HIDING IN PLAIN SIGHT: AN ABUNDANCE OF COMPACT MASSIVE SPHEROIDS IN THE LOCAL UNIVERSE

While information about the surface brightness profile decompositions can be found in the papers mentioned in Table 1, we felt that it may be instructive to include an example of how the outer exponential profile can increase the galaxy size over the bulge size. We have somewhat randomly chosen NGC 5419 from Laurikainen et al. (2010). This was chosen because (a) the Laurikainen et al. paper simply contains the greatest number of compact massive spheroids in our Table 1, and (b) this particular galaxy was modeled by Dullo & Graham (2014) as an elliptical galaxy, while they noted that a disk might be present. Sandage & Tammann (1981) did not support the original elliptical galaxy classification in the Second Reference Catalogue of de Vaucouleurs et al. (1976), but instead considered NGC 5419 to be a lenticular galaxy, as did Laurikainen et al. (2010) based on their near-infrared K-band analysis.

Therefore, we re-investigate this galaxy using a Spitzer Space Telescope 3.6 μm image (see Figure 1), which was reduced following the procedures described in G. A. D. Savorgnan et al. (2015, in preparation). The light profile was extracted by allowing the ellipticity and position angle to vary about a fixed center using the IRAF task Ellipse (Jedrzejewski 1987) and is shown in Figure 2.

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Our modeling of the 3.6 μm light profile within 60'' matches the solution to the K-band data in Laurikainen et al. (2010). We also find that a single Sérsic function is inadequate; the curvature of the light profile and the residual light profile reveal the presence of additional components. Figure 2 shows how the addition of an outer exponential and a very faint lens (fit with a Ferrers function) provides a better fit. These were the components employed by Laurikainen et al. (2010). From this, one can see that the half-light radius of the galaxy (${{R}_{{\rm e},{\rm gal}}}=53\buildrel{\prime\prime}\over{.} 6$) is much greater than the half light radius of the inner spheroid (${{R}_{{\rm e},{\rm sph}}}=8\buildrel{\prime\prime}\over{.} 4$). Laurikainen et al. (2010) reported that their bulge+lens+disk model had a bulge Sérsic index n = 1.4 and half-light radius ${{R}_{{\rm e}}}=6\buildrel{\prime\prime}\over{.} 5$. They reported a disk scale length $h=32\buildrel{\prime\prime}\over{.} 3$, while our exponential model has $h=33\buildrel{\prime\prime}\over{.} 1$.

One may wonder if there is also a contribution from an extended envelope around this galaxy due to its location at the center of the poor cluster Abell S753. Indeed, Sandage & Bedke (1994) referred to this galaxy as having an extended outer envelope, and Seigar et al. (2007; see also Pierini et al. 2008) established that intracluster light tends to have an exponential profile, i.e., the same radial decline as seen in disks. However, Bettoni et al. (2001) have reported a rotational velocity reaching 90 km s⁻¹ by the inner 5'', betraying the presence of at least an inner disk. In an extreme scenario, one may speculate that this galaxy has an intermediate-scale disk (the "lens" component in Figure 2, which shows up in both the ellipticity and position angle profiles) plus intracluster stars that produce the near-exponential light profile at larger radii. More extended kinematics would be helpful in discriminating between these options.

The cluster-centric location of NGC 5419 is interesting, and it further prompted us to pursue the suggestion by L. Cortese (2015, private communication) to check on the environment (e.g., field, group, cluster) of our sample. Table 2 shows this information, along with the ${{R}_{{\rm e}}}/h$ size and $B/T$ flux ratios obtained by the papers given in Table 1. While a few of the galaxies are the brightest of their small galaxy group, NGC 1316 (the interacting galaxy Fornax A) is the only other member of a substantial-sized group. This rules out the idea that the compact massive spheroids might be encased in an exponential-like 3D envelope of intracluster light rather than a 2D disk.

Table 2.  Galaxy Properties

Gal.Id.	σ	${{R}_{{\rm e}}}/h$	$B/T$	Environment
Lenticular Galaxies
Laurikainen et al. (2010)
ESO 337-G10	...	0.25	0.41	?
NGC 484	233	0.29	0.62	Group
NGC 1161	295	0.40	0.65	?
NGC 3665	215	0.43	0.58	BGG, NGC 3665 Group (N = 11)
NGC 5266	201	0.23	0.45	Group
NGC 5419	351	0.20	0.24	BCG, poor cluster Abell S753
NGC 7796	259	0.27	0.48	Field
Cappellari et al. (2011); Krajnović et al. (2013)
NGC 4649b	329	0.45	0.32	Virgo cluster (N = 355)
NGC 3640	192	0.56	0.60	BGG, NGC 3640 Group (N = 12)
NGC 5493a	204	...	...	BGG, NGC 5493 Group (N = 2)
G. A. D. Savorgnan et al. (2015, in preparation)
NGC 1316	225	0.08	0.23	BGG, NGC 1316 Group (N = 111)
NGC 1332	321	0.52	0.95	BGG, NGC 1332 Group (N = 22)
Dullo & Graham (2013)
NGC 507	295	0.19	0.32	BGG, poor NGC 507 Group
van den Bosch et al. (2012)
NGC 1277a	333	...	...	Group
Spiral Galaxies
Graham & Worley (2008)
NGC 266	230	0.19	0.24	Field?
NGC 2599	...	0.24	0.51	Field?
NGC 3884	209	0.20	0.22	Abell 1367 cluster (N = 90)
NGC 7490	...	0.23	0.27	Field?
UGC 2862	...	0.11	0.55	Field?
NGC 3147	225	0.33	0.23	BGG, NGC 3147 Group (N = 5)
NGC 6504	185	0.23	0.42	Field?
Laurikainen et al. (2010)
NGC 6646	...	0.28	0.26	Field?

