THE RELATIVE ABUNDANCE OF COMPACT AND NORMAL MASSIVE EARLY-TYPE GALAXIES AND ITS EVOLUTION FROM REDSHIFT z ∼ 2 TO THE PRESENT^*

The epoch between z ∼ 3 and z ∼ 1 appears to be crucial for the assembly of massive galaxies, as many authors find that the number density of galaxies with masses around 10¹¹ M_☉ and larger evolves very rapidly over this period of time (Fontana et al. 2006; Marchesini et al. 2009; Ilbert et al. 2010; Conselice et al. 2011). By redshift z ∼ 1, however, the number density of early-types is comparable to the local one, with an increase of a factor of 1.5 allowed at most (Cimatti et al. 2006; Franceschini et al. 2006; Borch et al. 2006). There is also evidence that a substantial fraction of the massive elliptical galaxies at z > 1.5 are smaller than their local counterparts of the same mass (Daddi et al. 2005; Trujillo et al. 2007; Toft et al. 2007; Zirm et al. 2007; Van Dokkum et al. 2008; Buitrago et al. 2008; Cimatti et al. 2008), whereas some passively evolving galaxies may be already present at redshifts as high as ∼3 (Van Dokkum et al. 2010; Y. Guo et al. 2011, in preparation).

We still lack a comprehensive understanding of the formation of passively evolving galaxies and of their evolution in size and spatial abundance from z ∼ 3 to the present, including the physical mechanisms responsible for the quenching of star formation. Classically, hierarchical models of galaxy formation predict that the evolution of massive galaxies at early epochs is mostly driven by major mergers (e.g., Shankar et al. 2010, 2011) and that some form of feedback, from star formation itself or from active galactic nucleus activity, quenches star formation (e.g., Somerville et al. 2008). But highly turbulent disks with star formation rate (SFR) ∼100 M_☉ yr⁻¹ have been claimed to also be efficient into slowing accreting gas in recent works (Förster-Schreiber et al. 2006; Förster-Schreiber et al. 2009; Genzel et al. 2008). Others have suggested that at later epochs (z < 1), the evolution is dominated by less violent processes, like minor mergers and/or smooth accretion (Van Dokkum et al. 2010), that can possibly explain the size evolution as well (Hopkins et al. 2009). Recently, Peng et al. (2010) have shown that two independent processes are responsible for the quenching, one related to mass (or almost equivalently to the SFR), and another to the environment via the local overdensity, with the former dominating especially at high masses and early cosmic times, whereas the latter dominates at low masses and late times.

Observationally, there is still ongoing debate on the quantitative and qualitative features of the evolution of early-type galaxies (ETGs). For example, the detection of compact size, and thus large stellar density, is mostly based on morphological studies done either using Hubble Space Telescope (HST)/ACS z-band images, which at 1 < z < 2 sample the rest-frame UV and thus might not reflect the morphology of the bulk of the stellar mass (Daddi et al. 2005; Trujillo et al. 2007; Cimatti et al. 2008), or on HST/NICMOS or ground-based near-IR images, which have substantially worse resolution and/or image quality than ACS, and thus are potentially affected by systematic errors (Toft et al. 2007; Zirm et al. 2007; Van Dokkum et al. 2008; Buitrago et al. 2008). Even when taking advantage of modern, high-quality near-IR imagers such as HST/Wide Field Camera 3 (WFC3), only quite small samples have been studied so far (Cassata et al. 2010; Szomoru et al. 2010).

One essential step to map the evolution of passively evolving galaxies is the measure of the distribution function of their size at various cosmic epochs. While such distribution function has been studied in the local universe, at z ∼ 2 the measures remain uncertain. There is evidence that the size of high-redshift ETGs covers a range that overlaps with those in the present-day universe (e.g., Saracco et al. 2010), whereas selection effects might contribute to underestimate the contribution by more extended galaxies in the high-z samples (Mancini et al. 2010). In any case, the mass–size relation of passively evolving galaxies and its evolution with redshift still remains poorly constrained. Even at z ∼ 0, the distribution function of the effective radius of ETGs is not well characterized at the small end, with some groups suggesting that a compact population of early-types could be hidden among unresolved red objects (Shih & Stockton (2011). Moreover, Valentinuzzi et al. (2010a, 2010b) reported evidence of a rich population of compact passive galaxies at z ∼ 0.04 and z ∼ 0.7, and Saracco et al. (2010) pointed out that the number density of z ∼ 2 compact galaxies is comparable with the local density of similarly small early-types.

Recently, various groups have analyzed the morphology of massive ETGs at z ∼ 2 using WFC3 images in the Hubble Ultra Deep Field (HUDF) and/or ERS field (both located within the boundaries of GOODS-South) and found that the size of passive galaxies at z ∼ 2 is almost independent of the wavelength, confirming previous results on the compactness of such galaxies (e.g., Cassata et al. 2010; Ryan et al. 2011; Szomoru et al. 2010). If indeed the rest-frame UV morphology of these galaxies is similar to that at optical wavelength this allows us to use the wider ACS database for statistically significant studies of the distribution function of their effective radius, its dependence on the stellar mass, and its evolution with redshift.

The aim of this paper is to compare the size distribution in the same rest-frame optical for homogeneous samples of ETGs at 0 < z < 2.5, selected in a consistent way, and to constrain the number evolution of normal and compact early-types over the same epoch. In particular, we exploit the GOODS multi-band data set to build a robust sample of passive ETGs at 1.2 < z < 2.5, and a similar sample of galaxies at 0 < z < 1.2. We complement those two with a sample of local ETGs from the Sloan Digital Sky Survey (SDSS) selected using the same criteria. Using the SDSS sample, we establish the local mass–size relation, and we identify local compact ETGs. Classically, authors in literature consider compact any galaxy 1σ below the local SDSS relation (Valentinuzzi et al. 2010a, 2010b; Saracco et al. 2010). This definition of compactness implies that 16% of the local galaxies are compact. In this paper, we use this definition, but we identify as well a class of ultra-compact early-type (at all redshifts) with size 0.4 dex below the local average relation. Virtually, there are no such dense galaxies in the local universe. With the aim of constraining the evolutionary path that ETGs follow from z ∼ 2 to the present, we compute the mass–density in normal, compact, and ultra-compact early-types at 0 < z < 2.5.

