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Stellar Population Diagnostics of Elliptical Galaxy Formation

Major progress has been achieved in recent years in mapping the properties of passively-evolving, early-type galaxies (ETG) from the local universe all the way to redshift ~2. Here, age and metallicity estimates for local cluster and field ETGs are reviewed as based on color-magnitude, color-sigma, and fundamental plane relations, as well as on spectral-line indices diagnostics. The results of applying the same tools at high redshifts are then discussed, and their consistency with the low-redshift results is assessed. Most low- as well as high-redshift (z~1) observations consistently indicate 1) a formation redshift z>~3 for the bulk of stars in cluster ETGs, with their counterparts in low-density environments being on average ~1-2 Gyr younger, i.e., formed at z>~1.5-2, 2) the duration of the major star formation phase anticorrelates with galaxy mass, and the oldest stellar populations are found in the most massive galaxies. With increasing redshift there is evidence for a decrease in the number density of ETGs, especially of the less massive ones, whereas existing data appear to suggest that most of the most-massive ETGs were already fully assembled at z~1. Beyond this redshift, the space density of ETGs starts dropping significantly, and as ETGs disappear, a population of massive, strongly clustered, starburst galaxies progressively becomes more and more prominent, which makes them the likely progenitors to ETGs.


INTRODUCTION
Following Hubble (1936), we still classify galaxies as ellipticals, spirals and irregulars (see Sandage 2005, and references therein). This was an eyeball, purely morphological scheme; however, morphology correlates with the stellar population content of these galaxies, with typical ellipticals being redder than the others, and showing purely stellar absorption-line spectra with no or very weak nebular emissions. As a consequence, one often refers to early-type galaxies (ETG), even if they are color (or spectral type) selected rather than morphologically selected. Furthermore, the bulges of spirals of the earlier types show morphological as well as spectral similarities with ellipticals, and one often includes both ellipticals and bulges under the category of galactic spheroids.
Morphologically-selected and color-, or spectrum-selected samples do not fully overlap. For example, in a recent study of local (z ∼ 0) ETGs from the Sloan Digital Sky Survey (SDSS) all three criteria were adopted (Bernardi et al. 2006), and the result is reported in Table 1 (M. Bernardi, private communication). 1 From a sample including ∼123,000 galaxies with 14.5 < r Petrosian < 17.77 and 0.004 < z < 0.08, ETGs have been selected in turn by each of the three criteria (MOR, COL, SPE), and the resulting numbers of galaxies fulfilling each of them is given on the diagonal of the matrix. Out of the diagonal are the fractions of galaxies that satisfy two of the criteria, as labelled in the corresponding row and column. So, out of the morphologically-selected ETGs, 70% satisfy also the color selection, etc. The correlation between color and morphology selection persists at high redshift, e.g., at z ∼ 0.7 about 85% of color-selected, red-sequence galaxies are also morphologically early-type, i.e., E/S0/Sa (Bell et al 2004a), an estimate broadly consistent with the local one, when allowing for the wider morphological criterion. It is estimated that true ellipticals represent ∼ 22% of the total mass in stars in the local universe, a fraction amounting to ∼ 75% for spheroids (i.e., when including E0's and spiral bulges), whereas disks contribute only ∼ 25% and dwarfs an irrelevant fraction (Fukugita, Hogan, & Peebles 1998). Although earlier estimates gave slightly lower fractions for stars in spheroids vs. disks (e.g. Schechter Persic & Salucci 1992), it is now generally accepted that the majority of stars belong to spheroids. Figure 1 shows separately the mass functions of color-selected ETGs and of blue, star-forming galaxies, also based on the SDSS data (Baldry et al. 2004). Above ∼ 3 × 10 10 M ⊙ red-sequence galaxies start to increasingly outnumber blue galaxies by a factor that exceeds 10 above ∼ 3 × 10 11 M ⊙ . Figure 2, drawn from the same mass functions, shows the contributions to the total stellar mass by red and blue galaxies in the various mass bins, along with the contributions to the total number of galaxies. Then, ETGs Elliptical Galaxy Formation 3 Figure 1: The mass function of local (z ∼ 0) early-type (red) galaxies and late-type (blue) galaxies from the Sloan Digital Sky Survey (Baldry et al. 2004). The solid lines represent best fit Schechter functions. For the blue galaxies the sum of two different Schechter functions is required to provide a good fit. Dotted lines show the mass functions from Bell et al. (2003).
represent only 17% of the total number of galaxies in the sample, but contribute ∼ 57% of the total mass. Moreover, > ∼ 80% of the stellar mass in ETGs belongs to galaxies more massive than ∼ 3 × 10 10 M ⊙ . Dwarfs are sometimes seen as the "building blocks" of galaxies, but at least in the present universe one can not build much with them.
With spheroids holding the major share of stellar mass in galaxies, understanding their evolution -from formation to their present state -is central to the galaxy evolution problem in general. Historically, two main scenarios have confronted each other, the so-called Monolithic Collapse model (Eggen, Lynden-Bell & Sandage 1962, Larson 1974, Arimoto & Yoshii 1987, Bressan, Chiosi & Fagotto 1994, and the Hierarchical Merging model (e.g., Toomre 1977;White & Rees 1978). In the former scenario spheroids form at a very early epoch as a result of a global starburst, and then passively evolve to the present. If the local conditions are appropriate, a spheroid can gradually grow a disk by accreting gas from the environment, hence spheroids precede disks. In the merging model, big spheroids result from the mutual disruption of disks in a merging event, hence disks precede spheroids.
The two scenarios appear to sharply contradict each other, but the contradiction has progressively blurred in recent years. Evidence has accumulated that the bulk of stars in spheroids are old, and most likely formed in major merging events. In the hierarchical merging scenario (the only one rooted in a solid cosmological context) successive generations of models have struggled to increase their predicted stellar ages, so as to produce results resembling the opposite sce-4 Alvio Renzini Figure 2: The contributions to the total stellar mass and to the number of galaxies by early-type (red) and late-type (blue) galaxies in the various mass bins, as derived from the best-fit mass functions of Baldry et al. (2004) shown in Figure 1. The relative areas are proportional to the contributions of the early-and late-type galaxies to the total stellar mass and to the number of galaxies. (Courtesy of D. Thomas).
nario. This review will not attempt to trace an history of theoretical efforts to understand the formation and evolution of ellipticals and spheroids. It will rather concentrate on reviewing the accumulating observational evidences coming from the stellar component of these galaxies. Other extremely interesting properties of ellipticals, such as their structural and dynamical properties, their hot gas content, central supermassive black holes, etc., will not be touched in this review, even if they are certainly needed to complete the picture and likely play an important role in the evolution of these galaxies. Also untouched are the internal properties of ETGs, such as color and line-strength gradients indicative of spatial inhomogeneities of the stellar populations across the body of ETGs. A complementary view of ETG formation based on the globular cluster populations of these galaxies is presented in the article by J. Brodie & J. Strader (this volume).

SYNTHETIC STELLAR POPULATIONS
The ETGs treated in this review can only be studied in integrated light, hence the interpretation of their photometric and spectroscopic properties needs population synthesis tools. Pioneering unconstrained synthesis using "quadratic programming" (e.g., Faber 1972), was soon abandoned in favor of evolutionary population synthesis, whose foundations were laid down by Beatrice Tinsley in the Elliptical Galaxy Formation 5 1970s (Tinsley & Gunn 1976, Tinsley 1980, Gunn, Stryker & Tinsley 1981. Much progress has been made in the course of the subsequent quarter of a century, especially thanks to the systematic production of fairly complete libraries of stellar evolutionary sequences and stellar spectra. Several modern population synthesis tools are commonly in use today, including those of Worthey (1994), Buzzoni (1995), , Maraston (1998Maraston ( , 2005, Bruzual Vazdekis et al. (2003), and González Delgado et al. (2005). Though far more reliable than earlier generations of models, even the most recent tools still may suffer from incomplete spectral libraries (especially at high metallicity and for nonsolar abundance ratios), and poorly calibrated mass loss in advanced stages, such as the asymptotic giant branch (AGB). Yet, there is fair agreement among the various models, with the exception of those for ages around ∼ 1 Gyr, when the contribution by AGB stars is at maximum, and Maraston's models (calibrated on Magellanic Cloud clusters) give appreciably higher near-IR fluxes than the other models.
Only a few "rules of thumb" regarding population synthesis models can be recalled here, which may be useful in guiding the reader through some of the subtleties of their comparison with the observations. • No evolutionary population synthesis code is perfect. Evolutionary tracks are not perfect and stellar libraries are never really complete. So, any code deficiency will leave its imprint on the results, generating a distortion of the age/metallicity grids used to map plots of one observable versus another. Inevitably, such distortions will leave their imprint in the results, and to some extent may lead to spurious correlations/anticorrelations when reading ages and metallicities from overplotted data points.
• Ages derived from best fits to simple stellar populations (SSPs, i.e., single burst populations) are always luminosity-weighted ages, and in general are more sensitive to the youngest component of the real age distribution. SSP ages should be regarded as lower limits.
• Spectra and colors of SSPs are fairly insensitive to the initial mass function (IMF), because most of the light comes from stars in a narrow mass interval around the mass of stars at the main sequence turnoff.
• The time evolution of the luminosity of a SSP does depend on the IMF, and so does the mass-to-light ratio (M/L). For example, a now fashionable IMF that flattens below ∼ 0.6 M ⊙ (e.g., Chabrier 2003) gives M/L ratios a factor of ∼ 2 lower than a straight Salpeter IMF.
• Stellar ages and metallicities are the main quantities that the analyses of colors and integrated spectra of galaxies are aimed to determine. Yet, for many observables, age and metallicity are largely degenerate, with a reduced age coupled to an increased metallicity conjuring to leave the spectral energy distribution nearly unchanged. This results primarily from the color (temperature) of the main sequence turnoff, e.g., (B − V ) TO , (the true clock of SSPs) being almost equally sensitive to age and metallicity changes. Indeed, from stellar isochrones one can derive that (∂log t/∂[Fe/H]) (B−V ) TO ≃ −0.9 − 0.35[Fe/H], and a factor of 2 error in estimated metallicity produces a factor ∼ 2 error in age (Renzini 1992). Red giant branch stars are the major contributors of bolometric luminosity in old stellar populations, and their locus shifts to lower temperatures with both increasing age and metallicity, further contributing to the degeneracy. Thus, from full SSPs, Worthey (1994) estimated that a factor of 3 error in metallicity generates a factor of 2 error in age when using optical colors as age indicators, the so-called 2/3 rule. Several strategies have been devised to circumvent this difficulty and break the age-metallicity degeneracy (see below).
• There are occasionally ambiguities in what is meant by the M/L ratio in the tabulated values. The mass M can be defined either as the mass of gas that went into stars, or the mass of the residual population at age t, including the mass in dead remnants (i.e., the original mass diminished by the mass lost by stars in the course of their evolution), or even the mass of the surviving stars, i.e., without including the mass in remnants. Caution should be paid when using tabular values, as different authors may adopt different definitions.
The power of stellar population diagnostics stems from the opportunity to agedate the stellar content of galaxies in a fashion that is independent of cosmological parameters. Then, once a cosmology is adopted, ages derived from observations at a lower redshift can be used to predict the properties of the stellar populations of ETGs at a higher one, including their formation redshift. Thus, ages derived for the local elliptical galaxies imply a well-defined color, spectral, and luminosity evolution with redshifts, which all can be subject to direct observational test. The extent to which a consistent picture of ETG formation is emerging from low-and high-redshift observations is the main underlying theme of this review.

