The fundamental plane of EDisCS galaxies

Astronomy & Astrophysics manuscript no. ediscs˙sigma˙sissa September 6, 2010 c ESO 20101 The fundamental plane of EDisCS galaxies ⋆ The effect of size evolution R.P. Saglia1,2 , P. Sánchez-Blázquez3,4 , R. Bender2,1 , L. Simard5 , V. Desai6 , A. Aragón-Salamanca7 , B. Milvang-Jensen8 , C. Halliday9 , P. Jablonka10,11 S. Noll12 , B. Poggianti13 , D. I. Clowe14 , G. De Lucia15 , R. Pelló16 , G. Rudnick17 , T. Valentinuzzi18 , S. D. M. White19 , and D. Zaritsky20 arXiv:1009.0645v1 [astro-ph.CO] 3 Sep 2010 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Max-Planck Institut für extraterrestrische Physik, Giessenbachstraße, D-85741 Garching, Germany e-mail: [email protected] Universitäts-Sternwarte München, Scheinerstr. 1, D-81679 München, Germany Departamento de Fsica Terica, Universidad Autnoma de Madrid, 28049 Madrid, Spain Departamento de Astrofı́sica, Universidad de La Laguna, E-38205 La Laguna, Tenerife, Spain Herzberg Institute of Astrophysics, National Research Council of Canada, Victoria, BC V9E 2E7, Canada Spitzer Science Center, Caltech, Pasadena CA91125, USA School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen, Denmark Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, I-50125 Firenze, Italy Observatoire de Genève, Laboratoire d’Astrophysique Ecole Polytechnique Federale de Lausanne (EPFL), CH-1290 Sauverny, Switzerland GEPI, Observatoire de Paris, CNRS UMR 8111, Université Paris Diderot, F-92125, Meudon, Cedex, France Institut für Astro- und Teilchenphysik, Universität Innsbruck, Technikerstr.25/8, 6020 Innsbruck, Austria Osservatorio Astronomico, vicolo dell’Osservatorio 5, I-35122 Padova Italy Ohio University, Department of Physics and Astronomy, Clippinger Labs 251B, Athens, OH 45701, USA INAF, Astronomical Observatory of Trieste, via Tiepolo 11, I-34143 Trieste, Italy Laboratoire d’Astrophysique de Toulouse-Tarbes, CNRS, Université de Toulouse, 14 Avenue Edouard Belin, 31400-Toulouse, France The University of Kansas, Malott room 1082, 1251 Wescoe Hall Drive, Lawrence, KS 66045, USA Astronomy Department, University of Padova, Vicolo dell’Osservatorio, 3 - 35122 Padova, Italy Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, Postfach 1317, D-85741 Garching, Germany Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721 Received ; accepted Abstract We study the evolution of spectral early-type galaxies in clusters, groups and the field up to redshift 0.9 using the ESO Distant Cluster SUrvey (EDisCS) dataset. We measure structural parameters (circularized half-luminosity radii Re , surface brightness Ie , and velocity dispersions σ) for 154 cluster and 68 field galaxies. On average, we achieve precisions of 10% in Re , 0.1 dex in log Ie and 10% in σ. We sample ≈ 20% of cluster and ≈ 10% of field spectral early-type galaxies down to an I band magnitude in a 1 arcsec radius aperture of I1 = 22. We study the evolution of the zero point of the fundamental plane (FP) and confirm results in the literature, but now also for the low cluster velocity dispersion regime. Taken at face value, the mass-to-light ratio varies as ∆ log M/L B = (−0.54 ± 0.01)z = (−1.61 ± 0.01) log(1 + z) in clusters, independent of their velocity dispersion. The evolution is stronger (∆ log M/L B = (−0.76 ± 0.01)z = (−2.27 ± 0.03) log(1 + z)) for field galaxies. A somewhat milder evolution is derived if a correction for incompleteness is applied. A rotation in the FP with redshift is detected with low statistical significance. The α and β FP coefficients decrease with redshift, or, equivalently, the FP residuals correlate with galaxy mass and become progressively negative at low masses. The effect is visible at z ≥ 0.7 for cluster galaxies and at lower redshifts z ≥ 0.5 for field galaxies. We investigate the size evolution of our galaxy sample. In agreement with previous results, we find that the half-luminosity radius for a galaxy with a dynamical or stellar mass of 2 × 1011 M⊙ varies as (1 + z)−1.0±0.3 for both cluster and field galaxies. At the same time, stellar velocity dispersions grow with redshift, as (1 + z)0.59±0.10 at constant dynamical mass, and as (1 + z)0.34±0.14 at constant stellar mass. The measured size evolution reduces to Re ∝ (1 + z)−0.5±0.2 and σ ∝ (1 + z)0.41±0.08 , at fixed dynamical masses, and Re ∝ (1 + z)−0.68±0.4 and σ ∝ (1 + z)0.19±0.10 , at fixed stellar masses, when the progenitor bias (PB, galaxies that locally are of spectroscopic early-type, but are not very old, disappear progressively from the EDisCS high-redshift sample; often these galaxies happen to be large in size) is taken into account. Taken together, the variations in size and velocity dispersion imply that the luminosity evolution with redshift derived from the zero point of the FP is somewhat milder than that derived without taking these variations into account. When considering dynamical masses, the effects of size and velocity dispersion variations almost cancel out. For stellar masses, the luminosity evolution is reduced to L B ∝ (1 + z)1.0 for cluster galaxies and L B ∝ (1 + z)1.67 for field galaxies. Using simple stellar population models to translate the observed luminosity evolution into a formation age, we find that massive (> 1011 M⊙ ) cluster galaxies are old (with a formation redshift z f > 1.5) and lower mass galaxies are 3-4 Gyr younger, in agreement with previous EDisCS results from color and line index analyses. This confirms the picture of a progressive build-up of the red sequence in clusters with time. Field galaxies follow the same trend, but are ≈ 1Gyr younger at a given redshift and mass. Taking into account the size and velocity dispersion evolution quoted above pushes all formation ages upwards by 1 to 4 Gyr. Key words. Galaxies: elliptical and lenticular, cD – evolution – formation – fundamental parameters 1. Introduction Despite their apparent simplicity, the physical processes involved in the formation of early-type galaxies (E/S0) remain unclear. The tightness of their scaling relations, such as the color-magnitude relation, and their slow evolution with redshift, are indicative of a very early and coordinated formation of their stars (e.g., van Dokkum et al. 2000; Blakeslee et al. 2003; Menanteau et al. 2004). However, in the ΛCDM paradigm, these galaxies are expected to form through mergers of smaller subsystems over a wide redshift range, managing to obey these constraints (Kauffmann 1996; De Lucia et al. 2006). A particularly interesting relation is that of the fundamental plane (hereafter FP). In the parameter space of central velocity dispersion (σ), galaxy effective radius (Re ), and effective surface brightness (S Be = −2.5 log Ie ), elliptical galaxies occupy a plane, known as the FP (Dressler, et al. 1987; Djorgovski & Davis 1987), which exhibits very little scatter (∼0.1 dex). The FP is usually expressed in the form: log Re = α log σ + βS Be + ZP, (1) where the zero point, hereafter ZP, is computed from the mean values log Re , log σ, and S Be of the sample: ZP = log Re − αlog σ − βS Be. (2) Based on the assumption of homology, the existence of a FP implies that the ratio of the total mass to luminosity (M/L) scales with σ and Re . Since the galaxy M/L depends on both the star formation history of the galaxies and the cosmology, the study of the FP is a valuable tool for studying the evolution of the stellar population in early-type galaxies. Several studies of intermediate (z ∼0.3) and highredshift (z ∼0.85) clusters of galaxies have used the ZP shift of the plane to estimate the average formation redshifts of stars in early-type galaxies (e.g., Bender et al. 1998; van Dokkum et. al. 1998a; Jørgensen et al. 1999; Kelson et al. 2000; van Dokkum & Stanford 2003; Wuyts et al. 2004; Jørgensen et al. 2006). In general, they have all found values compatible with a redshift formation greater than 3. In the field, early studies found slow evolution, compatible with that in clusters (e.g., van Dokkum et al. 2001; Treu et al. 2001; Kochanek et al. 2000). However, evidence of more rapid evolution in the field has been found by other authors (Treu et al. 2002; Gebhardt et al. 2003; Treu et al. 2005a). Taking into account the so-called progenitor bias (for which lower redshift early-type samples contain galaxies that have stopped their star formation only recently and that will not be recognised as early-types at higher redshifts), forces a revision to slightly lower formation redshifts (van Dokkum & Franx 2001, z ≈ 2). The current view is that both the evolution of earlytype galaxies with redshift and the dependence of this evolution on environment is different for galaxies of different mass. These differences manifest themselves as an evolution in the FP coefficient α at increasing redshift, from 1.2 (in the B band) at redshift 0.0 to 0.8 at z∼0.81.3 (van der Wel et al. 2004; Treu et al. 2005a; Treu et al. 2005b; van der Wel et al. 2005; di Serego Alighieri et al. 2005; Holden et al. 2005; Jørgensen et al. 2006). However, this change in the slope has not been observed at 0.2<z<0.8 (e.g., Send offprint requests to: R.P. Saglia ⋆ Based on observations collected at the European Southern Observatory, Paranal and La Silla, Chile, as part of the ESO LP 166.A0162. van Dokkum&Franx 1996; Kelson et al. 2000; Wuyts et al. 2004; van der Marel&van Dokkum 2007b; MacArthur et al. 2008). If interpreted as a M-M/L ratio relation, this rotation of the FP indicates that there is a greater evolution in the luminosity of low-mass galaxies with redshift. This interpretation was however questioned by van der Marel&van Dokkum (2007b). Dynamical models provide little evidence of a difference in M/L evolution between low- and high-mass galaxies, and the steepening of the FP may be affected by issues other than M/L evolution, such as an increasing importance of internal galaxy rotation at lower luminosities, not captured by the simple aperture-corrected velocity dispersion used in Eq. 1 (Zaritsky, Zabludoff & Gonzalez 2008), superimposed on the well known change with redshift in the fraction of S0 galaxies contributing to the early-type population (Dressler et al. 1997; Desai et al. 2007; Just et al. 2010). This so-called rotation of the FP, or change in the tilt of the FP, was originally found in field samples, but Jørgensen et al. (2006) claimed that is also exists for cluster galaxies at z=0.89. Most studies of evolution with redshift in cluster early-type galaxies have concentrated on single clusters. It remains unclear whether early-type galaxies in clusters at the same redshift share the same FP, or whether the FP coefficients vary systematically as a function of the global properties of the host cluster (e.g., richness, optical and X-ray luminosity, velocity dispersions, concentration, and subclustering). D’Onofrio et al. (2008) demonstrated that the universality of the FP has yet to be proven and that to avoid causing any biases by comparing the FP relation of clusters at different redshifts a larger number of clusters should be studied. Furthermore, the ZP evolution of the FP with redshift has been interpreted as an evolution in the M/L ratio. However, this may not be entirely true if there is a structural evolution in the size of the galaxies. At face value, observations seem to show that the most massive (M∗ > 1011 M⊙ ) spheroid-like galaxies at z>1.5, irrespective of their star-formation activity (Pérez-González et al. 2008) were much smaller (a factor of ∼4) than their local counterparts (Daddi et al. 2005; Trujillo et al. 2006, 2007; Longhetti et al. 2007; Zirm et al. 2007; Toft et al. 2007; Cimatti et al. 2008; van Dokkum et al. 2008; Buitrago et al. 2008; Saracco, Longhetti, & Andreon 2009; Damjanov et al. 2009; Ferreras et al. 2009). van Dokkum et al. (2010) argue that the growth in size with decreasing redshift is due to the progressive build-up of the outer (R > 5 kpc) stellar component of galaxies, while the inner core is already in place at redshift ≈ 2. We note also that these conclusions have been questioned by Mancini et al. (2010), who find evidence for galaxies as large as local ones at redshifts higher than 1.4. Complementing our discussion above about the evolution of the zero point of the FP, if galaxy size were to vary with redshift, we should expect an accompanying partial revision of the importance of the effect when taking into account the progenitor bias (Valentinuzzi et al. 2010a). Finally, if a variation in galaxy size with redshift were to occur, we should expect an accompanying increase in the central velocity dispersion with redshift (Cenarro & Trujillo 2009; van Dokkum, Kriek & Franx 2009). Both the evolution in size and velocity dispersion are predicted by theoretical models that take into account internal feedback ’puffing’ mechanisms (Biermann & Shapiro 1979; Fan, et al. 2008) or the effect of merging (Khochfar & Silk 2006; Hopkins et al. 2009). As one can read from Eq. 2, a change in log Re , log σ, and S Be with redshift due to structural evolution will change the amount of stellar population evolution needed to explain the ZP variation R.P. Saglia et al.: The fundamental plane of EDisCS galaxies and therefore needs to be taken into account when deriving constraints on the formation epoch of early-type galaxies. In this paper, we present the evolution of the FP in a sample of 154 spectral early-type galaxies in 28 clusters or groups and 62 in the field using spectra and images from the ESO Distant Cluster Survey of galaxies (White et al. 2005, EDisCS). The clusters have redshifts between ∼0.4 and 0.9 and velocity dispersions between 166 and 1080 km/s (Halliday et al. 2004; Clowe et al. 2006; Milvang-Jensen et al. 2008). Our clusters have generally lower velocity dispersions than those typically studied at similar redshifts and represent an intermediateredshift sample for which a majority of the clusters may be progenitors of typical low-redshift clusters (see Poggianti et al. 2006; Milvang-Jensen et al. 2008). The paper is organized as follows. Section 2 presents the data set. In particular, Sect. 2.1 describes the measurements of the galaxy velocity dispersions. Section 2.2 describes the measurement of the structural parameters, their errors, and the photometric calibration. Section 2.3 characterizes the statistical properties of the sample. Section 3 presents the FP of EDisCS galaxies. We start in Sect. 3.1 with the FP for 25 clusters and discuss the evolution of the FP zero point as a function of redshift and cluster velocity dispersion. Section 3.2 considers the differences between the FP of galaxies in clusters and the field and the dependence on galaxy mass. Section 3.3 discusses the related problem of the rotation of the FP. In Sect. 4, we consider the size evolution of galaxies and how this affects the stellar population time-dependence implied by the evolution of the FP. In Sect. 5, we draw our conclusions. Appendix A explains in detail how we compute circularized half-luminosity radii. Throughout the paper, we assume that Ω M = 0.3, ΩΛ = 0.7, and H0 = 70km/s/Mpc. 2. Data analysis The sample of galaxies analyzed in this paper consists of spectroscopic early-type objects. We considered the fluxcalibrated spectra reduced in Halliday et al. (2004) and Milvang-Jensen et al. (2008) of galaxies with early spectral type (1 or 2). This indicates the total absence (type 1) or the presence of only weak (with equivalent width smaller than 5 Å) [OII] lines (Sánchez-Blázquez et al. 2009). We derive galaxy velocity dispersions from these spectra (Sect. 2.1). We match this dataset with HST and VLT photometry (Sect. 2.2). The HST images (Desai et al. 2007) provide visual classification and structural parameters for 70% of our galaxies. For the remaining 30%, we use VLT photometry, where no visual classification is available (Simard et al. 2009). Approximately 70% of the galaxies with HST photometry have early-type morphology (Sect. 2.3). 