Note. Column 1: Galaxy identification.

^aThe galaxy rather than bulge parameters were used. ^bBulge/disk parameters may not be reliable. ^cNGC 1332 has had its disk fit with a Sérsic model having n = 0.5, for which the scale length $h={{R}_{{\rm e},{\rm disk}}}/0.82$ (rather than ${{R}_{{\rm e},{\rm disk}}}/1.68$ as is the case when n = 1). Column 2: Velocity dispersion (km s⁻¹) from HyperLeda (Makarov et al. 2014), except for NGC 1277 (van den Bosch et al. 2012). Columns 3 and 4: Bulge-to-disk size ratio and bulge-to-total flux ratio, respectively. For the lenticular galaxies (and NGC 6646), values were taken from the respective papers. For the spiral galaxies, the dust-corrected values were derived in Graham & Worley (2008). Column 5: Environment of the galaxy. BCG = Brightest Cluster Galaxy. BGG = Brightest Group Galaxy. N represents the number of galaxies with known radial velocities in the group (Makarov & Karachentsev 2011; Tully et al. 2013). Field? = No group known to authors, and the galaxy appears to be in the field from looking at Digitized Sky Survey images available via NED.

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In Figure 3(a) we do not compare our data with the size–mass relation for early-type galaxies as given by Shen et al. (2003) because of the biases in their data, which are explained in Graham & Worley (2008). Lange et al. (2015) have, however, fit the double power-law model from Shen et al. (2003) to the galaxy size–mass data from several thousand nearby ($0.01\leqslant z\leqslant 0.1$) early-type (morphologically identified diskless) galaxies taken from the Galaxy And Mass Assembly (GAMA) survey (Driver et al. 2011). The galaxy magnitudes had been converted into stellar masses by Taylor et al. (2011), and the effective half-light galaxy sizes derived by Kelvin et al. (2012) who fit single Sérsic models to images in 10 bands (ugrizZY JHK_s). We have taken the K_s-band results from Lange et al. (2015) and show their mass–size relation in Figure 3(a). Given that Figure 6 from Lange et al. (2015) reveals that the double power law cannot fully capture the curvature in the GAMA data at ${{M}_{*}}\;\gt$ (1–2) $\times \;{{10}^{11}}\;{{M}_{\odot }}$—where galaxies have larger radii than the double power-law model—we have therefore additionally included the mass–size relation from Graham et al. (2006); see Equation (2.11) in Graham 2013). While Figure 3(a) reveals that the mass–size relation of local early-type galaxies has larger radii at a given mass than the distant spheroids, it also reveals that the masses and sizes of our local bulges overlap with those of the distant spheroids (Damjanov et al. 2011). Our data appear more clustered in Figure 3(a) simply because we have been stricter with the mass and size limit for our local bulge sample.

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In Figure 3(b) we show the sizes and Sérsic indices of our local compact massive systems and the overlap with galaxies in the redshift interval 1.4 $\lt \;z\;\lt$ 2.7, as given by Damjanov et al. (2011, their Table 2). We have excluded from Damjanov et al. those galaxies with no reported Sérsic index and those fit with an ${{R}^{1/n}}$ surface brightness model having a fixed value of n, such as 4. As with our bulge data, the high-z galaxy data in Damjanov et al. have also been taken from a compilation of different surveys: 17 in their case. Their galaxy selection criteria are thus varied, and it can be seen in Figure 3 to contain a much larger range of sizes and masses than our data. Comparing the data points, we conclude that not all compact, massive spheroids need to have undergone significant structural and size evolution since $z\lesssim 2.5$.

Twenty-one of the 22 systems (20 bulges plus 2 galaxies) are within 90 Mpc, with the additional system at 103.6 Mpc. Excluding this furthest bulge gives a number density of $(6.9\pm 1.5)\times {{10}^{-6}}$ Mpc⁻³ for the sample of 21. All of these systems have stellar masses in the range $0.7\times {{10}^{11}}\lt {{M}_{*}}/\;{{M}_{\odot }}\lt 1.4\times {{10}^{11}}$. Ten of the 13 systems with ${{M}_{*}}\geqslant {{10}^{11}}\;{{M}_{\odot }}$ are within 70 Mpc, giving a similar number density⁴ of $(7.0\pm 2.2)\times {{10}^{-6}}$ Mpc⁻³. It needs to be remembered that these densities are a lower limit because we have not conducted a volume-limited, all-sky survey for compact massive spheroids. However, the ATLAS$^{3{\rm D}}$ survey did sample all of the bright galaxies over half the sky to a depth of 42 Mpc. Given that it contains three compact, massive systems, this corresponds to a number density of $(1.9\pm 1.1)\times {{10}^{-5}}$ Mpc⁻³. This value is 2.75(±58%) times higher, but there is a larger uncertainty assuming Poissonian errors.