ELLIPTICAL GALAXIES IN THE LOCAL UNIVERSE
Observations at high redshift are certainly the most direct way to look at the forming galaxies, and a great observational effort is currently being made in this direction. Yet, high-redshift galaxies are very faint, and only few of their global properties can now be measured. Nearby galaxies can instead be studied in far greater detail, and their fossil evidence can provide a view of galaxy formation and evolution that is fully complementary to that given by high-redshift observations. By fossil evidence one refers to those observables that are not related to ongoing, active star formation, and which are instead the result of the integrated past star formation history. At first studies attempted to estimate ages and metallicities of the dominant stellar populations on a galaxy-by-galaxy basis. But the tools used were still quite rudimentary, being based on largely incomplete libraries of stellar spectra and evolutionary sequences. Hence, through the 1980s progress was relatively slow, and opinions could widely diverge as to whether ellipticals were dominated by old stellar populations -as old as galactic globular clustersor by intermediate age ones, several billion years younger than globulars (see e.g. O'Connell 1986, Renzini 1986) -with much of the diverging interpretations being a result of the age-metallicity degeneracy. From the beginning of the 1990s progress has been constantly accelerating, and much of this review concentrates on the developments that took place over the past 15 years.

Color-Magnitude Relation, Fundamental-Plane and Line-Indices
3.1.1 THE COLOR-MAGNITUDE AND COLOR-σ RELATIONS That elliptical galaxies follow a tight color-magnitude (C-M) relation was first recognized by Baum (1959), and in a massive exploration Visvanathan & Sandage (1977) and Sandage & Visvanathan (1978a,b) established the universality of this relation with what continues to be the culmination of ETG studies in the pre-CCD era. The C-M relation looked the same in all nine studied clusters, and much the same in the field as well, though with larger dispersion (at least in part due to larger distance errors). The focus was on the possible use of the C-M relation as a distance indicator; however, Sandage & Visvanathan documented the tightness of the relation and noted that it implies the stellar content of the galaxies to be very uniform. They also estimated that both S0's and ellipticals had to be evolving passively since at least ∼ 1 Gyr ago. Figure 3 shows a modern rendition for the C-M plot for the Coma cluster galaxies, showing how tight it is, as well as how closely both S0's and ellipticals follow the same relation, as indeed Sandage & Visvanathan had anticipated.