2.1. Velocity dispersions Velocity dispersions were measured in all galaxy spectra using the IDL routine pPXF (Cappellari & Emsellem 2004). This routine is based on a maximum penalized likelihood technique that employs an optimal template, and also performs well when applied to spectra of low signal-to-noise ratio (Cappellari et al. 2009). The algorithm works in pixel space, estimating the best fit to a galaxy spectrum by combining stellar templates that are convolved with the appropriate mean galaxy velocity and velocity dispersion. The results depend critically on how well the spectra are matched by the template. To compile an optimal template, we use 35 synthetic spectra from the library of single stellar popula- 3 tion models of Vazdekis et at. (2010), which uses the new stellar library MILES (Sánchez-Blázquez et al. 2006). These spectra have been degraded to the wavelength-dependent resolution of the EDisCS spectra, determined from the widths of the lines in the arc lamp spectra, slit by slit, and matching well the widths of the sky lines on the science spectra. The library contains spectra spanning an age range from 0.13 to 17 Gyr and metallicities from [Z/H] = −0.68 to [Z/H] = +0.2. Operating in pixel space, the code allows the masking of regions of the galaxy spectra during the measurements. We use this to mask regions affected by skyline residuals. Although the code allows the measurement of the higher Gauss-Hermite order moments (Bender et al. 1994), we only fit the velocity and σ, which stabilises the fits in our spectra of low signal-to-noise ratio. Errors were calculated by means of Monte Carlo simulations in which each point was perturbed with the typical observed error, following a Gaussian distribution. Because the template mismatch affects the measurement of the velocity and σ determined with pPXF, a new optical template was used in each simulation. The errors were assumed to be the standard deviation in measurements inferred from 20 simulations. Owing to limitations caused by the instrumental resolution, only velocity dispersions larger than 100 km/s are reliable and unbiased. Therefore, galaxies with smaller σ, as well as velocity dispersions with uncertainties larger than 20%, the approximate intrinsic scatter of the local FP (see Introduction), will not be considered further. We note that the velocity dispersions measured here are ≈ 10% lower than those given in Sánchez-Blázquez et al. (2009). The difference is caused by the fact that the instrumental resolution in that paper was assumed to be constant with wavelength at the value of 6 Å. In reality, this is just the best resolution possible with our setup, that extends up to 8 Å. The change is important here, but does not affect any of the results presented in Sánchez-Blázquez et al. (2009). We measured velocity dispersions for 192 cluster and 78 field galaxies. Figure 1 shows the histograms of the statistical and systematic errors. The statistical errors are on average 10% and are a function of magnitude. The systematic errors are more difficult to estimate, as they depend on the template mismatch, continuum variations, and filtering schemes. They have been extensively studied in the past (Cappellari & Emsellem 2004) and can be as large as 5-10%. To check the size of systematic errors, we derived the galaxy velocity dispersions using the FCQ method of Bender et al. (1994), which is less prone to template mismatching systematics and operates in Fourier space. We focused on the G band region at z ≈ 0.5, the Mgb region at lower redshifts, or the largest available continuous range redder than the 4000 Å break, similar to the approach of Ziegler et al. (2005). The two methods agree well, with 68% of the values differing by less than the combined 1-σ error, and 96% by less than 3-σ, but smaller errors are derived using the pixel fitting approach, partially because most of each spectrum can be used. This allow us to conclude that our residual systematic errors are always smaller than the statistical ones. Finally, an aperture correction following Jørgensen et al. (1995) log σcor = log σmes + 0.04 ∗ log(Ap/3.4kpc), (3) where Ap represents the average aperture of our observations, 1.15 arcsec, scaled with the distances of the objects, was applied to the measured velocity dispersions σmes to place them on the Coma cluster standard aperture system of 3.4 kpc. Figure 4 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Figure 1. The velocity dispersion errors. First row: the histograms of statistical errors on velocity dispersions. Second row: the statistical errors as a function of apparent I band magnitude in a 1 arcsec radius aperture. Colors code the spectroscopic type (black: 1; red: 2). Figure 2. The histogram of the fractional aperture corrections σcor /σmes for cluster (left) and field (right) galaxies. 2 shows that, on average, this correction amounts to 3% with ≈ 0.5% spread. From this point on, we drop the cor and indicate with σ the aperture-corrected value of the velocity dispersion. Figure 3 presents the velocity dispersions as a function of redshift and their distribution. On average, the galaxy velocity dispersion is ≈ 200 km/s, with a mildly increasing trend with redshift. Weighting each galaxy with the inverse of its completeness value (see Sect. 2.3) in general changes the mean by no more than its error. 2.2. Photometry The photometric part of the FP, i.e., the half-luminosity radius Re L and average effective surface brightness hS Bei = −2.5 log 2πR 2, e where L is the total luminosity, was derived by fitting either HST ACS images (Desai et al. 2007) or I-band VLT images (White et al. 2005) using the GIM2D software (Simard et al. 2002). Simard et al. (2009) provide an extensive description of the methods and tests performed to assess the accuracy of the derived structural parameters, using exhaustive Monte Carlo sim- Figure 3. The velocity dispersions of the galaxy sample. Top: the measured galaxy velocity dispersions as a function of redshift in clusters (left) and the field (right). The green lines show the mean values in 0.1 redshift bins and the relative errors. The dotted lines show the mean values weighting each galaxy with the inverse of its completeness value. Bottom: the histogram of galaxy velocity dispersions in clusters (left) and the field (right). Colors code the spectral type (black: 1; red:2). The dotted lines show the histogram for the entire sample irrespective of spectral type. ulations. To summarize, a two-component two-dimensional fit was performed, adopting an R1/4 bulge plus an exponential disk convolved to the PSF of the images. From the parameters of the fit, we measured the (circularized) Re and effective surface brightness from curves of growth constructed from the best fit models using the procedure described in Appendix A. Historically, effective radii were derived from fits to curves of growths, constructed from photoelectric photometry using circular apertures of increazing sizes (Burstein et al. 1987). Our procedure reproduces this approach and is identical to that followed by Gebhardt et al. (2003) to study the evolution of the FP of field galaxies with redshift. We prefer it to less sophisticated approaches (such as the straight R1/4 fit often used in the literature) as it provides far superior fits to the images. As Gebhardt et al. (2003) do, we note that in the past a variety of methods have been adopted to measure the structural parameters that enter in the FP: curve of growth, isophotal photometry or 2dimensional fitting, pure R1/4 , Sersic or bulge+disk (B+D) functions. The derived effective radii and surface brightness, however, when combined in Eq. 1 of the FP, deliver the same ZP to a high degree of accuracy (Saglia et al 1993). This has been proven for a large set of local clusters, including the Coma cluster (Saglia et al. 1997b; de Jong et al. 2004), and remains valid for the present data set (see below). This justifies the comparisons with FP samples from the literature presented below. We later use effective radii to probe the size evolution of galaxies. Without doubt, the scale length along the major axis of a pure disk galaxy is the correct measurement of its size, and our circularized Re progressively underestimates the effective semi-major axis length as the inclination increases (see Fig. R.P. Saglia et al.: The fundamental plane of EDisCS galaxies 4). However, for a pure bulge the inverse is true, and our Re then averages out projection effects, producing the equivalent circularized size of each spheroid. On the other hand, the resolution and signal-to-noise ratio of the images considered here is too low to allow us to perform an accurate and unbiased determination of the sizes of the bulge and the disk components separately for our galaxies. Since the percentage of disk-dominated, highly inclined objects in the galaxy sample considered here is low, as it is in the low redshift comparison, we conclude that our choice is reasonable. In particular, the mean axial ratios of our sample and the low redshift comparison are identical, as discussed in Valentinuzzi et al. (2010b). We now consider the quantitative question of the extent to which our procedure for computing structural parameters is equivalent to other approaches discussed in the literature. In analogy with procedures followed for local galaxies (Saglia et al. 1997a), where systematic errors are gauged by comparing different photometric fits, we assess the robustness of the structural parameters to the chosen R1/4 bulge plus exponential disk surface brightness model by considering a second two-dimensional fitting approach to the HST images. We fit a single-component Sersic profile (with 0.5 ≤ nS er ≤ 4.5) to the HST ACS imaging in the F814W band, available for 10 of the EDisCS clusters. Again, the circularized half-luminosity radius Re (S er) is computed from curves of growth constructed from the best fit model as described in Appendix A. Figure 4 summarizes the results of our B+D and Sersic fits. The galaxies of our HST sample have on average a flattening 1 − be /ae of 0.37 (0.33 without spirals), with some diskdominated, nearly edge-on spiral galaxies reaching 1 − be /ae ≈ 0.8. As a consequence, our circularized effective radii are on average 39% (33 % without spirals) smaller than the effective semimajor lengths ae . On average, our objects are bulge-dominated (hB/T i = 0.59, 0.64 without spirals) and reasonably well described by a de Vaucouleurs law (hnS er i = 3.7, 3.9 without spirals). Figures 5, 6 and 7 (top and middle panels) assess the robustness of the derived structural parameters derived for the galaxies with measured velocity dispersions. For this purpose, we also consider the harmonic radius Rhar = (ae be )1/2 , often used in the literature as a proxy for Re (sometimes fixing the Sersic index to 4, the R1/4 law) and the related average surface brightness hS Bhar e i, where ae and be are the effective semi-major and minor axis of the Sersic fits. The evaluated harmonic and circularized Sersic radii are on average very similar to our adopted Re , as well as the resulting effective surface brightness. When combined into the quantity orthogonal to the FP log Re − 0.27hS Bei, they show minimal systematic differences and scatter. As discussed in Appendix A, only at high flattening (i.e. for almost edge-on disk-dominated galaxies) do the harmonic quantities show the expected stronger deviations. Figure 8 quantifies the differences δ log Re = log Re (B + D) − log Re (S ersic), δhS Bei = hS Bei(B + D) − hS Bei(S ersic), and the direction orthogonal to the FP, δFP = δ log Re − 0.27δhS Bei by showing their histograms, separately for cluster and field galaxies. In summary, the median differences are small (the Sersic Re are 9% larger, the Sersic effective surface brightnesses are ≈ 0.13 mag brighter). The widths at the 68% of the distributions are δ68 log Re ∼ 0.07, δ68 hS Bei ∼ 0.24, and δ68 FP ∼ 0.005 for cluster and (slightly smaller for) field galaxies with measured velocity dispersions. Given the quality of our HST ACS images, we conclude that we measure the structural parameters of galax- 5 Figure 4. The properties of the bulge+disk fits to galaxies with HST photometry and a measured velocity dispersion. We plot the ratio ae /Re between the semi-major effective scale length ae of the best-fitting Sersic profile to the circularized effective radius Re of the best fits B+D model (top), the bulge-to-total ratio B/T (middle), and the Sersic index nS er (bottom) as a function of the ellipticity 1 − be /ae (where be is the semi-minor effective scale length) of the Sersic fit. Objects with B/T > 0.5 are plotted in red, the remainder in blue. Symbols code the morphology: filled ellipses show T ≤ −4, filled circles crossed by a line −3 ≤ T ≤ 0, spirals T > 0. ies with a precision similar to that of local galaxies (Saglia et al. 1997b; de Jong et al. 2004). For the remaining clusters with only ground-based images, we derive the structural parameters as described above (Simard et al. 2009), i.e., by fitting an R1/4 bulge plus an exponential disk 2D model to the I-band VLT deep images that were obtained in excellent seeing conditions. Circularized halfluminosity radii are derived from curves of growth constructed from the best fits as described in Appendix A. In general, simulations show that the structural parameters derived from the fits to VLT images are of reasonably good precision when nearlyisolated galaxies (i.e., those for which the segmentation area has little contamination by nearby objects) are considered. Statistical errors smaller than 0.27 mag in total magnitudes and smaller than 0.36 dex in log Re are derived, in addition to systematic errors smaller than 0.15 mag and 0.2 dex, respectively, if bright objects (Imag< 22.5) are examined (Simard et al. 2009). The galaxies in our sample are typically at least one magnitude brighter than this limit. The bottom panels of Figs. 5, 6, and 7 show the comparison of the VLT-derived structural parameters with the HST derived structural parameters as a function of galaxy flattening, while Fig. 9 shows the histograms of the differences δ log Re = log Re (HS T )−log Re (VLT ), δhS Be i = hS Bei(HS T )− hS Bei(VLT ), and δFP = δ log Re − 0.27δhS Bei for objects with measured velocity dispersions where HST images are also available. For cluster objects that are isolated or have only relatively small companions (SExtractor flags 0 or 2, Bertin & Arnouts 1996), the comparison is reasonable, with median hδ log Re imed ∼ −0.08, δ68 log Re ∼ 0.14, (i.e., VLT half- 6 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Figure 5. The comparison between different estimations of the half-luminosity radii of all galaxies with HST photometry and a measured velocity dispersion. We plot the ratio of the harmonic radius (ae be )1/2 to the circularized effective radius Re of the best fits HST B+D model (top), the ratio of the circularized effective radius Re (S er) of the Sersic fit to Re (middle), and the ratio of the circularized effective radius Re (VLT ) of the best fits VLT B+D model to Re (bottom) as a function of 1 − be /ae . Symbols and color coding are as in Fig. 4. Figure 6. The comparison between different estimates of the effective surface brightness of all galaxies with HST photometry and a measured velocity dispersion. We plot the difference ∆hS Be (ae be )i between the average surface brightness within (ae be )1/2 and Re (top), the difference ∆hS Be (S er)i between the average surface brightness within Re (S er) and Re (middle), and the difference between the average surface brightness within Re (VLT ) and Re (bottom) as a function of 1 − be /ae . Symbols and color coding are as in Fig. 4. Figure 7. The comparison between different estimations of the quantity FP = log Re − 0.27hS Bei for all galaxies with HST photometry and a measured velocity dispersion. We plot ∆FP(ae be )1/2 = log((ae be )1/2 /Re ) − 0.27(hS Bei(ae be )1/2 ) − hS Bei) (top), ∆FP = log(Re (S er)/Re) − 0.27(hS Bei(S er) − hS Bei) (middle), and ∆FP = log(Re (VLT )/Re ) − 0.27(hS Bei(VLT ) − hS Be i) (bottom) as a function of 1 − be /ae . Symbols and color coding are as in Fig. 4. luminosity radii are on average 20% larger than HST Re with ≤ 25% scatter), and median difference hδhS Be iimed ∼ −0.32, δ68 hS Bei ∼ 0.53 (i.e., VLT effective surface brightnesses are on average 0.32 mag brighter than those from HST hS Bei with ≤ 0.53 mag scatter). The errors δ log Re and δhS Bei are correlated, with minimal scatter in the direction almost orthogonal to the FP, i.e., δFP = δ log Re − 0.27δhS Bei and δ68 FP ∼ 0.025 and there is a small median shift. No trend with redshift is seen. These values agree with or are of higher precision than those derived from simulations (see above). Very similar results are obtained for field objects. Therefore, the VLT dataset can be merged with the HST-based one to study