While Taylor et al. (2010) reported a reduction, at fixed size and mass, of at least 5000 in the co-moving number density of compact massive galaxies from $z\sim 2.3$ to $z\sim 0.1$, we find that there is a roughly comparable (within a factor of a few) number density of compact massive systems at z = 0 and $z\sim 2.5$. Bezanson et al. (2009) report a number density of $(3\pm 1)\times {{10}^{-5}}$ Mpc⁻³ at this higher redshift, for systems with stellar mass densities greater than one billion solar masses within their innermost sphere of radius 1 kpc (or ${{M}_{*}}\gt {{10}^{11}}\;{{M}_{\odot }},$ ${{R}_{{\rm e}}}\lt 2.88$ kpc). Muzzin et al. (2013, their Figure 5) report a number density of $\sim 5\times {{10}^{-5}}$ Mpc⁻³ at $2\lt z\lt 3$ for all (compact and extended) quiescent galaxies with ${{M}_{*}}\sim {{10}^{11}}\;{{M}_{\odot }}$, in fair agreement with the value of $\sim 4\times {{10}^{-5}}$ Mpc⁻³ for the quiescent galaxies at $z=3\pm 0.5$ with ${{M}_{*}}\gt 0.4\times {{10}^{11}}\;{{M}_{\odot }}$ reported by Straatman et al. (2014). At these high redshifts, it is speculated here that the bulk of the disk formation (which will remove "galaxies" from satisfying the compactness criteria), may be yet to occur, and thus one may have a cleaner sample of "nakedbulges" with which to make a comparison with the number density of bulges in the local universe. At yet higher redshifts the "nakedbulges" may likely still be developing themselves (e.g., Dekel & Burkert 2014).

Barro et al. (2013) report a similar number density as Bezanson et al. (2009) at z = 2.5, even though Barro et al. used a lower stellar mass limit of 0.1 $\times \;{{10}^{11}}\;{{M}_{\odot }}$ for their sample (cf. 1.0 $\times {{10}^{11}}\;{{M}_{\odot }}$ used by Bezanson et al. 2009). Barro et al. reported that their number density increased as the redshift dropped, peaking at about 2.3 × 10⁻⁴ Mpc⁻³ by z = 1.2, before dropping to lower densities as the redshift decreased further. Taken together, this suggests that the most massive, quiescent spheroids were in place first, with the less massive spheroids appearing later at lower redshifts (possibly connecting with the luminous blue compact galaxies forming at $z\lt 1.4$; Guzmán et al. 1997). The above peak density at z = 1.2 is, at least in part, larger than the value we have found because Barro et al.included galaxies having a much broader range in stellar mass than we did. In a separate study, van der Wel et al. (2014) used a stellar mass limit $\gt 0.5\times {{10}^{11}}\;{{M}_{\odot }}$ and found a peak density at $z\sim 1.2$ of 1 × 10⁻⁴ Mpc⁻³.

The mass range sampled in our study only spans a factor of two, from 0.7 to $1.4\times {{10}^{11}}\;{{M}_{\odot }}$. Our number density per unit dex in mass, as recorded in mass functions, is therefore five times higher, giving 3.5 × 10⁻⁵ Mpc⁻³ dex⁻¹ (or $\approx {{10}^{-4}}$ Mpc⁻³ dex⁻¹ if using the volume-limited ATLAS$^{3{\rm D}}$ results) at ${{M}_{*}}\approx {{10}^{11}}\;{{M}_{\odot }}.$ These values are roughly 2–6 times lower than that from Barro et al. (2013), whose galaxy mass range exceeded 1 dex, and roughly 1–3 times lower than that from van der Wel et al. (2014), whose mass range was less than 1 dex. A proper comparison is, however, complicated because the local bulge mass function is not quite flat from 0.1 to 1.4 $\times \;{{10}^{11}}\;{{M}_{\odot }}$, but increases as one moves to the lower-mass end (e.g., Driver et al. 2007). For this reason, our number density for local compact massive bulges, as estimated above, is expected to be less than the actual number density in the decade-wide mass range from, say, 0.14 to $1.4\times {{10}^{11}}\;{{M}_{\odot }}$. Using a constant stellar $M/L$ ratio across this mass range, to convert the bulge luminosity function in Driver et al. (2007) into a mass function, the actual number density in this decade range might be ∼40% higher, although predicting this properly requires knowledge of the slope of the mass function for local compact bulges. We hope to perform a more complete, volume-limited investigation of compact massive bulges within 100 Mpc in a forthcoming paper, enabling us to construct the mass function of local compact bulges with ${{M}_{*}}\gt {{10}^{10}}\;{{M}_{\odot }}$. This can then be better compared with the mass function at higher redshifts.

The WIde-field Nearby Galaxy-cluster Survey (WINGS) has reported the existence of many compact massive galaxies in nearby ($0.04\lt z\lt 0.07$) clusters. Including substantially lower mass galaxies than us, Valentinuzzi et al. (2010) reported that 22% of the WINGS galaxies with $0.3\times {{10}^{11}}\lt {{M}_{*}}/\;{{M}_{\odot }}\lt 4\times {{10}^{11}}$ are compact, with a median size of 1.61 ± 0.29 kpc (and a median Sérsic index of $3\pm 0.6$). For their cluster galaxy sample they derived a lower limit (because they excluded field galaxies) for the number density of $(1.31\pm 0.09)\times {{10}^{-5}}$ Mpc⁻³ within the co-moving volume between z = 0.04 and z = 0.07. This density drops to $(0.46\pm 0.05)\times {{10}^{-5}}$ Mpc⁻³ when they increase their lower mass limit from 0.3$\times {{10}^{11}}\;{{M}_{\odot }}$ to 0.8 $\times {{10}^{11}}\;{{M}_{\odot }}$ (their Table 1). They observed that the bulk of their compact galaxies are lenticular galaxies, which are known to have ∼30% smaller disk sizes in galaxy cluster environments (e.g., Gutiérrez et al. 2004; Head et al. 2014).