Elliptical Galaxy Formation
In a major breakthrough in galaxy dating, Bower, Lucey, & Ellis (1992), rather than trying to age-date galaxies one by one, were able to set tight age constraints on all ETGs in Virgo and Coma at once. Noting the remarkable homogeneity of ETGs in these clusters, they estimated the intrinsic color scatter in the color-σ relation (see Figure 4) to be δ(U − V ) < ∼ 0.04 mag, where σ is the central stellar velocity dispersion of these galaxies. They further argued that -if due entirely to an age dispersion δt = β(t H − t F ), such color scatter should be equal to the time scatter in formation epochs, times ∂(U − V )/∂t, i.e.: where t H is the age of the universe at z = 0, and galaxies are assumed to form before a lookback time t F . Bower and colleagues introduced the parameter β, such that β(t H − t F ) is the fraction of the available time during which galaxies actually form. Thus, for β = 1 galaxy formation is uniformly distributed between t ∼ 0 and t = t H − t F , whereas for β < 1 it is more and more synchronized, i.e., restricted to the fraction β of time interval t H − t F . Adopting ∂(U − V )/∂t from the models of Bruzual (1983), they derived t H − t F < 2 Gyr for β = 1 and t H − t F < 8 Gyr for β = 0.1, corresponding respectively to formation redshifts 8 Alvio Renzini z F > ∼ 2.8 and > ∼ 1.1 for their adopted cosmology (t H = 15 Gyr, q • = 0.5). For the concordance cosmology, the same age constraints imply z F > ∼ 3.3 and > ∼ 0.8, respectively. A value β = 0.1 implies an extreme synchronization, with all Virgo and Coma galaxies forming their stars within less than 1 Gyr when the universe had half its present age, which seems rather implausible. Bower and colleagues concluded that ellipticals in clusters formed the bulk of their stars at z > ∼ 2, and later additions should not provide more than ∼ 10% of their present luminosity. Making minimal use of stellar population models, this approach provided for the first time a robust demonstration that cluster ellipticals are made of very old stars, with the bulk of them having formed at z > ∼ 2. As the narrowness of the C-M and color-σ relations sets constraints on the ages of stellar populations in ETGs, their slope can set useful constraints on the amount of merging that may have led to the present-day galaxies. The reason is that merging without star formation increases luminosity and σ, but leaves colors unchanged, thus broadening and flattening the relations. Moreover, merging with star formation makes bluer galaxies, thus broadening and flattening the relations even more. Then, from the constraints set by the slope of the C-M relation, Bower, Kodama, & Terlevich (1998) concluded that not only the bulk of stars in clusters must have formed at high redshift, but also that they cannot have formed in mass units much less than about half their present mass. 3.1.2 THE FUNDAMENTAL PLANE Three key observables of elliptical galaxies, namely the effective radius R e , the central velocity dispersion σ, and the luminosity L (or equivalently the effective surface brightness I e = L/2πR e 2 ) relate their structural/dynamical status to their stellar content. Indeed, elliptical galaxies are not randomly distributed within the 3D space (R e , σ, I e ), but rather cluster close to a plane, thus known as the fundamental plane (FP), with R e ∝ σ a I e b Djorgovski & Davis 1987), where the exponents a and b depend on the specific band used for measuring the luminosity. The projection of Elliptical Galaxy Formation 9 the FP over the (R e , I e ) coordinate plane generates the Kormendy relation (Kormendy 1977), whereas a projection over the (σ, L = 2πR e 2 I e ) plane generates the Faber-Jackson relation (Faber & Jackson 1976). At a time when testing the Ω M = 1 standard cosmology had high priority, the FP was first used to estimate distances, in order to map deviations from the local Hubble flow and construct the gravitational potential on large scales. Its use to infer the properties of the stellar content of galaxies, and set constraints on their formation, came later. Yet, by relating the luminosity to the structural-dynamical parameters of a galaxy, the FP offers a precious tool to gather information on the ages and metallicities of galaxies, at low as well as at high redshifts.
The mere existence of a FP implies that ellipticals (a) are virialised systems, (b) have self-similar (homologous) structures, or their structures (e.g., the shape of the mass distribution) vary in a systematic fashion along the plane, and (c) contain stellar populations which must fulfill tight age and metallicity constraints.
Here we concentrate on this latter aspect.
To better appreciate the physical implications of the FP, Bender, Burnstein, & Faber (1992) introduced an orthogonal coordinate system (κ 1 , κ 2 , κ 3 ), in which each new variable is a linear combination of log σ 2 , log R e and log I e . The transformation corresponds to a rotation of the coordinate system such that in the (κ 1 , κ 3 ) projection the FP is seen almost perfectly edge-on. Moreover, if structural homology holds all along the plane, then log M/L = √ 3κ 3 + const. If σ is (almost) unaffected by the dark matter distribution (as currently understood, Rix et al. 1997), then κ 3 provides a measure of the stellar M/L ratio, and κ 1 ∝ log (σ 2 R e ) ∝ log M a measure of the stellar mass. Bender and colleagues showed that in Virgo and Coma the FP is remarkably "thin", with a 1-σ dispersion perpendicular to the plane of only σ(κ 3 ) ≃ 0.05, corresponding to a dispersion in the M/L ratio < ∼ 10% at any position along the plane. Moreover, the FP itself is "tilted", with the M/L ratio apparently increasing by a factor ∼ 3 along the plane, while the mass is increasing by a factor ∼ 100. Note that the tilt does not imply a departure from virialization, but rather a systematic trend of the stellar content with galaxy mass, possibly coupled with a systematic departure from structural homology (e.g., Bender, Burstein & Faber 1992, Ciotti 1997, Busarello et al. 1997. The narrowness of the FP, coupled to the relatively large tilt (∆κ 3 /σ(κ 3 ) ≃ 0.35/0.05 = 7) requires some sort of fine tuning, which is perhaps the most intriguing property of the FP (Renzini & Ciotti 1993). Although unable to identify one specific origin for the FP tilt, Renzini & Ciotti argued that the small scatter perpendicular to the FP implied a small age dispersion ( < ∼ 15%) and high formation redshift, fully consistent with the Bower, Lucey & Ellis (1992) argument based on the narrowness of the C-M and color-σ relations.
The remarkable properties of the FP for the Virgo and Coma clusters were soon shown to be shared by all studied clusters in the local universe. Jørgensen, Franx, & Kjaergaard (1996) constructed the FP for 230 ETGs in 10 clusters (including Coma), showing that the FP tilt and scatter are just about the same in all local clusters, thus strengthening the case for the high formation redshift of cluster ETGs being universal. However, Worthey, Trager, & Faber (1995) countered that the thinness of the FP, C-M, and color-σ relations could be preserved, even with a large age spread, provided age and metallicity are anticorrelated (with old galaxies being metal poor and young ones being metal rich). This is indeed what Worthey and colleagues reported from their line-indices analysis (see below), indicating a factor of ∼ 6 for the range in age balanced by a factor ∼ 10 in metallicity (from solar to ∼ 10 times solar). If so, then the FP should be thicker in the near infrared, because the compensating effect of metallicity would be much lower at longer wavelength, thus unmasking the full effect of a large age spread (Pahre, Djorgovski, & De Carvalho 1995). But Pahre and colleagues found the scatter of the FP K-band to be the same as in the optical. In addition, its slope implied a sizable variation of M/L K ∝ M 0. 16   , who finally concluded that the origin of the FP tilt defies a simple explanation, but is likely the result of combined age and metallicity trends along the plane (with the most metal rich galaxies being actually the oldest), plus an unidentified systematic deviation from structural homology. Several possibilities for the homology breaking have been proposed and investigated, such as variation in stellar and/or dark matter content and/or distribution, anisotropy, and rotational support (e.g., Ciotti   argued that one fourth of the tilt is due to stellar population (i.e., a combination of metallicity and age), and three quarters of it to structural nonhomology in the distribution of the visible matter.
Of special interest is the comparison of the FP in clusters and in the field, because one expects all formation processes to be faster in high density peaks of the matter distribution. This was tested by Bernardi et al. (2003bBernardi et al. ( , 2006) with a sample of ∼ 40, 000 SDSS morphology-and color-selected ETGs spanning a wide range of environmental conditions, from dense cluster cores to very low densities. Bernardi and colleagues found very small, but detectable differences in the FP zero point; the average surface brightness is ∼ 0.08 mag brighter at the lowest density extreme compared to the opposite extreme. As the sample galaxies are distributed in redshift up to z ∼ 0.3, they used the observed lookback time to empirically determine the time derivative of the surface brightness (hence in a model-independent fashion) and estimated that the 0.08 mag difference in surface brightness implies an age difference of ∼ 1 Gyr, and therefore that galaxies in low density environments are ∼ 1 Gyr younger compared to those in cluster cores. 3.1.3 THE LINE-STRENGTH DIAGNOSTICS Optical spectra of ETGs present a number of absorption features whose strength must depend on the distributions of stellar ages, metallicities and abundance ratios, and therefore may give insight over such distributions. To exploit this opportunity, Burstein et al. (1984) introduced a set of indices now known as the Lick/IDS system, and started taking measurements for a number of galaxies. The most widely used indices have been the Mg 2 (or Mgb), < Fe >, and the Hβ indices, measuring respectively the strength of MgH+MgI at λ ≃ 5156 − 5197Å, the average of two FeI lines at λ ≃ 5248 and 5315Å, and of H β .
A first important result was the discovery that theoretical models based on solar abundance ratios adequately describe the combinations of the values of the < Fe > and Mg 2 indices in low-luminosity ETGs, but fail for bright galaxies (Peletier 1989 , Jørgensen 1997). This implies either that population synthesis models suffered from some inadequacy at high metallicity (possibly due to incomplete stellar libraries), or that massive ellipticals were genuinely enriched in magnesium relative to iron, not unlike the halo stars of the Milky Way (e.g., Wheeler, Sneden, & Truran 1989). As for the Milky Way halo, such an α-element overabundance may signal a prompt enrichment in heavy elements from Type II supernovae, with the short star-formation timescale having prevented most Type Ia supernovae from contributing their iron while star formation was still active. Yet, a star-formation timescale decreasing with increasing mass was contrary to the expectations of galactic wind/monolithic models (e.g., Arimoto & Yoshii 1987), where the star formation timescale increases with the depth of the potential well . However, as noted by Thomas (1999), the contemporary semi-analytical models did not predict any α-element enhancement at all, no matter whether in low-or high-mass ETGs. Indeed, Thomas, Greggio, & Bender (1999) argued that the α-enhancement, if real, was also at variance with a scenario in which massive ellipticals form by merging spirals, and required instead that star formation was completed in less than ∼ 1 Gyr. Therefore, assessing whether the α-enhancement was real, and in that case measuring it, had potentially far reaching implications for the formation of ETGs.
Two limitations had to be overcome in order to reach a credible interpretation of the < Fe > − Mgb plots: (a) existing synthetic models for the Lick/IDS indices were based on stellar libraries with fixed [α/Fe] (Worthey 1994, Buzzoni 1995, and (b) an empirical verification of the reality of the α-enhancement was lacking.
In an attempt to overcome the first limitation, Greggio (1997) developed a scaling algorithm that allowed one to use existing models with solar abundance ratios to estimate the Mg overabundance, and she concluded that an enhancement up to [Mg/Fe]≃ +0.4 was required for the nuclei of the most massive ellipticals (see also Weiss, Peletier, & Matteucci 1995). She also concluded that a closed-box model for chemical evolution failed to explain the very high values of the Mg 2 index of these galaxies. Indeed, the numerous metal-poor stars predicted by the model would obliterate the Mg 2 feature, hence the nuclei of ellipticals had to lack substantial numbers of stars more metal poor than ∼ 0.5Z ⊙ . Besides, very old ages ( > ∼ 10 Gyr) and α-enhancement were jointly required to account for galaxies with strong Mg 2 . Eventually, Thomas, Maraston, & Bender (2003) produced a full set of synthetic models with variable [α/Fe], and Maraston et al. (2003) compared such models to the indices of ETGs and of metal-rich globular clusters of the Galactic bulge, for which the α-enhancement has been demonstarted on a star-by-star basis by high resolution spectroscopy. The result is displayed in Figure 5, showing that indeed the new models indicate for the bulge globulars an enhancement of [α/Fe]∼ +0.3, in agreement with the stellar spectroscopy results, and similar to that indicated for massive ETGs.
Other widely used diagnostic diagrams involved the Hβ index along with < Fe > and Mg 2 or Mgb. The Balmer lines had been suggested as good age indicators (e.g., O'Connell 1980; Dressler & Gunn 1983), an expectation that was confirmed by the set of synthetic models constructed by Worthey (1994) with the aim of breaking the age-metallicity degeneracy that affects the broad-band colors of galaxies. Worthey's models were applied by Jørgensen (1999)   indices. From these samples, and using the Hβ − Mgb and Hβ − < Fe > plots from Worthey's models, both Jørgensen and Trager and colleagues concluded that ages ranged from a few to almost 20 Gyr, but age and metallicity were anticorrelated in such a way that the Mgb − σ, C-M, and FP relations may be kept very tight. Moreover, there was a tendency for ETGs in the field to appear younger than those in clusters. Yet, Trager and colleagues cautioned that Hβ is most sensitive to even low levels of recent star formation, and suggested that the bulk of stars in ETGs may well be old, but a small "frosting" of younger stars drives some galaxies toward areas in the Hβ − Mgb and Hβ − < Fe > plots with younger SSP ages. Finally, for the origin of the α-enhancement Trager and colleagues favored a tight correlation of the IMF with σ, in the sense of more massive galaxies having a flatter IMF, hence more Type II supernovae. However, with a flatter IMF more massive galaxies would evolve faster in luminosity with increasing redshift, compared to less massive galaxies, which appears to be at variance with the observations (see below).
These conclusions had the merit of promoting further debates. Maraston & Thomas (2000) argued that even a small old, metal-poor component with a blue horizontal branch (like in galactic globulars) would increase the Hβ index thus making galaxies look significantly younger than they are. Even more embarrassing for the use of the Hβ − Mgb and Hβ − < Fe > plots is that a perverse circulation of the errors automatically generates an apparent anticorrelation of age and metallicity, even where it does not exist. For example, if Hβ is overestimated by observational errors, then age is underestimated, which in turn would reduce Mgb below the observed value unless the younger age is balanced by an artificial increase of metallicity. Trager and colleagues were fully aware of the problem, and concluded that only data with very small errors could safely be used. Kuntschner et al. (2001) investigated the effect by means of Monte Carlo simulations, and indeed showed that much of the apparent age-metallicity anticorrelation is a mere result of the tight correlation of their errors. They concluded that only a few outliers among the 72 ETGs in their study are likely to have few-billion-year-old luminosity-weighted ages, and these were typically galaxies in the field or loose groups, whereas a uniformly old age was derived for the vast majority of the studied galaxies. Moreover, younger ages were more frequently indicated for S0 galaxies (Kuntschner & Davies 1998). Nevertheless, in a cluster with very tight C-M and FP relations such as Coma, a large age spread at all magnitudes was found for a sample of 247 cluster members (Poggianti et al. 2001), and a sizable age-metallicity anticorrelation was also found for a large sample of SDSS galaxies (Bernardi et al. 2005).
As already alluded to, the main pitfall of the procedure is that the various indices depend on all three population parameters one is seeking to estimate: thus Hβ is primarily sensitive to age, but also to [ are all tightly correlated, and one is left with the suspicion that apparent correlations or anticorrelations may be an artifact of the procedure, rather than reflecting the real properties of galaxies. In an effort to circumvent these difficulties, Thomas et al. (2005) renounced to trust the results galaxy by galaxy. They rather looked at patterns in the various index-index plots and compared them to mock galaxy samples generated via Monte Carlo simulations that fully incorporated the circulation of the errors. The real result was not a set of ages and metallicities assigned to individual galaxies, but rather age and metallicity trends with velocity dispersion, mass and environments. Having analyzed a sample of 124 ETGs in high-and low-density environments, Thomas and colleagues reached the following conclusions: (a) all three parameters -age, metallicity and [α/Fe]-correlate strongly with σ, and, on average, follow the relations: where quantities in brackets/not in brackets refer to low-density/high-density environments, respectively. (c) By and large this picture applies to both cluster and field ETGs, with cluster galaxies having experienced the bulk of their star formation between z ∼ 5 and 2, and this activity appears to have been delayed by ∼ 2 Gyr in the lowest density environments, i.e., between z ∼ 2 and ∼ 1. Figure 6 qualitatively summarizes this scenario, in which the duration of star formation activity decreases with increasing mass (as required by the [Mg/Fe] trend with σ), and extends to younger ages for decreasing mass (as forced by the Hβ − σ relation). Note that the smooth starformation histories in this figure should be regarded as probability distributions, rather than as the actual history of individual galaxies, where star formation may indeed take place in a series of bursts. Qualitatively similar conclusions were reached by Nelan et al. (2005), from a study of ∼ 4000 red-sequence galaxies in ∼ 90 clusters as part of the National Astronomical Observatory Fundamental Plane Survey. Assuming the most massive galaxies (σ ∼ 400 km s −1 ) to be 13 Gyr old, they derived an age of only 5.5 Gyr for less massive galaxies (σ ∼ 100 km s −1 ). Note that the age-σ scaling of Thomas and colleagues would have given a much older age (∼ 9.5 Gyr). Taken together, Equations 2 and 3 imply a trend of M/L V by a factor ∼ 1.8 along the FP (from σ = 100 to 350 km s −1 ), thus accounting for almost two thirds of the FP tilt. As extensively discussed by Thomas et al. (2005), one residual concern comes from the possibility that part of the Hβ strength may be due to blue HB stars. Besides a blue HB contribution by low-metallicity stars (especially in less massive galaxies), blue HB stars may also be produced by old, metal-rich populations, and appear to be responsible for the UV upturn in the spectrum of local ETGs (Brown et al. 2000, Greggio & Renzini 1990). In the Thomas et al. sample, some S0 outliers with strong Hβ and strong metal lines would require very young ages and extremely high metallicity (up to ∼ 10 times solar), and may better be accounted for by an old, metal-rich population with a well-developed blue HB.
The Mg 2 − σ relation has also been used to quantify environmental differences in the stellar population content. The cluster/field difference turns out to be small, with ∆Mg 2 ∼ 0.007 mag, corresponding to ∼ 1 Gyr difference -field galaxies being younger -within a sample including ∼ 900 ETGs (Bernardi et al. 1998), though no statistically significant environmental dependence of both Mg 2 and Hβ was detected within a sample of ∼ 9, 000 ETGs from the SDSS (Bernardi et al. 2003a). Still from SDSS, coadding thousands of ETG spectra in various luminosity and environment bins, Eisenstein et al. (2003) detect clear trends with the environment thanks to the resulting exquisite S/N, but the differences are very small, and Eisenstein and colleagues refrain from interpreting them in terms of age/metallicity differences.
These results from the analysis of the Lick/IDS indices, including large trends of age with σ, or even large age-metallicity anticorrelations, have yet to be proven consistent with the FP and C-M relations of the same galaxies as established specifically for the studied clusters. Feeding the values of the indices, the synthetic models return ages, metallicities, and α-enhancements. But along with them the same models also give the colors and the stellar M/L ratio of each galaxy in the various bands, hence allowing one to construct implied FP and C-M relations. It would be reassuring for the soundness of the whole procedure if such relations were found to be consistent with the observed ones. To our knowledge, this sanity check has not been attempted yet. The mentioned trends and correlations, if real, would also have profound implications for the evolution of the FP and C-M relations with redshift, an opportunity that will be exploited below. Figure 6: The scenario proposed by Thomas et al. (2005) for the average star formation history of early-type galaxies of different masses, from 5 × 10 9 M ⊙ up to 10 12 M ⊙ , corresponding to σ ≃ 100 to ∼ 320 km s −1 , for the highest and lowest environmental densities, respectively, in the upper and lower panel.