the evolution of the FP (Sect. 3). The systematic and random errors increase dramatically if objects with sizable companions (VLT SExtractor flag 3) are considered. In these cases, the VLT segmentation areas fitted by GIM2D are heavily contaminated by the companions. As a consequence, Re (VLT ) and VLT total magnitudes are systematically larger and brighter, respectively, than those derived from HST fits. There are 38 cluster and 10 field galaxies with early spectral type and measured velocity dispersion that have only VLT imaging and a SExtractor flag equal to 3. Given the already sizeable systematics in Re detected for the ’isolated’ objects, we refrain from attempting an iterative fit and just exclude the affected galaxies from the FP analysis. In Sect. 4, we use the half-luminosity radii discussed above to constrain the size evolution of our galaxies. The highprecision (≈ 10% systematic) HST half-luminosity radii are certainly good enough and our results are based on this dataset only. A number of caveats have to be kept in mind when considering the VLT radii. According to the Monte Carlo simulations discussed by Simard et al. (2009, Fig.1), the VLT radii of the R.P. Saglia et al.: The fundamental plane of EDisCS galaxies 7 Figure 8. The quality of the photometry parameters derived from HST images for cluster (left) and field (right) galaxies. We show histograms of the differences between structural parameters derived from bulge plus disk (B+D) and Sersic GIM2D fits to the HST ACS images of the galaxies with measured velocity dispersions. The mean, rms, and the widths at the 68% of the distributions are given. Figure 9. The quality of the photometry parameters derived from VLT images for cluster (left) and field (right) galaxies. Histograms of the differences between structural parameters derived from bulge plus disk GIM2D fits to the HST ACS and VLT I band images of the isolated, undisturbed galaxies with measured velocity dispersions. The mean, rms and the widths at the 68% of the distributions are given. largest galaxies of the sample (larger than 1.8 arcsec) might underestimate the true radii by up to 40%. But only 2.5% of our sample has Re > 1.8”. Sizes below 0.1 arcsec are probably unreliable because of a lack of resolution, but only 3% of cluster galaxies and 5% of field galaxies fall into this category. Finally, if galaxies have strong color gradients, our half-luminosity radii, derived from I band images (i.e., approximately rest-frame V band at redshift 0.5 and rest-frame B band at redshift 0.8) might be affected differentially with redshift. However, we do not detect any significant trend with redshift in the sizes derived from our VLT B and V band images relative to the ones used here from the I band images. Despite all these systematic differences between HST and VLT Re radii (on average 20%), Sect. 4 shows that the size evolution derived from VLT Re radii is very similar. As a last step, effective surface brightnesses were calibrated as follows. Corrections to rest-frame Johnson B band were applied based on the spectroscopic redshift z and an interpolation of the best-fit spectral energy distribution, according to our photometric redshift procedure (Rudnick et al. 2009; Pelló et al. 2009). Moreover, the Tolman correction (1 + z)4 was taken into account. Finally, to be able to compare our results with those of Wuyts et al. (2004) and related papers, we transformed effective surface brightness to surface brightness at Re using the con- version factor valid for a pure R1/4 law, i.e. Ie = hIe i/3.61 and loghIe i(L⊙ /pc2 ) = −0.4(hS Bei − 27). Figure 10 shows log Re , log Ie , and dynamical mass log Mdyn as a function of redshift. Following van Dokkum & van der Marel (2007), we compute dynamical masses to be Mdyn = 5Re σ2 /G = 1.16 × 106 (Re /kpc), ×(σ/kms−1 )2 M⊙ (4) (see also Sect. 3.2). The mean size of the half-luminosity radius remains approximately constant at values of ≈ 2.5 kpc. In contrast, the surface brightness at Re increases on average by a factor 2 from redshift 0.4 (where it is ≈ 250L⊙ /pc2 ) to redshift 0.8. This matches the differential luminosity evolution inferred from the FP zero point evolution with redshift (see Sect. 3.1). Weighting each galaxy with the inverse of its selection value to correct for incompleteness (see Sect. 2.3) pushes the sample averages of log Re and log Ie to slightly lower and higher values, respectively. As for the velocity dispersions, the effect is however on the order of the error in the averages. We note that the situation changes when we consider the size evolution of massselected samples (see Sect. 4). We study cluster galaxies with dynamical masses higher than 1.5 × 1010 M⊙ and field galaxies 8 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Figure 10. The distribution with redshift of sizes, surface luminosities, and dynamical masses of the galaxy sample. We show the half-luminosity radii log Re (top), effective surface brightness log Ie (middle), and dynamical mass log Mdyn (bottom) as a function of redshift for cluster (left) and field (right) galaxies. Black and red points show spectroscopic types 1 and 2, respectively. Crosses and circles show galaxies with HST and VLT photometry, respectively. The solid green lines show the mean values in 0.1 redshift bins with the errors. The dotted lines show the averages obtained by weighting each galaxy with the inverse of its selection value. The blue lines show the mean luminosity evolution derived from Fig. 17: log Ie = 2.4 + 1.66 log 1+z 1.4 /0.83 for /0.83 for the field. cluster galaxies and log Ie = 2.4 + 2.27 log 1+z 1.4 with dynamical masses higher than 2.5 × 1010 M⊙ . Both cluster and field galaxies have on average a dynamical mass of 1011 M⊙ . 2.3. Selection function Figure 11 describes the final sample. We measured velocity dispersions for 113 cluster and 41 field spectral early-type galaxies with HST photometry, and 41 cluster and 27 field galaxies with only VLT good photometry. A large fraction of galaxies with HST photometry also have early-type morphology: 67% of the objects in clusters and 78% in the field have been classified as either Es or S0. Moreover, 77% of galaxies in clusters and 68% in the field do not exhibit [OII] emission, being of spectral type 1. Figure 11. Statistics of the sample of galaxies with measured velocity dispersions and photometric parameters. To quantify the selection function of our sample, we assign a selection probability PS to each galaxy. This is computed in two steps. First, the σ-completeness probability Pσ of the velocity dispersion measurements is determined. This is shown in Fig. 12. For each given spectral type, we compute the ratio of the number of galaxies with a measured velocity dispersion and reliable photometric structural photometry (see above) to the number of galaxies with a spectrum in a given magnitude bin. In a way similar to Milvang-Jensen et al. (2008), we use the I band magnitude in a 1 arcsec radius aperture I1 . We compute these curves separately for cluster and field galaxies, and for galaxies with redshifts either lower than or equal to or higher than 0.6. Finally, we assign the probability Pσ (I1 , z, S T, F/C) to each galaxy by linearly interpolating the appropriate curve for its redshift z, spectral type S T , and field or cluster environment (F/C) as a function of magnitude. The σ-completeness is high at bright magnitudes and declines toward fainter objects. In this regime, the σ completeness is also slightly higher for higher redshift galaxies, where the exposure times are longer. The differences between cluster and field galaxies are not as pronounced. As a second step, following Milvang-Jensen et al. (2008) we consider the total number of spectroscopically targeted galaxies NT (drawn from a photometric magnitude-limited sample far deeper than that considered here; see Milvang-Jensen et al. 2008) in a given magnitude bin, separately for each of the 19 fields we observed. In the given field, we then consider the number of galaxies for which we were able to derive a secure redshift NR (with a success rate of essentially 100%; see R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Figure 12. The relative completeness functions. The fraction of galaxies with an observed spectrum of spectroscopic type 1 or 2 for which we could measure velocity dispersions and obtain reliable photometric structural parameters. This relative completeness is shown for the clusters (top row) and the field (bottom row) as a function of galaxy magnitude in the I band in a 1 arcsec radius aperture. Colors code the spectral type (black: 1; red: 2). The full lines show the full redshift range, the dotted lines galaxies with z < 0.6, the dashed lines galaxies with z ≥ 0.6. The dots show the magnitudes of the single galaxies and the assigned completeness weight. Milvang-Jensen et al. 2008), the number of galaxies spectroscopically found to be members of any cluster NC , and the number of galaxies found in the field, NF = NR − NC . We conC struct the ratio functions RC = NNCT and RF = NRN−N and interT polate them at the magnitude of each galaxy. Finally, we assign to each galaxy the selection probability PS (Cluster) = Pσ × RC or PS (Field) = Pσ × RF if the galaxy belongs to a cluster or to the field. Figure 13 shows the resulting probabilities as a function of I1 and dynamical mass (see Eq. 4 and Sect. 3.2). In clusters, we sample 10 to 30% of the spectral early-type population. The selection probability is almost flat as a function of mass for Mdyn ≥ 4 × 1010 M⊙ . This is above the stellar mass completeness limit of our parent stellar catalogue. In this mass range, the selection probability has no dependence on the galaxy colors. We become progressively more incomplete at lower masses, where we sample just 10% of the population. The effect is less pronounced at higher redshifts. In the field, the average completeness is lower (≈ 15 %) and similar trends are observed. In general, Pσ traces PS quite well, with PS ≈ (0.29 ± 0.12)Pσ. In the abstract and in the following, we quote first results obtained ignoring selection effects, and then illustrate the effect of the selection correction. Tables 1 and 2 summarize the velocity dispersions and the structural parameters of the cluster and field galaxies, respectively. For each galaxy, we list its name (White et al. 2005), the number of the cluster to which it belongs (if it is a cluster galaxy, see Table 4 for the correspondence between cluster name and number), spectroscopic redshift and type (Halliday et al. 2004; Milvang-Jensen et al. 2008), raw and aperture-corrected veloc- 9 Figure 13. The completeness function of the galaxy sample. The completeness weight for the galaxies with a velocity dispersion for clusters (top row) and the field (bottom row). Left: as a function of galaxy magnitude in the I band in a 1 arcsec radius aperture; Right: as a function of dynamical mass. Colors code the spectral type (black: 1; red: 2). Filled circles show galaxies with redshift either equal or higher than 0.6, open circles galaxies with redshift lower than 0.6. The green full lines with error bars show the bin averages and rms over the full redshift range. The dotted lines refer to the sample with z < 0.6, the dashed lines to the sample with z ≥ 0.6. ity dispersion σmes and σcor with estimated statistical error, circularized half-luminosity radius Re , surface brightness log Ie in the rest-frame B-band, and, when HST images are available, morphological type. When VLT-only images are available, the morphological flag is set to be ∗ when the SExtractor flag is equal to 3, i.e., when the photometric parameters are expected to be contaminated by companions. Moreover, we list the selection probabilities PS and the stellar masses (see Sect. 3.2). In addition, Table 3 gives the circularized Re and log Ie derived from Sersic fits (to HST images) and bulge+disk fits to VLT images for the galaxies for which both HST and VLT images are available. 3. The fundamental plane of the EDisCS galaxies 3.1. The FP of EDisCS clusters Figure 14 shows the FP of the 14 EDisCS clusters with HST photometry, while Fig. 15 provides the FP of the additional 12 clusters with VLT-only photometry. In each cluster, good FP parameters are available for only a small number of galaxies (< 9), the exceptions being cl1232.5-1144, cl1054.4-1146, cl1054.7-1245, and cl1216.8-1201. Therefore, at this stage we do not attempt to fit the parameters of the FP except for the zero point, keeping the velocity dispersion and surface brightness slopes fixed to the local values (α0 = 1.2, β0 = −0.83/(−2.5) = 0.33, Wuyts et al. 2004). In Sect. 3.3, we argue that this is a good approximation up to redshift 0.7. Following van Dokkum & van der Marel (2007), we compute the zero point as ZP = Σw(1.2 log σ(km/s) − 0.83 log Ie (L⊙ /pc2 ) 10 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies − log Re (kpc))/Σw, (5) where the sum comprises all N galaxies in a cluster with measured velocity dispersion, early spectroscopic type (1 or 2), and (for clusters with only VLT photometry) SExtractor flag 0 or 2, irrespective of morphology. At this stage, we weight each point with w = (1/1.2dσ)2, where dσ is the error on σ, and do not apply selection weighting to be consistent with the procedures adopted in the literature and minimize scatter. We note that this could generate systematic differences, given that the considered surveys have different selection functions. We explore the influence of our selection function on the √ results below. The error in the zero point is δZP = rms(ZP)/ N. Following Wuyts et al. (2004), we use the Coma cluster as a reference point for the whole sample with ZP = 0.65. All past studies measuring the peculiar motions of the local universe of early-type galaxies (Lynden-Bell et al. 1988; Colless et al. 2001; Hudson et al. 2004, and references therein) agree with the conclusion that Coma, the richest and, in the FP context, the most well-studied local cluster, is at rest with respect to the cosmic microwave background and therefore the best suited as a reference. We convert the variation in the FP zero point into a variation in the mean mass-to-light ratio of galaxies in the B band with respect to Coma using the relation ∆ log M/LB = (ZP − 0.65)/0.83 (where 0.83=β0 × 2.5, see Eqs. 7 and 8). We note that at this stage we still implicitly assume, as in the past, that no evolution in size or velocity dispersion is taking place. Figure 16, left, shows ∆ log M/LB as a function of redshift. Only clusters with 4 or more (N ≥ 4) galaxies are considered. Table 4 gives the relevant quantities: cluster number (Col. 1), cluster name (Col. 2, from Milvang-Jensen et al. 2008), cluster short name (Col. 3), type of photometry used (HST or VLT, Col. 4), cluster velocity dispersion (Col. 5), ∆ log M/LB (Col. 6), scatter (Col. 7), and number of galaxies considered (Col. 8). Table 4 also lists the first six columns for the remaining clusters without FP ZPs. If we compute ∆ log M/LB using the VLT photometry for the 12 clusters with both HST and VLT photometry, we derive a mean value ∆ log M/LB (VLT − HS T ) = −0.04 (-0.02 if two outliers, CL1354 and CL1138, are not considered) with an rms of 0.06 or an error in the mean of 0.02 (see also Sect. 3.2). We add to the EDisCS sample 15 clusters from the literature (van Dokkum & van der Marel 2007), plus A370 from Bender et al. (1998). They span the redshift range z = 0.109 − 1.28 and sample the high cluster velocity dispersion (σclus > 800km/s) regime only. Moreover, as a common zero-redshift comparison we add the Coma cluster. A linear weighted fit to the whole sample gives ∆ log M/LB = (−0.54 ± 0.01)z. Applying selection weighting reduces the slope to −0.47. A fit restricted to the literature sample alone gives −0.49 ± 0.02. Wuyts et al. (2004) derive −0.47, whereas van Dokkum & van der Marel (2007) find −0.555 ± 0.042. In view of the size evolution discussion of Sect. 4, where dependencies of log(1 + z) are considered, we also fit the slope η of the form ∆ log M/LB = η log(1 +z). The results are summarized in Table 5. The residuals of the EDisCS cluster sample have an rms of 0.08 dex. The literature sample, which does not probe clusters with small velocity dispersions (see below), has an rms of 0.06 dex, the clusters at low redshift (z ≤ 0.2) having systematically positive residuals. The combined sample has an rms scatter of 0.07. Taking into account the measurement errors, this implies an intrinsic scatter of 0.06 dex or 15% in M/L. The best-fit line closely matches the prediction of simple stellar population models (Maraston 2005) with high formation redshift (2 ≤ z f ≤ 2.5) and solar metallicities. Here and below we make use of Maraston (2005) models to translate mass-tolight or luminosity variations into formation ages or redshifts. Similar conclusions would be obtained using other models (e.g., Bruzual & Charlot 2003), see for example Jaffé et al. (2010). However, we bear in mind that systematic errors still affect the SPP approach (see Maraston et al. 2009; Conroy & Gunn 2010, for the difficulties in reproducing the colors of real galaxies). Trimming the sample to high-precision data only (for example, considering only velocity dispersions determined to a precision higher than 10%) does not change the overall picture. We discuss the effects of cutting the sample according to mass, spectroscopic type, or morphology in Sect. 3.2, where we consider the sample on a galaxy by galaxy basis, since any selection drastically reduces the number of clusters with at least 4 galaxies. Figure 16 (right panel) shows the residuals ∆ log M/LB + 0.54z as a function of the cluster velocity dispersion. No convincing correlation is seen (the Pearson coefficient is 0.21, the Spearman coefficient 0.39 with a probability of 2.5% that a correlation exists), confirming that cluster massive early-type galaxies follow passive evolution up to high redshifts not only in massive clusters, as has been established (see discussion in the Introduction), but also in lower mass structures down to the group size. There is a hint that the scatter could increase in the low velocity dispersion clusters: while the combined EDisCS+Literature sample of high velocity dispersion clusters (σclus > 800 km/s) exhibit an rms of the residuals ∆ log M/LB + 0.54z of 0.06 dex, the lower σclus EDisCS clusters exhibit an rms of 0.08 dex. We note that the scatter in M/L measured in each cluster is larger (up to 0.3 dex) and intrinsic (i.e., not caused by measurement errors). 