Using the Padova Millennium Galaxy and Group Catalogue (PM2GC) spanning $0.03\lt z\lt 0.11$, Poggianti et al. (2013a, 2013b) explored outside of clusters—most galaxies reside in the field or group environment—and concluded that 4.4% of local field and group galaxies with stellar masses $0.3\times {{10}^{11}}\lt {{M}_{*}}/\;{{M}_{\odot }}\lt 4\times {{10}^{11}}$ are compact, and that this 4.4%—most of which are lenticular galaxies—has a median mass-weighted age of 9.2 Gyr, and corresponds to a number density of $(4.3)\times {{10}^{-4}}$ Mpc⁻³, or basically $3.2\times {{10}^{-4}}$ Mpc⁻³ dex⁻¹ given their mass range sampled.

Although the above two studies treated the lenticular galaxies as single-component systems when measuring both their ages and their circularized half-light radii, we suspect that it is the bulges of these galaxies that are the primary, compact massive spheroidal component. In a sense, we may therefore be dealing with the same type of galaxy as they are. While we do not try to resolve the question as to why their compact, massive galaxies were not found by others who searched in the SDSS database, we do provide a couple of comments. Disk galaxies viewed edge-on will of course have circularized half-light radii that are notably smaller than the values obtained if they are viewed face-on. It may be of interest to see if the Valentinuzzi et al. (2010) and Poggianti et al. (2013a, 2013b) detections are dominated by massive, edge-on disk galaxies. It may additionally be interesting to see the results (sizes, masses, number densities) after careful bulge/disk decompositions have been performed for these WINGS and PM2GC samples.

To recap our findings, we measure a lower limit of 3.5 × 10⁻⁵ Mpc⁻³ dex⁻¹ (or $\approx {{10}^{-4}}$ Mpc⁻³ dex⁻¹ if using the volume-limited ATLAS$^{3{\rm D}}$ results) for compact (${{R}_{{\rm e}}}\lesssim 2$ kpc) bulges with ${{M}_{*}}\approx {{10}^{11}}\;{{M}_{\odot }}$.

As noted in the Introduction, within the literature, minor mergers are the overwhelmingly preferred, albeit still problematic, solution to try to transform the compact, massive spheroids at high redshifts into larger spheroids by today. While our discovery of numerous compact massive spheroids at z = 0 suggests that this evolutionary path did not always transpire, we can still ask about minor mergers. If (wet or dry) minor mergers had built a large fraction of each disk around today's compact massive spheroids, then it may be telling us that there is something not quite right with ΛCDM simulations.⁵ This is because the simulations contain somewhat random orientations of satellite galaxies that would not result in the formation of a disk, although see Tempel et al. (2015). However, if minor mergers have built the disks, the observations may then be telling us that most central galaxies have had preferred "Great Planes" on which their minor neighbors were located prior to infall and disk (rather than bulge) building. Some support for this idea can be found in the disks-of-satellites around the Milky Way and Andromeda (Kroupa et al. 2005; Metz et al. 2007; Ibata et al. 2013; Pawlowski et al. 2014). What is of course different in our scenario is that these Great Planes are not just a recent, local phenomenon but would need to have always been present over the past 10–13 Gyr (see Goerdt et al. 2013).

Hammer et al. (2005, 2009) have reasoned that many rotating stellar disks could have been built in major gas-rich mergers, with the disk forming due to the net angular momentum of the gas in the merger event (e.g., Barnes 2002; Robertson et al. 2006). Even in gas-poor (dry) mergers, Naab & Burkert (2003) report that disks can form if the net angular momentum is not canceled out (Fall 1979). Given that rotating spiral galaxies at $z\approx 0.65$ are half as abundant as they are today (Neichel et al. 2008), disk growth since $z=2\pm 0.6$ has obviously occurred, and the outer regions of galaxies with prominent bulges are known to be younger (e.g., Pérez et al. 2013; Li et al. 2015). Arnold et al. (2011) additionally remarked that lenticular galaxies might form through a two-phase inside-out assembly with the inner regions built early via a violent major merger, and wet minor mergers (rather than gas accretion) subsequently contributing to their outer parts.

It is recognized that there have not been enough galaxy merger events to transform the distant compact massive galaxies into today's ordinary-sized elliptical galaxies (e.g., Man et al. 2015), and therefore the above mechanisms cannot, on their own, be invoked to fully explain the growth of disks around the compact massive galaxies seen at high, z such that they have become today's lenticular galaxies with typical disk-to-bulge flux ratios of 3 (i.e., bulge/total $=\;1/4$). Observing higher gas fractions of lower metallicity at higher redshifts, Béthermin et al. (2015) favor large gas reservoirs over major mergers as the cause of the intense star formation observed in massive galaxies at high redshifts. Following the idea of cyclical galaxy metamorphosis (White & Rees 1978; Navarro & Benz 1991; White & Frenk 1991; Steinmetz & Navarro 2002; see also Bournaud & Combes 2002), Graham (2013) advocated earlier suggestions that "cold" gas flows may have contributed to the development of these disks, via either spherical accretion of ∼10⁴–10⁵ K gas (e.g., Birnboim & Dekel 2003; Birnboim et al. 2007) or streams (e.g., Kereš et al. 2005; Dekel et al. 2009; Kereš & Hernquist 2009; Danovich et al. 2014).