Ellipticals Versus Spiral Bulges
The bulges of spiral galaxies are distinguished in "true bulges", typically hosted by S0-Sb galaxies, and "pseudobulges" usually (but not exclusively) in later-type galaxies (Kormendy & Kennicutt 2004). True (classical) bulges have long been known as similar to ellipticals of comparable luminosity, in both structure, line strengths and colors (e.g., Bender, Burnstein & Faber 1992, Jablonka, Martin, & Arimoto 1996, Renzini 1999, and references therein). Peletier et al. (1999) were able to quantify this similarity using Hubble Space Telescope (HST) WFPC2 (Wide Field Planetary Camera 2) and NICMOS (Near Infrared Camera and Multiobject Spectrometer) observations, and concluded that most (true) bulges in their sample of 20 spirals (including only 3 galaxies later than Sb) had optical and optical-IR colors similar to those of Coma ellipticals. Hence, like in Coma ellipticals their stellar populations formed at z > ∼ 3, even if most of the galaxies in their sample are in small groups or in the field. More recently, Falcon-Barroso, Peletier, & Balcells (2002) measured the central velocity dispersion for the same sample observed by Peletier and colleagues, and constructed the FP for these bulges, showing that bulges in this sample tightly follow the same FP relation as cluster ellipticals, and therefore had to form their stars at nearly the same epoch. The similarity of true bulges and ellipticals includes the tendency of less massive objects to have experienced recent star formation, as indicated by their location in the Mg 2 − σ diagram in Figure 7. These similarities between true (classical) bulges and ellipticals suggest a similar origin, possibly in mergerdriven starbursts at high redshifts. Pseudobulges, instead, are more likely to Alvio Renzini have originated via secular evolution of disks driven by bars and other deviations from axial symmetry, as extensively discussed and documented by Kormendy & Kennicutt (2004). Several of the objects in the Prugniel and colleagues sample in Figure 7 are likely to belong to the pseudobulge group. From the Lick/IDS indices of a sample of bulges, Thomas and Davies (2006) argue that the same scenario depicted in Figure 6 for ETGs, applies to bulges as well, the main difference being that bulges are on average less massive, hence on average younger than ETGs.
Looking near to us, HST and ground based photometry of individual stars in the Galactic bulge have shown that they are older than at least 10 Gyr, with no detectable trace of an intermediate age component (Ortolani et al. 1995, Kuijken & Rich 2002, Zoccali et al. 2003. HST/NICMOS photometry of stars in the bulge of M31 has also shown that their H-band luminosity function is virtually identical to that of the Galactic bulge, and by inference should have nearly identical ages (Stephens et al. 2003). These two bulges belong to spirals in a rather small group, and yet appear to have formed their stars at an epoch corresponding to z > ∼ 2, not unlike most ellipticals.

Summary of the Low-Redshift (Fossil) Evidence
The main observational constraints on the epoch of formation of the stellar populations of ETGs in the near universe can be summarized as follows: • The C-M, color-σ and FP relations for ETGs in clusters indicate that the bulk of stars in these galaxies formed at z > ∼ 2 − 3.
• The same relations for the field ETGs suggest that star formation in low density environments was delayed by ∼ 1 − 2 Gyr. • The more massive galaxies appear to be enhanced in Mg relative to iron, which indicates that the duration of the star-formation phase decreases with increasing galaxy mass, having been shorter than ∼ 1 Gyr in the most massive galaxies.
• Interpretations of the Lick/IDS indices remains partly controversial, with either an age-metallicity anticorrelation, or an increase of both age and metallicity with increasing σ.
These trends are qualitatively illustrated in Figure 6, showing that the higher the final mass of the system, the sooner star formation starts and more promptly subsides, in an apparently "antihierarchical" fashion. A trend in which the stellar population age and metallicity are tightly correlated to the depth of the potential well (as measured by σ) argues for star formation, metal enrichment, supernova feedback, merging, and violent relaxation having been all concomitant processes rather than having taken place sequentially.
The fossil evidence illustrated so far is in qualitative agreement with complementary evidence at low as well as high redshift, now relative to star-forming galaxies as opposed to quiescent ones. At low z, Gavazzi (1993) and Gavazzi, Pierini, & Boselli (1996) showed that in local (disk) galaxies the specific starformation rate anticorrelates with galaxy mass, a trend that can well be extended to include fully quiescent ellipticals. On this basis, Gavazzi and collaborators emphasized that mass is the primary parameter controlling the star-formation history of galaxies, with a sharp transition at L H ≃ 2 × 10 10 L ⊙ (corresponding to ∼ 2×10 10 M ⊙ ) between late-type, star-forming galaxies and mostly passive, earlytype galaxies (Scodeggio et al. 2002). This transition mass has then been precisely located at ∼ 3 × 10 10 M ⊙ with the thorough analysis of the SDSS database (Kauffmann et al. 2003). In parallel, high redshift observations have shown that the near-IR luminosity (i.e., mass) of galaxies undergoing rapid star formation has declined monotonically from z ∼ 1 to the present, a trend for which Cowie et al. (1996) coined the term down-sizing. This is becoming a new paradigm for galaxy formation, as the anticorrelation of the specific star-formation rate with mass is now recognized to persist well beyond z ∼ 2 (e.g., Juneau et al. 2005, Feulner et al. 2006).

ELLIPTICAL GALAXIES AT HIGH REDSHIFT
Perhaps the best way of breaking the age-metallicity degeneracy is by looking back in time, studying galaxies at higher and higher redshifts. In the 1990s this was attempted first with 4m-class telescopes, and later, with impressive success, with 8-10m-class telescopes and HST. Studies first focused on cluster ellipticals, and their extension to field galaxies followed with some delay. Thus, the evolution with redshift of various galaxy properties were thoroughly investigated, such as the C-M and Kormendy relations, the luminosity and mass functions, and the FP. Various ongoing surveys are designed to map the evolution with redshift and local environment of all these properties, along with the number density of these galaxies.

Cluster Ellipticals
Up to z ∼ 1 4.1.1 THE COLOR-MAGNITUDE RELATION With the identification of clusters at higher and higher redshifts, from the mid-1990s it became possible to construct their C-M relation, hence to directly assess the rate of evolution of cluster ETGs. Pioneering studies showed a clearly recognizable red sequence in high-redshift clusters, and gave hints that the color evolution up to z ∼ 1 was broadly consistent with pure passive evolution of the galaxies formed at high redshift (Dressler & Gunn 1990; Aragón-Salamanca et al. 1993; Rakos & Schombert 1995). Subsequent studies fully confirmed these early hints and provided accurate estimates for the formation redshift of the bulk of stars in cluster ellipticals. Thus, replicating the Bower, Lucey & Ellis (1992) procedure for a sample of morphologically-selected ETGs in clusters at z ∼ 0.5, Ellis et al. (1997) were able to conclude that most of the star formation in ellipticals in dense clusters was completed 5-6 Gyr earlier than the cosmic time at which they are observed, i.e., at z > ∼ 3. Extending these studies to clusters up to z ∼ 0.9, Stanford, Eisenhardt, and Dickinson (1998) showed that pure passive evolution continues all the way to such higher redshift, while the dispersion of the C-M relation remains as small as it is in Virgo and Coma (see Figure 8). Thus, Stanford and colleagues concluded that cluster ellipticals formed the bulk of their stars at z > ∼ 3, with the small color dispersion arguing for highly synchronized star-formation histories among galaxies within each cluster, and from one cluster to another. These conclusions were reinforced by several other investigators, e.g., Gladders et al. The redshift evolution of the color of the red sequence in clusters proved to be a very powerful tool in disentangling ambiguities that are difficult to eliminate based only on z ∼ 0 observations. From the color evolution of the red sequence in two Abell clusters at z ∼ 0.2 and ∼ 0.4, Kodama & Arimoto (1997) were able to break the age-metallicity degeneracy plaguing most of the global observables of local ellipticals. In principle, because colors depend both on age and metallicity, the slope of the C-M relation could equally well be reproduced with either age or metallicity increasing with increasing luminosity (or σ). However, if age were the dominant effect, then the C-M relation would steepen with lookback time (redshift), as the color of the young galaxies would get more rapidly bluer compared to that of the old galaxies. Instead, the slope of the relation remains nearly the same (see Figure 8). Actually, the Kodama & Arimoto argument can be applied also to the color dispersion within a cluster, demonstrating that the tightness of the C-M (and FP) relation in low-z clusters cannot be due to a conspiracy of age and metallicity being anticorrelated (as advocated e.g., by Worthey, Trager & Faber 1995). If so, the color dispersion would rapidly increase with redshift, contrary to what is seen in clusters up to z ∼ 1 (see Figure 8). 4.1.2 THE LUMINOSITY FUNCTION A cross check of the high formation redshift of ETGs can be provided by looking at their luminosity in distant clusters. If ETGs evolve passively, following a pure luminosity evolution, then their luminosities should increase with increasing redshift by an amount that depends on the formation redshift and on the slope of the IMF.
Initial attempts to detect the expected brightening of the characteristic luminosity (M * ) of the luminosity function (LF) were inconclusive, as  failed to detect any appreciable change between clusters at z = 0.31 and z = 0.56, possibly owing to the small redshift baseline. On the other hand, comparing the LF of z ∼ 0 clusters to the LF of a sample of 8 clusters at 0.40 < z < 0. 48 Barrientos & Lilly (2003) found a brightening of the characteristic luminosity M * consistent with passive evolution and high formation redshift, also in agreement with the (U −V ) color evolution of the red sequence. In a major cluster survey, De Propris et al. (1999) explored the evolution of the observed K-band LF in 38 clusters with 0.1 < z < 1, and compared the results to the Coma LF. With this much larger redshift baseline, De Propris et al. found the trend of K * with redshift to be consistent with passive evolution and z F > ∼ 2. They pointed out the agreement with the results based on the color evolution of the red sequence galaxies, but emphasized that this behavior of the LF implies that "not only their stellar population formed at high redshift, but that the assembly of the galaxies themselves was largely complete by z ∼ 1". Kodama & Bower (2003) and Toft, Soucail, & Hjorth (2003) came to the same conclusions by studying the K-band LF of (respectively two and one) clusters at z ∼ 1. Breaking the z = 1 barrier, Toft et al. (2004) constructed a very deep K-band LF of a rich RDCS cluster at z = 1.237, and concluded that the most massive ellipticals that dominate the top end of the LF were already in place in this cluster. They compared the cluster K-band LF (corresponding to the rest-frame z-band LF) to the z-band LF of local clusters (Popesso et al. 2005) and derived a brightening by ∼ 1.4 mag in the rest-frame z-band characteristic magnitude, indeed as expected from pure passive evolution. Toft and colleagues also found a substantial deficit of fainter ETGs, which could be seen as a manifestation of the down-sizing effect in a high redshift cluster, a hint of which was also noticed in other clusters at However, a more complete study of 3 rich clusters at 1.1 < ∼ z < ∼ 1.3, including the z = 1.237 cluster studied by Toft et al. (2004), did not produce evidence of a down-sizing effect, down to at least 4 magnitudes below K * (Strazzullo et al. 2006). This study confirmed the brightening of M * z and M * K by ∼ 1.3 mag, consistent with passive evolution of a population that formed at z > ∼ 2, and showed that the massive galaxies were already fully assembled at z ∼ 1.2, at least in the central regions of the 3 clusters. 4.1.3 THE KORMENDY RELATION An alternative way of detecting the expected brightening of old stellar populations at high redshift is by tracing the evolution of the Kormendy relation, which became relatively easy only after the full image quality of HST was restored. Thus, from HST data, the ETGs in a cluster at z = 0.41 were found brighter by ∆M K = 0.36 ± 0.14 mag (Pahre, Djorgovski, & de Carvalho 1996) or by 0.64 ± 0.3 mag (Barrientos, Schade, & Lopez-Cruz 1996) with respect to local galaxies, consistent (within such large errors) with passive evolution of an old, single-burst stellar population. Schade et al. (1996) using excellent-seeing CFHT (Canada-France-Hawaii Telescope) imaging data for 3 clusters at z = 0.23, 0.43 and 0.55 detected a progressive brightening in galaxy luminosity at a fixed effective radius that once more was estimated to be consistent with passive evolution and formation at high redshift. No differential evolution with respect to ETGs in the cluster surrounding fields was detected.
Turning to HST data, a systematic brightening in the Kormendy relation, again consistent with passive evolution and high formation redshift, was found by several other groups, eventually reaching redshifts ∼ 1 (see Schade