The issue that we try to clarify in this study is to what extent the evolution of the average mass–size relation with cosmic time is driven by the size growth of individual galaxies or by the progressive appearance of ETGs with larger size, as suggested by Valentinuzzi et al. (2010b).

Throughout the paper, we use a standard ΛCDM cosmology, with Ω_Λ = 0.7, Ω_M = 0.3, and H₀ = 70 km s⁻¹ Mpc⁻¹, and we assume a Salpeter initial mass function (IMF; Salpeter 1955).

The Great Observatories Origins Deep Surveys-North (GOODS-N) and GOODS-South (GOODS-S), centered on the Hubble Deep Field North (HDFN) and the Chandra Deep Field South (CDFS), respectively, provide an unique resource of data to study the distant universe. The two fields cover a total area of about 300 arcmin², and have now been imaged with all the largest available telescopes (Hubble, Spitzer, Very Large Telescope (VLT), Chandra, XMM-Newton, Herschel, Canada–France–Hawaii Telescope (CFHT)). The GOODS HST Treasury Program (Giavalisco et al. 2004) provides ultradeep high-resolution images in the B-, V-, i- and z-bands. Deep ground-based imaging in the U-band is provided by VIMOS/VLT for the CDFS (Nonino et al. 2009), and at the Kitt Peak National Observatory for the HDFN. Moreover, VLT/ISAAC imaged the CDFS in J-, H- and K-bands, while CFHT/WIRCAM imaged the HDFN in J- and K-bands (L. Lin et al. 2011, in preparation; also see Wang et al. 2010). Ultradeep Spitzer/Infrared Array Camera imaging is also available in the 3.6, 4.5, 5.6 and 8.0 μm NIR channels.

We built a multiwavelength catalog (GUTFIT, Grand Unified TFIT catalog) for each of the GOODS-N and GOODS-S using the TFIT procedures by Laidler et al. (2007). This procedure allows us to point-spread function (PSF) match images having different resolutions, and uses the ACS/z-band (version 2.0) as detection image. The positions and profiles of galaxies in the ACS/z-band high-resolution image are used as a prior to reconstruct the flux in the lower resolution images. This is useful for objects that are deblended in the high-resolution images but are close enough in the sky to overlap in the low-resolution ones. In these cases, TFIT is able to reconstruct the flux of each object, and is accurate down to the limiting sensitivities of images (Laidler et al. 2007).

We included all the WFC3 data available in the GOODS-S field to 2010 July, namely the HUDF observations (GO 11563, PI: Illingworth) and the Early Release Science Program 2 (ERS2: GO 11359. PI: McConnell; see Windhorst et al. 2011 for further details). The former observed one WFC3 field (∼4 arcmin²) centered in the HUDF in the F105W (Y), F125W (J), and F160W (H) filters, imaged, respectively, for 16, 16, and 28 orbits, reaching 1σ fluctuations of 27.2, 26.6, and 26.3 AB arcsec⁻² in the three bands, respectively. The latter covers 40 arcmin² on the north part of the GOODS-S field, imaged with the same filters as the HUDF/WFC3, with integration times of 2, 2, and 3 orbits, respectively, for the F105W (Y), F125W (J), and F160W (H) filters, producing 1σ fluctuations of 25, 24.4, and 24.1 AB arcsec⁻² in the three bands, respectively. We used a version of these data sets that had been processed as described in more detail in Koekemoer et al. (2011), which were combined using MultiDrizzle (Koekemoer et al. 2002) to a 006 pixel scale, aligned to the existing GOODS and HUDF astrometric grid, and obtaining a PSF of ∼016 in our resulting WFC3 images.

The sample was complemented with the 6000 spectroscopic redshifts available to date (3000 in the south and 3000 in the north), among which 2500 are at z > 1 (Cimatti et al. 2008; Vanzella et al. 2008; Popesso et al. 2009).

We fitted the spectral energy distribution (SED) of the galaxies in the two samples to measure accurate photo-z, using the PEGASE 2.0 templates (Fioc & Rocca-Volmerange 1997). By comparing photo-z and spectro-z, we estimate that the scatter of our photo-z is of the order of σ[Δz/(1 + z)] ∼ 0.04.

Once a redshift has been assigned to each galaxy (either spectroscopic or photometric), we fitted the SEDs from the UV to 8 μm to a set of models by S. Charlot & G. Bruzual (2009, in preparation, CB09 hereafter) in order to get accurate measurements of the stellar mass, E(B − V), age, and SFR of the sources. In particular, we use a Salpeter IMF (Salpeter 1955) with lower and upper masses of 0.1 and 100 M_☉, we apply the Calzetti law (Calzetti et al. 2000) to describe the dust extinction, and we use exponentially declining star formation histories (SFHs). Maraston et al. (2010) showed that these models tend to overestimate the SFRs and underestimate stellar masses for a sample of star-forming galaxies at z ∼2, and that exponentially increasing SFHs instead give less biased results. We will explore if such biases are present for ETGs as well in a forthcoming paper. The stellar mass that we derive does not include the mass loss from stars, but includes the stellar mass of remnants (white dwarfs, neutron stars, etc.). The specific star formation rates (SSFRs), i.e., the SFR for unit mass, are derived by dividing the SFRs by stellar masses. The stellar masses (and all the derived quantities) based on different IMFs that we cite and use as a comparison throughout the paper were homogenized to match our assumptions, using the offsets measured by Salimbeni et al. (2009): log (M_CB09) = log (M_BC03) − 0.2 and log (M_Salp) = log (M_Chab) + 0.25, where BC03 stands for Bruzual & Charlot (2003). This process of homogenization is essential to ensure meaningful comparison among different samples at different redshifts.

We then extracted our sample of passive galaxies, selecting only objects with stellar mass M > 10¹⁰ M_☉ and SSFR<10⁻² Gyr⁻¹ at 0 < z < 2.5. These criteria ensure that only the most massive and less star-forming objects at those redshifts are selected. This selection has resulted in a sample of about 900 candidate ETGs at redshifts between ∼0.1 and ∼2.5. As we want to have an optical high-resolution image for each candidate, we kept only those z > 1.2 galaxies that lie within either the ERS or HUDF WFC3 areas.

