STELLAR POPULATIONS AND EVOLUTION OF EARLY-TYPE CLUSTER GALAXIES: CONSTRAINTS FROM OPTICAL IMAGING AND SPECTROSCOPY OF z = 0.5−0.9 GALAXY CLUSTERS

The GMOS-N imaging data for MS0451.6−0305 and RXJ1226.9+3332 were reduced and co-added using the same methods as for the RXJ0152.7−1357 imaging data (Jørgensen et al. 2005). One co-added image was produced for each filter and field. The co-added images were then processed with SExtractor v.2.1.6 (Bertin & Arnouts 1996) as described in Jørgensen et al.

The photometry was standard calibrated using the magnitude zero points and color terms derived in Jørgensen (2009). The absolute accuracy of the standard calibration is expected to be 0.035–0.05 mag, as described in that paper. Tables 13 and 14 list the photometry for MS0451.6−0305 and RXJ1226.9+3332 calibrated to the Sloan Digital Sky Survey (SDSS) system. Similar photometry for RXJ0152.7−1357 can be found in Jørgensen et al. (2005). The r'-band imaging for MS0451.6−0305 was obtained in significantly better seeing than the other bands, and therefore is significantly deeper. Object detection was done in the r' band. Due to the difference in seeing the colors involving the r' band are expected to be affected by a systematic error of ≈0.05 mag, with the galaxies being too blue. As this systematic error has no significant effect on our analysis, we have chosen not to correct the colors for the difference in seeing.

The Galactic extinction in the direction of the three clusters is A_B = 0.14, 0.064, and 0.085 for MS0451.6−0305, RXJ0152.7−1357, and RXJ1226.9+3332, respectively (Schlegel et al. 1998). Using the effective wavelength of the filters used for the photometry and the calibration from Cardelli et al. (1989) we derive the extinction on those filters; see Table 4. The photometry in Tables 13 and 14 has not been corrected for the Galactic extinction.

We have compared the GMOS-N photometry with available literature data for the fields; details can be found in Appendix A. Based on these comparisons, we conclude that the photometry is calibrated to an external accuracy of 0.05 mag.

The principles of the spectroscopic sample selection for the project are described in Jørgensen et al. (2005). In brief, sample selection is based on the GMOS photometry. Stars and galaxies are separated using the SExtractor classification parameter class_star derived from the image in the i' filter. For the purpose of selecting targets for the spectroscopic observations we choose a threshold of 0.80, i.e., objects with class_star < 0.80 in the i'-image are considered galaxies. In practice, this excludes galaxies with effective radius r_e ⩽ 015 (r_e ⩽ 1 kpc). However, it was more important for the planning of our observations that the selected spectroscopic targets had a high probability of being galaxies rather than foreground stars. Then we use the total magnitude in i' and the available colors to define four classes of objects in each field. The aim is to use a color selection that includes likely cluster members. Table 6 summarizes the definition of these four classes for each of the three clusters. The classes are shown in Figures 3 and 4. For RXJ1226.9+3332 the (i' − z') colors are used as the primary color selection, while for MS0451.6−0305 both (r' − z') and (i' − z') colors are used. The classes are used in the selection of the spectroscopic sample as described in Jørgensen et al. (2005). Objects in classes 1 and 2 are likely to be cluster members. For each field, roughly equal numbers of objects from each of these two classes are included. Empty spaces in the mask designs are filled with class 3 objects if possible. This class may include blue cluster members or cluster members too faint to derive all spectroscopic parameters due to the resulting S/N of the spectroscopic observations. Any remaining space in the mask designs is filled with class 4 objects. The brighter and bluer objects in this class are in general not expected to be members of the cluster, while the fainter and redder objects in this class may be faint cluster members. The selection criteria for galaxies included in the analysis are described in Section 8. Here we note that any observed galaxy for which the properties meet the final selection criteria is included in the analysis, independent of its class in this initial selection used for the spectroscopic observations. We have visualized this by marking galaxies included in the analysis with red triangles in Figures 3(a) and 4(a).