THE FUNDAMENTAL PLANE
Besides the high spatial resolution, constructing the FP of high redshift cluster (and field) galaxies requires moderately high-resolution spectroscopy (to get σ), hence a telescope with large collective area. With one exception, for a few years this was monopolized by the Keck Telescope, and FP studies of high-z ellipticals first flourished at this observatory. In a crescendo toward higher and higher redshifts, the FP was constructed for clusters at z The redshift evolution of the FP depends on a variety of factors. For passive evolution the FP shifts by amounts that depend on a combination of IMF slope, formation redshift, and cosmological parameters. A systematic trend of the IMF slope with galaxy mass would cause the FP to rotate with increasing redshift (Renzini & Ciotti 1993), as it would do for a similar trend in galaxy age. An age dispersion (∆t) would cause the scatter perpendicular to the FP to increase with redshift, as, for fixed ∆t, ∆t/t increases for increasing redshift, i.e. decreasing galaxy age (t). Clearly, the behavior of the FP with redshift can give a wealth of precious information on the formation of ellipticals, their stellar populations, and to some extent on cosmology also (Bender et al. 1998).
All the quoted FP studies of high-z clusters conclude that the FP actually shifts nearly parallel to itself by an amount that increases with redshift and is consistent with the passive evolution of stellar populations that formed at high redshifts. The FP shifts imply a decrease of the rest-frame M/L ratio ∆log M/L B ≃ −0.46z (van Dokkum & Stanford 2003), but -as emphasized above -the formation redshift one can derive from it depends on both cosmology and the IMF. Figure  9 illustrates the dependence on the adopted cosmology. Note that for the "old  standard" cosmology (Ω M = 1) galaxies would be older than the universe and therefore the observed FP evolution can effectively rule out this option (see also Bender et al. 1998). Figure 10 shows the effect of the IMF slope and formation redshift on the expected evolution of the M/L B ratio. The redshift range z = 0 to 1.5 only probes the IMF between ∼ 1 and ∼ 1.4 M ⊙ , which correspond to the masses at the main sequence turnoff M TO of oldest populations at z = 0 (age ∼ 13 Gyr, M TO ≃ M ⊙ ) and of those at z = 1.5 (age ∼ 4.5 Gyr and M TO ≃ 1.4 M ⊙ ). Together, Figure  9 and 10 illustrate the formation redshift/IMF/cosmology degeneracies in the FP diagnostics. However, the cosmological parameters are now fixed by other observational evidences, whereas the formation redshift as determined by the color evolution of the cluster red sequence is independent of the IMF slope. In summary, in the frame of the current concordance cosmology, when combining the color and FP evolution of cluster ellipticals one can conclude that the best evidence indicates a formation redshift z F ∼ 3 and a Salpeter IMF slope in the pertinent stellar mass range (1 < M < 1.4 M ⊙ ).
The fact that the cluster FP does not appreciably rotate with increasing redshift is documented down to σ ∼ 100 km s −1 for clusters out to z ∼ 0. ). If the large age trends with σ derived in some of the studies using the Lick/IDS indices were real (see Section 3.1), this would result in a very large rotation of the FP in these clusters. For example, if age were to increase along the FP from 5.5 Gyr to 13 Gyr (at z = 0, and for σ = 100 and 320 km s −1 , respectively, see Nelan et al. 2005), then at a lookback time of 4 Gyr (z ∼ 0.4) the younger population would have brightened by ∆M B ∼ 1.33 mag, and the older one only by ∼ 0.46 mag (using models from Maraston 2005), which results in a FP rotation of ∼ 0.9 mag in surface brightness. Alternatively, the much shallower age−σ relation derived by Thomas et al. (2005) implies an age increase from ∼ 9.5 Gyr to ∼ 11.5 Gyr for σ increasing from 180 to 350 km s −1 , which implies a rotation of the FP by ∼ 0.36 mag in surface brightness by z = 0.8, which is still consistent with the hint that in fact there may be a small FP rotation in a cluster at this redshift (Wuyts et al. 2004).
The scatter about the FP of clusters also remains virtually unchanged with increasing redshift, however some of the claimed age-metallicity anticorrelations derived from the Lick/IDS indices would result in a dramatic increase of the scatter with redshift, causing the FP itself to rapidly blur away. 4.1.5 THE LINE INDICES The intermediate resolution spectra used for constructing the FP of distant cluster ETGs, were also used to measure age-sensitive line indices that can provide further constraints on the formation epoch. Thus, Bender, Ziegler, & Bruzual (1996) and Ziegler & Bender (1997) measured the Mgb index of 16 ETGs in their two clusters at z = 0.375, and found that the Mgb − σ relation was shifted toward lower values of the index. From such differences in Mgb index, Ziegler & Bender inferred that the age of the z = 0.375 galaxies is about two thirds of that of ETGs in Coma and Virgo. Therefore, t(z = 0) − t F = 1.5 × [t(z = 0.375) − t F ], where t is the cosmic time and t F the cosmic time when the local and distant cluster ETGs formed (which is assumed to be the same). Adopting the t − z relation for the concordance cosmology, one derives t F ∼ 1.7 Gyr, corresponding to z F > ∼ 3.
From the strength of the Balmer absorption lines (H δ and H γ ) as age indicators, Kelson et al. (2001) used data for several clusters up to z = 0.83 and were able to set a lower limit to the formation redshift z F > ∼ 2.5, consistent with the above result from the Mgb index.
In summary, the study of the stellar populations in ETGs belonging to distant clusters up to z ∼ 1.3 have unambiguously shown that these objects have evolved passively from at least z ∼ 2 − 3. This came from the color, line strength, and luminosity evolution. Moreover, the brightest cluster members at z ∼ 1 − 1.3 and the characteristic luminosity of the LF appear to be brighter than their local counterpart by an amount that is fully consistent with pure passive evolution, indicating that these galaxies were already fully assembled at this high redshift. This may not have been the case for less massive galaxies, as their counts may be affected by incompleteness. 4.1.6 CAVEATS Although it is well established that ETGs in distant clusters are progenitors to their local analogs and formed at high redshift, some caveats are nevertheless in order. First, as frequently emphasized, the evidence summarized above only proves that at least some cluster galaxies evolved passively from z > ∼ 1 to the present, but other local ETGs may have z ∼ 1 progenitors that would not qualify as ETGs at that redshift, either morphologically or photometrically. This "progenitor bias" (e.g., van Dokkum & Franx 1996) would therefore pre-vent us from identifying all the z ∼ 1 progenitors of local cluster ETGs, some of which may well be still star forming. Second, the slope of the FP is progressively less accurately constrained in higher and higher redshift clusters, because the central velocity dispersion has been measured only for very few cluster members (generally the brightest ones). Third, it is always worth recalling that all luminosity-weighted ages tend to be biased toward lower values by even minor late episodes of star formation. Last, stellar population dating alone only shows when stars were formed, not when the galaxy itself was assembled and reached its observed mass.

Field versus Cluster Ellipticals up to z ∼ 1
In the local universe field ellipticals show small, yet detectable differences compared to their cluster counterpart, being possibly ∼ 1 Gyr younger, on average. This ∆t difference, if real, should magnify in relative terms and become more readily apparent when moving to high redshift (∆t/t is increasing). Using the color evolution of the red sequence and the shift of the FP with redshift, progress in investigating high−z ETGs in the field has been dramatic in recent years, along with the cluster versus field comparison. Schade et al. (1999) selected ETGs by morphology from the Canada-France Redshift Survey (CFRS, Lilly et al. 1995a,b) and Low Dispersion Survey Spectrograph (LDSS) redshift survey (Ellis et al. 1996), and constructed the restframe (U − V ) C-M relation for field ETGs in the 0.2 < z < 1.0 range. They found that the C-M relation becomes progressively bluer with redshift, with ∆(U − V ) ≃ −0.68 ± 0.11 at z = 0.92 with respect to the relation in Coma, accompanied by a brightening by ∼ 1 mag in the rest-frame B band, as derived from the Kormendy relation. To be consistent with the color evolution, this brightening should have been much larger than observed if the color evolution were due entirely to the passive evolution of stellar populations formed at high z. Thus, Schade and colleagues reconciled color and luminosity evolution by invoking a residual amount of star formation (adding only ∼ 2.5% of the stellar mass from z = 1 to the present), yet enough to produce the observed fast color evolution. Support for such an interpretation comes from about one third of the galaxies exhibiting weak [OII] emission, which indicates that low-level star formation is indeed fairly widespread. The rate of luminosity evolution was found to be identical to that of cluster ellipticals at the same redshifts, hence no major environmental effect was detected besides the mentioned low level of star formation and a color dispersion slightly broader than in clusters at the same redshift.
With COMBO-17, the major imaging survey project undertaken with the ESO/MPG 2.2m telescope, Wolf et al. (2003) secured deep optical imaging in 17 broad and intermediate bands over a total 0.78 square degree area, from which Bell et al. (2004b) derived photometric redshifts accurate to within δz ∼ 0.03. The bimodality of the C-M relation, so evident at z ∼ 0 (e.g., Baldry et al. 2004), clearly persists all the way to z ∼ 1.1 in the COMBO-17 data, and this allowed Bell and colleagues to isolate ∼ 5, 000 "red sequence" ETGs down to R < 24. As mentioned above, ∼ 85% of such color-selected galaxies appear also morphologically early-type on the ACS images of the GEMS (Galaxy Evolution from Morphology and SED) survey , Bell et al. 2004a). The rest-frame (U − V ) color of ETGs in the COMBO-17 survey evolves by a much smaller amount than that reported by Schade et al. (1999) for the morphologically-selected ETGs, i.e., by only ∼ 0.4 mag between z = 0 and 1, as expected for an old stellar population that formed at high redshift (z F > ∼ 2). This color evolution is also in agreement with the ∼ 1.  Kodama et al. (2004) selected ETGs for having the R − z and i − z colors in a narrow range as expected for passively evolving galaxies in the range 0.9 < ∼ z < ∼ 1.1, and the sampled population included both field and cluster ETGs. They found a deficit of red galaxies in the C-M sequence ∼ 2 mag fainter than the characteristic magnitude (corresponding to stellar masses below ∼ 10 10 M ⊙ ). Less massive galaxies appear to be still actively star-forming, while above ∼ 8 × 10 10 M ⊙ galaxies are predominantly passively evolving. This was interpreted as evidence for down-sizing in galaxy formation (à la Cowie et al. 1996), with massive galaxies having experienced most of their star formation at early times and being passive by z ∼ 1, and many among the less massive galaxies experience extended star formation histories.
In a comprehensive study also based on deep, wide-field imaging with the Suprime-Cam at the Subaru Telescope, Tanaka et al. (2005) obtained photometric redshifts based on four or five optical bands and constructed the C-M relations for the two clusters (at z = 0.55 and 0.83) included in the field, and for their extended environment. Tanaka and colleagues further distinguished galaxies in the cluster environment as belonging either to recognized "groups", or otherwise to the "field". The results are shown in Figure 11, where the various plots allow one to visually explore trends with redshift for given environment, or with environment for given redshift. The red sequence appears already in place in the "field" in the highest redshift sample, but no clear color bimodality is apparent. (Note that COMBO-17 does find bimodality at this redshift, possibly due to its photometric redshifts based on many more bands being more accurate.) The color bimodality is instead clearly recognizable in the z = 0.55 "field" sample. At higher environmental densities (labelled "group") the C-M relation of the red sequence is clearly recognizable already in the z = 0.83 sample, and even more so in the "cluster" sample. Tanaka and colleagues argue that the bright and the faint ends of the red sequence are populated at a different pace in all three environments; the more massive red galaxies are assembled first, i.e., the C-M relation grows from the bright end to the faint end in all three environments (not in the opposite way, as one may naively expect in a hierarchical scenario), which is interpreted in terms of down-sizing. Note also that the faint end appears to be well in place in "clusters" at z = 0 while virtually still lacking in the field (see also Popesso et al. 2005). Using HST/WFPC2 imaging over a ∼ 30 arcmin 2 field including the same z = 0.83 cluster, Koo et al. (2005) were able to measure the rest-frame (U − B) colors of the sole bulge component of 92 galaxies with M B < −19.5, part in the cluster itself, part in the surrounding field. Their very 26 Alvio Renzini Figure 11: The C-M relations of two high redshift clusters and their surrounding fields at progressive lower density (labelled "group" and "field") are compared to their local counterparts from the Sloan Digital Sky Survey. The red line marks the adopted separation between the red sequence galaxies, and the blue, star-forming galaxies. In the cluster panels the blue dashed lines show the approximate location of galaxies with stellar mass of 10 10 (right) and 10 11 M ⊙ (left). From Tanaka et al. (2005). red color does not show any environmental dependence, suggesting similarly old ages and high formation redshifts.
The public delivery of the Hubble Deep Field data (HDF, Williams et al. 1996) spurred several studies of field ETGs. Thus, Fasano et al. (1998) applied the Kormendy relation to a sample of morphologically selected ETGs in HDF-North and estimated an increase of the surface brightness at a fixed effective radius that was consistent with a high formation redshift (z F ∼ 5), according to the galaxy models by Bressan, Chiosi & Fagotto (1994) and Tantalo et al. (1996).
Although the LF and the C-M and Kormendy relations had already given useful indications on the analogies and differences between cluster and field ETGs, major progress came with the study of the differential evolution (field versus cluster) of the FP with redshift. In early studies, no field/cluster difference had clearly emerged at z = 0.3 (Treu et al. 1999 (Treu et al. 2002). But already at these modest redshifts there were hints that the brightest, most massive ETGs in the field closely follow the FP evolution of their cluster counterparts, while less massive ETGs (especially S0's) appear to evolve slightly faster, and hence look younger. This was more accurately quantified for morphologically-selected ETGs up to z ∼ 1 in the HDF-North by van Dokkum & Ellis (2003), showing a field versus cluster difference ∆lnM/L B = −0.14 ± 0.13 in the FP. This implies that field ETGs are on average younger by only 16% ± 15% at < z >= 0.88. Van Dokkum & Ellis also inferred that the bulk of stellar mass in the observed ETGs must have formed at z > ∼ 2 even in the field, with only minor star formation at lower redshifts. Then, moving to the wider GOODS (Great Observatories Origin Deep Survey)-South field (Giavalisco et al. 2004a), van der Wel et al. (2004, 2005a) constructed the FP for a total of 33 color and morphology-selected ETGs at 0.60 < z < 1.15, using intermediate resolution spectra taken at the ESO Very Large Telescope (VLT). They also found the most massive galaxies (M * > 2×10 11 M ⊙ ) to behave much like their cluster analogs at the same redshifts, while less massive galaxies appeared to be substantially younger. Moreover, all these studies noted the higher proportion of weak [OII] emitters among the field ETGs (∼ 20%) compared to their cluster counterparts, as well as the higher proportion of galaxies with strong Balmer lines (the K+A Galaxies).
The main limitations of all these early studies was in the small number of objects observed at each redshift, which must go a long way toward accounting for occasional discrepancies in the results. In a major effort to overcome this limitation, Treu et al. (2005a,b) obtained high-resolution spectra at the Keck telescope for 163 morphologically-selected ETGs in the GOODS-North field, which were distributed over the redshift range 0.2 < z < 1.2. The main results of this study are displayed in Figure 12, showing that the most massive ellipticals in the field do not differ appreciably from their cluster analogs in having luminosity-weighted ages implying z F > ∼ 3. However, the lower the mass the larger the dispersion in the M/L B ratio, with a definite trend toward lower values with decreasing mass, implying lower and lower formation redshift. This demonstrates that completion of star formation in field galaxies proceeds from the most massive to the less massive ones, as is indeed expected from the down-sizing effect (Cowie et al. 1996, Kodama et al. 2004) and is consistent with the scenario shown in Figure 6. This systematic trend in the M/L ratio with galaxy mass results in a "rotation" of the FP with increasing redshift, as less massive galaxies evolve faster in luminosity compared to the more massive, older ones (but one should beware of possible Alvio Renzini where the rotation with respect to the Coma FP is apparent. Note that a similar FP rotation in two clusters at z = 0.83 and 0.89 has been recently unambiguously detected by Jørgensen et al. (2006), having extended the σ measurements below ∼ 100 km s −1 . Somewhat at variance with the FP studies reported above was the Deep Groth Strip Survey result (Gebhardt et al. 2003), in which no difference in the slope was found up to z ∼ 1 compared to the local FP (hence no downsizing), which was coupled to a much faster luminosity evolution compared to all other results. Treu et al. (2005b) discuss the possible origins of the discrepancy, and attribute it to a combination of selection bias, small number statistics, and relatively low S/N spectra.
From population synthesis models one expects the rate of evolution of the M/L ratio to be slower at longer wavelengths compared to the B band, because it is less affected by the main sequence turnoff moving to cooler temperatures with increasing age. This expectation was qualitatively confirmed by van der Wel et al. appear to be similar to those of cluster ETGs, although with more scatter, and indicate < z F > > ∼ 1.5 for the bulk of the stars in the lensing galaxies. In summary, like at low redshifts, also at z ∼ 1 there appear to be small detectable differences between ETGs in high-and low-density regions, but such differences are more evident for faint/low-mass galaxies than for the bright ones.