This alternative process, which can operate in parallel with mergers (e.g., Welker et al. 2015), involves the accretion of gas from not just the halo (e.g., Kauffmann et al. 1993, their Section 2.7; Kauffmann et al. 1999, their Section 4.5; Genzel et al. 2006) and possible molecular gas reservoirs for some galaxies (e.g., Tacconi et al. 2008; Santini et al. 2014; Chapman et al. 2015) but also cold filamentary flows from the cosmic web (e.g., Ceverino et al. 2010, 2012; Goerdt et al. 2012; Rubin et al. 2012; Stewart et al. 2013). Although such cold gas accretion is yet to be convincingly demonstrated as a common phenomenon, it has the power to subsequently build a disk that transforms into stars. Indeed, it has been noted for well over a decade that the mass of a galaxy could double, due to gas accretion, in just a few Gyr (e.g., Katz et al. 1996; Bournaud & Combes 2002). The discovery of very low metallicity gas (0.02 solar) 37 kpc from a sub-L_* galaxy with solar metallicity by Ribaudo et al. (2011) revealed the presence of such gas, and we now know that there is lots of low metallicity gas in the halos of galaxies (e.g., Lehner et al. 2013; Prochaska et al. 2014). Furthermore, Bouché et al. (2013) have revealed the inflow (as opposed to just presence) of this material around a z = 2.3 galaxy that has kinematics, metallicity, and star formation typical of a rotationally supported disk, and it is such that the gas accretion rate is well matched to the star formation rate (see also Conselice et al. 2013). It has also been established that there is a high spatial covering fraction of Lyα gas clouds within 300 kpc of all galaxy types at high z (Wakker & Savage 2009; Prochaska et al. 2011; Thom et al. 2011; Stocke et al. 2013; Tumlinson et al. 2013), and a review of cool gas in high-z galaxies can be found in Carilli & Walter (2013). In particular, even quiescent elliptical galaxies can have a massive cool reservoir around them (Thom et al. 2012; Tumlinson et al. 2013; Zhu et al. 2014; O'Sullivan et al. 2015). Although not surrounding a pre-existing compact, massive bulge, Prescott et al. (2015) report on the rotation of an 80 kpc Lyα nebula at $z\sim 1.67$ with an implied total mass of $3\times {{10}^{11}}\;{{M}_{\odot }}$ within a 20 kpc radius. While this is a developing field, extensive evidence for gas accretion at many redshifts is reviewed by Combes (2014, 2015b).

It seems likely that the compact massive galaxies would act as natural gravitational seeds around which filaments or streams of cold gas would flow inward and build disks that form stars. The existence of early-type galaxies with dual, large-scale counter-rotating stellar disks (e.g., NGC 4550, Rubin et al. 1992; NGC 3032, Young et al. 2008) supports the idea of disk growth via the accretion of external gas clouds (e.g., Coccato et al. 2015, and references therein), although it may also be due to minor mergers. Presumably feeding is usually from the same direction, given the low frequency of significant (by mass) counter-rotation, and after settling to the mid-plane the rotation is aligned. Small counter-rotating stellar disks and kinematically decoupled cores do, however, reveal that this is not always the case, and gas accretion can form interesting features such as warps, gas-star misalignments, and polar rings (e.g., Briggs 1990; Jog & Combes 2009; Davis et al. 2011; Mapelli et al. 2015). However, rather than only random accretion orientations, Pichon et al. (2011) explain how cold streams can build a disk in a coherent planer manner (see also Danovich et al. 2012, 2014; Prieto et al. 2013; Stewart et al. 2013; Cen 2014; Wang et al. 2014), which is of key importance. A second key aspect is the rapid formation of some of these disks (e.g., Agertz et al. 2009; Brooks et al. 2009), which would naturally explain the older ages of many lenticular galaxy disks today. It also implies significant galaxy growth independent of the merging of distinct entities such as dark matter halos. This process of gas accretion is still observed today in massive early-type galaxies (e.g., Davis et al. 2011).

Disk growth in early-type galaxies is an ongoing phenomenon (e.g., Yi et al. 2005; Kaviraj et al. 2007; Fabricius et al. 2014), albeit at lower levels today as less gas is available (e.g., Combes et al. 2007; Sage et al. 2007; Huang et al. 2012; Catinella et al. 2013). The molecular gas usually resides in kpc-scale, rotating disks (e.g., Inoue et al. 1996; Wiklind et al. 1997; Das et al. 2005; Okuda et al. 2005), as does the Hi gas (e.g., Serra et al. 2012, 2014, and references therein). Young et al. (2008), for example, detail the slow ongoing growth of the disk in NGC 4526, a galaxy whose bulge has a half-light radius equal to 1.43 kpc (Krajnović et al. 2013) and a stellar mass⁶ of $0.55\times {{10}^{11}}$ (which, along with other bulges, was not massive enough to be included in our sample). Perseus A is yet another example that is also still accreting cold gas (Salomé et al. 2006).

As noted in Section 2, NGC 1277, NGC 1332, NGC 5493 and NGC 5845 are examples of local early-type galaxies where the disk does not dominate the light at large radii, as in proto-typical lenticular galaxies. These disks are an order of magnitude larger than nuclear disks and referred to as intermediate-sized disks. Given that the amount of gas accretion can vary, it would be natural for such disks to exist. They are not a new phenomenon (e.g., Scorza & van den Bosch 1998 and references therein), but some readers may not be familiar with their existence. At $z\approx 2$, the lower-mass spheroids, with less gravitational pull, and which likely formed from a smaller overdensity in the early universe, may naturally experience a smaller subsequent supply of gas from cold streams and build their disks more gradually. Free-floating, "compact elliptical" dwarf galaxies (e.g., Huxor et al. 2013; Paudel et al. 2014) might represent spheroids that never acquired a significant disk, while those in the vicinity of much larger neighbors are thought to have been largely stripped of their disks.