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Redshift data for MS0451.6−0305 from the CNOC survey (Ellingson et al. 1998) were used to optimize inclusion of cluster members. In the mask design galaxies that are known cluster members based on these data were given preference over galaxies without redshift information. Known non-members were assigned to class 4 and only included in the mask if no object from the other classes could be used to fill the available space.

The masks for MS0451.6−0305 also include 12 objects selected to have (i' − z') ⩾ 0.7 and (r' − z') ⩾ 1.1 and therefore be candidate background galaxies with redshifts larger than about 0.75 and passive stellar populations. These are enclosed by the red box in Figures 3(a), (e), and (f), and are not discussed further in this paper though we do derive and list their redshifts.

The sample selection for the GSA data used for RXJ1226.9+3332 is not known. We note that in addition to cluster members on the red sequence, the data contain a number of bluer member and non-member galaxies, as well as some AGNs.

The spectroscopic samples are marked in Figures 1 and 2. For each mask in the GCP observations, two blue stars were included in order to obtain a good correction for the telluric absorption lines. The blue stars are also marked in figures.

The MS0451.6−0305 spectroscopic data were reduced in the same way as done for the RXJ0152.7−1357 data (Jørgensen et al. 2005). The only difference was that we applied our established correction for the charge diffusion in the red as described in Appendix B. The correction slightly improves the sky subtraction for these short slits.

The RXJ1226.9+3332 GSA data were reduced in a similar way, with the exception that for some of the very short slitlets with the objects very close to the end of the slitlet, sky subtraction was possible only after the wavelength calibration had been applied. This in general leads to poorer sky subtraction as the (strong) skylines are being interpolated onto the rectified wavelength scale before the sky signal is subtracted out.

The RXJ1226.9+3332 GCP data were obtained using GMOS-N in the nod-and-shuffle mode (Glazebrook & Bland-Hawthorn 2001). The reduction of these data involved construction of special flat fields that take into account the shuffling of the data on the detector array, as well as a correction for the effect of charge diffusion in the far-red wavelength region.

The details of the reductions of all the spectroscopic data are described in Appendix B. The final data products are cleaned and averaged spectra that have been wavelength calibrated and calibrated to a relative flux scale. Both the extracted one-dimensional (1D) and the 2D spectra are kept after the basic reductions. However, in this paper we use only the 1D spectra.

The co-added 1D spectra were used for deriving the redshifts, velocity dispersions, absorption line indices, and emission line equivalent widths of the galaxies. The details are described in Jørgensen et al. (2005) and in Appendix B. In the following analysis we use the Lick/IDS absorption line indices for CN₂, Fe4383, C4668, Mgb, Fe5270, and Fe5335 (Worthey et al. 1994). We use Hβ_G (see González 1993; Jørgensen 1997) in place of the Lick/IDS definition for Hβ. We also use the higher order Balmer line indices Hδ_A and Hγ_A (Worthey & Ottaviani 1997) and the CN3883 index defined by Davidge & Clark (1994). The uncertainties on the line indices were estimated both from the local S/N of the spectra and from internal comparisons of indices derived from stacking subsets of the frames available for each cluster. In the following we use the uncertainties from the latter method as these are larger than uncertainties based on the S/N. Table 19 in Appendix B summarizes the uncertainties.

For galaxies with detectable emission from [O ii] we determined the equivalent width of the [O ii]λλ3726,3729 doublet, in the following referred to as the "[O ii] line."

Tables 22 and 24 in Appendix B list the derived line indices and the measurements of the [O ii] equivalent widths for members of MS0451.6−0305 and RXJ1226.9+3336. The data for RXJ0152.7−1357 are available in Jørgensen et al. (2005).