We visually classified both the z < 1.2 and z > 1.2 samples in the z- and H-bands, respectively, and we kept only galaxies with a spheroidal morphology, i.e., galaxies with no signs of asymmetry and centrally concentrated. About 60% of all passive galaxies were classified as morphologically spheroidal and were kept in the sample. We also checked the Spitzer/MIPS images, and we found a negligible fraction of objects detected at 24 μm (∼10 objects at z < 1.2 and 2 at z > 1.2) that we removed from the sample. In the end, we end up with 563 passive galaxies, 52 of which are at z > 1.2. We stress once again that the 511 early-types at z < 1.2 are extracted from the 300 arcmin² of GOODS-S and N, while the 52 at 1.2 < z < 2.5 are extracted from the ERS and HUDF WFC3 fields (for a total area of 49 arcmin²). Figure 1 shows the redshift distribution in the highest redshift bin, 1.2 < z < 2.5, peaked around z ∼ 1.6. Among the 52 galaxies in this redshift range, 20 have spectroscopic redshifts.

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In Figure 2 we show the stellar mass as a function of the ACS/z-band magnitude for galaxies at z > 1.2, with the aim of assessing the incompleteness of our selection at those redshifts. For three redshift bins (1.2 < z < 1.6, 1.6 < z < 2, and 2 < z < 2.5) we compare the stellar mass vs. m_z of objects in the sample with the models used to fit their SEDs. By definition, we can detect in our sample only galaxies falling between the two diagonal lines in Figure 2, which represent the bluest and reddest models. We used a Monte Carlo approach, simulating galaxies with deVaucouleurs profiles and different sizes, to establish the detection limit of the z-band imaging version 2.0 that is used by GUTFIT as detection image. The objects are then placed on the real z-band images, and the same SExtractor procedure used to extract real objects is run on the simulated images. Ignoring for now the dependence of the completeness on the size of the galaxies (which will be discussed in Section 4), we find that our selection achieves 80% completeness at m_z = 26.5 for compact objects. At 1.2 < z < 1.6 the mass vs. m_z relation for the reddest model and the 80% completeness magnitude intersect around M/M_☉ = 10¹⁰: this implies that up to z ∼ 1.6 we detect all passive galaxies with any color down to M/M_☉ = 10¹⁰. At higher redshift the model and the 80% completeness line intersect at higher masses, implying that our selection misses part of the galaxies with M/M_☉ > 10¹⁰. In particular, at 1.6 < z < 2 and at 2 < z < 2.5 our sample is complete only down to M/M_☉ > 10^10.5 and M/M_☉ > 10^10.8, respectively.

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For both samples we used the GALFIT package (Peng et al. 2002) to fit the light profile in the rest-frame UV and optical to the Sérsic model:

$$\begin{equation} I(r)=I_e\exp \left\lbrace -b_n\left[\left(\frac{r}{r_e}\right)^{1/s}-1\right]\right\rbrace, \end{equation} \tag{ 1 }$$

where I(r) is the surface brightness measured at distance r, I_e is the surface brightness at the effective radius r_e, and b_n is a parameter related to the Sérsic index s. For s = 1 and s = 4 the Sérsic profile reduces, respectively, to an exponential and deVaucouleurs profile. Bulge-dominated objects typically have high s values (e.g., s > 2) and disk-dominated objects have s around unity. Ravindranath et al. (2006), Cimatti et al. (2008), and Trujillo et al. (2007) showed that GALFIT yields unbiased estimates of the Sérsic index and effective radius for galaxies with a signal-to-noise ratio (S/N) >10 and r_e > 003, independently of the redshift of the source, thus demonstrating that surface brightness dimming is not an issue for this kind of study.

The PSF was obtained in each passband needed by averaging well-exposed, unsaturated stars. We run GALFIT, experimenting on various sizes of the fitting region around each galaxy, and with the sky either set to a pre-measured value or left as a free parameter. We verified that the sizes and Sérsic indices do not vary by more than 10% in the various cases. The values that we show throughout the paper were obtained with a free sky and 6 × 6 arcsec² fitting regions. Any close-by object detected by SExtractor within each fitting region was automatically masked out during the fitting procedure.

Finally, we selected a sample of local galaxies from the SDSS, for which masses, SFRs, and morphological parameters are available in the literature. In particular, we combined the MPA SDSS DR7 catalog, which contains stellar masses and SFRs (Kauffmann et al. 2003; Brinchmann et al. 2004) with the DR7 NYU Value-Added Galaxy Catalog, which contains the GALFIT Sérsic best fit to the u, g, r, i, and z SDSS images (Blanton et al. 2005). We defined the local sample of massive and passive ETGs by applying the same criteria used for the high-z ones: stellar mass M_☉ > 10¹⁰ and SSFR <10⁻² Gyr⁻¹. Instead of visually inspecting the whole sample, we eliminated the disk-dominated objects removing all objects (5% of the total) with Sérsic index s < 2 in the r-band. We verified with a random sample of 200 SDSS galaxies that the contamination of disk-dominated objects among objects with s > 2 is below 5%.

In Figure 3 we compare the Sérsic indices and the physical sizes in the UV and optical rest frames, for the high and low-redshift samples. Since the errors on the sizes and Sérsic indices given by GALFIT are the formal errors derived by the fitting procedure and do not take into account any systematic uncertainty, in this figure and in the following we set the error bars to a minimum value of 20%. For the low-redshift sample we restricted the analysis at z > 0.6, and we used the ACS v-band and z-band, matching the rest-frame UV and optical, respectively. We did not include galaxies at lower redshift, as the UV rest frame at z < 0.6 would be matched by the ACS/B-band, which provides a worse S/N than the other ACS bands. As we already mentioned in the previous section, the z ∼ 2 sample contains the 52 galaxies for which the WFC3 imaging is available: at that redshift, the z- and the H-bands correspond, respectively, to the rest-frame UV at ∼3000 Å and optical at ∼5700 Å. First, 95% of the passive galaxies at z < 1.2 and z ∼ 2 have a Sérsic index s > 2, both at UV and optical wavelengths. This is not surprising, as the sample has been restricted to contain only visually classified spheroidals. Second, the sizes measured in the UV and in the optical correlate almost perfectly with each other, with a scatter smaller than ±20%. The Sérsic indices in the two rest-frame bands correlate as well but show a larger scatter (∼40%). However, we do see systematic offsets for both sizes and Sérsic indices in the two rest frames, which become more evident when checking the fractional differences between optical and UV, shown in the insets of Figure 3. We see that on average galaxies at 1.2 < z < 2.5 have sizes 20% smaller and Sérsic indices 25% larger in the optical than in the UV rest frame. Similarly, galaxies at 0.6 < z < 1.2 galaxies have sizes 10% smaller and Sérsic indices 10% larger in the optical than in the UV rest frame.