3.2. Environment and mass dependence We now consider the sample on a galaxy by galaxy basis. As in Eq. 5, in Fig. 17 we show the evolution with redshift of ∆ log M/LB = (1.2 log σ − 0.83 log Ie − log Re − 0.65)/0.83 for the EDisCS cluster (left) and field (right) galaxies. For the 74 galaxies with both HST and VLT photometry, we derive a mean difference ∆ log M/LB (VLT − HS T ) = −0.02 with an rms of 0.06 or an error in the mean of 0.02, similar to that quoted for clusters in Sect. 3.1. In general, there is scatter in the galaxy data that falls even below the SPP model line for a formation redshift z f = 1.2 with twice-solar metallicity, or to positive values that are impossible to explain with simple stellar population models. Many of these deviant points are galaxies with late-type morphology. Their measured velocity dispersion might not be capturing their dynamical state dominated by rotation. First, we turn our attention to galaxies belonging to clusters. Averaging the points in redshift bins 0.1 wide shows that cluster galaxies closely follow the mean linear fit derived for clusters as a whole. This corresponds to a solar metallicity SPP model with formation redshift z f = 2 or formation lookback time of 10 Gyr (see Sect. 4.4 for a detailed discussion). The average values do not change within the errors if a cut either in mass (Mdyn > 1011 M⊙ ) or morphology (T ≤ 0) is applied. Table 5 lists the slope η and η′ of ∆ log M/L = η log(1 + z) = η′ z derived by cutting the sample in a progressively more selective way. In general, PS selection weighting produces shallower slopes. Shallower slopes are also obtained when only massive galaxies or spectral types ST=1 are considered. The steepest slope (η′ = −0.56) is obtained by considering only galaxies with HST early-type morphologies, no restrictions on spectral type or mass, and no selection weighting. The shallowest slope (η′ = −0.32) is obtained considering only galaxies more massive R.P. Saglia et al.: The fundamental plane of EDisCS galaxies 11 Figure 14. The FP of the EDisCS clusters with HST photometry. Each cluster is identified by its short name for clarity, see Table 4 for the full name. Colors code the spectroscopic type (black = 1, red = 2). Symbols code the morphology: filled ellipses show T ≤ −4, filled circles crossed by a line −3 ≤ T ≤ 0, spirals T > 0. The magenta line shows the best-fit FP line with no selection weighting. The full line shows the Coma cluster at zero redshift. The black dotted and dashed lines show data for the clusters MS2053-04 at z = 0.58 and MS1054-03 at z = 0.83, respectively, from Wuyts et al. (2004). than 1011 M⊙ , with spectral type ST=1, no constraints on morphology and PS weighting. Finally, considering galaxies with HST photometry and no constraints on morphology or mass, but with ellipticity less than 1 − be /ae ≤ 0.6 changes the slopes only minimally, from η′ = −0.53 (for 113 objects) to η′ = −0.56 (for 88 objects). In contrast, galaxies in the field have values of ∆ log M/LB more negative than the corresponding cluster bins starting from z ≈ 0.45. For our sample, a solar metallicity SSP model with formation redshift z f = 1.2 is an accurate representation of the data. This corresponds to a formation age of 8.4 Gyr or a mean age difference of 1.6 Gyr between cluster and field galaxies (see Sect. 4.4 for a detailed discussion). The slopes η listed in Table 5 for field galaxies are always steeper than the ones derived for cluster galaxies. The shallowest (η′ = −0.67) is obtained when considering only galaxies more massive than 1011 M⊙ with ST=2. Here we approach the result of van Dokkum & van der Marel (2007), who detect only a very small age difference between cluster and field galaxies of these masses and morphologies. Still, our shallowest slope for field galaxies is steeper than the steepest slope for cluster galaxies. We compute dynamical masses as in Eq. 4. As discussed in the Introduction, the validity of this equation can be questioned in many respects. The value of the appropriate structural constant need not to be the same for every galaxy. If ordered motions dominate the dynamics of a galaxy, as must be the case for disk galaxies, the use of velocity dispersion is inappropriate. Moreover, we also assume that the structure proportional- 12 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Figure 15. The FP of the EDisCS clusters with VLT only photometry. Each cluster is identified by its short name for clarity, see Table 4 for the full name. Colors code the spectroscopic type. The black squares show galaxies with SExtractor flags different from 0 or 2 and therefore unreliable photometric parameters. The dotted magenta line shows the best-fitting FP line to all galaxies. The solid magenta line shows the best-fitting FP line considering only galaxies with spectroscopy type ≤ 2 and SExtractor flag 0 or 2. The full line shows the Coma cluster at zero redshift. The black dotted and dashed lines show the clusters MS2053-04 at z = 0.58 and MS1054-03 at z = 0.83 from Wuyts et al. (2004), respectively. ity constant does not vary with redshift, which might not be true. Nevertheless, on average Eq. 4 delivers values that compare reasonably with stellar masses. We compute the (total) stellar masses from ground-based, rest-frame absolute photometry derived from SED fitting (Rudnick et al. 2009), adopting the calibrations of Bell & de Jong (2001), with a ’diet’ Salpeter IMF (with constant fractions of stars of mass less than 0.6M⊙ ) and B-V colors, and renormalized using the corrections for an elliptical galaxy given in de Jong & Bell (2007). The method to calculate the rest-frame luminosities and colors is described in Rudnick et al. (2003), and the rest-frame filters have been taken from Bessel (1990). Although the photometric redshifts and rest-frame SEDs have been computed from the matched aperture photometry of White et al. (2005), the rest-frame luminosities have been adjusted to total values, as described in Rudnick et al. (2009). In general, the dynamical masses are somewhat lower than the stellar ones (Mdyn /M∗ = 0.91 for cluster galaxies, 0.75 for field galaxies), with an intrinsic scatter of a factor of two, on the order of the typical combined precision achieved for dynamical and stellar masses. If we consider only galaxies with HST morphology T < 0, the ratio Mdyn /M∗ drops to 0.74 for cluster and 0.56 for field galaxies. Moreover, a possible decreasing trend with redshift of the ratio Mdyn /M∗ is seen at the 2 − σ level, which is not unexpected given the size and velocity dispersion evolution discussed in Sect. 4.2. To conclude, the tendency to have Mdyn /M∗ < 1 may indicate that the structural constant used in Eq. 4 is too low. However, we note that the structural constant is the one that dynamical studies at low redshifts prefer (Cappellari et al. 2006; Thomas et al. 2010). Alternatively, our adopted IMF contains too high a fraction of low mass stars (Baldry et al. 2008). Finally, we refer to Thomas et al. (2010) for a discussion of the role of dark matter in the estimation of Mdyn . In the following, we consider relations as a function of both dynamical and stellar masses to assess the robustness of each result. Figure 18 shows the residuals ∆ log M/LB + 1.66 log(1 + z) as a function of galaxy dynamical mass, for cluster (top) and field galaxies (bottom), at low (left) and high (right) redshifts. We divided the sample into three redshift bins of z < 0.5, 0.5 ≤ z < 0.7, and z ≥ 0.7. Averaging the points in mass bins 0.25 dex wide, one derives the following (see also Fig. 25). At low redshifts (z < 0.5), there is no convincing systematic trend between mass and residuals from the passively evolved FP, for both cluster (where the Pearson coefficient is 0.55 with a 2.5 σ deviation from the no correlation hypothesis) and field galaxies (where the Pearson coefficient is 0.15 for a t-value of 0.58 in agreement with the absence of a correlation). Within the er- R.P. Saglia et al.: The fundamental plane of EDisCS galaxies 13 Figure 16. Left: the redshift evolution of the B band mass-to-light ratio. The full black lines show the simple stellar population (SSP) predictions for a Salpeter IMF and formation redshift of either z f = 2 (lower) or 2.5 (upper curve) and solar metallicity from Maraston (2005). The blue line shows the SSP for z f = 1.5 and twice-solar metallicity, the magenta line the SSP for z f = 2.5 and half-solar metallicity. The dotted line shows the best-fit linear relation and the 1σ errors dashed. Right: the (absence of) correlation of the M/L residuals ∆ log M/LB + 0.54z with cluster velocity dispersion. Black points are EDisCS clusters with HST photometry, cyan points with VLT photometry. Each EDisCS cluster is identified by its short name for clarity, see Table 4 for the full name. Red points are from the literature, Bender et al. (1998) and van Dokkum & van der Marel (2007). Cluster velocity dispersions come from Halliday et al. (2004) and Milvang-Jensen et al. (2008) for EDisCS clusters and from Edwards et al. (2002) (Coma), Le Borgne, Pello & Sanahuja (1992) (A2218), Gómez, Hughes & Birkinshaw (2000) (A665), Carlberg et al. (1996) (A2390), Fisher et al. (1998) (CL1358+62), Mellier et al. (1988) (A370), Poggianti et al. (2006) (MS105403 and CL0024+16), van Dokkum & van der Marel (2007) (3C295, CL1601+42, CL0016+16), Tran et al. (2005) (MS2053-04), Jørgensen et al. (2005) (RXJ0152-13), and Jørgensen et al. (2006) (RXJ1226+33) for the literature clusters. We estimate σclus for RDCS1252-29 and RDCS084+44 from their bolometric X-ray luminosity and the relation of Johnson et al. (2006). Circles mark cluster at redshift > 0.7. rors, the solar metallicity SSP model with z f = 2 provides a reasonable description of the evolution of luminosity of all cluster and field early-type galaxies more massive than 1010 M⊙ . At intermediate redshifts (0.5 ≤ z < 0.7), field (and to a lower extent cluster) galaxies with dynamical masses lower than 1011 M⊙ show systematically negative mean residuals. At higher redshifts (z ≥ 0.7), both cluster and field galaxies with masses lower than 1011 M⊙ show systematically negative mean residuals, i.e., are brighter than predicted by the passively evolved FP at zero redshift, with Spearman correlation coefficients between mass and residuals larger than 0.66 and a t-value of 6.3 for cluster galaxies. The trends are stronger if we restrict the sample to galaxies with HST early-type (T < 0) morphology. We note that down to masses ≈ 4 × 1010 M⊙ we sample a constant fraction (≈ 20%) of the existing galaxy population (see Fig. 13). At lower masses, however, this drops to just 10% and we might expect residual selection effects to play a role, as discussed in van der Wel et al. (2005). We do not detect any additional dependence on cluster velocity dispersion. 3.3. The rotation of the fundamental plane As discussed by di Serego Alighieri et al. (2005), a mass dependence of the ∆ log M/L residuals implies a rotation of the FP as a function of redshift. Here we investigate the effect by assuming that the zero point variation ∆ log M/LB = −1.66 × log(1 + z) for cluster and ∆ log M/LB = −2.27 × log(1 + z) for field galaxies is caused entirely by pure luminosity evolution. Accordingly, we correct the surface brightnesses of cluster galaxies by applying the offset ∆ log Ie = −1.66 × log(1 + z)/0.83 and of field galaxies by applying ∆ log Ie = −2.27 × log(1 + z)/0.83. This agrees with the observed evolution of the average effective surface brightness (see dotted line in Fig. 10), except for the highest redshift bins. We then fit the parameters α and β of Eq. 1 using the maximum likelihood algorithm of Saglia et al. (2001), which uses multi-gaussian functions to describe the distribution of data points, taking into account the full error covariance matrix and selection effects (for a Bayesian approach to the modeling of systematic effects see Treu et al. 2001). To ensure uniformity with the procedures adopted in the literature, the results are derived with and without taking into account selection effects, but the differences between the two approaches are always smaller than the large statistical errors. We fit three redshift ranges for cluster galaxies and two for field galaxies. The results are shown in Table 6. The errors are computed as the 68% percentiles of the results of Monte Carlo simulations of each fitted sample as in Saglia et al. (2001). The low redshift bins (up to z=0.7) infer α coefficients that are compatible with local values (α ≈ 1.2) and β coefficients (β ≈ 0.23 −0.3) slightly smaller than the local value (β ≈ 0.33). In contrast, the highest redshift bins produce shallower log σ slopes. Given the relatively low number of galaxies per bin, especially in the low velocity dispersion regime, the statistical significance is just ≈ 1σ, but the trend 14 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Figure 17. The redshift evolution of the mass-to-light ratio for cluster (left) and field (right) galaxies. Top: Black and red indicate galaxies with spectroscopic types 1 and 2, respectively. Morphologies for galaxies with HST photometry are coded as in Fig. 14. Galaxies with VLT photometry only are shown as crosses. Only galaxies with good VLT photometry (i.e., SExtractor flag 0 or 2) are plotted. The solid black lines show the solar metallicity SSP for z f = 2 (cluster) and z f = 1.2 (field). The solid red line shows the SSP for z f = 3.5 and half-solar metallicity, the cyan line shows the SSP for z f = 1.2 and twice-solar metallicity. The dotted line shows the best-fit linear relation (-0.55z for cluster and -0.76z for field galaxies) and the 1σ errors dashed. Bottom: The blue points show averages over redshift bins 0.1 wide. The cyan points are average field galaxies from van Dokkum & van der Marel (2007). Only field galaxies (plot to the right) with dynamical masses higher than 1011 M⊙ are considered. confirms the claims of the literature (see Sect. 1). In particular, both values of α and β decrease at high redshift, as observed by di Serego Alighieri et al. (2005), a consequence of the flattening with redshift of the power-law relation between luminosity and mass (see Sect. 4). by a variation in the luminosity. As discussed in the Introduction, there is growing evidence that early-type galaxies evolve not only in terms of luminosity, but also in size and velocity dispersion. Here we examine the consequences of these findings. 