Ellipticals Beyond z ∼ 1.3
Up to z ∼ 1.3 the strongest features in the optical spectrum of ETGs are the CaII H&K lines and the 4000Å break. But at higher redshifts these features first become contaminated by OH atmospheric lines, and then move to the near-IR, out of reach of CCD detectors. The lack of efficient near-IR multi-object spectrographs (even in just the J band) has greatly delayed the mapping of the ETG population beyond z ∼ 1.3. Thus, for almost a decade the most distant spectroscopically confirmed old spheroid was an object at z = 1.55 selected for being a radiogalaxy (Dunlop et al. 1996, Spinrad et al. 1997). The spectral features that made the identification possible included a set of FeII, MgII and MgI lines in the rest-frame near-UV, in the range of ∼ 2580 − 2850Å, which is typical of F-type stars. The UV Fe-Mg feature offers at once both the opportunity to measure the redshift, and to age-date the galaxy, because it appears only in populations that have been passively evolving since at least a few 10 8 years. It Figure 14: The rest-frame coadded spectrum of the four passively evolving galaxies at 1.6 < z < 1.9 with the identification of the main spectral features (blue spectrum). The spectrum from Bruzual & Charlot (2003) for a 1-Gyr-old SSP (simple stellar population) model of solar metallicity is also shown (red spectrum). (From Cimatti et al. 2004) has been also used to age-date local ETGs (e.g., Buson et al. 2004). Thus, using this feature, Spinrad and colleagues inferred an age of ∼ 3.5 Gyr, implying z F > 5 (even in modern cosmology).
This record for the highest redshift ETG was eventually broken by Glazebrook et al. (2004) and Cimatti et al. (2004), using the same features in the rest-frame UV (see Figure 14). They reported the discovery of, respectively, five passively evolving galaxies at 1.57 < ∼ z < ∼ 1.85, and four other such objects at 1.6 < ∼ z < ∼ 1.9. All being brighter than K = 20, these galaxies are quite massive (M > ∼ 10 11 M ⊙ ), and hence would rank among the most massive galaxies even in the local universe. This suggests that they were (almost) fully assembled already at this early epoch, and having been passive since at least ∼ 1.1 Gyr had to form at redshift > ∼ 2.7 . The four objects found by Cimatti and colleagues are included in the GOODS-South field, and the GOODS deep HST/ACS imaging showed that two objects are definitely elliptical galaxies, and the two others are likely to be S0's.
Though breaking the old redshift record was certainly an exciting result, perhaps far more important was the discovery that the surface density of z > 1.5 ETGs is indeed much higher than one would have expected from just the single object found by Dunlop et al. (1996). Indeed, this galaxy was selected from a catalog of radiogalaxies covering a major fraction of the whole sky, whereas the nine galaxies in the Cimatti  Altogether, these are virtually all the spectroscopically confirmed ETGs at z > 1.3 known to date. Given the long integration time needed to get spectroscopic redshifts, it became clear that an effective criterion was indispensable to select high-z ETG candidates. To this end, Daddi et al. (2004) introduced a robust criterion based on the B −z and z −K colors, that very effectively selects galaxies at 1.4 < ∼ z < ∼ 2.5 (the so-called BzKs), and among them separates the star forming BzKs with BzK ≡ (z − K) AB − (B − z) AB ≥ −0.2, from the passive ones, with BzK < −0.2 and (z − K) AB > 2.5. The criterion is primarily an empirical one, based on the spectroscopic redshifts from the K20 survey (Cimatti et al. 2002b) and other publicly available data sets. However, Daddi and colleagues showed that synthetic stellar populations of the two kinds (i.e., star forming and passive) do indeed occupy the corresponding areas in this plot, when redshifted to 1.4 < z < 2.5. An application of the method to a 320 arcmin 2 field is shown in Figure 15  ). In this latter study, it is estimated that the space density of massive and passive BzKs (with K < 20, stellar mass > ∼ 10 11 M ⊙ and < z >≃ 1.7) is 20 ± 7% that of z = 0 ETGs within the same mass limit. Then there appears to be a sharp drop of passive BzKs beyond z = 2, which in part may be due to the available B-band data being not deep enough  Further candidate ETGs with masses up to a few 10 11 M ⊙ have been identified at even higher redshifts, such as six objects within the HUDF at a (photometric) redshift > 2.8 (Chen & Marzke 2004), where both the redshift and the old age are inferred from the observed break between the J (F110W) and the H (F160W) band being interpreted as the 4000Å break. One of these objects is undetected in the deep GOODS optical data, but is prominent in the GOODS Spitzer/IRAC 3.5 − 8 µm images (M. Dickinson et al., in preparation). Thus its SED shows two breaks, one between the z and the J band, and one between the K and the 3.5 µm IRAC band. Identifying them respectively with the Lyman and Balmer breaks, the object would be placed at z ∼ 6.5, it would be passively evolving with z F > 9, and would have the uncomfortably large mass of a few 10 11 M ⊙ . Lower redshift alternatives give much worse fits to the data, whereas the use of models with strong AGB contribution (Maraston 2005) results in a somewhat less extreme mass and formation redshift.