In the analysis involving the two higher order Balmer line indices Hδ_A and Hγ_A, we use the combined index as defined by Kuntschner (2000) (Hδ_A + Hγ_A)' ≡ −2.5log (1 − (Hδ_A + Hγ_A)/(43.75 + 38.75)). For the iron indices in the visible region, we use the average iron index 〈Fe〉 ≡ (Fe5270 + Fe5335)/2 rather than the individual indices.

In the analysis of the line index strengths we use the SSP models from Thomas et al. (2011) for a Salpeter (1955) initial mass function (IMF). These authors model the Lick/IDS indices on a flux-calibrated system, which makes them ideal for comparison with our data. They also provide models for different abundance ratios. We use their base models for different values of [α/Fe], where the α-elements should be understood as including the carbon, nitrogen, and sodium. Further, we use the carbon and nitrogen enhanced models. We downloaded the model tables from the Web site provided by D. Thomas (http://www.icg.port.ac.uk/~thomasd).

The models do not provide predictions for the M/L ratios and CN3883. Maraston (2005) modeled the M/L ratios for solar abundance ratios and otherwise used the same model ingredients as Thomas et al. The dependency of the M/L ratios on varying abundance ratios (at fixed metallicity) are in general poorly understood and often assumed to be insignificant as done by Maraston. In our discussion we also investigate the effect of differences in the IMF slope. To do so, we use the models from Vazdekis et al. (2010), but note that these models cover solar abundance ratios only.

The strong index CN3883 is not yet modeled by any of the commonly used stellar population models, which also vary the abundance ratios. Rather than use the weaker indices CN₁ and CN₂ we instead estimate how CN3883 depends on age, metallicity, and abundance ratios using two approaches. First, we use the model spectra used by Maraston & Strömbäck (2011) to derive CN3883 and CN₂. The models are based on the same ingredients as the models from Thomas et al. (2011), but cover only solar [α/Fe]. Second, we determine an empirical relation between CN3883 and CN₂ and then transform the stellar population model values for CN₂ to the equivalent CN3883. CN₁ and CN₂ probe the same features in the spectra. However, CN₂ excludes Hδ in its blue continuum passband and is therefore preferred over CN₁ (Worthey et al. 1994).

Figure 5 shows CN3883 versus CN₂ and the best-fit relation

$$\begin{equation} {\rm CN3883} = (0.84 \pm 0.13)\, {\rm CN_2} +0.146 \end{equation} \tag{ 4 }$$

with an rms scatter of 0.041. The residuals were minimized in CN3883 as the goal is to predict CN3883 based on the CN₂ values. The relation has an intrinsic scatter of about 0.03 in CN3883. This relation has not previously been established in the literature. As the passbands for CN3883 contain some higher order Balmer lines, one might expect that (part of) the intrinsic scatter of the relation is due to differences in the strengths of the Balmer lines. However, we found no dependence of the residuals on the Balmer line index (Hδ_A + Hγ_A)'. Similarly including (Hδ_A + Hγ_A)' as a parameter in the fit does not lower the scatter of the established relation. For the redshifts of RXJ0152.7−1357 and RXJ1226.9+3332, the passband for CN₂ coincides with the strong telluric absorption around 760–770 nm. However, CN₂ is only used to establish Equation (4) and not in the analysis itself. Excluding RXJ0152.7−1357 and RXJ1226.9+3332 from the fit results in slightly steeper relation with a slope of 1.00 ± 0.13. This relation is also shown in Figure 5. None of the results in our analysis change significantly if we were to adopt this steeper slope. Thus, we adopt Equation (4) as the best fit. Figure 5 also shows the model values based on Maraston & Strömbäck (2011). These implicate stronger CN3883 at CN₂ > 0.08 than found from the data. It is beyond the scope of this paper to investigate the reason for this. However, we note that CN3883 derived from the Maraston & Strömbäck model spectra would indicate roughly a factor of two stronger dependency on age and metallicity than if instead we use the transformation in Equation (4). However, because the values from the Maraston & Strömbäck model spectra do not reproduce our data, we choose to use Equation (4) to transform the model values for CN₂ (from Thomas et al. 2011) to CN3883, and through that transformation achieve estimates of how CN3883 depends on age, metallicity, and [α/Fe].