4. Size and velocity dispersion evolution In general, if sizes were shrinking with increasing redshift, we would expect the surface brightness to increase. Therefore, if the velocity dispersions do not increase a lot, the net effect will be to reduce the net amount of brightening with redshift caused by stellar population evolution. In detail, setting ∆ZP = 4.1. Setting the stage Up to this point, we have analyzed and interpreted the ZP variations of the FP based on the assumption that it is caused mainly R.P. Saglia et al.: The fundamental plane of EDisCS galaxies 15 Figure 18. The mass dependence of FP mass-to-light ratios. Top: the residuals ∆ log M/LB + 1.66 log(1 + z) as a function of galaxy mass for cluster galaxies at low (left, z < 0.5), intermediate (middle, 0.5 ≤ z < 0.7), and high (right, z > 0.7) redshift. The arrow in the top left panel shows the how points change due to the typical 10% error in velocity dispersion. Bottom: the residuals ∆ log M/LB + 1.66 log(1 + z) as a function of galaxy dynamical mass for field galaxies at low (left, z < 0.5), intermediate (middle, 0.5 ≤ z < 0.7), and high (right, z ≥ 0.7) redshift. Colors and symbols as in Fig. 17. The green points show averages over log Mdyn bins 0.25 dex wide. ZP(z) − ZP(0) and using the fact that hS Be i = −2.5 log(L/2πR2e ), we derive ∆ZP = α0 ∆ log σ − 2.5β0 ∆ log L + (5β0 − 1)∆ log Re , (6) where ∆ log Re = log Re (z) − log Re (0) and ∆ log σ = log σ(z) − log σ(0) are the variations with redshifts in the mean halfluminosity radius and average surface brightness. Therefore, the redshift variation in the luminosity, taking into account the size and velocity dispersion evolution of galaxies is: ∆ log L = 10β0 − 1 2α0 2∆ZP ∆ log Re + ∆ log σ − . 5β0 5β0 5β0 (7) We note that the ZP variations have been determined by assuming constant α0 and β0 coefficients, which is probably not true at the high redshift end of our sample (see Sect. 3.3). If the variations are computed at constant dynamical mass, then ∆ log σ = −∆ log Re /2, as in the “puffing”scenario of Fan, et al. (2008), see below, Eq. 7 becomes ∆ log L pu = 10β0 − 2 − α0 2∆ZP ∆ log Re − . 5β0 5β0 (8) In this case, the contribution of the size evolution to the luminosity evolution at constant mass derived from the FP is zero if A0 = 10β0 − 2 − α0 , 5β0 (9) is zero, i.e., α0 = 10β0 − 2. This is the expected relation between α and β if the mass-to-light ratio M/L varies as a power law of 1 the luminosity M/L ∝ Lǫ , in which case one has L ∝ M 1+ǫ = 2 1+ǫ M λ , α = 1+2ǫ , and β = 25 1+2ǫ . Table 6 lists the values of ǫ, λ, and A implied by the fits of the FP coefficients performed in Sect. 3.3. If we parametrize all variations as a function of log(1 + z) as ∆ log Re = ν log(1 + z), ∆ log σ = µ log(1 + z), and ∆ZP = κ log(1 + z), we find that ∆ log L = ( 10β0 − 1 2α0 2 ν+ µ− κ) log(1 + z) + φz, 5β0 5β0 5β0 (10) where φz is the correction for progenitor bias estimated by van Dokkum & Franx (2001) to be φ = +0.09. Their result can be applied to our work directly, since our redshift dependence of the FP ZP matches closely that considered there. As discussed in the Introduction, the size and σ evolution of galaxies is usually interpreted as a result of the merging history of galaxies. The merger models of Hopkins et al. (2009) predict νme ≈ −0.5 and µme = 0.1 for galaxies with constant stellar mass M∗ ≈ 1011 with (Mhalo /Rhalo )/(M∗ /Re ) ≈ 2. This means that ∆ log Re = −0.2∆ log σ. As an alternative explanation, Fan, et al. (2008) proposed the ’puffing’ scenario, where galaxies grow in size conserving their mass as a result of quasar activity. In this case, one has σ pu ∝ R−1/2 . We note, however, that e this mechanism should already have come to an end at redshift 0.8. Moreover, the strong velocity dispersion evolution predicted 16 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies by the puffing scenario at redshifts higher than 1 was ruled out by Cenarro & Trujillo (2009). Using ν = −0.5, µ = +0.1, the change in the slope ∆τ = 10β0 −1 2α0 5β0 ν + 5β0 µ of the luminosity evolution ∆ log L = τ log(1 + z) (see Eq. 7) is ≈ −0.5 units. We now attempt to determine the values of ν and µ implied by our dataset. 4.2. The redshift evolution of Re and σ Following van der Wel et al. (2008), we investigated the size evolution of EDisCS galaxies by considering the Mass − Re relation for objects with masses higher that 3 × 1010 M⊙ . In Fig. 19, we divided our sample into 8 redshift bins (centered on redshifts from 0.25 to 0.95 of bin size ∆z = 0.1) and fit the relation Re = Rc (M/Mc )b . We considered both dynamical (Mdyn , left) and stellar (M∗ , right) masses, and we weighted each galaxy with 1/PS . Within the errors, b does not vary much and is compatible with the values b = 0.56 found locally. In Fig. 19 we therefore keep its value fixed and determine Rc at the mass Mc = 2 × 1011 M⊙ . We fitted the function Rc (z) = Rc (0) × (1 + z)ν and summarize the values of the parameters resulting from the fits in Table 7. As becomes clear below, this does not necessarily describe the evolution in size of a galaxy of fixed mass, but rather at any given redshift the mean value of the size of the evolving population of galaxies with this given mass. Given the larger uncertainties in the Re values derived from VLT photometry, we first fitted the HST dataset alone (entries 1 and 2 of Table 7). Within the errors, both Rc (0) and the slope are very similar to the values reported by van der Wel et al. (2008, Rc (0.06) = 4.8 kpc, ν = 0.98 ± 0.11) for both dynamical and stellar mass fits. Our results do not change within the errors if we separately fit galaxies belonging to clusters or to the field. If we add the galaxies with VLT photometry only (entries 3 and 4 of Table 7), we derive larger Rc and steeper slopes. Figure 20 shows Rc as a function of redshift when we apply a correction for progenitor bias as in Valentinuzzi et al. (2010a). The EDisCS galaxies considered here are a sample of spectroscopically selected passive objects. In contrast, a morphologically selected local sample of early-type galaxies contains objects with relatively young ages that, when evolved to EDisCS redshifts, would not be recognized as being spectroscopically passive. Valentinuzzi et al. (2010a) analyze the WINGS sample of local galaxies and determine their ages by means of a spectral analysis. They select objects that were already passive (i.e., have an age ≥ 1.5 Gyr) at the cosmic time of the redshifts z = 0, 0.25, 0.5, 0.75 and 1, and compute the median halfluminosity radii of massive galaxies. The resulting Re vary as Re = (4.1 ± 0.1) − (0.8 ± 0.2)z (kpc), when selecting galaxies with dynamical masses 1011 < Mdyn /M⊙ < 3 × 1011 , and as (4.3 ± 0.1) − (0.9 ± 0.2)z when selecting galaxies with stellar masses 1011 < M∗ /M⊙ < 3 × 1011 . Therefore, we multi4.1 ply the Rc (z) derived at Mdyn = 1011 M⊙ by 4.1−0.8z , and those 4.3 at M∗ = 1011 M⊙ by 4.3−0.9z . With these corrections, the residual evolution is small, and even compatible with no evolution up to redshift z ≈ 0.7 with dynamical masses, and 0.5 with stellar masses. Similar results are derived if we also consider the galaxies with VLT photometry, with the caveats discussed above. Our correction for progenitor bias is of course somewhat model-dependent, since objects might cross the boundaries between populations. For example, there might be z ∼ 0.6 passive galaxies that produce z = 0 descendants with some younger stars, after accreting gas or gas-rich objects. In Figs. 21 and 22, we show the analogous plots and fits for the velocity dispersion. Table 7 lists the relative results. We 0.23 find that σ scales as ≈ Mdyn . The trend weakens at low masses and high redshifts, especially when stellar masses are considered. The fit at constant dynamical mass is just a consistency check, which should infer a slope of the redshift dependence of opposite sign to and half the value of the one measured for Rc (µ = +0.68) and this is the case. In contrast, a weaker redshift evolution (µ = 0.39) is derived if stellar masses are considered, in agreement with Cenarro & Trujillo (2009). This is expected, since, as discussed above, σc at fixed M∗ should certainly be smaller than σc at fixed Mdyn given that Mdyn /M∗ < 1. Following the procedure of Valentinuzzi et al. (2010a) described above, we construct the local sample of WINGS galaxies with velocity dispersions, trimmed to have only massive spectroscopically passive galaxies at the redshifts z = 0, 0.25, 0.5, 0.75 and 1, and compute the median σ of massive galaxies. The resulting σ vary as σ = (197 ± 2) + (6 ± 4)z km/s, when selecting galaxies with dynamical masses 1011 < Mdyn /M⊙ < 3 × 1011 , and is constant at (210 ± 1.5) km/s when selecting galaxies with stellar masses 1011 < M∗ /M⊙ < 3 × 1011 . Therefore, we correct the measured σc for the progenitor bias by multiplying the 197 values derived at Mdyn = 1011 M⊙ by 197+6z , and no correction is applied at constant stellar mass. The residual redshift evolution after the correction and fitting the point at zero redshift is small. 0 Table 9 lists the changes in the slope ∆τ = 10β5β00−1 ν + 2α 5β0 µ of the luminosity evolution ∆ log L = τ log(1 + z) (see Eq. 7) derived from the measured variation in the FP ZP caused by the size and velocity dispersion evolution, coding the different cases listed in Table 7. For example, “case 1+9 Mdyn ” uses the value of ν derived for the redshift evolution of Rc constructed using the Re − Mdyn relation with HST data, without both selection weighting and progenitor bias correction (case 1 of Table 7), and the value of µ derived from the redshift evolution of σ inferred in turn from the σ − Mdyn relation, without both selection weighting and progenitor bias correction (case 9 of Table 7), getting ∆τ = −0.39. This implies that the luminosity evolution inferred from the ZP evolution of the EDisCS clusters without selection weighting (L ∼ (1 + z)1.61 , see Table 5) would reduce to L ∼ (1 + z)1.22 . To summarize, none of the values of ∆τ listed in Table 9 differ statistically from zero. However, without taking into account the progenitor bias (rows two to five of Table 9), the values of ν and µ are much larger than inferred by the merger scenario of Hopkins et al. (2009) and when used in Eq. 10 reduce the predicted luminosity evolution with redshift drastically. In contrast, by taking into account the progenitor bias (rows six to nine of Table 9), the correction ∆τ to the redshift slope of the luminosity evolution inferred from the FP is far smaller. 4.3. Luminosity evolution: the direct fit To close the loop, in Fig. 23 we directly considered the relation between total luminosity LB and dynamical mass as a function of redshift. In general, the power law L = LC (M/MC )0.75 provides a reasonable fit to the data. Without selection weighting, we derived LC as a function of redshift as shown in Fig. 24 for dynamical and stellar masses. Fitting the power-law relation LC = LC (0)(1 + z)τ to z > 0.4 data points, separately for cluster and field galaxies, we derived the results listed in Table 7. The zero-redshift extrapolations compare well to the local values derived by considering the sample of Faber et al. (1989) (LC = 2.2×1010 L⊙ and M/LB = 8.9M⊙ /L⊙ ). As for the σc −z re- R.P. Saglia et al.: The fundamental plane of EDisCS galaxies 17 Figure 19. The evolution in the Re − mass relation with redshift. Left: dynamical masses. Right: stellar masses. Colors and symbols are as in Fig. 17. The numbers give the average redshift in each bin. The full lines show the best-fit relation Re = Rc (M/2 × 1011 M⊙ )0.56 with uniform galaxy weighting, the dashed lines with selection weighting. The blue lines show the reference line at zero redshifts. The vertical lines show the 2 × 1011 M⊙ mass. Figure 20. The size evolution with redshift of EDisCS galaxies corrected for progenitor bias (see text). Left: Rc as a function of redshift at 2 × 1011 M⊙ (see Fig. 19, left) derived using Mdyn . Right: Rc at 2 × 1011 M⊙ (see Fig. 19, right) as a function of redshift derived using M∗ . The full lines show the best-fit function to the galaxies with HST photometry (yellow points) Rc = R0c × (1 + z)−ν without selection weighting (see Table 7, case 1). The open dots show the local sample of Valentinuzzi et al. (2010a) evolved at the redshifts 0, 0.25, 0.5, 0.75, and 1, after having applied the progenitor bias correction. The dashed line shows the local value. lation, we inferred a shallower luminosity evolution when measuring Lc at constant M∗ . The luminosity evolution with redshift is steeper for field galaxies. Given the large errors in the luminosity fits, the derived luminosity evolution agrees with the ones derived from the FP analysis. At face value, the FP ZPs without size and velocity dispersion evolution corrections slightly overestimate the luminosity evolution at constant stellar mass and underestimate that at constant dynamical mass. This corroborates the conclusion that the corrections ∆τ for size and velocity dispersion evolution must be small, as one finds when the progenitor bias is taken into account. 18 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Figure 21. The evolution of the σ-mass relation with redshift. Left: dynamical masses. Right: stellar masses. Colors and symbols as in Fig. 17. The numbers give the average redshift in each bin. The full lines show the best-fit relation σ = σC (M/MC )0.23 with uniform galaxy weighting, the dashed line with selection weighting. The blue lines show the reference line at zero redshifts. The vertical line marks the 2 × 1011 M⊙ mass. Figure 22. The σ evolution with redshift of EDisCS galaxies corrected for progenitor bias (see text). Left: σc as a function of redshift derived using Mdyn . Right: σc as a function of redshift derived using M∗ . The full lines show the best-fit function σc = σ0c × (1 + z)µ without selection weighting (see Table 7). The open dots show the local sample of Valentinuzzi et al. (2010a) evolved to the redshifts 0, 0.25, 0.5, 0.75, and 1, and after having applied the progenitor bias correction. The dashed line shows the local value. 4.4. Ages As a final step, we translated the observed evolution in the FP zero points, into an age estimate. We examined three cases that define the realistic range of possible luminosity evolutions: (1) minimal evolution, using ∆τ = −0.7 (M∗ , case 6+12, of Table7) and φ = 0; (2) ∆τ = 0 and φ = 0, where the small size and velocity dispersion correction compensates the progenitor bias of van Dokkum & Franx (2001); (c) ∆ log L = φz, where the size and velocity dispersion correction is zero and we take into account the progenitor bias of van Dokkum & Franx (2001). We convert the mean ∆ log M/LB for cluster and field galaxies measured in the mass bins of Fig. 18 into an age, by considering the various options for size evolution discussed above. We use the solar-metallicity (motivated by the analysis of the averaged line indices discussed below), Salpeter IMF SSP models of Maraston (2005) at the appropriate mean redshift of the bin. R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Ages older than the age of the universe at that redshift are set to the age of the universe. Figure 25 shows the results, Table 8 gives the average values for Mdyn < 1011 M⊙ and Mdyn > 1011 M⊙ . Cluster galaxies more massive than 1011 M⊙ are 6 to 8 Gyr old, with formation redshifts higher than 1.5, while galaxies of lower masses are some 3-4 Gyr younger. This parallels the findings of Sánchez-Blázquez et al. (2009), where the analysis of spectral indices of EDisCs cluster galaxies with velocity dispersion larger than 175 km/s assigns them formation redshifts > 1.4. Galaxies with lower velocity dispersions have instead younger ages, compatible with continuous low levels of star formation. Alternatively, the low-mass, spectroscopic early-type cluster sample is building up progressively with the acquisition of new and young objects, as discussed in De Lucia et al. (2004, 2007) and Rudnick et al. (2009). The result also agrees with the analysis of the scatter in the color-magnitude relation of EDisC clusters of Jaffé et al. (2010). Field galaxies are slightly younger than cluster galaxies at the same redshift and mass. Taking into account the size and velocity dispersion evolution considered above in the case 6+12 pushes all formation ages upwards by 1 to 4 Gyr. Taking into account the progenitor bias of van Dokkum & Franx (2001) reduces the ages by 1 to 2 Gyr. Table 8 lists mean ages for the HST sample of galaxies with morphologies T < 0. The differences between low and high mass galaxies are smaller. We next correlated the FP ages of Fig. 25 with those derived from the analysis of the spectral indices. As performed in Sánchez-Blázquez et al. (2009), we averaged the spectra of the galaxies appearing in each mass bin shown in Fig. 18, measured the Fe4383, HdA, and CN2 indices, and recovered the ages and metallicities of SSP models that reproduce their values best. The derived metallicity averaged over the sample is solar, which justifies the choice above. We also estimated luminosity-weighted and mass-weighted ages directly by fitting the spectra with a library of model spectra. Within the large errors, there is overall agreement with the ages derived from the indices. The optimal match is achieved when considering the minimal evolution ages. As a final check, we derived the rest-frame U-B and B-V colors corresponding to a SSP of solar metallicity and age derived as above and compared them to the measured averaged colors. The agreement was fair, but either the colors predicted using the FP ages are too red or the spectral ages appear to be too high. The discrepancy is exacerbated when size evolution is taken into account. This could simply reflect the known difficulties for stellar population synthesis models in reproducing the colors of real galaxies (Maraston et al. 2009). 