Evolution of the Number Density of ETGs to z ∼ 1 and Beyond
The studies illustrated so far have shown that ETGs exist up to z ∼ 1, both in clusters and in the field, and are dominated by old stellar populations that formed at z > ∼ 2 − 3. Moreover, a handful of ETGs has also been identified (over small fields) well beyond z ∼ 1. Some of these ETGs appear to be as massive as the most massive ETGs in the local universe, demonstrating that at least some very massive ETGs are already fully assembled at z > ∼ 1. However, the expectation is for the number of ETGs to start dropping at some redshift, when indeed entering into the star formation phase of these galaxies, or when they were not fully assembled yet. Therefore, what remained to be mapped by direct observations was the evolution with redshift of the comoving number density of ETGs, and to do so as a function of mass and environment while covering wide enough areas of the sky in order to reduce the bias from cosmic variance. Only in this way one could really overcome the so-called progenitor bias. Because deep and wide surveys require so much telescope time, progress has been slow. Cosmic variance may still be responsible for the apparent discrepancies between galaxy counts from different surveys, but occasionally the interpretation itself of the counts may be prone to ambiguities.
One of the main results of the CFRS was that the number density of red galaxies shows very little evolution over the redshift range 0 < z < 1 (Lilly et al. 1995b). Following this study, in an attempt to map the number evolution of ETGs all the way to z ∼ 1 , Kauffmann, Charlot, & White (1996) extracted 90 color-selected ETGs without [OII] emission from the CFRS redshift catalog. They used a V /V max test and concluded that at z = 1 only ∼ 1/3 of bright ETGs had already assembled or had the colors expected for old, pure passively evolving galaxies. However, Im et al. (1996) identified ∼ 360 ETGs morphologically selected on archival HST images, and also conducted the V /V max test using photometric redshifts, finding no appreciable number density evolution up to z ∼ 1 and a brightening consistent with passive evolution. The V /V max test was repeatedagain using the CFRS sample -by Totani & Yoshii (1998) who concluded that there was no evolution in the number density up to z ∼ 0.8, and ascribed the apparent drop at z > 0.8 to a color selection bias. No evolution of the space density of morphologically-selected ETGs up to z ∼ 1 was found by Schade et al. (1999) too, who used the HST imaging of the CFRS and LDSS redshift surveys.
Several attempts to trace the evolution of the number density of morphologicallyselected ETGs to the highest possible redshifts were made using HDF data. In some of these studies very little, if any, change in the space density of ETGs was found up to z ∼ 1 (e.g., Driver et al. 1998, Franceschini et al. 1998, Im et al. 1999, or up to even higher redshifts when combining the HDF optical data with very deep near-IR data (Benitez et al 1999, Broadhurst & Bouwens 2000. These latter authors emphasized that without deep near-IR data many high-z ETGs are bound to remain undetected, and that spectroscopic incompleteness beyond z ∼ 0.8 is partly responsible for some of the previous discrepancies. Beyond z ∼ 1 a drop in the space density of ETGs was detected in several studies including the HDF (Zepf 1997, Franceschini et al. 1998, Barger et al. 1999, Rodighiero, Franceschini, & Fasano 2001). In particular, Stanford and colleagues applied the V /V max test to a sample of 34 ETGs from the HDF-North that includes deep NICMOS imaging in the H band (F160W), and concluded for a real drop at z > 1, but advocated the necessity to explore much wider  2004) is here shown for objects to a limiting magnitude K Vega = 20 from a 320 arcmin 2 field (from Kong et al. 2006). Black dots refer to galaxies at z <∼ 1.4, blue dots refer to starforming galaxies at ∼ 1.4 < z <∼ 2.5, orange dots refer to passively evolving galaxies at ∼ 1.4 < z <∼ 2.5. Green dots are Galactic stars in the same field and purple stars are local stellar standards.
fields in order to improve the statistics and cope with cosmic variance. Finally, the HDF-South optical data were complemented by ultra-deep JHK imaging at the VLT (the FIRES survey, Labbé et al. 2003, revealing a population of near-IR galaxies with very red colors (J − K > 2.3), called distant red galaxies (DRG), a fraction of which may be ETGs at very high redshifts (see below). Compared to HDF-North, its Southern equivalent appeared to be much richer in very red galaxies, e.g., including 7 objects with (V − H) AB > 3 and H AB < 25 while HDF-North has only one. Clearly, exploring much wider fields compared to HDF's ∼ 5 arcmin 2 field was imperative in order to make any significant progress.
Passive ETGs formed at very high redshift (e.g., z > 3) would indeed have very red colors at z > ∼ 1, and thus they should be found among the so-called extremely red objects (ERO), a class defined for having R − K > 5 (or similar color cut), and whose characteristics and relation to ETGs have been thoroughly reviewed by McCarthy (2004). Using a much shallower sample than that from the HDF, but one that covers an area ∼ 140 times wider than it,  and Firth et al. (2002) showed that EROs are much more abundant than previously found in smaller fields and are much more strongly clustered than generic galaxies to the same limiting magnitude K ∼ 19. This made them likely candidates for high-z ETGs, and assuming that ∼ 70% of EROs are indeed ETGs at z > 1, Daddi, Cimatti & Renzini (2000) concluded that most field ellipticals were fully assembled by z ∼ 1. However, Cimatti et al. (2002a) actually found that out of the 30 EROs with secure redshifts and K < 19.2, only 50% are passively evolving objects and these are distributed in the redshift interval 0.8 < ∼ z < ∼ 1.3, while the other 50% is made by highly-reddened, actively star-forming galaxies. Interestingly, precisely 50% among a sample of 129 EROs with K < 20.2 have been detected at 24 µm with Spitzer/MIPS, reinforcing the conclusion that up to one half of EROs are likely to be passive precursors to ETGs ). In fact, the fraction of passive EROs decreases to ∼ 35% on a spectroscopic complete sample to K = 20 . Nevertheless, the number density of passive EROs appeared to be broadly consistent with no density evolution of ETGs up to z ∼ 1, or a modest decrease.
With the COMBO-17 survey Bell et al. (2004b) went a long way toward coping with cosmic variance. With their 5,000 color-selected ETGs up to photometric redshift z ∼ 1.1, Bell and colleagues were able to construct their rest-frame Bband luminosity functions in nine redshift bins (0.2 < z < 1.1), and derived the best fit Schechter parameters for them using a fixed value of the faint-end slope, α = −0.6. They found that the characteristic luminosity M * B brightens by ∼ 1.0 mag between z = 0.25 and 1.05, consistent with passive evolution within the errors, and also with the brightening expected from the FP shift (∆log M/L B = −0.46∆z), which predicts ∼ 0.9 mag. At the same time, the normalization factor φ * drops by a factor of ∼ 4, but much of the drop is in the highest redshift bins which may be affected by incompleteness. More robust than either φ * or L * separately, is their product φ * L * B which is proportional to the B-band luminosity density, and this is found to be nearly constant up to z ∼ 0.8. This is at variance with a pure passive-evolution scenario, that would have predicted an increase by a factor of ∼ 2. Thus, the color of the COMBO-17 red sequence follows nicely the expectation from passive evolution (cf. section 4.2), but the number density of red sequence galaxies does not, and Bell and colleagues concluded that the stellar mass in red sequence galaxies has nearly doubled since z ∼ 1.
In a major observational effort at the Keck telescope, Faber et al. (2006, DEEP2 project) secured spectroscopic redshifts for ∼ 11, 000 galaxies with R < 24.1, and also reanalyzed the COMBO-17 data, finding separate best fit Schechter parameters in various redshift bins up to z ∼ 1.1. Faber and colleagues emphasize that φ * and M * are partly degenerate in these fits, for which the faint-end slope was fixed at α = −0.5. Thus, between z = 0.3 and 1.1, M * brightens by ∼ 0.47 mag and φ * drops by a factor of ∼ 2.5 for the DEEP2 data, and respectively up by ∼ 0.95 mag and down by a factor of ∼ 4 for the COMBO-17 data. Once more, much of the φ * drops are confined to the last redshift bin, and emphasis is placed on both DEEP2 and COMBO-17 confirming that the B-band luminosity density is nearly constant up to z ∼ 0.8, along with the implication that the mass density in ETGs has increased, presumably by a factor of ∼ 2, as estimated by Bell et al. (2004b). Extending the analysis from z = 0.3 to z = 0 (using SDSS data), Faber an colleagues find ∆M * ∼ 1.3 mag and a drop in φ * by a factor of ∼ 4 between z = 0 and 1.1, but caution that much of these changes occur between the z ∼ 0 survey and their first bin (at z = 0.3) at one end, and in the last redshift bin at the other end, where the data are said to be the weakest.
Both in COMBO-17 and DEEP2 the shape of the Schechter function for the red-sequence galaxies is assumed constant with redshift. As such, by construction this assumption virtually excludes down-sizing, for which ubiquitous indications have emerged both at low as well as high redshift. Indeed, as alluded in Kong et al. (2006) and documented by Cimatti, , COMBO-17 and DEEP2 results can also be read in a different way. Figure 16 shows the evolution of the rest frame B-band LF from COMBO-17, with the continuous line being the local LF for red-sequence galaxies from Baldry et al. ( Figure 16 it is apparent that the brightest part of the LF is fully consistent with pure passive evolution of the most massive galaxies, whereas the fainter part of the LF (below ∼ L * ) is progressively depopulated with increasing redshift, an effect that only in minor part could be attributed to incompleteness. Therefore, from these data it appears that virtually all the most massive ETGs have already joined the red sequence by z ∼ 1, whereas less massive galaxies join it later. This is what one would expect from the down-sizing scenario, as exemplified e.g., in Figure 6, as if downsizing was not limited to stellar ages (stars in massive galaxies are older), but it would work for the assembly itself, with massive galaxies being the first to be assembled to their full size. Being more directly connected to the evolution of dark matter halos, an apparent antihierarchical assembly of galaxies may provide a more fundamental test of the ΛCDM scenario than the mere down-sizing in star formation. The slow evolution with redshift of the number density of spectrum-selected bright ETGs was also one of the main results of the K20 survey (Pozzetti et al. 2003), and more recently of the VLT VIMOS Deep Survey (VVDS) where the rest-frame B-band LF of ETGs to I < 24 is found to be broadly consistent with passive evolution up to z ∼ 1, with the number density of bright ETGs decreasing by ∼ 40% between z = 0.3 and 1.1 (Zucca et al. 2006).
Quite the same scenario, in which the most massive ETGs are already in place at z ∼ 1 while less massive ones appear later, emerges from the study of the evolution of the stellar mass function for morphologically-selected ETGs in the GOODS fields ( Ferreras et al. (2005), who report instead a steep decrease in their number density with redshift. It seems fair to conclude that to fully prove (or disprove) down-sizing in mass assembly, and precisely quantify the effect, one needs to explore the luminosity and mass functions to deeper limits than reached so far, while extending the search to wider areas is needed to overcome cosmic variance. An endeavour of this size requires an unprecedented amount of observing time at virtually all major facilities, both in space and on the ground. The COSMOS project covering 2 square degrees (Scoville 2005) is deliberately targeted to this end, providing public multiwavelength data extending from X rays to radio wavelengths that will allow astronomers to map the evolution of galaxies and AGNs in their large scale structure context, and to derive photometric and spectroscopic redshifts (Lilly 2005) to substantially fainter limits than reached so far. Thus, it will be possible to directly assess the interplay be- tween AGN activity, star-formation onset and quenching, merging, mass growth, and morphological differentiation over the largest presently possible scale, hence promising substantial, perhaps definitive progress in mapping the evolution of ETGs and their progenitors.
It is worth emphasizing that even a low-level of ongoing star formation can make galaxies drop out of our ETG samples, and that theoretical models do not make solid predictions on when star formation is going to cease in a dark matter halo. Therefore, in a broader perspective, what is perhaps more fundamental than the early-type/late-type distinction, is the stellar mass of galaxies and the evolution of the galaxy mass function, irrespective of galaxy type. Several ongoing studies are moving in this directions (e.g., Fontana