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This reinforces our previous result presented in Cassata et al. (2010), where we showed a similar trend for the subset of galaxies at z ∼ 2 lying in the HUDF, and it is in good agreement with other studies of ETGs at z ∼ 2 (McCarthy et al. 2007; Trujillo et al. 2007; Ryan et al. 2011), as well as at lower redshift (Papovich et al. 2003; Cassata et al. 2005).

Interestingly, these biases basically imply that ETGs at z > 1.2 show a negative color gradient, with the center being redder than the outskirts. Early-types at lower redshift show a similar, but shallower, color gradient. This is in very good agreement with the results by Guo et al. (2011), who found negative color gradients for six passive galaxies in HUDF, steeper than those observed in local ETGs.

Based on these evidences, we can conclude that in the whole 0 < z < 2.5 interval the morphological K-correction is weak for passive spheroidals that have already ended their star formation activity.

In Figure 4 we show the mass–size relation for the 52 galaxies at 1.2 < z < 2.5 selected in the ERS+HUDF WFC3 fields, in the same three redshift bins of Figure 2. The sizes have been measured by GALFIT in the F160w filter, which at these redshifts corresponds to the optical rest-frame regime. We plot as well the mass–size relation for local ETGs drawn from the SDSS, in the same optical rest frame. We stress that here the mass measurements were homogenized to a Salpeter IMF (see Section 2 for details). The relation for SDSS passive galaxies is found to be in good agreement with results by Shen et al. (2003), which are widely used by many authors as a reference at z ∼ 0. At all redshifts, we call ultra-compact any ETGs 0.4 dex smaller than local SDSS galaxies of the same mass, and compact any galaxy 1σ below the local relation. The first definition comes out naturally as the maximum size without a counterpart in the local universe (see Section 5); the second is the least strict definition of compactness used in the literature and in this way we can compare our measurements with others. The normal ETGs are those lying on top of or above the local relation. If we define the mean mass density within the half-light radius as

$$\begin{equation} \Sigma _{50}=\frac{0.5 M_*}{\pi r_e^2}, \end{equation} \tag{ 2 }$$

we note that the local relation is roughly parallel to the loci of constant Σ₅₀. Compact and ultra-compact ETGs have mass densities Σ₅₀ ≳ 3 × 10⁹ M_☉ kpc⁻² and Σ₅₀ ≳ 1.2 × 10¹⁰ M_☉ kpc⁻², respectively.

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For each redshift bin we show the region of the plane where our selection detects at least 80% of the objects. To build this region we took the reddest template available in our sample, for which we know, at every redshift, the z-band magnitude as a function of the stellar mass (see Figure 2). We combine this with the output of the Monte Carlo simulation that we used to assess the completeness of the z-band detection images: in particular, we know the fraction of retrieved objects as a function of the magnitude m_z as well as of the half-light radius r_e. Finally, we built, at each redshift bin, the locus of the 80% completeness limit in the stellar mass vs. r_e plane. The detection fraction at smaller masses or larger sizes of this model drops really quickly: in practice, objects to the left of this line cannot be detected by our selection method (the few objects lying out of the forbidden region are bluer than the extreme template we used for this exercise); on the other hand, this work ensures that we detect at least 80% of the objects lying to the right of the line. At 1.2 < z < 1.6, our sample is complete down to M = 10¹⁰ M_☉ (as already discussed in Section 2 and Figure 2) and up to r_e ∼ 3–10 (depending on the mass). At 1.6 < z < 2 the limit moves to higher masses, but still we can detect 80% of the galaxies with M > 10^10.4 M_☉ and sizes r_e ∼ 3–10. Finally, at 2 < z < 2.5 we can detect 80% of the galaxies with M > 10^10.8 M_☉ and sizes r_e ∼ 3–10.

The first interesting result is that at 1.2 < z < 1.6, 1.6 < z < 2, and 2 < z < 2.5, about 65%, 95%, and 100%, respectively, of ETGs are more than 1σ below the local relation, and that about 25%, 50%, and 80%, respectively, are ultra-compact, according to our definition. The evolution of these fractions between 1.2 < z < 2.5 seems to be real: in fact, even considering only the part of the plane where the detection is higher than 80%, the result still holds. In particular, at M ≳ 10^{10.6 − 8} M_☉, we should detect "normal" ETGs with r_e ∼ 2–4 kpc at z > 1.6, if they were present, but we detect none. However, since at z > 1.6 we might progressively miss more and more large galaxies, it is possible that the compact and ultra-compact fractions at those redshifts are slightly overestimated. In the following sections and figures, in order to improve the statistics, we will combine the three redshift bins of Figure 4 in one. Note that the absence in our sample of very massive galaxies with large size is due to their rarity, as with a surface density of one every ∼500 arcmin² (Mancini et al. 2010) one does not expect to find any in the 40 arcmin² covered by the WFC3 data.

