depleted of stars.

The ATLAS 3D galaxy sample used by Lauer (2012) is dominated by early-type galaxies with magnitudes up to ∼3 mag fainter than M_B = −21 mag—many of which are two-component lenticular galaxies (Emsellem et al. 2011). As such, application of the Nuker model may identify many "cores" (γ < 0.3) among these galaxies which do not actually possess partially depleted cores relative to their spheroid's outer Sérsic profile. The Nuker model classification may therefore substantially blur the actual connection between the dry merger scenario, as described by Faber et al. (1997), and the existence of depleted cores from coalescing BHs. We thus advocate the core-Sérsic model and point readers to additional important reasons for this that are discussed in Graham et al. (2003) and Dullo & Graham (2012).

Figure 8 shows distinct features in NGC 3607 (left), NGC 3706 (middle), and NGC 6849 (right).

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