5. Conclusions We have examined the FP of EDisCS spectroscopic early-type galaxies, in both the cluster and the field. Combining structural parameters from HST and VLT images and velocity dispersions from VLT spectra, we have compiled a catalogue of 154 cluster and 68 field objects in the redshift range 0.2-0.9. For the first time, we have explored the FP of galaxy clusters of mediumto-low velocity dispersion in the redshift range 0.4-0.9. At facevalue, on average, the evolution of the zero point follows the predictions of simple stellar population models with high (≈ 2) formation redshift for all clusters, independent of their velocity dispersion, with a slight increase (from 15% to 18%) in the scatter in mass-to-light ratios for clusters with low (σclus < 600 km/s) velocity dispersions. The FP zero point of field galaxies follows similar tracks up to redshift ≈ 0.5, but implies brighter luminosities, or lower formation redshifts at higher redshifts. 19 We have determined dynamical and stellar masses for our galaxies. The ratio Mdyn /M∗ is ≈ 0.9 with a scatter of a factor 2 and a tendency to decrease with redshift. We investigated the FP residuals as a function of galaxy mass. At high redshifts (z > 0.7 for cluster galaxies, slightly below for field galaxies), galaxies with mass lower than ≈ 1011 M⊙ have lower mass-to-light ratios than a passive evolution of the ZP predicts. This implies that there is a rotation in the FP: we confirm that for cluster galaxies the velocity dispersion coefficient α is compatible with the local value up to a redshift z = 0.7 and decreases to α ≈ 0.7 ± 0.4 at higher redshifts, but this detection is of low statistical significance. We have investigated the size and velocity dispersion evolution of our sample. At a given mass, galaxy sizes decrease and velocity dispersions increase at increasing redshift. We fitted the relations Re ≈ (1 + z)−1.0±0.3 , and σ ≈ (1 + z)0.59±0.1 and σ ≈ (1 + z)0.34±0.14 at a constant dynamical or stellar mass of 2 × 1011 M⊙ , respectively, for both cluster and field galaxies. However, after taking into account the progenitor bias affecting our sample (large galaxies that joined the local early-type class only recently will progressively disappear in higher redshift samples), the effective size and velocity dispersion evolution reduced substantially (to Re ∝ (1 + z)−0.5±0.2 and σ ∝ (1 + z)0.41±0.08 for dynamical masses and Re ∝ (1 + z)−0.68±0.4 and σ ∝ (1 + z)0.19±0.10 for stellar masses). We computed the luminosity evolution predicted by the ZP variation with redshift of the FP when the size and velocity dispersion evolution are taken into account. The corrections computed at constant dynamical masses with a progenitor bias correction almost cancel out; at constant stellar mass, they reduce the slope of the (1 + z) dependence of luminosity by −0.6 units (case 5+11 of Table 7). Fitting directly the luminosity-mass relation, we derived a luminosity evolution that agrees with the one derived from the FP analysis and does not allow for large size and velocity dispersion corrections such as those derived without taking into account the progenitor bias, where a reduction of the slope of the (1 + z) dependence of luminosity by −0.8 is derived at constant M∗ (case 1+9 of Table 7) . Using simple stellar population models, we translated the variations in the FP ZP into formation ages as a function of redshift and galaxy mass. Massive (M > 1011 M⊙ ) cluster galaxies are old, with formation redshifts z f > 1.5. In contrast, lower mass galaxies are just 2 to 3 Gyr old. This agrees with the EDisCS results presented in De Lucia et al. (2004, 2007), Poggianti et al. (2006), Sánchez-Blázquez et al. (2009), and Rudnick et al. (2009), who argue from different points of view that the lower luminosity, lower mass population of earlytype galaxies comes in place only at later stages in clusters. Field galaxies at all masses are somewhat younger (by ≈ 1 Gyr) than the cluster ones with similar masses and redshifts. In general, the FP ages agree reasonably well with those derived from spectral indices. To conclude, our analysis of the FP, size, and velocity dispersion evolution of EDisCS galaxies points towards a picture where a large fraction of the population became passive only fairly recently. The high redshift passive galaxies are a biased subset of all the present passive galaxies. At any probed redshift, from 0 to 1, passive galaxies are an inhomogeneous population in terms of their formation paths, and as redshift increases, a subset of the population leaves the sample, with less massive galaxies dropping out of the sample more rapidly with redshift than the more massive ones, and with a somewhat accelerated pace in the field. Only when these effects are taken into account may coherent estimates of the luminosity evolution of early-type 20 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies galaxies from the colors, indices, and the FP zero point be derived. Acknowledgements. This work was supported by the Sonderforschungsbereich 375 of the German Research Foundation. The Dark Cosmology Centre is funded by the Danish National Research Foundation. GDL acknowledges financial support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement n. 202781. The anonymous referee report helped us improve the presentation of the results. 0 Table 9. The change in slope ∆τ = 10β5β00−1 ν+ 2α 5β0 µ of the luminosity evolution ∆ log L = τ log(1 + z) (see Eq. 7) derived from the measured variation in the FP ZP caused by the size and velocity dispersion evolution for the different cases listed in Table 7. Case Hopkins et al. (2009) 1+9 Mdyn 1+9 M∗ 2+10 Mdyn 2+10 M∗ 5+11 Mdyn 5+11 M∗ 6+12 Mdyn 6+12 M∗ ν -0.5 -1.0 -1.0 -1.3 -1.2 -0.46 -0.68 -0.67 -0.84 µ +0.1 +0.59 +0.34 +0.68 +0.39 +0.41 +0.19 +0.49 +0.27 ∆τ -0.51 −0.39 ± 0.43 −0.78 ± 0.83 −0.65 ± 0.60 −0.98 ± 1.01 +0.04 ± 0.30 −0.60 ± 0.55 −0.11 ± 0.43 −0.69 ± 0.59 References Baldry, I.K., Glazerbrook, K., Driver, S.P., 2008, MNRAS, 388, 945 Bell, E. 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The ages of cluster (top) and field (bottom) galaxies at low (left, z < 0.5 left), medium (0.5 < z < 0.7, middle), and high (z > 0.7, right) redshifts as a function of dynamical mass. The circles show the ages as derived from the bare FP zero point evolution. The triangles pointing upwards take into account size evolution at constant M∗ , case 3+7 (see Table 9). The triangles pointing downwards take into account the progenitor bias of van Dokkum & Franx (2001). The median redshifts are given and the corresponding ages of the universe are shown by the dotted lines. Treu, T., Ellis, R.S., Liao, T.X., van Dokkum, P.G., Tozzi, P., Coil, A., Newman, J., Cooper, M.C., Davis, M., 2005a, ApJ, 633, 174 Treu, T., Ellis, R.S., Liao, T. 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L., Thomas, D., Böhm, A., Bender, R., Fritz, A., Maraston, C., 2005, A&A, 433, 519 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies 23 Zirm, A.W., van der Wel, A., Franx, M., et al., 2007, ApJ, 656, 66 Appendix A: Circularized half-luminosity radii GIM2D delivers bulge ae and disk ah scale lengths along the major axis, bulge apparent flattening (b/a)B and disk inclination angles i (corresponding to an apparent flattening (b/a)D = 1 − cos i), and bulge-to-total ratios B/T . When fitting Sersic profiles, GIM2D delivers the n Sersic index, the major axis aSe er and the flattening (b/a)S er . We compute the circularized halfluminosity radius Re of the resulting galaxy model as follows. We determine the flux inside a circular aperture of radius R (the so-called curve of growth) of a model of apparent flattening b/a and p surface density distribution constant on ellipses f (x, y) = f ( x2 /a2 + y2 /b2 ) as Z 2π Z R q F(R) = f ( (R′ cos φ)2 /a2 + (R′ sin φ)2 /b2 R′ dR′ dφ.(A.1) 0 0 RR Using Fc (R) = 2π 0 r f (r)dr we get p Z π/2 Fc (r/b 1 − (1 − b2 /a2 ) cos2 φ) 2 dφ. F(R) = 4b 1 − (1 − b2 /a2 ) cos2 φ 0 (A.2) We perform the angular integration numerically, using P FcdeVauc (z) = 1 − (1 + 7i=1 zi /i!)e−z, with z = 7.67(r/ReB)1/4 , exp and Fc (x) = 1 − (1 + x)e−x , with x = R/h for the normalized de Vaucouleurs and exponential density laws respectively. For a Sersic profile of given n, we use Fcn = P(2n, X), where P is the incomplete Γ function and X = k(r/ReS er )1/n and k = 1.9992n − 0.3271 (Simard et al. 2002). We determine Re by solving the equation B/T × F deVauc (Re ) + (1 − B/T )F exp(Re ) = 0.5 (A.3) for the bulge plus disk models, and F n (Re ) = 0.5 (A.4) for the Sersic fits numerically. In general, the resulting Re agree within 1% with the half-luminosity radii derived by measuring the curves of growth directly from (ACS HST like) images generated by GIM2D with the fit parameters and no PSF convolution, but the image-based method overestimates Re by up to 10 % when it is smaller than 4 pixels (0.2 arcsec). Figure A.1 illustrates that a more accurate approximation of the circularized radius Re (S er) of Sersic profiles, more accurate than 2%, is obtained by taking the simple mean Rave = (ae +be )/2 of the major and minor axis √ scale lengths ae and be instead of the harmonic mean Rhar = ae × be . This is surprising only at a first sight, since Rhar goes to zero as the flattening increases, while Rave does not. Therefore Rave is bound to more closely approximate the half-luminosity radius derived from circular curves of growth at high ellipticities. On the other hand, the effective surface brightness within the ellipse of semi-major and minor axis ae and be is constant whatever the flattening, while this is not true for the surface brightness within the circle of radius Re (S er). Since in this exercise the total luminosity L is kept constant, we have log Re (S er)/Rhar = 0.2(hS Bei − hS Bhar e i, with L L hS Bei = −2.5 log 2πRe (S and hS Bhar e i = −2.5 log 2πR2 . This er)2 har is almost orthogonal to the FP (see Eq. 1), making the choice of method unimportant, as far as not too many disks seen edge-one (i.e. of very high flattening) are present in the sample (see Fig. 5 and discussion in Sect. 2.2). * Figure A.1. The circularized half-luminosity radius Re (S er) of the sample of EDisCS galaxies with HST photometry and velocity dispersions computed according to Eqs. A.2 and A.4 compared to the simple √ mean Rave = 0.5(ae + be ) (top) and harmonic mean Rhar = ae × be (bottom) as a function of the ellipticity 1 − be /ae . The simple mean approximates Re (S er) better. 24 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Table 1. The FP parameters of cluster galaxies. Name Nclus z EDCSNJ1040403-1156042 EDCSNJ1040407-1156015 EDCSNJ1040346-1157566 EDCSNJ1040396-1155183 EDCSNJ1040356-1156026 EDCSNJ1054244-1146194 EDCSNJ1054250-1146238 EDCSNJ1054309-1147095 EDCSNJ1054263-1148407 EDCSNJ1054338-1149299 EDCSNJ1054280-1149598 EDCSNJ1054296-1147123 EDCSNJ1054278-1149580 EDCSNJ1054305-1146536 EDCSNJ1054303-1149132 EDCSNJ1054237-1146107 EDCSNJ1054246-1146124 EDCSNJ1054467-1245035 EDCSNJ1054435-1245519 EDCSNJ1054451-1247336 EDCSNJ1054436-1244202 EDCSNJ1054438-1245409 EDCSNJ1054445-1246173 EDCSNJ1054440-1246390 EDCSNJ1054442-1245331 EDCSNJ1054439-1245556 EDCSNJ1054398-1246055 EDCSNJ1054396-1248241 EDCSNJ1054431-1246205 EDCSNJ1216470-1159267 EDCSNJ1216454-1200017 EDCSNJ1216490-1200091 EDCSNJ1216453-1201176 EDCSNJ1216420-1201509 EDCSNJ1216468-1202226 EDCSNJ1216401-1202352 EDCSNJ1216462-1200073 EDCSNJ1216418-1200449 EDCSNJ1216438-1200536 EDCSNJ1216461-1201143 EDCSNJ1216456-1201080 EDCSNJ1216453-1201209 EDCSNJ1216443-1201429 EDCSNJ1216438-1202155 EDCSNJ1216417-1203054 EDCSNJ1216359-1200294 EDCSNJ1216446-1201089 EDCSNJ1216449-1201203 EDCSNJ1216403-1202029 EDCSNJ1216522-1200595 EDCSNJ1216382-1202517 EDCSNJ1216387-1201503 EDCSNJ1232318-1249049 EDCSNJ1232280-1249353 EDCSNJ1232303-1250364 EDCSNJ1232250-1251551 EDCSNJ1232287-1252369 EDCSNJ1232271-1253013 EDCSNJ1232343-1249265 EDCSNJ1232350-1250103 9 9 9 9 9 8 8 8 8 8 8 8 8 8 8 8 8 10 10 10 10 10 10 10 10 10 10 10 10 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 4 4 4 4 4 4 4 4 0.702 0.703 0.7024 0.7046 0.7081 0.6965 0.6968 0.6998 0.7014 0.6945 0.6964 0.6981 0.6949 0.6986 0.6964 0.6962 0.7034 0.7304 0.7503 0.7305 0.7463 0.7568 0.7498 0.7496 0.7446 0.7531 0.7482 0.7478 0.7553 0.7971 0.7996 0.7863 0.7955 0.7941 0.7987 0.8022 0.7847 0.7967 0.7945 0.7997 0.8058 0.8054 0.7918 0.8028 0.8012 0.793 0.8001 0.8035 0.7976 0.7882 0.79 0.8008 0.5408 0.5449 0.5419 0.5399 0.5432 0.5445 0.5395 0.5397 S Type 1 1 1 2 2 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 2 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 σmes (km/s) 161.3 155.9 148.9 226.2 172.7 230.2 221.8 193.5 256.8 205.3 134.2 214.1 191.4 256.7 250.9 135.8 228.6 142.3 359.1 195.8 187.9 205.4 325.4 163.1 209.5 119.4 154.8 209.6 234.7 170.8 260.4 255 293.1 273.7 135.8 214.9 122.3 155.5 282.2 240.4 122.4 198.2 132.2 255.3 167.5 206.2 317.3 176.6 316.2 113.8 238.3 290.4 145.7 316.7 329.2 120.9 264.9 243.4 196.3 212.1 σcor (km/s) 167.1 161.5 154.3 234.4 178.9 238.5 229.8 200.5 266 212.7 139 221.8 198.3 265.9 259.9 140.7 236.8 147.5 372.4 203 194.8 213 337.5 169.1 217.2 123.8 160.5 217.4 243.4 177.3 270.3 264.6 304.2 284.1 141 223.1 126.9 161.4 292.9 249.5 127.1 205.8 137.2 265 173.9 214 329.4 183.3 328.2 118.1 247.3 301.4 150.2 326.6 339.5 124.7 273.2 251 202.4 218.7 dσ (km/s) 13.6 15.4 17.8 13.4 8.4 19.5 18 16.9 15 17.4 10.9 16.8 14.6 10.5 13.9 20 34.3 13.7 33.9 17.3 24.9 24.2 40.9 23 38.9 16.5 12.7 39.7 42.7 15.6 14.4 44 19.9 19.5 14.3 15.4 21.8 10.5 22.5 10 15.9 24.1 22.7 23.9 17.2 31.5 32.6 12 31.5 7 20.7 32.3 19.5 21.3 24.9 17.3 11.3 21.4 16.7 13.2 Re (kpc) 5.147 1.698 2.9 1.789 2.123 4.614 3.194 2.452 4.047 3.45 1.527 2.336 3.95 6.945 4.592 0.9097 5.657 1.774 7.076 1.371 0.9712 1.396 1.311 1.601 1.267 2.203 4.38 3.572 4.66 2.469 1.938 2.737 10.09 3.208 4.333 1.327 0.9628 3.027 2.414 4.545 4.794 3.969 1.73 0.6319 0.8983 0.9888 1.668 2.72 2.62 1.45 3.737 1.233 1.883 3.797 14.03 2.082 2.448 2.244 1.198 4.001 log Ie log L⊙ /pc2 2.092 2.807 2.404 2.68 2.703 2.307 2.477 2.396 1.98 2.393 2.635 2.707 2.428 2.15 2.22 2.755 1.805 2.716 2.031 2.872 3.22 2.991 2.741 2.539 2.327 2.454 2.428 2.204 1.64 2.47 2.6 2.369 1.972 2.692 2.149 3.176 3.026 2.304 2.728 2.477 2.018 2.209 2.647 3.291 3.397 3.221 2.638 2.457 2.089 2.607 2.365 3.091 2.363 2.314 1.621 2.503 2.479 2.462 2.872 2.14 T Type -5 -2 -5 -5 -5 -5 -5 -5 1 -5 -5 -5 1 -5 -5 -5 4 1 -5 -2 -2 -5 1 1 -2 -2 1 1 4 1 -5 1 1 -5 -2 -2 -5 -2 -5 -5 -5 2 -5 -2 -2 -2 -5 -5 1 -2 -5 -2 -5 5 -5 3 1 -5 -2 -5 PS 0.199 0.149 0.161 0.096 0.304 0.150 0.196 0.150 0.129 0.172 0.112 0.245 0.271 0.295 0.254 0.077 0.126 0.141 0.129 0.140 0.142 0.146 0.077 0.074 0.008 0.126 0.121 0.136 0.047 0.204 0.204 0.208 0.323 0.301 0.230 0.270 0.034 0.208 0.274 0.295 0.209 0.237 0.282 0.010 