At 1.2 < z < 2.5, passive galaxies appear to be on average three to five times smaller than local counterparts of the same mass. This result is in good agreement with our previous findings in Cassata et al. (2010) and with Ryan et al. (2011), obtained with WFC3 in the ERS and/or HUDF surveys. This result is also in agreement with previous studies at high-z using NICMOS data (Toft et al. 2007; Zirm et al. 2007; Van Dokkum et al. 2008; Buitrago et al. 2008) and ACS data (Trujillo et al. 2007; Cimatti et al. 2008). However, we do not find evidence for a population of "normal" passive z ∼ 2 galaxies as abundant as the one presented by Saracco et al. (2009, 2010): they claim that ∼60% of all early-types at 1 < z < 2 are indeed on top of the local relation. This discrepancy may in part be due to the slightly different redshift interval they use: if we select passive galaxies in the same redshift interval used by Saracco et al. (2010), 0.9 < z < 1.92, we find a fraction of compact galaxies of ∼60%. Moreover, we note that Saracco et al. (2009) claim that the normal early-types at z ∼ 2 (i.e., those lying on the local relation) have much younger ages than the compact ones. It is possible that we do not select such young ETGs because of our very conservative SSFR selection (SSFR < 10⁻² Gyr⁻¹). We also note that Mancini et al. (2010) find a predominance of normal-size ETGs in a sample of 12 very massive such galaxies at 1.4 < z_phot < 1.7, with M > 2.5 × 10¹¹ M_☉ (Chabrier IMF), a mass range not reached by the present sample.

We thus confirm that passive galaxies at z ∼ 2 are on average smaller than local counterparts, at least in the mass range 10¹⁰ < M/M_☉ < 10¹¹ in which our sample is representative, but we also confirm that compact and normal-size galaxies coexist up to this high redshift. The aim of this work, however, is to follow the global evolution of the passive galaxies in the mass–size plane from z ∼ 2.5 to z ∼ 0, using for the first time a homogeneous and complete data set. The evolution at z < 1.2 is illustrated by Figure 5, where we show the mass relation for four redshift bins: 0.3 < z < 0.68, 0.68 < z < 0.95, 0.95 < z < 1.2, and 1.2 < z < 2.5 (the fourth combines together the three redshift bins of Figure 4). It is evident that the average mass–size relation evolves continuously from z ∼ 2 to z ∼ 0. This migration is almost complete by z ∼ 0.4, as shown in the first panel of Figure 5, where the distribution of galaxies somehow overlaps with the z ∼ 0 SDSS relation (although the scatter is larger for the 0.3 < z < 0.68 galaxies). The fraction of "compact" galaxies, defined as the galaxies that at each redshift lie 1σ below the local relation (the gray strip in Figure 5) drops from z ∼ 2 to z ∼ 0 following such evolution, as we will see in more detail in the next section.

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Figure 6 shows the evolution of the average size of passive galaxies between z ∼ 2 and z ∼ 0 for three different mass intervals: 10¹⁰ < M/M_☉ < 10^10.5, 10^10.5 < M/M_☉ < 10¹¹, and M/M_☉ > 10¹¹. We stress that at 1.2 < z < 2.5 the sample is only complete down to M/M_☉ = 10^10.8.

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It is clear, once again, that the evolution is faster at z > 0.6 (or age of the universe <6–8 Gyr), while at z < 0.6 the average sizes remain almost unchanged. Our results are in quantitative agreements with Stott et al. (2011), who claimed that the average size of the most massive ETGs increases by 30% from z ∼ 1 to z ∼ 0. The shape of the evolution, in a logarithmic plane, is similar for the three mass bins, so the fractional size increment as a function of the cosmic time appears to be independent of the stellar mass. This implies that on a linear scale the size evolution is faster for the most massive galaxies than for less massive ones, in agreement with Ryan et al. (2011).

We note also that the evolution of the average size from z ∼ 2 to z ∼ 0 is in qualitative agreement with the prediction by Naab et al. (2009), who modeled the formation and evolution of a passive galaxy with a final mass of 1.5 × 10¹¹ M_☉ in a high-resolution hydrodynamical simulation. In such a simulation, the mass of the galaxy increases by a factor of two from z ∼ 2 to z ∼ 0 through a series of minor merger events, which at the same time are responsible for the decrease of the stellar density and increase of the size throughout the same redshift interval. The observed size evolution is not well reproduced by the model of Khochfar & Silk (2006), who used a semi-analytical technique in which the size evolution is the result of the amount of cold gas available during major merger events.

In the previous section, we have observed that the average mass–size relation of passively evolving ETGs undergoes significant evolution from z ∼ 2 to the present.

In principle, one can imagine that the evolution is driven by two independent mechanisms: one is the progressive appearance, as time evolves, of new ETGs due to the cessation of star formation activity; the other is the evolution of galaxies that are already passive, and whose stellar populations remains mostly passive, but whose mass and size change as the result of merging and interactions with other galaxies, passive or otherwise. Some models including these effects have been proposed recently; Khochfar & Silk (2006) suggested that the observed size evolution of passive galaxies can be explained by the variation of the amount of cold gas available during the major merger events that originate ETGs: the most massive ones formed at high-z, when major mergers were more gas rich than at later epochs. Naab et al. (2009), on the other hand, introduced a model in which the size of a passive galaxy increases, as time goes on, through the continuous merging activity with low mass objects.

At any redshift, the appearance of new passive galaxies modifies the mass–size relationship depending on the mass and size distribution of the galaxies that become passive. On the other hand, the morphological transformation of the old passive galaxies contributes to the modification of the mass–size relationship depending on how galaxies accrete stellar mass and/or grow in size, for example, either increasing stellar mass but remaining unchanged in size, or also growing by "puffing-up" (e.g., Hopkins et al. 2009).

Van der Wel et al. (2009) found that in the local universe small passive galaxies with M > 10¹¹ M_☉ are older than the larger ones, implying that at higher redshift such larger galaxies gradually disappear. They suggest that this effect, together with some dry merging activity, may account for the observed size evolution from z ∼ 2 to z ∼ 0.

In this paper, we document the evolution of the mass–size relation in terms of the relative importance of the size growth of individual passive galaxies and the appearance of new large ETGs at more recent epochs. For this purpose, we constrain the number density of ETGs for different sizes as a function of the redshift. We stress that as of the present the evidence that compact ETGs are more common at high-z than in the local universe is mainly based only on the fact that their "fraction" increases with z, irrespective of the fact that the total number of ETGs is not constant throughout the life of the universe (e.g., Trujillo et al. 2009). Nevertheless, some authors (Valentinuzzi et al. 2010a, 2010b; Taylor et al. 2010; Saracco et al. 2010) have compared the number density of compact ETGs at z ∼ 2 and z ∼ 0, but they used non homogeneous samples of ETGs selected with different techniques at high- and low-z. In this work, for the first time, we select in a homogeneous way a mass complete sample of ETGs and we measure the number density of compact and normal ETGs throughout the entire 0 < z < 2 redshift range.