The theoretical work of Steinmetz & Navarro (2002, and references therein) suggested that a galaxy's morphology is a transient phenomenon. Galaxies do not simply progress from the "blue cloud" to the "red sequence" (Faber et al. 2007) but can move in the opposite direction. While the latter pathway may not be traversed in full today, because less gas is available, there are fledged examples of galaxies in the "green valley" (e.g., Cortese & Hughes 2009; Marino et al. 2011). Elliptical galaxies may initially be built through major mergers of disk galaxies (and perhaps from a violent disk instability; Ceverino et al. 2015) and then proceed to grow a new stellar disk through gas accretion (White & Frenk 1991), which remains intact until the next significant merger (see Salim et al. 2012 and Conselice et al. 2013 for supporting arguments, and Fang et al. 2012 and Bresolin 2013 for caution in some cases). The number of cycles may, however, be low (i.e., 1 or 2) rather than several (3–5). Evidence for a bulge-then-disk scenario may exist within the Milky Way (e.g., Zoccali et al. 2006). Furthermore, the hierarchical models from Khochfar & Silk (2006), for example, present diskless galaxies at z = 2, which evolve into disk galaxies with a bulge-to-total mass ratio equal to 0.2 by z = 0 due to gas accretion from the halo, cold streams, and minor mergers.

There have recently been reports of infant, premature disks detected in some of the high-redshift, compact massive galaxies (Chevance et al. 2012 and references therein). In a study of 14 compact massive galaxies at $z=2.0\pm 0.5$, van der Wel et al. (2011) reported that 65(±15)% are disk dominated, appearing highly flattened on the sky and having disks with a median half-light radius of 2.5 kpc. This corresponds to a median scale length of 1.5 kpc, which is half the size of disks today, e.g., Graham & Worley (2008, their Figure 3). These high-z disks were observed to harbor compact central components, i.e., bulges. Although most early-type galaxies around us today are known to be lenticular disk galaxies—thanks to studies such as ATLAS3D$^{3{\rm D}}$ (Emsellem et al. 2011)—there are of course still some massive, slow or non-rotating, elliptical galaxies. Some of these may be the "ordinary-sized" elliptical galaxies,⁷ observed at high z, while others likely formed from more recent, major merger events. Some of the "ordinary-sized" elliptical galaxies at high z may have also acquired disks, but they would appear as intermediate-sized disks if insufficient gas was accreted to build a larger-scale disk around an already large galaxy.

Following the deep observations by Szomoru et al. (2010) to verify the compactness of a galaxy at z = 1.91 found by Daddi et al. (2005), we note that future work should be mindful that shallow surveys at any redshift could miss the outer disks of galaxies to varying degrees and may largely just recover the inner bulge if they are particularly shallow. If that was to occur, one would effectively, although accidentally, manage to identify higher number densities of compact massive systems.

The above scenario for disk growth around compact "bulges" requires the massive bulges of nearby disk galaxies to be old. Although beyond the scope of the current investigation, it will be of interest to explore the ages of the bulges and disks in the current sample of galaxies. However, MacArthur et al. (2009) have already shown that bulges in both early- and late-type disk galaxies do indeed have old mass-weighted ages, with less than 25% by mass of the stars being young, second- or third-generation stars built from metal-enriched gas. Based on stellar populations and radial gradients, MacArthur et al. (see also Fisher et al. 1996) concluded that early-formation processes are common to bulges and that secular processes or "rejuvenated" star formation generally contribute minimally to the stellar mass budget of bulges (see also Moorthy & Holtzman 2006; Thomas & Davies 2006; Jablonka et al. 2007), yet it has biased luminosity-weighted age estimates in the past. Such "frostings" of young stars, of up to 25% by mass, can give the impression of positive luminosity-weighted age gradients, i.e., bulges are younger at their centers, and have misled some studies (which assumed a single stellar population) into missing the fact that the bulk of the stellar mass in most bulges is old.⁸ This follows Kuntschner & Davies (1998), who revealed that the obvious lenticular galaxies in the Fornax cluster have ages that are younger than the more spheroid-dominated galaxies in the cluster.

These works imply that the bulk of the stellar mass in today's massive bulges already existed at high redshifts, and therefore these stellar systems should be what we are observing in deep images of our young universe. Curiously, Saracco et al. (2009) reported that there are two kinds of early-type galaxy at $z\approx 1.5$: an old (∼3.5 Gyr) population that needs to experience a factor of 2.5–3 size evolution to have sizes equal to today's early-type galaxies, and a young (∼1 Gyr) population (perhaps those that have recently acquired their disks) that already has sizes consistent with today's population of early-type galaxies. In this regard, it will be interesting to know if their old population is best described with a single Sérsic model, while their young population is better described by a bulge+disk model rather than a single-component Sérsic model. Furthermore, if a younger disk has formed, or bulges developed at different epochs, they may have different initial stellar mass functions (IMFs), resulting in differing composite IMFs for the early-type galaxies today (e.g., Dutton et al. 2013; McDermid 2015, and references therein).

Gradual stellar mass loss due to stellar winds is a part of the aging process for passively evolving spheroids (e.g., de Jager et al. 1988; Ciotti et al. 1991; Jungwiert et al. 2001), as is the conversion of visible stars into dark remnants such as neutron stars and stellar mass black holes. If a fraction x of the initial mass is lost from a galactic system due to stellar winds, or Type Ia supernovae clearing out gas, then there will be an adiabatic expansion because the galaxy is no longer as tightly bound and it will therefore reach a new equilibrium such that its size has increased by $1/(1-x)$ (e.g., Jeans 1961, p. 299; Hills 1980, their Equation (6)). Of course, if any stellar ejecta remains in a galaxy—which seems likely in massive galaxies with strong potential wells—perhaps eventually ending up as hot X-ray gas, then the expansion of the galaxy will be reduced depending on the radial expanse of this gas. After the young stars ($\lt 1$ Gyr) have evolved, stellar winds likely account for just a ≲10% reduction to the stellar mass of the passive, compact massive galaxies seen at $z\sim 2$ (Damjanov et al. 2009; but see Poggianti et al. 2013b). Fan et al. (2008) had previously suggested that AGN feedback may blow out the gas in distant massive galaxies and cause them to expand by factors of 3 or more. Of course, if this had happened, then we would be left having to explain where all of the compact massive bulges in the universe today came from.