CATCHING ELLIPTICALS IN FORMATION
Immediate precursors for cluster ETGs in the local universe were first identified with a population of blue, star-forming galaxies whose fraction in clusters increases very rapidly with redshift (Butcher & Oemler 1978, a trend known as the Butcher-Oemler effect), and therefore most such blue, star-forming galaxies had to subside to passive ETGs by z ∼ 0. Dressler el al. (1997) and Fasano et al. (2000) showed that in clusters up to z ∼ 0.5 the fraction of true ellipticals is fairly constant, while the fraction of (star-forming) spirals rapidly increases at the expense of the S0's. This was interpreted as evidence that galaxies in clusters that were star-forming spirals at z ∼ 0.5, have changed their morphology to become passively evolving S0's by z = 0, a transformation that may account for much of the Butcher-Oemler effect. In clusters in the same redshift range, a sizable population of ETGs with strong Balmer absorption lines was also identified by Dressler & Gunn (1983), hence called K+A galaxies after the appearance of their spectrum. These ETGs were recognized as poststarburst galaxies, as further documented by Dressler et al. (1999Dressler et al. ( , 2004 and Poggianti et al. (1999).
Thus, the metamorphosis from z ∼ 0.5 to z = 0 of a fraction of cluster galaxies from star forming to passive is well documented by these studies. However, these changes seem to affect more spirals and S0's than true ellipticals, and if the bulk of star formation in ETGs took place at very high redshift, then we need to look further out to catch them in formation. From the low-redshift studies we have learned that ETGs are massive, highly clustered, and had to form the bulk of their stars at z > ∼ 1.5−3 (depending on mass and environment) within a short time interval. Indeed, fast star formation is required by the α-overabundance, and by the mere high formation redshift. At z ∼ 3 the universe is only ∼ 2 Gyr old, hence forming ∼ 10 11 M ⊙ of stars in one object between z = 5 and z = 3 (∆t ∼ 1 Gyr) requires a star-formation rate (SFR) of > ∼ 100 M ⊙ yr −1 . Altogether, possible precursors of massive ETGs at low z could be searched among high-z massive, highly clustered, starburst galaxies with very high SFRs ( > ∼ 100 M ⊙ yr −1 ). The rest of this section is dedicated to mentioning the main results in searching for such objects.
Lyman break galaxies (LBGs) were the first ubiquitous population of galaxies to be identified at z ∼ 3, and their SFRs often in excess of ∼ 100 M ⊙ yr −1 , plus their relatively small size (R e ∼ 1 − 3 kpc), made them natural precursors to local bulges and ETGs (e.g., Giavalisco, Steidel, & Macchetto 1996, Giavalisco 2002, but see also Giavalisco et al. 1995 for an even earlier attempt to identify a z = 3.4 precursor to ETGs). Recently, Adelberger et al. (2005) show that the 3D correlation length (r • ) of LBGs is such to match that of local lesser spheroids (M < ∼ 10 11 M ⊙ ) when the secular increase of r • is taken into account. However, Adelberger et al. note that the most massive and most rapidly star forming galaxies at high redshifts are likely to be lost by the Lyman break selection. From Figure 2 we see that local ETGs with M > 10 11 M ⊙ include almost 50% of the mass in this kind of galaxies, and ∼ 1/4 of the total stellar mass at z = 0. Therefore, looking at the starforming precursors of the most massive ETGs refers to a major component of the whole galaxy population. Hence the search was not limited to the LBG technique.
Other obvious candidates are the ultraluminous infrared galaxies (ULIRG, Sanders et al. 1988, Genzel & Cesarsky 2000, detected in mm or sub-mm surveys (e.g., Ivison et al. 1998), a class defined for their infrared luminosity (8 − 1000 µm) exceeding ∼ 10 12 L ⊙ , and whose typical SFRs ( > ∼ 200 M ⊙ yr −1 ) well qualify them for being precursors to massive spheroids, as does their very high (stellar) density ensuring that they would "land" on the fundamental plane as star formation subsides (Kormendy& Sanders 1992, Doyon et al. 1994). ULIRGs as ETG in formation are also advocated by Genzel et al. (2001), who from the resolved kinematics for 12 of them argue that typical ULIRGs are likely precursors to intermediate-mass ETGs rather than to giant ellipticals. However, the internal kinematics of one ULIRG at z = 2.8 indicates a mass > ∼ 3 × 10 11 M ⊙ (Genzel et al. 2003) making it a likely precursor to a very massive ETG. Blain et al. (2004) note that submillimeter-selected galaxies at z = 2 − 3 appear to be more strongly clustered than LBGs at the same redshifts, which makes them more attractive candidates than LBGs for being the progenitors of the most massive ETGs. Still, their space density falls short by a factor of ∼ 10 compared to passive EROs at z ∼ 1, and they could be the main precursors to EROs only if their duty cycle is very short. Nevertheless, Chapman et al. (2005) argue that the sub-mm galaxies may well be the dominant site of massive star formation at z = 2 − 3, once more making them excellent candidates for being ETG in formation.
The survey and characterization of sub-mm galaxies are currently limited by the modest sensitivity and resolution of existing sub-mm facilities, hence optical/near-IR selections are still the most efficient way of identifying large samples of massive star-forming galaxies at high redshift. For the star-forming BzKselected objects, Daddi et al. (2004) estimate < SFR >≃ 200 M ⊙ yr −1 , which is typical of ULIRGs, and most of them are clearly mergers on ACS images. Indeed, out of 131 non-AGN (i.e., non X-ray emitter) star-forming BzKs with K < 20 in the GOODS-North field (Dickinson et al. in preparation), 82% were individually detected with Spitzer/MIPS at 24 µm (Daddi et al. 2005a). Moreover, by stacking the fluxes of the 131 objects (< z >= 1.9) from radio to X-rays (i.e., VLA 1.4 GHz, SCUBA 850 and 450 µm, MIPS 24 µm, IRAC 8-3.5 µm, near-IR and optical bands, and Chandra's 0.5-8 keV) Daddi and colleagues showed that the resulting composite SED is an excellent match to that of a template ULIRG with L IR = 1.7 × 10 12 L ⊙ and < SFR >≃ 250 M ⊙ yr −1 , in agreement with the typical SFRs derived from the extinction-corrected UV flux. Two of these BzKs have also been detected at 1.2 mm with MAMBO, implying a SFR∼ 1000 M ⊙ yr −1 (Dannerbauer et al. 2006). So, the BzK selection proves to be an excellent way of finding large numbers of ULIRGs at high redshift, whose space density at z ∼ 2 (∼ 1 − 2 × 10 −4 Mpc −3 ) is about three orders of magnitudes higher than the local density of ULIRGs, and a factor of 2-3 higher than that at z = 1. Moreover, the number of star-forming BzKs with M > 10 11 M ⊙ is close to that of passive BzKs of similar mass, and added together nearly match the space density of massive ETGs at z = 0 . Hence, it is tantalizing to conclude that as star formation subsides in star-forming BzKs the number of passive ETGs will approach their local density. Finally, worth mentioning is that the majority among samples of J − K > 2.3 DRGs in the Extended HDF-South field (Webb et al. 2006) and GOODS-South field (Papovich et al. 2006) have been recently detected at 24 µm with Spitzer/MIPS, indicating that the majority of DRGs are likely to be dusty starburst precursors to ETGs, rather than having already turned into passive ETGs themselves. Moreover, DRGs appear to be distributed over a very broad and nearly flat redshift distribution, from less than 1 to over ∼ 3.5 (Reddy et al. 2006).
Moderate redshift precursors to local ETGs are not necessarily star-forming. They may also be less massive ETGs that will merge by z = 0, an event now called "dry merging". The merger rate since z ∼ 1.2 has been estimated by Lin et al. (2004) as part of the DEEP2 survey, concluding that only ∼ 9% of presentday M * galaxies have undergone a major merger during the corresponding time interval. However, Bell et al. (2006) searched for dry merger candidates over the GEMS field, and based on 7 ETG-ETG pairs estimated that each present-day ETG with M v < −20.5 has undergone 0.5-1 major dry merger since z ∼ 0.7. This may be at variance with the estimate based on the 3D two-point correlation function of local ETGs in the overwhelming SDSS database. Indeed, each local ETG is found to have less than 1% probability per Gyr of merging with another ETG, hence the dry merging rate appears to be "lower, much lower than the rate at which ETG-hosting DM halos merge with one another" ), at least for z < ∼ 0.36 (Masjedi et al. 2006).
The history of star formation in ETGs has been deduced from the properties of their passively evolving stellar populations in low and high redshifts galaxies, and we know that ETGs and bulges hold at least ∼ 50% of the stellar mass at z = 0. Threfore, it is worth addressing here one last issue, even if only in a cursory way: is such an inferred history of star formation consistent with the direct measurements of the star-formation density and stellar mass density at high redshifts? Based on the estimate that the bulk of stars in spheroids formed at z > ∼ 3, it has been suggested that at least ∼ 30% of all stars (and metals) have formed by z = 3 (Renzini 1999). This appears to be at least a factor of ∼ 3 higher than the direct estimate based on the HDF-North, according to which only 3% − 14% of today's stars were in place by z = 3 (Dickinson et al. 2003). Data from HDF-South give the higher value 10% − 40% (Fontana et al. 2003), most likely as a result of cosmic variance affecting both HDF fields. Based on the ∼ 10 times wider field of the K20 survey, ∼ 30% of the stellar mass appears to be in place by z ∼ 2 ), but the corrections for incompleteness are large. Drory et al. (2005) find that over the ∼ 200 arcmin 2 area of the combined GOODS-South and FORS Deep Field, ∼ 50%, ∼ 25%, and at least ∼ 15% of the mass in stars is in place, respectively at z = 1, 2, and 3. So, no gross discrepancy has emerged so far between the mass density at z ∼ 3 as directly measured and as estimated from the fossil evidence at lower redshift. The same holds for the comparison between the star-formation densities as a function of redshift, as inferred from the distribution of stellar ages of ETGs on the one hand, and as directly measured by observations on the other hand (e.g., Madau et al. 1996, Steidel et al. 1999, Giavalisco et al. 2004b). Errors on both sides are still as large as a factor of 2 or 3, but this should rapidly improve thanks to the deep and wide surveys currently under way.
Almost thirty years ago Toomre (1977) remarked that star formation was observed only in galaxy disks, and further that the final state of merging spirals must be something resembling an elliptical galaxy. Thus, merging spirals to form ellipticals at relatively low redshifts became very popular, especially following the success of CDM theories in accounting for the growth of large scale structure from tiny initial perturbations.
However, in the intervening three decades an impressive body of evidence on galaxies at low as well as high redshift has accumulated, that at least in part contradicts Toomre's assumption. While in the local universe most of the star formation is indeed confined to disks; at z > 1 − 1.5 most of it appears to take place in starburst galaxies, such as ULIRGs, whose space density is orders of magnitude higher than in the local universe. Moreover, ∼ 50% of all stars seem to have formed at z < ∼ 1 (Dickinson et al. 2003), and to have occurred mostly in disks (Hammer et al. 2005), whereas, if the scenario shown in Figure 6 is basically correct, then the bulk of star formation in ETGs took place at much higher redshift. At the risk of some simplification, we can say that the era of ETG/spheroid/elliptical formation was largely finished by z ∼ 1 (if not before), just when the major build up of disks was beginning (see also Papovich et al. 2005).
The evidence for the stellar populations in ETGs being old, and older in massive galaxies than in less massive ones, has been known for over ten years, along with the evidence for down-sizing and for the anticorrelation of mass and SFR. Theoretical models based on the CDM paradigm have recently incorporated these observational constraints, and have been tuned to successfully reproduce the down-sizing effect in star formation (e.g., De Lucia et al. 2006). In a hierarchical scenario, down-sizing in star formation is indeed natural. Star formation starts firsts in the highest density peaks, which in turn are destined to become the most massive galaxies later on. But until recently models predicted that star formation was continuing all the way to low redshift, as cooling flows were left uncontrasted, thus failing to even produce a red sequence. To get the old and dead massive galaxies we see in nature, such cooling flows (and the accompanying star formation) had to be suppressed in the models, which is now generally accomplished by invoking strong AGN feedback, as first incorporated in ΛCDM simulations by Granato et al. (2001) 2 . Yet, the AGN responsibility in switching off star formation remains conjectural at this time, but we became aware that galaxies and supermassive black holes co-evolve, which means we must understand their formation as one and the same problem.
Baryon physics, including star formation, black hole formation and their feedbacks, is highly nonlinear, and it is no surprise if modelling of galaxy evolution relies heavily on many heuristic algorithms, their parameterization, and trials and errors. Dark matter physics, on the contrary, is extremely simple by comparison. Once DM halos are set into motion, there is nothing preventing them from merging with each other under the sole action of gravity, and growing bigger and bigger "galaxies" in an up-sizing process. Thus, the vindication of the ΛCDM paradigm should be found in observations demonstrating that the biggest, most massive galaxies are the first to disappear when going to higher and higher redshifts. This is indeed what has not been seen yet, and actually there may be hints for the contrary.