0.233 0.211 0.145 0.218 0.021 0.057 0.250 0.221 0.092 0.171 0.147 0.160 0.268 0.174 0.163 0.268 log M∗ log M⊙ 11.54 11.28 11.25 11.09 11.35 11.72 11.53 11.04 11.09 11.4 11.8 11.45 11.4 11.71 11.7 10.7 11.1 11.06 11.65 11.01 11.01 11.27 10.92 10.92 10.18 10.98 11.45 11.06 11 10.91 11.12 11.07 11.82 11.59 11.18 11.23 10.72 11.15 11.47 11.71 11.31 11.45 11.42 10.69 10.83 11.05 11.01 11.65 10.75 10.8 11.28 11.15 10.73 11.37 11.86 10.78 11.23 11.04 10.93 11.09 dlog M∗ log M⊙ 0.06 0.05 0.08 0.09 0.12 0.05 0.06 0.08 0.08 0.06 0.03 0.05 0.44 0.15 0.06 0.08 0.15 0.10 0.04 0.04 0.05 0.04 0.04 0.05 0.07 0.05 0.07 0.06 0.08 0.06 0.07 0.07 0.05 0.07 0.05 0.07 0.06 0.06 0.04 0.05 0.04 0.06 0.05 0.07 0.06 0.05 0.06 0.05 0.08 0.07 0.07 0.04 0.10 0.09 0.08 0.16 0.08 0.12 0.12 0.11 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies 25 Table 1. Continued Name Nclus z EDCSNJ1232313-1250327 EDCSNJ1232317-1249275 EDCSNJ1232309-1249408 EDCSNJ1232303-1251092 EDCSNJ1232303-1251441 EDCSNJ1232370-1248239 EDCSNJ1232372-1249258 EDCSNJ1232296-1250119 EDCSNJ1232301-1250362 EDCSNJ1232288-1250490 EDCSNJ1232299-1251034 EDCSNJ1232207-1252016 EDCSNJ1232204-1249547 EDCSNJ1037527-1243456 EDCSNJ1037548-1245113 EDCSNJ1037447-1246050 EDCSNJ1037552-1246368 EDCSNJ1037535-1241538 EDCSNJ1037525-1243541 EDCSNJ1037428-1245573 EDCSNJ1037527-1244485 EDCSNJ1037473-1246245 EDCSNJ1103365-1244223 EDCSNJ1103372-1245215 EDCSNJ1103363-1246220 EDCSNJ1103444-1245153 EDCSNJ1103349-1246462 EDCSNJ1103413-1244379 EDCSNJ1103357-1246398 EDCSNJ1138068-1132285 EDCSNJ1138102-1133379 EDCSNJ1138069-1134314 EDCSNJ1138074-1137138 EDCSNJ1138104-1133319 EDCSNJ1138107-1133431 EDCSNJ1138127-1134211 EDCSNJ1138116-1134448 EDCSNJ1138069-1132044 EDCSNJ1138130-1132345 EDCSNJ1138110-1133411 EDCSNJ1138022-1135459 EDCSNJ1138065-1136018 EDCSNJ1138031-1134278 EDCSNJ1354098-1231098 EDCSNJ1354098-1231015 EDCSNJ1354097-1230579 EDCSNJ1354026-1230127 EDCSNJ1354114-1230452 EDCSNJ1354159-1232272 EDCSNJ1354102-1230527 EDCSNJ1354101-1231041 EDCSNJ1354204-1234286 EDCSNJ1354106-1230499 EDCSNJ1018471-1210513 EDCSNJ1018464-1211205 EDCSNJ1018467-1211527 EDCSNJ1018489-1211357 EDCSNJ1018474-1211537 EDCSNJ1018464-1211392 EDCSNJ1018470-1212483 EDCSNJ1059100-1251390 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 1 5 5 1 1 1 18 7 7 17 7 18 7 3 3 3 2 3 3 3 2 3 3 3 2 2 2 11 11 11 6 6 6 11 11 6 11 14 14 14 14 14 14 14 13 0.5496 0.542 0.5485 0.5428 0.55 0.5401 0.5377 0.5509 0.5424 0.547 0.5493 0.5416 0.546 0.5807 0.5789 0.4222 0.4245 0.5789 0.5772 0.4225 0.4223 0.4229 0.7031 0.6251 0.6288 0.964 0.6257 0.7038 0.6278 0.4787 0.4801 0.4819 0.4528 0.4844 0.4764 0.4804 0.4571 0.4798 0.4791 0.4825 0.4541 0.4561 0.4549 0.7568 0.7562 0.7565 0.5942 0.5947 0.5929 0.7593 0.7612 0.6006 0.7634 0.4716 0.4717 0.4716 0.4779 0.4746 0.4696 0.4704 0.4517 S Type 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 2 1 1 2 1 2 1 1 1 2 2 1 2 1 1 2 1 1 1 1 2 1 1 1 1 1 2 2 1 1 2 1 2 1 1 1 2 1 1 1 1 1 1 2 σmes (km/s) 162.6 138.2 251.6 140.8 169.9 142.1 219.4 135.1 218.4 164.7 207.4 238.9 245.7 262.5 187.3 106 175.8 257.9 182.7 142.9 223.7 193.7 268.7 160.5 164.1 284.5 231.7 148.8 270.9 134.9 224 220.4 256.6 159.5 262.8 172.8 157.9 177.4 127.4 115 171.9 165 231.2 141.9 310.3 300.9 152.1 141 191.7 293.1 314.3 249.3 198.4 197.1 115.5 236.2 172.9 284.8 179 177.9 164 σcor (km/s) 167.7 142.5 259.5 145.2 175.2 146.5 226.2 139.4 225.2 169.9 213.9 246.3 253.4 271 193.4 108.7 180.3 266.3 188.6 146.6 229.4 198.7 278.4 166 169.7 296 239.6 154.2 280.1 138.7 230.4 226.7 263.6 164.1 270.3 177.7 162.2 182.5 131 118.3 176.6 169.5 237.5 147.2 321.8 312.1 157.1 145.7 198 304 326 257.6 205.8 202.6 118.8 242.8 177.8 292.9 184 182.9 168.5 dσ (km/s) 18.5 13.1 22.9 25.1 19.8 7.7 29.9 9.3 29.5 6.4 14.7 17.7 18.2 20.1 13.6 11.6 11.6 14.8 5 7.2 9.3 23.7 11.1 8.9 10.5 49.3 10 28.1 33.6 24.2 9.1 14.1 20 24.9 15.3 25 8.9 8.1 8.3 13.7 7 29.9 16.7 11.8 8.3 8.5 11.4 7.2 12.5 53.7 9.4 14.8 11.2 15.8 22.3 9.7 19.4 40.3 15 26.9 5.5 Re (kpc) 1.373 4.564 3.559 1.128 1.976 1.812 0.8342 3.48 2.542 2.121 1.452 5.822 3.916 1.206 1.618 1.288 1.529 3.322 1.56 2.778 2.183 1.326 6.336 2.113 2.71 2.097 6.083 2.272 1.564 3.589 5.841 1.539 3.661 2.675 1.523 0.9325 1.285 1.589 2.788 2.681 2.59 3.729 1.163 1.002 5.41 1.89 1.312 4.694 0.672 7.373 1.691 2.212 1.896 4.213 1.243 14.77 3.588 1.33 0.8029 0.6736 5.845 log Ie log L⊙ /pc2 2.549 2.143 2.485 2.613 2.331 2.612 2.688 2.242 2.039 2.55 2.555 2.076 2.278 2.841 2.934 2.373 2.295 2.012 2.724 2.109 2.367 2.347 2.189 2.447 2.182 2.918 2.004 2.527 2.545 1.75 1.937 2.62 2.181 1.824 2.52 2.673 2.727 2.428 2.004 1.936 2.278 1.471 2.602 2.84 2.195 2.864 2.661 2.168 3.041 1.648 2.73 2.61 2.703 1.969 2.6 1.493 1.997 2.785 2.811 2.935 1.885 T Type -5 1 -2 -2 3 -2 1 3 -5 -2 -5 -5 3 -5 -5 -5 -2 1 2 2 -2 -5 3 -5 2 -5 -5 -5 1 3 -2 -5 -2 -2 1 -5 -2 -2 3 3 2 4 -2 -2 1 -5 -5 2 -5 3 -2 -5 -5 * * * PS 0.084 0.238 0.071 0.085 0.103 0.163 0.023 0.252 0.119 0.215 0.092 0.140 0.187 0.089 0.129 0.129 0.141 0.076 0.138 0.219 0.123 0.102 0.306 0.154 0.172 0.085 0.264 0.130 0.159 0.114 0.294 0.157 0.318 0.175 0.169 0.175 0.171 0.123 0.198 0.158 0.228 0.159 0.195 0.049 0.130 0.110 0.069 0.128 0.027 0.108 0.117 0.121 0.120 0.343 0.133 0.000 0.193 0.000 0.094 0.088 0.000 log M∗ log M⊙ 10.82 11.21 11.57 10.59 10.8 11.02 10.4 11.22 10.87 11.18 10.73 11.6 11.33 10.98 11.3 10.67 10.74 11.07 11.04 11.06 10.98 10.7 11.95 10.98 11.17 11.43 11.54 11.21 10.94 10.85 11.51 10.9 11.21 10.6 11 10.56 10.85 10.84 10.88 10.78 11.06 10.74 10.69 10.73 11.7 11.32 10.72 11.11 10.57 11.36 11.16 11.35 11.1 11.16 10.78 11.85 10.87 11 10.61 10.44 11.42 dlog M∗ log M⊙ 0.12 0.10 0.05 0.11 0.11 0.12 0.12 0.11 0.08 0.11 0.09 0.08 0.09 0.07 0.06 0.07 0.09 0.07 0.06 0.06 0.09 0.13 0.08 0.10 0.13 0.04 0.07 0.08 0.08 0.21 0.11 0.10 0.08 0.14 0.12 0.23 0.12 0.11 0.13 0.19 0.12 0.21 0.12 0.04 0.06 0.05 0.08 0.17 0.10 0.08 0.06 0.56 0.05 0.12 0.06 0.08 0.07 0.09 0.08 0.07 0.07 26 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Table 1. Continued Name Nclus z EDCSNJ1059107-1253020 EDCSNJ1059096-1253197 EDCSNJ1059053-1255535 EDCSNJ1059046-1251583 EDCSNJ1059093-1253065 EDCSNJ1059075-1253351 EDCSNJ1059069-1253531 EDCSNJ1059102-1254115 EDCSNJ1059135-1254337 EDCSNJ1059106-1253118 EDCSNJ1059102-1253260 EDCSNJ1059104-1253211 EDCSNJ1059022-1253465 EDCSNJ1059060-1253574 EDCSNJ1059086-1255576 EDCSNJ1119168-1130290 EDCSNJ1119166-1130442 EDCSNJ1119165-1130541 EDCSNJ1119173-1129304 EDCSNJ1119173-1129425 EDCSNJ1119168-1129376 EDCSNJ1202411-1222495 EDCSNJ1202430-1223461 EDCSNJ1202430-1224044 EDCSNJ1202433-1224301 EDCSNJ1202432-1224227 EDCSNJ1202478-1226383 EDCSNJ1227589-1135135 EDCSNJ1227539-1138173 EDCSNJ1227531-1138340 EDCSNJ1227587-1135089 EDCSNJ1227541-1138174 EDCSNJ1227447-1140544 EDCSNJ1228003-1135243 EDCSNJ1227551-1136202 EDCSNJ1227537-1138210 EDCSNJ1227581-1135364 EDCSNJ1227566-1136545 EDCSNJ1238330-1144307 EDCSNJ1301351-1138356 EDCSNJ1301372-1139069 EDCSNJ1301402-1139229 EDCSNJ1301420-1139379 EDCSNJ1301414-1140081 EDCSNJ1301302-1138187 EDCSNJ1301304-1138266 EDCSNJ1301397-1139048 EDCSNJ1353021-1135395 EDCSNJ1353017-1137285 EDCSNJ1353055-1137581 EDCSNJ1353019-1137290 EDCSNJ1352599-1138256 EDCSNJ1352562-1136567 EDCSNJ1411078-1146452 EDCSNJ1411047-1148287 EDCSNJ1411038-1151014 EDCSNJ1411160-1151292 EDCSNJ1411037-1147286 EDCSNJ1411059-1147515 EDCSNJ1411041-1148232 EDCSNJ1420104-1233451 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 19 19 19 19 19 19 20 20 20 20 20 20 16 16 16 16 16 21 16 16 16 16 16 22 24 24 23 23 23 23 23 23 25 25 25 25 25 25 26 26 26 26 26 26 26 15 0.4552 0.455 0.4572 0.4561 0.4537 0.4565 0.4573 0.4598 0.4559 0.4511 0.4559 0.4553 0.4582 0.4559 0.4515 0.5491 0.551 0.5492 0.5482 0.5503 0.5497 0.4267 0.4244 0.4228 0.4246 0.423 0.4244 0.6375 0.6339 0.6345 0.641 0.6345 0.5822 0.6376 0.639 0.6309 0.6383 0.6391 0.4606 0.3976 0.394 0.4828 0.4835 0.4792 0.4856 0.4893 0.4795 0.5887 0.5889 0.5916 0.5877 0.5892 0.5865 0.5191 0.52 0.5214 0.5199 0.5161 0.5229 0.5177 0.4944 S Type 1 2 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 2 1 2 1 1 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 σmes (km/s) 169.2 214 204.4 115.9 270.4 242.3 147.1 200.2 146.3 111.5 140.7 263.7 317.6 271.7 114.3 288 152.8 283.3 150.8 265.9 111.2 128.3 188.9 157.3 239.9 170 150.3 211.1 142.4 137.4 155.8 219.1 119.6 105.2 233.7 139.9 166 124.7 408.4 225.8 124.8 271.9 150.7 105.1 218.9 113.9 247.9 177.3 240.7 112.8 292.2 158.8 165.8 157 230 144.1 210.7 155.9 142.7 150.5 177.5 σcor (km/s) 173.8 219.8 210 119.1 277.8 248.9 151.1 205.7 150.3 114.5 144.6 270.9 326.3 279.1 117.4 297.1 157.6 292.2 155.5 274.3 114.7 131.6 193.7 161.3 246.1 174.3 154.2 218.3 147.3 142.1 161.2 226.6 123.5 108.8 241.7 144.7 171.7 129 419.7 231.2 127.8 279.7 155 108.1 225.2 117.2 255 183.1 248.6 116.5 301.8 164 171.2 161.8 237 148.5 217.1 160.6 147 155 182.7 dσ (km/s) 21 17.6 19.2 14.3 30.9 10.9 17.1 8.7 9.9 16.5 12.9 10.3 21.1 10.3 22.3 10.9 15.7 29.1 16.6 16.4 17.9 16.9 23.4 25.5 11.3 27.1 9.4 7.7 19.1 12.1 12.1 12.7 14.7 16.9 17.6 21.5 10.1 8.8 64.3 17 22.8 17.7 19.9 15.9 15.7 17 12.9 14.2 12.7 22.4 24.8 21.3 16.5 14.7 13.9 15.5 17.2 8.2 21.5 7.2 13.6 Re (kpc) 0.8354 8.433 3.187 2.335 4.667 9.692 1.617 1.412 1.719 3.44 3.53 3.783 80.52 4.227 3.303 3.975 0.7064 0.7822 0.4868 2.785 4.054 4.259 0.1114 3.179 10.98 1.801 2.206 12.29 5.542 1.235 0.9511 8.193 0.9498 1.843 1.955 3.299 1.692 1.267 6.26 12.06 1.598 12.96 1.236 3.116 2.982 3.828 3.069 8.501 14.44 3.35 5.367 0.7164 2.833 1.906 11.54 2.81 3.803 4.186 0.9881 20.58 2.283 log Ie log L⊙ /pc2 2.711 1.665 2.057 2.243 1.405 1.559 2.478 2.785 2.577 1.779 2.04 2.007 0.08597 2.172 1.995 2.342 3.469 3.229 3.885 2.464 1.97 1.868 4.404 1.873 1.473 2.303 2.397 1.484 1.768 2.79 3.167 1.58 2.759 2.354 2.387 2.038 2.733 2.642 2.03 1.517 2.29 1.565 2.679 2.147 2.27 2.214 2.448 1.745 1.607 2.094 2.19 3.018 2.479 2.51 1.753 2.192 2.045 2.199 2.857 0.8911 2.511 T Type * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * - PS 0.080 0.000 0.196 0.199 0.058 0.000 0.129 0.283 0.000 0.079 0.000 0.000 0.000 0.118 0.145 0.000 0.138 0.127 0.000 0.196 0.000 0.000 0.058 0.194 0.000 0.000 0.198 0.000 0.000 0.000 0.000 0.000 0.026 0.065 0.166 0.000 0.140 0.167 0.000 0.000 0.000 0.000 0.209 0.000 0.000 0.000 0.140 0.000 0.000 0.076 0.000 0.067 0.250 0.113 0.000 0.113 0.000 0.139 0.000 0.000 0.243 log M∗ log M⊙ 10.53 11.46 10.84 10.87 10.49 11.42 10.74 11.07 11.05 10.52 11.13 11.19 11.63 11.34 10.65 11.37 10.93 10.98 11.12 11.23 11.39 11.16 10.41 10.73 11.48 10.78 10.9 11.55 11.04 10.76 10.94 11.67 10.66 10.5 10.88 10.79 11.13 10.87 11.76 11.71 10.65 11.73 10.78 11.17 11.05 11.17 11.45 11.42 11.83 10.72 11.57 10.75 11.2 10.94 11.75 10.74 11.16 11.19 10.65 11.29 11.15 dlog M∗ log M⊙ 0.11 0.10 0.10 0.11 0.14 0.09 0.13 0.09 0.10 0.13 0.09 0.07 0.11 0.09 0.38 0.11 0.08 0.17 0.11 0.08 0.21 0.12 0.15 0.15 0.13 0.13 0.12 0.07 0.13 0.08 0.08 0.09 0.10 0.16 0.12 0.08 0.08 0.06 0.14 0.09 0.14 0.08 0.12 0.09 0.09 0.11 0.06 0.05 0.05 0.09 0.04 0.06 0.04 0.12 0.06 0.10 0.15 0.11 0.09 0.11 0.13 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies 27 Table 1. Continued Name Nclus z EDCSNJ1420098-1233566 EDCSNJ1420164-1235291 EDCSNJ1420201-1236297 EDCSNJ1420219-1237051 EDCSNJ1420235-1237178 EDCSNJ1420228-1233529 EDCSNJ1420181-1236230 EDCSNJ1420184-1236427 EDCSNJ1420132-1237440 EDCSNJ1420202-1236281 15 15 15 15 15 15 15 15 15 15 0.4958 0.4958 0.4969 0.4956 0.4957 0.4954 0.489 0.4965 0.4976 0.4938 S Type 1 1 1 1 1 2 1 1 1 1 σmes (km/s) 143.6 119.9 268.4 212.6 148.8 189.3 234 219.9 159.3 284.1 σcor (km/s) 147.8 123.4 276.3 218.8 153.2 194.8 240.8 226.3 164 292.4 dσ (km/s) 11.5 17.7 7 28.5 14.8 10.1 15.2 19 19.6 22.8 Re (kpc) 1.909 2.87 11.91 0.8876 2.639 3.781 4.454 5.343 2.303 5.752 log Ie log L⊙ /pc2 2.6 2.099 1.639 2.781 2.209 2.192 1.94 1.847 2.405 2.075 T Type * * * PS 0.213 0.127 0.000 0.055 0.133 0.191 0.000 0.197 0.162 0.000 log M∗ log M⊙ 10.99 10.78 11.67 10.61 10.81 11.17 11.28 11.24 11.06 11.6 Table 2. The FP parameters of field galaxies Name z EDCSNJ1040391-1155167 EDCSNJ1040343-1155414 EDCSNJ1040476-1158184 EDCSNJ1054253-1148349 EDCSNJ1054289-1146428 EDCSNJ1054239-1145236 EDCSNJ1054339-1147352 EDCSNJ1054240-1147364 EDCSNJ1054525-1244189 EDCSNJ1054353-1246528 EDCSNJ1054487-1245052 EDCSNJ1216402-1201593 EDCSNJ1216508-1157576 EDCSNJ1216476-1202280 EDCSNJ1216445-1203359 EDCSNJ1216364-1200087 EDCSNJ1216449-1202139 EDCSNJ1216527-1202553 EDCSNJ1216548-1157451 EDCSNJ1232326-1249355 EDCSNJ1232285-1252553 EDCSNJ1232315-1251578 EDCSNJ1037540-1241435 EDCSNJ1037448-1245026 EDCSNJ1037534-1246259 EDCSNJ1037595-1245095 EDCSNJ1037529-1246428 EDCSNJ1103531-1243328 EDCSNJ1103418-1244344 EDCSNJ1103430-1245370 EDCSNJ1138100-1136361 EDCSNJ1138126-1131500 EDCSNJ1138078-1134468 EDCSNJ1354144-1228536 EDCSNJ1354107-1231236 EDCSNJ1354016-1231578 EDCSNJ1354055-1234136 EDCSNJ1354139-1229474 EDCSNJ1354161-1234210 EDCSNJ1354164-1229192 0.766 0.7807 0.6171 0.8657 0.2491 0.7408 0.8608 0.6124 0.7283 0.6932 0.6189 0.3463 0.6501 0.5434 0.2344 0.7868 0.6691 0.8263 0.8746 0.4186 0.8457 0.4171 0.4329 0.4456 0.4948 0.8736 0.6452 0.7221 0.3539 0.6584 0.4389 0.9079 0.5282 0.8245 0.6183 0.4783 0.5142 0.6865 0.5391 0.6846 S Type 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 2 1 1 2 1 1 2 2 1 1 1 1 2 1 2 2 2 1 2 2 1 2 σmes (km/s) 177.8 290.4 161.9 231.8 258.6 200.8 153 201.7 211.9 191.2 136.2 224.5 132 209.9 139.5 166.4 160.5 226.9 169.8 235 144.3 117.7 126.2 113.5 212.5 356.8 178.8 134.7 146.9 205.6 160.6 202.3 129 188.7 207.3 129.4 205.4 127.4 139.5 164.6 σcor (km/s) 184.4 301.3 167.4 240.9 261.5 208.2 159 208.5 219.7 198 140.8 229.1 136.6 216.5 140.8 172.7 166.1 235.6 176.5 241 149.9 120.7 129.5 116.5 218.7 370.8 185 139.6 150 212.8 164.9 210.3 133 196 214.3 133.1 211.6 131.9 143.8 170.5 dσ (km/s) 29.9 17.1 10.4 43.6 5.5 9.4 14.4 12.9 6.9 13.1 10.4 6.3 24.5 20.1 6.3 16.6 12.8 20.4 26.9 35.4 22.8 22.8 15.6 17.3 13 21.6 18.8 14.7 11.9 10.8 20.9 20.4 13.3 11.4 14.9 12.9 12.9 20.3 18.9 12.3 Re (kpc) 0.9953 3.494 1.745 1.646 4.418 2.376 1.65 3.552 3.174 3.102 1.462 2.229 0.9882 1.164 3.83 1.065 2.109 0.8582 2.799 0.9256 2.747 4.337 2.111 1.029 1.285 1.878 1.365 2.711 1.222 2.085 1.378 1.665 1.798 2.607 1.089 1.539 2.483 1.66 1.521 3.108 log Ie log L⊙ /pc2 2.842 2.562 2.561 2.916 2.225 2.901 2.947 2.402 2.527 2.342 2.753 2.456 3.072 3.015 2.089 3.115 2.618 3.428 2.704 2.944 2.544 1.952 2.102 2.615 2.724 2.961 2.617 2.679 2.353 2.601 2.708 3.256 2.453 2.664 2.915 2.429 2.363 2.631 2.753 2.463 T Type -5 -5 -2 -5 -2 -5 3 -5 1 1 -2 -5 -5 -2 -5 -2 -5 -5 3 -2 -5 -2 -5 -5 -2 1 -5 -5 -2 -2 -2 -2 -2 1 -2 -2 1 -5 1 -2 PS 0.049 0.369 0.276 0.057 0.090 0.169 0.073 0.190 0.185 0.166 0.070 0.174 0.068 0.191 0.082 0.031 0.155 0.039 0.047 0.111 0.065 0.099 0.122 0.053 0.058 0.060 0.068 0.330 0.188 0.297 0.096 0.064 0.030 0.231 0.216 0.117 0.068 0.076 0.162 0.167 log M∗ log M⊙ 10.78 11.58 10.99 11.11 11.51 11.37 11.13 11.73 11.38 11.61 10.96 11.45 10.92 11.21 11.09 10.97 11.1 10.99 11.27 11.09 11.16 11.13 10.67 10.57 10.98 11.35 10.79 11.23 10.71 11.2 10.78 11.24 10.96 11.47 10.87 10.78 11 10.88 10.53 11.45 dlog M∗ log M⊙ 0.07 0.05 0.08 0.07 0.55 0.07 0.09 0.04 0.04 0.06 0.08 0.23 0.08 0.09 0.87 0.06 0.07 0.05 0.69 0.12 0.07 0.15 0.09 0.11 0.06 0.04 0.08 0.10 0.28 0.07 0.16 0.08 0.11 0.08 0.09 0.08 0.09 0.14 0.05 0.06 dlog M∗ log M⊙ 0.10 0.13 0.08 0.13 0.12 0.13 0.10 0.10 0.09 0.07 28 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Table 2. Continued Name z EDCSNJ1354130-1230263 EDCSNJ1054143-1144503 EDCSNJ1054499-1247587 EDCSNJ1216435-1203502 EDCSNJ1232293-1254348 EDCSNJ1018465-1213510 EDCSNJ1059233-1251010 EDCSNJ1059055-1249491 EDCSNJ1059149-1251030 EDCSNJ1059198-1252101 EDCSNJ1059132-1250585 EDCSNJ1059225-1251279 EDCSNJ1059224-1254492 EDCSNJ1119226-1128488 EDCSNJ1119216-1132475 EDCSNJ1119194-1133231 EDCSNJ1119271-1130174 EDCSNJ1202496-1222081 EDCSNJ1227589-1139039 EDCSNJ1227539-1140303 EDCSNJ1227578-1136570 EDCSNJ1227552-1137559 EDCSNJ1227496-1138046 EDCSNJ1228009-1138122 EDCSNJ1301413-1138172 EDCSNJ1353107-1135521 EDCSNJ1353037-1136152 EDCSNJ1352578-1138286 EDCSNJ1353108-1139340 EDCSNJ1410565-1146209 EDCSNJ1410570-1147052 EDCSNJ1411028-1149063 EDCSNJ1411143-1149241 EDCSNJ1411171-1150200 EDCSNJ1420242-1233126 EDCSNJ1420185-1235026 EDCSNJ1420224-1235422 EDCSNJ1420231-1239076 0.8223 0.3976 0.802 0.6693 0.7518 0.4888 0.5182 0.675 0.6248 0.6319 0.8506 0.2966 0.5184 0.5269 0.4764 0.7092 0.6439 0.3791 0.4911 0.834 0.4679 0.4893 0.4879 0.7081 0.3534 0.5559 0.5705 0.6292 0.424 0.3252 0.3179 0.4001 0.4291 0.4102 0.4656 0.7022 0.6071 0.3964 S Type 1 2 1 2 1 1 