Given the smaller half-light radii that early-type galaxies had at higher redshifts, before they acquired their disks, the stellar densities within those half-light radii were 1 to 2 orders of magnitude greater than the stellar densities inside the half-light radii of today's large early-type galaxies. This led Zirm et al. (2007) to conclude that it is a problem for models of early-type galaxy formation and evolution. Buitrago et al. (2008) claimed that within the inner 1 kpc of the high-z galaxies, they have densities equal to globular clusters. This led them to advocate a scenario in which globular clusters and distant compact massive galaxies may have a similar origin, while at the same time suggesting that the more massive halos (not the globular clusters) started collapsing earlier and dragged along a larger amount of baryonic matter that later formed stars. However, they overestimated the typical globular cluster size by a factor of 10/3 and thus underestimated a typical globular cluster's density by a factor of 37, undermining their conclusions.

Bezanson et al. (2009) revealed that the inner regions ($\lt 1$ kpc) of today's early-type galaxies have stellar densities that are 2–3 times lower than those of the distant compact massive galaxies of the same mass. However, the majority of galaxies in our sample have bulge-to-total ratios of 1/2–1/4 (Table 2), while Laurikainen et al. (2010) found an average ratio of 1/4 for their sample of lenticular galaxies. That is, the local massive bulges are 2–4 times less massive than the galaxy within which they reside. In comparing galaxies of the same mass in Figure 2d from Bezanson et al. (2009), one is effectively comparing the high-redshift galaxies with local bulges that are 2–4 times less massive, possibly accounting for the lower density observed in these lower-mass bulges. If one compares the quiescent, compact massive galaxies at high redshift with today's bulges of the same mass, one may find that they have the same density within the inner kpc.

Hopkins et al. (2009) reported that there is no central ($\lt 1$ kpc) density mismatch (van Dokkum et al. 2014). They suggested that "the entire population of compact, high-redshift red galaxies may be the progenitors of the high-density cores of present-day ellipticals," by which they mean spheroids. We, however, consider the evolution to have been very different, such that a 2D disk is built within and around the spheroid that undergoes no substantial size evolution, rather than the continual development of a 3D envelope around a spheroid that effectively undergoes significant size growth.

If there is indeed no evolution of the distant spheroids, then their velocity dispersion should remain the same. Now, if a stellar disk builds within and around them, then the galaxy mass today will have increased. As a result, if one was to compare the velocity dispersions of the distant compact spheroids with the velocity dispersions of z = 0 disk galaxies having the same total stellar mass, one would actually be sampling local bulges that are less massive than the distant spheroids. The local galaxies of the same mass, containing compact bulges of 2–4× lower mass, are naturally expected to have lower velocity dispersions. Indeed, this general behavior has been observed (e.g., Cenarro & Trujillo 2009; Cappellari et al. 2009; Newman et al. 2010).

If one assumes ${{M}_{*}}\propto {{\sigma }^{4}}$, then a 2–4× difference in stellar mass will be associated with a ∼1.2–1.4× difference in velocity dispersion. If one attempts to bypass the photometric stellar mass estimate and use a dynamical/virial mass estimate (${{\sigma }^{2}}{{R}_{{\rm e},{\rm gal}}}$) for the lenticular galaxies, the same issue occurs. This is because of the enhanced ${{R}_{{\rm e},{\rm gal}}}$ value due to the presence of the disk component. If a galaxy's half-light radius is 3–6 times larger than the half-light radius of its central bulge, then the velocity dispersion of the bulge coupled with the galaxy size will produce a galaxy virial mass that is 3–6 times larger than what one would obtain for the bulge. This will act to artificially separate the compact high-z spheroids from local massive bulges in a diagram of dynamical mass versus velocity dispersion. A note to keep in mind is that disk growth, as with envelope growth, may lead to the compression of the original inner bulge and a slight enhancement in the central velocity dispersion (Andredakis 1998; Debattista et al. 2013).

The presence of partially depleted cores in massive spheroids is thought to be a result of major, dry merger events (e.g., Begelman et al. 1980; Faber et al. 1997; Merritt et al. 2007). The large elliptical galaxies with sizes several times that of the high-z, compact massive spheroids, and with a deficit of stars over their inner tens of parsecs to a few hundred parsecs, likely formed this way. The orbital decay of the binary supermassive black hole, created by the galaxy merger, proceeds by slingshotting the central stars out of the core of the newly formed galaxy. However, as noted by Dullo & Graham (2013), the presence of such partially depleted cores in the bulges of massive disk galaxies (e.g., Dullo & Graham 2013) presents a conundrum because these disk galaxies may be unlikely to have formed from such major merger events.⁹ One potential solution is that the bulges may have formed first, and the disks were subsequently accreted and grew (Driver et al. 2013; Graham 2013). It may therefore be interesting to check for partially depleted cores in the current sample of disk galaxies in Table 1. Application of the core-Sérsic model (Graham et al. 2003) to Hubble Space Telescope images—due to their superior spatial resolution over a sufficiently wide field of view—will reveal which bulges have an inner deficit of flux relative to the inward extrapolation of their outer Sérsic light profile. Knowledge of which bulges have partially depleted cores, coupled with information about their stellar age, should shed even further light on the formation history.