We used a simple V/V_max formalism to measure the number and mass densities in early-types with M > 10¹⁰ M_☉ in the same four redshifts of Figure 5 and for the local SDSS sample at z ∼ 0. Our sample is complete down to this mass limit just to z = 1.6, while at z > 1.6 the sample is only complete down to M = 10^10.8 M_☉ (see Figure 2). The V/V_max, however, takes into account such incompleteness and corrects for it. In particular, our method assumes that the density of galaxies in the yellow region of Figure 2 is the same as the one that we measure for galaxies with m_z < 26.5.

In Figure 7 we show the size distribution of ETGs in the same four redshift bins as Figure 5, scaled to the number density of galaxies in each bin and compared with the distribution of galaxies in the local universe derived from our SDSS sample. For each galaxy in the GOODS and SDSS sample we calculated the ratio of its size to the average size of SDSS ETGs with the same stellar mass, and then we plotted the histograms of such a ratio. The local size distribution is almost perfectly lognormal, with virtually no ultra-compact ETGs (e.g., galaxies with sizes 0.4 dex smaller than the local average). However, some authors suggested that a compact population of ETGs could be hidden among unresolved red objects in SDSS, and thus their number density could be somewhat underestimated (Valentinuzzi et al. 2010a; Shih & Stockton 2011). The size distribution at higher redshift is approaching a lognormal as well, even though it is broader than the z ∼ 0 one. The standard deviation of the distribution is in fact σ ∼ 0.22–0.26 at 0.3 < z < 2.5, while it is σ ∼ 0.17 at z ∼ 0. This effect might be due to the fact that z > 0.3 size measurements are noisier than the z ∼ 0 ones, thus producing a broader distribution.

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The bottom right panel of Figure 7 shows that at the same stellar mass ETGs at 1.2 < z < 2.5 are on average 0.5 dex smaller than their local counterparts. This indicates that ETGs assembled at those epochs are preferentially small. Note that we are not suggesting that the size distribution at high redshift is truncated: galaxies with large sizes become rarer at z > 1.2, implying that surveys with larger area coverage than ours are required to find them in significant numbers (e.g., Mancini et al. 2010).

By redshift z ∼ 1, the number density of ETGs has increased by a factor of five (see also Figure 8). We note that the number density of ETGs increased significantly at all sizes from 1.2 < z < 2.5 to 0.95 < z < 1.2: if for a moment assume that the galaxies already present at z > 1.3 do not grow in size, the ETGs formed during this epoch would have a size distribution spanning from −0.5 dex smaller to 0.5 dex larger than local counterparts. This indicates that the new galaxies formed over this period have typically larger sizes than those already present at z > 1.2. Even though the size distribution in the 0.95 < z < 1.2 bin is significantly different than the local one, the number density of galaxies 0.3 dex larger than local counterparts is now similar to the local value.

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The evolution at later epochs is much milder, with the histogram progressively skewing towards larger sizes, and with the total number density of ETGs increasing by a factor of ∼1.5. The ultra-compact objects, i.e., those with size 0.4 dex smaller than local counterparts, gradually disappear, while the number of galaxies with sizes comparable to the local value (log (r_e)  −  log (< r_e > _{z = 0}) ∼ 0) steadily increases. This indicates that in this phase the smallest galaxies grow in size, and that the new galaxies formed have sizes comparable to the local counterparts. We note that the evolution in the lowest redshift bin is not yet complete: even though the peak of the histogram is close to the peak of the local SDSS one, and the tail at large size is quite similar to the local one, still some ultra-compact galaxies are present. In the next 5 Gyr, i.e., between z ∼ 0.5 and z ∼ 0, they keep growing in size and reach the present distribution, with essentially negligible new ETGs added (the area enclosed by the two histogram is almost the same; see also Figure 8). As already noted before, the size distribution at z ∼ 0 is much narrower than that at 0.3 < z < 2.5: this can be in part due to the errors on the size measurements at high-z. However, while the distribution at large sizes is quite similar at z > 0.3 and z ∼ 0 (and the small difference can be explained with a 5% of outliers), the excess of small galaxies at z > 0.3 is much more significant, and, if not true, would imply an unlikely large number of small-size outliers (50% of the objects at z > 1.2 and 15%–20% at 0.3 < z < 1.2.

Figures 8 and 9 show the evolution of the number density n* and stellar mass density ρ* contributed by normal, compact, and ultra-compact ETGs with M > 10¹⁰ M_☉ as a function of redshift and cosmic time, together with the evolution of the fraction of passive galaxies that are also compact and ultra-compact (bottom panel in Figure 8). The data at 〈z〉 =0.1 have been derived using the SDSS local sample defined in Section 2. Our high- and low-z samples probe ∼6 Gyr of cosmic time, from the epoch when the universe was 4 Gyr old to the epoch it was 10 Gyr old. Including the point at z ∼ 0, we can follow the evolution up to 13.6 Gyr after the big bang.

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In order to estimate a reliable error to assign to the mass and number density at each redshift we used a simple Monte Carlo simulation. In particular, we built 1000 realizations of our sample by perturbing the stellar mass of each galaxy assuming a typical (quite conservative) random error of ±0.4 dex, and we thus measured 1000 realizations of the mass density as a function of the redshift. In Figures 8 and 9 we use the median and standard deviation of 1000 such measurements as the value of the mass density and relative error, which thus do not include any estimate of the cosmic variance.