1 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 2 1 1 2 1 1 1 1 2 2 1 1 1 2 1 σmes (km/s) 251.3 243.9 248.3 231.1 175 251.6 209.9 174.8 140.9 206.1 109.3 214.1 192 252.6 132.1 210.7 216.2 125.9 105.2 163.5 159.3 146.5 169.4 184.8 123.8 176.4 203.1 185.9 130.1 148.9 164.8 159.1 163.4 161.4 128 254.4 135.9 173.8 σcor (km/s) 260.9 249.8 257.7 239.2 181.5 258.9 216.2 181 145.7 213.1 113.5 217.6 197.8 260.3 135.8 218.3 223.7 128.8 108.3 169.8 163.8 150.7 174.3 191.5 126.4 182 209.6 192.2 133.4 151.7 167.8 163 167.6 165.4 131.6 263.6 140.4 178 dσ (km/s) 17.6 34.4 13.1 21.3 25.7 36.4 12.8 22.2 16.8 19.9 10.5 6.2 11.1 23.6 18.4 37.7 14.7 18.3 12.2 21.3 10.2 8.1 17 21 21.4 28.5 19.3 16.3 10.4 25.5 16.1 19 23.9 6.9 15.3 12.8 17.8 27.9 Re (kpc) 1.244 1.361 6.362 2.57 1.543 1.714 2.378 2.297 0.6406 3.192 1.089 2.874 3.387 2.235 1.071 2.386 2.555 2.32 1.162 3.916 5.679 2.536 4.618 6.839 3.472 1.458 5.696 1.313 7.238 2.515 1.308 2.57 5.562 2.129 2.914 5.828 2.193 6.128 log Ie log L⊙ /pc2 3.174 2.142 2.041 2.296 2.885 2.557 2.235 2.218 3.543 2.212 3.219 2.481 2.47 2.676 3.256 2.639 2.547 1.883 2.817 2.297 1.581 2.317 1.77 1.702 1.962 2.687 1.845 2.966 1.792 1.821 2.221 2.281 1.552 2.65 2.231 2.252 2.668 1.673 T Type 3 * * * * * * * * * * - PS 0.229 0.045 0.165 0.000 0.066 0.091 0.153 0.023 0.174 0.106 0.081 0.081 0.166 0.148 0.000 0.167 0.358 0.000 0.000 0.096 0.128 0.000 0.000 0.097 0.105 0.235 0.000 0.366 0.264 0.000 0.126 0.156 0.106 0.083 0.181 0.000 0.330 0.180 log M∗ log M⊙ 11.09 10.64 11.39 11.08 11.69 11.03 11.1 10.56 10.8 11.2 10.7 11.48 11.41 11.29 11.25 11.09 11.14 10.54 10.73 11.34 11.15 11.09 11.18 11.32 10.98 10.89 11.1 10.9 11.17 10.41 10.21 10.79 10.27 11.12 11.03 11.4 10.96 10.83 dlog M∗ log M⊙ 0.05 0.11 0.04 0.07 0.26 0.05 0.10 0.06 0.05 0.20 0.06 0.13 0.12 0.13 0.12 0.25 0.12 0.30 0.14 0.04 0.09 0.13 0.09 0.07 0.15 0.07 0.06 0.06 0.16 0.25 0.30 0.15 1.56 0.17 0.13 0.05 0.07 0.14 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies 29 Table 3. The structural parameters of galaxies with measured velocity dispersions and HST photometry derived from Sersic fits to HST images and bulge+disk fits to VLT images. Name EDCSNJ1040403-1156042 EDCSNJ1040407-1156015 EDCSNJ1040346-1157566 EDCSNJ1040396-1155183 EDCSNJ1040356-1156026 EDCSNJ1054244-1146194 EDCSNJ1054250-1146238 EDCSNJ1054309-1147095 EDCSNJ1054263-1148407 EDCSNJ1054338-1149299 EDCSNJ1054280-1149598 EDCSNJ1054296-1147123 EDCSNJ1054278-1149580 EDCSNJ1054305-1146536 EDCSNJ1054303-1149132 EDCSNJ1054237-1146107 EDCSNJ1054246-1146124 EDCSNJ1054467-1245035 EDCSNJ1054435-1245519 EDCSNJ1054451-1247336 EDCSNJ1054436-1244202 EDCSNJ1054438-1245409 EDCSNJ1054445-1246173 EDCSNJ1054440-1246390 EDCSNJ1054442-1245331 EDCSNJ1054439-1245556 EDCSNJ1054398-1246055 EDCSNJ1054396-1248241 EDCSNJ1054431-1246205 EDCSNJ1216470-1159267 EDCSNJ1216454-1200017 EDCSNJ1216490-1200091 EDCSNJ1216453-1201176 EDCSNJ1216420-1201509 EDCSNJ1216468-1202226 EDCSNJ1216401-1202352 EDCSNJ1216462-1200073 EDCSNJ1216418-1200449 EDCSNJ1216438-1200536 EDCSNJ1216461-1201143 EDCSNJ1216456-1201080 EDCSNJ1216453-1201209 EDCSNJ1216443-1201429 EDCSNJ1216438-1202155 EDCSNJ1216417-1203054 EDCSNJ1216359-1200294 EDCSNJ1216446-1201089 EDCSNJ1216449-1201203 EDCSNJ1216403-1202029 EDCSNJ1216522-1200595 EDCSNJ1216382-1202517 EDCSNJ1216387-1201503 EDCSNJ1232318-1249049 EDCSNJ1232280-1249353 EDCSNJ1232303-1250364 EDCSNJ1232250-1251551 EDCSNJ1232287-1252369 EDCSNJ1232271-1253013 EDCSNJ1232343-1249265 EDCSNJ1232350-1250103 Re (S ersic) (kpc) 6.153 1.698 3.348 2.244 2.345 5.945 3.465 3.84 4.523 2.965 1.802 2.547 3.372 9.346 4.856 0.9561 6.194 1.883 9.555 1.516 1.297 1.606 1.373 1.692 1.684 2.806 5.88 2.259 5.025 2.12 2.494 4.425 8.92 3.867 6.409 1.41 1.052 2.802 1.855 4.748 7.863 5.509 1.846 0.6206 0.9622 0.9401 1.6 2.972 1.948 1.641 3.456 1.297 2.125 4.062 19.73 2.304 2.445 2.554 1.42 5.685 log Ie (S ersic) log L⊙ /pc2 1.986 2.808 2.319 2.549 2.659 2.155 2.431 2.125 1.927 2.484 2.533 2.657 2.522 1.969 2.191 2.729 1.753 2.68 1.849 2.809 2.993 2.906 2.713 2.513 2.142 2.311 2.251 2.484 1.601 2.563 2.451 2.075 2.033 2.58 1.907 3.14 2.957 2.35 2.876 2.453 1.718 2.012 2.612 3.296 3.347 3.255 2.664 2.406 2.247 2.53 2.409 3.06 2.291 2.283 1.414 2.438 2.483 2.383 2.767 1.928 Re (V LT ) (kpc) 9.822 2.923 5.857 2.624 2.543 12.3 8.08 3.461 5.196 3.749 2.298 4.457 5.019 10.06 9.448 0.9133 5.918 2.574 15.48 1.716 0 7.235 1.057 10.37 1.377 3.648 4.916 2.934 4.152 1.696 3.876 2.017 16.17 5.471 4.355 2.046 0.8956 5.177 2.129 6.957 11.69 10.02 7.068 0 0.5713 0.8689 4.238 27.13 14.17 0 9.366 1.834 4.021 4.521 20.46 2.034 2.691 3.256 0.8388 3.762 log Ie (V LT ) log L⊙ /pc2 1.682 2.448 1.885 2.411 2.606 1.648 1.855 2.182 1.854 2.325 2.386 2.251 2.268 1.911 1.797 2.674 1.761 2.456 1.566 2.758 -1948 1.813 2.955 1.287 2.184 2.133 2.329 2.332 1.686 2.724 2.146 2.579 1.716 2.308 2.11 2.876 3.072 1.936 2.798 2.158 1.457 1.7 1.966 -1997 3.766 3.258 2.017 0.9842 1.035 -1949 1.727 2.811 1.839 2.151 1.404 2.483 2.409 2.208 3.2 2.147 30 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Table 3. Continued Name EDCSNJ1232313-1250327 EDCSNJ1232317-1249275 EDCSNJ1232309-1249408 EDCSNJ1232303-1251092 EDCSNJ1232303-1251441 EDCSNJ1232370-1248239 EDCSNJ1232372-1249258 EDCSNJ1232296-1250119 EDCSNJ1232301-1250362 EDCSNJ1232288-1250490 EDCSNJ1232299-1251034 EDCSNJ1232207-1252016 EDCSNJ1232204-1249547 EDCSNJ1037527-1243456 EDCSNJ1037548-1245113 EDCSNJ1037447-1246050 EDCSNJ1037552-1246368 EDCSNJ1037535-1241538 EDCSNJ1037525-1243541 EDCSNJ1037428-1245573 EDCSNJ1037527-1244485 EDCSNJ1037473-1246245 EDCSNJ1103365-1244223 EDCSNJ1103372-1245215 EDCSNJ1103363-1246220 EDCSNJ1103444-1245153 EDCSNJ1103349-1246462 EDCSNJ1103413-1244379 EDCSNJ1103357-1246398 EDCSNJ1138068-1132285 EDCSNJ1138102-1133379 EDCSNJ1138069-1134314 EDCSNJ1138074-1137138 EDCSNJ1138104-1133319 EDCSNJ1138107-1133431 EDCSNJ1138127-1134211 EDCSNJ1138116-1134448 EDCSNJ1138069-1132044 EDCSNJ1138130-1132345 EDCSNJ1138110-1133411 EDCSNJ1138022-1135459 EDCSNJ1138065-1136018 EDCSNJ1138031-1134278 EDCSNJ1354098-1231098 EDCSNJ1354098-1231015 EDCSNJ1354097-1230579 EDCSNJ1354026-1230127 EDCSNJ1354114-1230452 EDCSNJ1354159-1232272 EDCSNJ1354102-1230527 EDCSNJ1354101-1231041 EDCSNJ1354204-1234286 EDCSNJ1354106-1230499 EDCSNJ1040391-1155167 EDCSNJ1040343-1155414 EDCSNJ1040476-1158184 EDCSNJ1054253-1148349 EDCSNJ1054289-1146428 EDCSNJ1054239-1145236 EDCSNJ1054339-1147352 Re (S ersic) (kpc) 1.44 5.449 3.62 1.087 2.704 1.831 0.6312 5.102 1.105 2.169 1.526 7.029 4.347 1.268 1.74 1.483 1.942 3.661 1.731 3.259 2.494 0.7199 6.787 2.682 2.645 2.327 5.823 2.637 1.741 3.893 6.071 1.692 2.877 4.137 1.604 0.9056 1.442 1.138 2.817 2.813 3.447 3.032 1.293 0.9136 7.568 1.926 1.385 5.69 0.7318 11.84 1.595 3.009 2.117 1.025 3.543 2.091 1.526 5.073 2.635 1.916 log Ie (S ersic) log L⊙ /pc2 2.523 2.049 2.476 2.637 2.14 2.605 2.869 2.011 2.615 2.539 2.526 1.96 2.223 2.81 2.889 2.292 2.157 1.954 2.666 2.02 2.284 2.772 2.159 2.305 2.199 2.852 2.037 2.441 2.484 1.703 1.917 2.565 2.326 1.562 2.492 2.695 2.664 2.66 2.003 1.917 2.107 1.584 2.54 2.895 1.99 2.854 2.64 2.065 2.989 1.369 2.766 2.424 2.635 2.833 2.558 2.45 2.977 2.15 2.842 2.865 Re (V LT ) (kpc) 19.95 5.643 4.613 1.262 2.002 2.289 1.396 6.447 8.984 2.457 1.231 9.614 3.337 2.49 1.263 1.433 1.75 5.46 1.616 3.723 2.444 3.525 7.192 2.563 3.895 2.526 7.501 3.182 1.871 3.365 16.73 2.575 3.817 5.453 1.916 0.9804 1.291 3.871 3.307 3.308 5.677 5.204 1.485 2.151 13.64 7.646 1.492 5.024 0.4524 10.15 8.668 5.488 3.311 1.14 5.096 2.047 1.711 6.876 2.251 1.939 log Ie (V LT ) log L⊙ /pc2 0.6675 1.964 2.269 2.472 2.294 2.428 2.254 1.831 1.332 2.449 2.712 1.73 2.403 2.363 3.175 2.391 2.205 1.674 2.716 1.927 2.284 1.637 2.075 2.316 1.941 2.764 1.855 2.319 2.374 1.705 1.246 2.224 2.124 1.361 2.312 2.659 2.715 1.74 1.839 1.763 1.747 1.243 2.428 2.317 1.666 1.883 2.564 2.096 3.394 1.433 1.542 2.006 2.334 2.71 2.307 2.434 2.915 1.932 2.971 2.78 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Table 3. Continued Name EDCSNJ1054240-1147364 EDCSNJ1054525-1244189 EDCSNJ1054353-1246528 EDCSNJ1054487-1245052 EDCSNJ1216402-1201593 EDCSNJ1216508-1157576 EDCSNJ1216476-1202280 EDCSNJ1216445-1203359 EDCSNJ1216364-1200087 EDCSNJ1216449-1202139 EDCSNJ1216527-1202553 EDCSNJ1216548-1157451 EDCSNJ1232326-1249355 EDCSNJ1232285-1252553 EDCSNJ1232315-1251578 EDCSNJ1037540-1241435 EDCSNJ1037448-1245026 EDCSNJ1037534-1246259 EDCSNJ1037595-1245095 EDCSNJ1037529-1246428 EDCSNJ1103531-1243328 EDCSNJ1103418-1244344 EDCSNJ1103430-1245370 EDCSNJ1138100-1136361 EDCSNJ1138126-1131500 EDCSNJ1138078-1134468 EDCSNJ1354144-1228536 EDCSNJ1354107-1231236 EDCSNJ1354016-1231578 EDCSNJ1354055-1234136 EDCSNJ1354139-1229474 EDCSNJ1354161-1234210 EDCSNJ1354164-1229192 EDCSNJ1354130-1230263 Re (S ersic) (kpc) 4.464 4.663 3.469 1.629 2.423 1.096 1.228 4.625 1.345 2.355 0.919 4.144 1.116 3.761 5.594 2.322 0.9972 1.655 2.377 1.555 3.073 1.272 2.203 1.381 1.649 1.974 2.011 1.085 1.583 2.393 1.504 1.061 3.845 1.183 log Ie (S ersic) log L⊙ /pc2 2.263 2.296 2.282 2.695 2.402 3.011 2.982 1.977 2.958 2.549 3.384 2.472 2.822 2.359 1.801 2.05 2.636 2.569 2.815 2.538 2.597 2.336 2.571 2.709 3.264 2.407 2.852 2.919 2.409 2.395 2.698 3.002 2.33 3.204 Re (V LT ) (kpc) 10.7 6.144 28.39 0 3.819 0.9015 1.173 6.214 1.076 1.783 0.881 2.953 1.658 5.188 4.918 2.705 0.7565 1.057 1.824 1.12 6.066 1.036 1.966 1.227 1.438 3.269 6.39 0.7461 1.085 3.174 2.739 5.412 20.08 2.775 log Ie (V LT ) log L⊙ /pc2 1.664 2.093 1.085 -1949 2.033 3.123 3.013 1.723 3.08 2.712 3.438 2.653 2.505 2.112 1.82 1.955 2.923 2.891 2.981 2.822 2.141 2.474 2.665 2.774 3.312 2.041 2.076 3.224 2.713 2.201 2.278 1.854 1.206 2.572 31 32 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Table 4. The parameters of the EDisCS clusters with measured FP zero points ∆ log M/LB , without selection weighting. Nclus Cluster Short Name Phota zclus 1 cl1037.9-1243a CL1037a 1 0.4252 2 cl1138.2-1133a CL1138a 1 0.4548 3 cl1138.2-1133 CL1138 1 0.4796 4 cl1232.5-1144 CL1232 1 0.5414 5 cl1037.9-1243 CL1037 1 0.5783 6 cl1354.2-1230a CL1354a 1 0.5952 7 cl1103.7-1245a CL1103a 1 0.6261 8 cl1054.4-1146 CL105411 1 0.6972 9 cl1040.7-1155 CL1040 1 0.7043 10 cl1054.7-1245 CL105412 1 0.7498 11 cl1354.2-1230 CL1354 1 0.762 12 cl1216.8-1201 CL1216 1 0.7943 13 cl1059.2-1253 CL1059 0 0.4564 14 cl1018.8-1211 CL1018 0 0.4734 15 cl1420.3-1236 CL1420 0 0.4962 16 cl1227.9-1138 CL1227 0 0.6357 17 cl1103.7-1245 CL1103 1 0.9586 18 cl1103.7-1245b CL1103b 1 0.7031 19 cl1119.3-1129 CL1119 0 0.5500 20 cl1202.7-1224 CL1202 0 0.424 21 cl1227.9-1138a CL1227a 0 0.5826 22 cl1238.5-1144 CL1238 0 0.4602 23 cl1301.7-1139 CL1301 0 0.4828 24 cl1301.7-1139a CL1301a 0 0.3969 25 cl1353.0-1137 CL1353 0 0.5882 26 cl1411.1-1148 CL1411 0 0.5195 (a) 1: with HST photometry, 0: with VLT photometry. σclus (km/s) 537+46 −48 542+63 −71 732+72 −76 1080+119 −89 319+53 −52 +95 433−104 336+36 −40 589+78 −70 418+55 −46 504+113 −65 +105 648−110 1018+73 −77 510+52 −56 486+59 −63 218+43 −50 574+72 −75 534+101 −120 +65 252−85 166+27 −29 518+92 −104 341+42 −46 447+135 −181 687+81 −86 391+63 −69 +136 666−139 710+125 −133 ∆ log M/L B (dex) −0.16 ± 0.02 −0.27 ± 0.02 −0.18 ± 0.02 −0.35 ± 0.01 −0.36 ± 0.02 −0.44 ± 0.02 −0.30 ± 0.02 −0.38 ± 0.02 −0.53 ± 0.02 −0.47 ± 0.03 −0.28 ± 0.01 −0.46 ± 0.01 −0.27 ± 0.02 −0.21 ± 0.04 −0.37 ± 0.02 −0.42 ± 0.03 - Scatter (dex) 0.13 0.27 0.08 0.17 0.27 0.14 0.15 0.17 0.11 0.30 0.22 0.23 0.10 0.12 0.14 0.21 - N 4 5 9 20 5 4 4 12 5 11 6 23 8 4 8 4 - Table 5. The slopes of the zero point evolution of the FP ∆ log M/L = 0.4(ZP(z) − ZP(0))/β0 = η′ z = η log(1 + z). Type Clusters Clusters Cluster galaxies Cluster galaxies Cluster galaxies Cluster galaxies Cluster galaxies Cluster galaxies Cluster galaxies Cluster galaxies Cluster galaxies Cluster galaxies Cluster galaxies Cluster galaxies Field galaxies Field galaxies Field galaxies Field galaxies Field galaxies Field galaxies Field galaxies Field galaxies Field galaxies Field galaxies Field galaxies Field galaxies Ngal 132 132 154 154 67 67 43 43 76 76 33 33 24 24 68 68 28 28 16 16 32 32 8 8 6 6 PS No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes HST Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes VLT Yes Yes Yes Yes Yes Yes Yes Yes No No No No No No Yes Yes Yes Yes Yes Yes No No No No No No ST 2 2 2 2 2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 1 Morph 10 10 10 10 10 10 10 10 0 0 0 0 0 0 10 10 10 10 10 10 0 0 0 0 0 0 Mdyn All All All All 1011 M⊙ 1011 M⊙ 1011 M⊙ 1011 M⊙ All All 1011 M⊙ 1011 M⊙ 1011 M⊙ 1011 M⊙ All All 1011 M⊙ 1011 M⊙ 1011 M⊙ 1011 M⊙ All All 1011 M⊙ 1011 M⊙ 1011 M⊙ 1011 M⊙ η′ −0.54 ± 0.01 −0.47 ± 0.003 −0.55 ± 0.006 −0.48 ± 0.01 −0.44 ± 0.01 −0.36 ± 0.01 −0.41 ± 0.01 −0.32 ± 0.01 −0.56 ± 0.01 −0.51 ± 0.01 −0.47 ± 0.01 −0.44 ± 0.01 −0.46 ± 0.01 −0.43 ± 0.01 −0.76 ± 0.01 −0.76 ± 0.01 −0.68 ± 0.01 −0.67 ± 0.01 −0.70 ± 0.01 −0.73 ± 0.02 −0.83 ± 0.01 −0.87 ± 0.02 −0.83 ± 0.02 −0.90 ± 0.02 −0.82 ± 0.02 −0.91 ± 0.02 η −1.61 ± 0.01 −1.43 ± 0.01 −1.66 ± 0.02 −1.45 ± 0.03 −1.34 ± 0.02 −1.10 ± 0.02 −1.24 ± 0.03 −0.97 ± 0.03 −1.70 ± 0.02 −1.54 ± 0.04 −1.44 ± 0.03 −1.34 ± 0.03 −1.41 ± 0.03 −1.32 ± 0.03 −2.27 ± 0.03 −2.28 ± 0.03 −2.05 ± 0.03 −1.99 ± 0.04 −2.10 ± 0.04 −2.16 ± 0.04 −2.46 ± 0.04 −2.58 ± 0.05 −2.43 ± 0.06 −2.59 ± 0.07 −2.40 ± 0.06 −2.59 ± 0.07 R.P. Saglia et al.: The fundamental plane of EDisCS galaxies Table 6. The coefficients α and β of the EDisCS FP as a function redshift and the derived quantities ǫ = 1 λ = 1+ǫ (with L ∝ M λ ), A = 10β−2−α . 5β z range 0 0.4-0.5 0.5-0.7 0.7-1.0 0.4-0.7 0.7-1.0 0.4-0.5 0.5-0.7 0.7-1.0 0.4-0.7 0.7-1.0 Ngal 46 57 50 39 21 46 57 50 39 21 PS No No No No No Yes Yes Yes Yes Yes α 1.2 1.09 ± 0.33 1.04 ± 0.24 0.69 ± 0.42 1.05 ± 0.6 0.37 ± 0.27 1.06 ± 0.25 1.09 ± 0.30 0.44 ± 0.20 1.00 ± 0.7 0.22 ± 0.7 β 0.33 0.23 ± 0.02 0.30 ± 0.02 0.23 ± 0.02 0.23 ± 0.02 0.23 ± 0.02 0.27 ± 0.02 0.32 ± 0.03 0.25 ± 0.03 0.23 ± 0.02 0.20 ± 0.02 ǫ 0.33 0.42 ± 0.30 0.46 ± 0.24 0.95 ± 1.07 0.45 ± 0.63 2.20 ± 2.09 0.44 ± 0.24 0.42 ± 0.27 1.77 ± 1.21 0.50 ± 0.75 4.04 ± 3.42 λ 0.75 0.71 ± 0.14 0.68 ± 0.11 0.51 ± 0.24 0.69 ± 0.27 0.31 ± 0.20 0.69 ± 0.11 0.70 ± 0.13 0.36 ± 0.13 0.67 ± 0.32 0.20 ± 0.13 A 0.06 −0.69 ± 0.37 −0.03 ± 0.21 −0.35 ± 0.42 −0.67 ± 0.58 −0.06 ± 0.30 −0.29 ± 0.25 +0.07 ± 0.26 +0.02 ± 0.28 −1.03 ± 0.76 +0.15 ± 0.20 33 2−α 2α (with M/L ∝ Lǫ ), Environment Local Sample Cluster Cluster Cluster Field Field Cluster Cluster Cluster Field Field Table 7. The redshift evolution of the mass correlation fits. Selection weighting and progenitor bias correction are applied when PS =Yes and PB=Yes. Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Parameter PS Re (kpc) HST Re (kpc) HST Re (kpc) Re (kpc) Re (kpc) HST Re (kpc) HST Re (kpc) Re (kpc) σ(km/s) σ(km/s) σ(km/s) σ(km/s) L(1010 L⊙ ) Cluster L(1010 L⊙ ) Cluster L(1010 L⊙ ) Field L(1010 L⊙ ) Field No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes PB No No No No Yes Yes Yes Yes No No Yes Yes No No No No log M slope 0.56 0.56 0.56 0.56 0.56 0.56 0.56 0.56 0.23 0.23 0.23 0.23 0.75 0.75 0.75 0.75 z=0 5.1 ± 0.7 5.5 ± 0.9 5.7 ± 0.5 5.7 ± 0.8 4.4 ± 0.4 4.6 ± 0.5 4.6 ± 0.4 4.6 ± 0.5 175 ± 8 175 ± 14 188 ± 7 188 ± 10 2.1 ± 0.4 1.9 ± 1.4 2.4 ± 0.2 2.0 ± 0.7 Mdyn (1+z)ˆ Slope −1.0 ± 0.3 −1.3 ± 0.4 −1.2 ± 0.2 −1.3 ± 0.3 −0.46 ± 0.2 −0.67 ± 0.3 −0.5 ± 0.2 −0.65 ± 0.2 +0.59 ± 0.10 +0.68 ± 0.17 +0.41 ± 0.08 +0.49 ± 0.11 +2.1 ± 0.4 +1.9 ± 1.2 +2.4 ± 0.2 +2.7 ± 0.6 z=0 4.3 ± 1.1 4.6 ± 1.3 6.1 ± 0.6 6.4 ± 0.9 4.3 ± 0.7 4.3 ± 0.7 4.8 ± 0.4 4.9 ± 0.5 185 ± 13 189 ± 23 199 ± 9 201 ± 15 2.8 ± 0.7 2.5 ± 0.6 2.3 ± 0.5 2.0 ± 0.8 M∗ (1+z) ˆ Slope −1.0 ± 0.6 −1.2 ± 0.7 −1.6 ± 0.2 −1.7 ± 0.4 −0.68 ± 0.4 −0.84 ± 0.4 −0.75 ± 0.2 −0.86 ± 0.3 +0.34 ± 0.14 +0.39 ± 0.24 +0.19 ± 0.1 +0.27 ± 0.16 +1.2 ± 0.4 +1.4 ± 0.4 +1.9 ± 0.4 +2.1 ± 0.8 Table 8. The ages derived from the evolution of the FP ZP, averaged for Mdyn < 1011 M⊙ and Mdyn > 1011 M⊙ . The variations for the case of maximal evolution and the progenitor bias of van Dokkum & Franx (2001) are also given. Type Cluster Cluster Cluster Cluster Field Field Field Field HST Yes Yes Yes Yes Yes Yes Yes Yes View publication stats VLT Yes Yes No No Yes Yes No No Morph 10 10 0 0 10 10 0 0 Mass < > < > < > < > z < 0.5 +3.1 4.7−1.2 +0 8.6−0.3 +0.7 7.2−0.1 +0.2 8.5−1.0 +3.2 3.9−0.8 +2.7 6.72.0 +2.8 3.4−0.7 +3.3 3.3−0.4 Age (Gyr) 0.5 < z < 0.7 +2.7 2.40.4 +2.0 5.7−1.7 +4.1 3.2−0.7 +3.2 4.4−1.1 +1.6 1.7−0.3 +4.0 3.8−0.9 +2.3 2.2−0.4 +2.0 2.1−0.3 z > 0.7 +2.1 1.8−0.3 +0.5 6.3−0.3 +1.9 1.8−0.3 +2.1 4.6−1.3 +0.9 1.1−0.2 +1.1 4.5−1.0 +1.1 1.4−0.3 +1.8 2.4−0.6