Surveying predominantly compact, passive, spheroidal galaxies at $1.4\lt z\lt 2.0$, with ${{10}^{10}}\lt {{M}_{*}}/\;{{M}_{\odot }}\lt {{10}^{11}}$, Cimatti et al. (2008, see van Dokkum et al. 2008 for higher redshifts and higher masses) noted that the galaxy sizes are typically such that ${{R}_{{\rm e}}}\lesssim 1$ kpc and are thus much smaller than early-type galaxies of comparable mass in the present-day universe. However, the bulges of most disk galaxies at $z\approx 0$ have compact sizes with ${{R}_{{\rm e}}}\lesssim 2$ kpc, and many bulges with ${{10}^{10}}\lt {{M}_{*}}/\;{{M}_{\odot }}\lt {{10}^{11}}$ have ${{R}_{{\rm e}}}\lesssim 1$ kpc (e.g., Graham & Worley 2008; Graham 2013). The growth of disks in and around the compact, high-z spheroids could therefore explain their apparent disappearance by today.

This possible explanation may at first glance appear somewhat at odds with the claim in the interesting paper by van Dokkum et al. (2013) that disk models, in which bulges were fully assembled at high redshift and disks gradually formed around them, can be ruled out. However, the first distinction in these two remarks is of course that disks do not simply form around spheroids but are additionally embedded within them, which is why bulge/disk decompositions continue the disk all the way into the centers of galaxies. It would therefore be of interest to perform a bulge/disk decomposition of the average surface density profiles, at different redshift intervals, that were constructed by Dokkum et al. (2013, their Figure 3). This would allow one to check how well their z = 0 Milky-Way-like galaxy profile that they built resembles the Milky Way, and thus to know if their stacked profiles are reliable or perhaps effected by dust or some other issue.¹⁰ A reliable decomposition of an evolving population (free from "progenitor bias") would of course enable one to quantify how much the disk and bulge (including pseudobulge) components have changed between the different redshifts. The second point of distinction is that van Dokkum et al. (2013) were referring to the inner 2 kpc radius of Milky-Way-mass spiral galaxies, rather than ${{10}^{11}}\;{{M}_{\odot }}$ galaxies. The Milky Way has a bulge mass of $0.91\times {{10}^{10}}\;{{M}_{\odot }}$ and a bulge-to-total stellar mass ratio of 0.15 (Licquia & Newman 2014); it also has a half-light radius of 0.66 kpc (Graham & Driver 2007). Therefore, within an inner radius of 2 kpc, the masses of Milky-Way-like galaxies are dominated by the disk rather than the bulge. Due to the greater prominence of bulges in early-type disk galaxies than in late-type disk galaxies (see Figure 21 in Graham 2001), the inner regions of today's massive galaxies—which host the once distant, compact massive spheroids—are expected to have changed less over time, as already observed by van Dokkum et al. (2010, their Figure 6).

Within the bulge-then-disk growth scenario, the existence of the distant massive spheroids having $n\lt 2$ implies that local galaxies with bulges having $n\lt 2$ need not be pseudobulges formed from the secular evolution of a stellar disk. This topic is reviewed in Graham (2013, 2014), where it is noted that bulges with Sérsic $n\lt 2$ need not be pseudobulges even if they are also rotating (e.g., Eliche-Moral et al. 2011; Scannapieco et al. 2011; Keselman & Nusser 2012; Saha et al. 2012; dos Anjos & da Silva 2013; Graham 2014; Querejeta et al. 2015).

In passing, we remark that formation paths in galaxy clusters in which the disks of spiral galaxies fade and lose their pattern, and possibly end up with relatively brighter bulges (e.g., Johnston et al. 2012, and references therein), to become lenticular galaxies can still operate. That is, lenticular galaxies likely have more than one evolutionary path, as can their bulges (e. g., Cole et al. 2000; Springel et al. 2005), and the presence of both classical and pseudobulges in the same lenticular galaxy would seem to support this (e.g., Erwin et al. 2003). At the same time, the preservation, i.e., the lack of evolution, of compact massive spheroids from $z=2\pm 0.6$ until today has implications for studies of the evolution of the black hole–bulge mass scaling relations (reviewed in Graham 2015, and references therein). The ${{M}_{{\rm bh}}}/{{M}_{{\rm bulge}}}$ ratio would not be expected to decrease in these particular systems since ≈$1.4$.

McLure et al. (2013) reported that 44% ± 12% of their $z=1.4\pm 0.1$ sample of relatively passive galaxies (specific star formation rate, sSFR $\leqslant 0.1$ Gyr⁻¹) with ${{M}_{*}}\geqslant 0.6\times {{10}^{11}}\;{{M}_{\odot }}$ have a disk-like morphology. While at face value this claim may appear to support the notion that flattened 2D disks have developed, their morphological (disk-like) claim was based on a Sérsic index divide at n = 2.5 such that they labeled galaxies with $n\lt 2.5$ to be late-type galaxies. They adopted this divide because Shen et al. (2003) had used it to separate the bright, local galaxy population. Shen et al. (2003) could do this because their SDSS sample contained relatively few dwarf early-type galaxies that have $n\lt 2.5$. However, bulges can have $n\lt 2.5$. Therefore, some/many(?) of the galaxies in the sample of McLure et al. (2013) with $n\lt 2.5$ may still be rather "naked bulges," rather than disk-dominated galaxies. Indeed, the similar distributions for their passive sample with $n\lt 2.5$ and $n\geqslant 2.5$ in the size–mass diagram (their Figure 8) would suggest this.

The practice of considering all high-z, compact, massive objects to be disk galaxies if their Sérsic index is less than 2–2.5 is unfortunately rather common (e.g., Hathi et al. 2008; Chevance et al. 2012; Fathi et al. 2012; Muzzin et al. 2012) and may have effectively misled many researchers. For this reason we have provided this cautionary text against this practice.