We compared our measurements with results in the literature for samples of similarly selected passive galaxies. In particular, we took the best-fit Schechter parameters by Ilbert et al. (2010), Borch et al. (2006), and Bell et al. (2003), we homogenized their masses to our assumptions, and we integrated their Schechter function down to our mass limit (M_* > 10¹⁰ M_☉) in order to have homogeneous measurements. However, since the mass functions of passively evolving galaxies all have moderate slopes at low mass values, both the number density n* and the mass density ρ* are dominated by galaxies around M*, that is typically M* ≃ 10^10.6 M_☉ (Ilbert et al. 2010; Peng et al. 2010). Thus, the contribution to the number and mass density of galaxies with M* < 10¹⁰ M_☉ is negligible, and the values presented here can be considered total values. The measurements by Saracco et al. (2010) are instead for galaxies with ∼4.5 × 10⁹ M_☉, but again this different limit should not affect our comparison. The incompleteness of our sample at z > 1.2 does not strongly affect the conclusions of this discussion. Even if we eliminated all galaxies with z > 1.6 (the redshift at which the sample is complete down to M = 10¹⁰ M_☉), we would have found a comparable number density of ETGs.

Our results for the global population of passive galaxies at 0.5 < z < 2.5, both in Figures 8 and 9, are in fair agreement with the results for quiescent and red elliptical galaxies by Ilbert et al. (2010). We do see, however, a gap between our measurements at z < 1 and those by Borch et al. (2006) and Bell et al. (2003). These differences are probably due to the different selection criteria: our selection is very conservative, and just at all redshifts selects galaxies with a tight upper limit to their SFR, and an early-type morphology, whereas Borch et al. (2006) refer to the mass density for all galaxies on the red sequence, which can be easily contaminated by dusty star forming galaxies (Cassata et al. 2008). On the other hand, Bell et al. (2003) select as early-types the galaxies with concentration in the r-band c_r > 2.6, which can thus be contaminated by bulge-dominated spirals.

By comparing Figures 8 and 9 we can draw interesting conclusions on the evolution of the passive population from 〈z〉 =1.6 to z ∼ 0. In particular, both the mass density and the number density of ETGs increases by a factor of ∼5 from 〈z〉 =1.6 to z ∼ 1, similarly to what has been found by Franceschini et al. (2006), Arnouts et al. (2007), and Abraham et al. (2007). This indicates that the bulk of the quenching of star formation of such galaxies takes place around that epoch. The evolution at later epochs is much milder. While the number density increases by a factor of 1.5 between z ∼ 1 and z ∼ 0.5, the mass density remains constant over the same interval. This implies that new ETGs are constantly added from z ∼ 1 to z ∼ 0.5, as already seen in Figure 7, but they are not massive enough to modify significantly the mass density. In other words, the new ETGs added from z ∼ 1 to z ∼ 0.5 are low mass objects, in good agreement with the "downsizing" scenario for the evolution of such galaxies (e.g., Thomas et al. 2010). We note that the data by Ilbert et al. (2010) show a similar behavior.

However, we cannot draw any strong conclusions, based on our data, about the evolution of the number density and mass density of ETGs from z ∼ 0.5 (the smallest GOODS redshift bin) and z ∼ 0 (the local SDSS value), since the GOODS fields are too small to minimize the effects of the cosmic variance.

Figures 8 and 9 distinguish the number and density evolution of compact, ultra-compact, and normal ETGs as a function of redshift. In particular, Figure 8 shows that the number densities of the compact and ultra-compact ETGs are not constant through the explored redshift range. We stress that at z ∼ 0 the classical definition of compactness sets the fraction of compact galaxies at 16%. At first, the number densities of compact and ultra-compact ETGs increase following the strong evolution of the global passive population: by z ∼ 1 there appears to be ∼3 times more compact and ultra-compact galaxies than those we found at 〈z〉 =1.6. At z < 1, conversely, their number density slowly decreases with cosmic time, decoupling from the evolution observed for the general population. At z ∼ 0, the number density of compact ETGs has decreased to 16% of the total density (by definition), reaching a value that is, just by chance, comparable to the number density at 〈z〉 =1.6 (e.g., Saracco et al. 2010). Similarly, the number density of the ultra-compact ETGs drops by a factor of ∼100 from z ∼ 1 to z ∼ 0, and in the local universe ultra-compact ETGs are ∼500 times rarer than normal ETGs. Similar behaviors are exhibited by the mass density in compact ETGs as a function of the redshift in Figure 9.

It is interesting to note that in Figure 8 the number of normal early-types from z ∼ 1 to z ∼ 0.5 increases at a faster rate than the one at which the compact ones disappear. As a result, the total number density increases, as already described. This result implies once again that both the mechanisms mentioned at the beginning of this section are at work from z ∼ 1 to z ∼ 0. On one side, some of the compact galaxies gradually increase in size, moving onto the local relation, and causing number (and mass) density of compact early-types to decrease; the compact galaxies that become normal support in part the growth of the mass and number density of normal early-types; but since the total number (compact+normal) increases as well, it means that new passive galaxies with sizes comparable to local counterparts are formed.

In the bottom panel of Figure 8 we show the fraction of compact and ultra-compact ETGs as a function of the redshift and cosmic time. The fraction of compact ETGs decreases from 80% at 〈z〉 =1.6 to 16% at z = 0, while the fraction of ultra-compact ETGs drops from 40% at 〈z〉 =1.6 to zero at z = 0. We stress that these fractions can be slightly overestimated at 1.2 < z < 2.5 as a result of the incompleteness of our selection at z > 1.6. Anyway, strong lower limits to these fractions (if we limit the sample to 1.2 < z < 1.6) are set to 65 and 25%, respectively. We note again that Saracco et al. (2010) found a much smaller fraction of compact early-types at z ∼ 2, and we tried to explain such difference in the previous section. However, our estimates for the compact fraction are in quite good agreement at later epochs with the measurements by Valentinuzzi et al. (2010a, 2010b). In particular, Valentinuzzi et al. (2010a) analyzed a sample of z ∼ 0.04 massive galaxies in clusters (WIde-field Nearby Galaxy-cluster Survey (WINGS), Fasano et al. 2006) and found a significant fraction of very compact galaxies. Valentinuzzi et al. (2010b) found a similar rich population of compact galaxies in clusters at z ∼ 0.7 (ESO Distant Clusters Survey, EDisCS; White et al. 2005), and claimed that 17% and 44% of all cluster galaxies are compact in WINGS and EDisCS clusters, respectively. By knowing the fraction of galaxies in the two surveys that are not morphologically early-type, we could reconstruct the fraction of compact early-types that we report in the bottom panel of Figure 8.

In this paper we have analyzed a complete and homogeneous sample of passive galaxies from z ∼ 0 to z ∼ 2.5, with the aim of observationally constraining the mass and size evolution of such systems during the last 10 Gyr of cosmic time. In particular, we estimated the evolution of the relative abundance of compact, ultra-compact, and normal ETGs throughout this redshift range.

We selected a homogeneous and robust sample of 563 passive galaxies using the multi-band photometry available in the GOODS-N+S fields, selecting galaxies with M > 10¹⁰ M_☉ and SSFR < 10⁻² Gyr⁻¹. We studied the morphological properties of the sample in the optical rest frame, using the ACS z-band for objects at z < 1.2 and the WFC3 H-band for galaxies at z > 1.2, and we discarded galaxies with late-type morphologies. We then run GALFIT to measure the Sérsic indices and physical sizes.

We found that, at all redshifts, the morphology traced by the rest-frame UV light is, within the statistical uncertainties, very close to that traced by the optical light, at least when parameters such as the Sérsic indices and effective radii are used. In fact, the sizes and Sérsic indices measured in the UV and optical rest frame correlate quite well with each other, with the sizes measured in the optical rest frame being slightly smaller (by ∼20% and ∼10% at z ≳ 1 and z ≲ 1, respectively) than those derived from the UV rest frame. This shows that, at least for galaxies that are not currently forming stars, the morphological K-correction is weak, and thus that ACS/z-band observations, if deep enough, can indeed be used to measure the size of passive galaxies at z > 1. This is in good agreement with previous results by Trujillo et al. (2007) and Cassata et al. (2010) and, at lower redshift, by Cassata et al. (2005) and Papovich et al. (2003).

We showed that the mass–size relation of ETGs evolves significantly from 〈z〉 1.6 to z ∼ 0: ∼80% of ETGs at 〈z〉 =1.6 in our sample are smaller than local counterparts of the same mass, and at later epochs ETGs are increasingly larger. We showed as well that the fractional increase of the average size is almost independent on the stellar mass.

With the aim of understanding whether the evolution of the mass–size relation is driven by the size growth of each individual galaxy or by the appearance of new large ETGs, we have built the size distribution in four redshift bins, scaled to the number density of ETGs in each bin. We observed that ETGs at 1.2 < z < 2.5 are on average 0.5 dex smaller than local counterparts of the same mass, and we identified a rich population of ultra-compact ETGs that have no identified counterparts in terms of size and density in the local universe. As time goes on, at 0.95 < z < 1.2 the number of ETGs is increased by a factor of five, and the new ETGs have a broad range of sizes, from 0.5 dex smaller to 0.5 dex larger than local counterparts of the same mass. At z < 0.95 the evolution is milder, with the number of ETGs increasing another factor of 1.5 down to z ∼ 0; the sizes of the new ETGs formed in this phase are similar to the average local value; at the same time the small ETGs gradually disappear, growing in size and skewing the size distribution towards large sizes. These results show that both the mechanisms driving the evolution of the mass–size relation are at work at the same time.

We measured the mass and number density of ETGs as a function of redshift, including the evolution of the relative fraction of normal, compact, and ultra-compact ones. In more detail, we showed that the number and mass density of massive and passive early-types increase by a factor of ∼5 within the ∼2 Gyr between 〈z〉 =1.6 to z ∼ 1, in agreement with Arnouts et al. (2007) and Ilbert et al. (2010). In the following 4 Gyr, from z ∼ 1 to z ∼ 0.5, the number density increases by at most another factor of ∼1.5, while in the same interval the mass density remains constant. This implies that, as expected in a "downsizing" scenario, the added galaxies that drive the number evolution have small masses and do not contribute too much to the mass density. These findings are in good agreement with Franceschini et al. (2006), Borch et al. (2006), and Abraham et al. (2007), and similar to the results of Cimatti et al. (2006) and Scarlata et al. (2007).

From z ∼ 1 to z ∼ 0, we also showed that the number (and mass) density of compact early-types decreases by a factor of two, while the number density of normal-size ETGs increases much faster, indicating once again that the overall increase of the average size at fixed mass is only partly due to a size increase of individual galaxies, whereas part of the effect is due to the appearance of new ETGs with large size.

We interpret these results as evidence that the phases at z > 1 and z < 1 are dominated by distinct and different physical mechanisms. The scenario that comes out is the following: the epoch at 1 < z < 3 is when the bulk of the stellar mass in local ETGs is assembled. This process of assembly is quite rapid: the stellar mass locked in passive ETGs increases by a factor of five over a period of ∼2 Gyr. Whatever the mechanism responsible for this huge mass density increase (gas-rich major merger, collapse of unstable disks, monolithic collapse), it produces a remnant that is compact and small with respect to local counterparts: ∼80% of early-types in this redshift interval are smaller than galaxies of the same mass in the local universe. Interestingly, Targett et al. (2011) found that submillimeter galaxies at z ∼ 2 have similar sizes to those that we measure for ETGs at the same epoch, suggesting a possible evolutionary connection between the two classes of galaxies. On the other hand the evolution at z < 1 is much milder. In this phase, the compact galaxies continuously increase in size, eventually disappearing, most likely undergoing a series of dry and wet minor mergers or by slowing accreting a small amount of mass in their outskirts (e.g., Van Dokkum et al. 2010; Hopkins et al. 2009). At the same time, new ETGs are formed, driving the number density increase of a factor 1.5 that we observe from z ∼ 1 to z ∼ 0. These new ETGs have small masses and large sizes, indicating that the mechanism through which they are formed is different from the one that at z > 1 generated the compact ETGs.

P.C., M.G., Y.G., and S.S. acknowledge support from NASA grants HST-GO-9425.36-A, HST-GO-9822.45-A, and HST-GO-10189.15-A, awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under NASA contract NAS 5-26555. The work presented here is partly based on observations obtained with WIRCam, a joint project of Canada–France–Hawaii Telescope (CFHT), Taiwan, Korea, Canada, France, at the CFHT which is operated by the National Research Council (NRC) of Canada, the Institute National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii. We are grateful to the anonymous referee for the useful comments.