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To enable studying the metallicity independent of the [α/Fe] abundance ratios, we use the combined magnesium–iron index [MgFe] ≡ (Mgb × 〈Fe〉)^1/2 first used by González (1993). The models predict this index to be independent of the [α/Fe] abundance ratios. Similarly we experimented to find a combination of C4668 and Fe4383, which the models also predict to be independent of [α/Fe]. The combined index

$$\begin{equation} \rm {[C4668\,Fe4383] \equiv C4668 \times (Fe4383)^{1/3} } \end{equation} \tag{ 5 }$$

has this property, as fitting this index as a function of age, metallicity, and [α/Fe] shows in an insignificant dependence on [α/Fe]. This combined index makes it possible for us to carry out similarly [α/Fe] independent analysis of the higher redshift clusters as is possible at lower redshift using [MgFe]. We have also tested a similarly defined index using CN3883 in place of C4668,

$$\begin{equation} \rm {[CN3883\,Fe4383] \equiv CN3883 + 0.33 \log Fe4383. } \end{equation} \tag{ 6 }$$

Under the assumption that the transformation from CN₂ to CN3883 is valid (Equation (4)), then fitting this index as a function of age, metallicity, and [α/Fe] also results in an insignificant dependence on [α/Fe]. While this index is independent of [α/Fe], its metallicity dependency relative to its age dependency is only about a factor of 1.5, while for [C4668 Fe4383] the same ratio is about 2.8. Thus, the models are better separated in age and metallicity in the [C4668 Fe4383] versus (Hδ_A + Hγ_A)' diagram than when using [CN3883 Fe4383] versus (Hδ_A + Hγ_A)'.

Because our data for the clusters RXJ0152.7−0152 and RXJ1226.9+3332 do not include line indices in the visible (Hβ_G, Mgb, and 〈Fe〉), we have evaluated to what extent line indices in the blue can be used to trace the same properties of the stellar populations as traced by the indices in the visible wavelength region. Figure 6 shows the best choices in the blue versus the line indices in the visible. The higher order Balmer lines and Hβ_G are expected to be closely correlated (Figure 6(a)). However, the data show galaxies with weaker Hβ_G than expected from their (Hδ_A + Hγ_A)' indices. While this may be due to Hβ_G being partly filled in by (very) weak emission, we choose to still include these galaxies in the analysis as the strength of their [O ii] emission meets the sample selection criteria; see Section 8.

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C4668 and CN3883 versus Mgb both approximately follow the locations predicted by the stellar populations' models for [α/Fe] = 0.3 (Figures 6(b) and (c)) and we therefore consider them both as viable candidates for use in the blue in place of Mgb. However, it is important to note that the models assume that the carbon and nitrogen abundance ratios, [C/Fe] and [N/Fe], follow the [α/Fe] abundance ratio. As C4668 and CN3883 both depend on the carbon and nitrogen abundances, the two indices trace [C/Fe] and [N/Fe], which are then assumed to be the same as [α/Fe]. We return to the question of additional enhancement of carbon or nitrogen in Section 10. The two iron indices 〈Fe〉 and Fe4383 are expected to be closely correlated, see Figure 6(d). The low-redshift data are in agreement with this prediction, while the MS0451.6−0305 sample show a larger scatter relative to the predicted relation between 〈Fe〉 and Fe4383. This can be explained by the larger uncertainties on the iron indices for MS0451.6−0305. The indices [C4668 Fe4383] and [CN3883 Fe4383] trace metallicity as well as [MgFe]; see Figures 6(e) and (f).

In our analysis, we will use the models to identify general trends of the indices with varying ages, metallicities, and abundance ratios. To make this more straightforward we fit the model index values as a function of age, total metallicity [M/H] and abundance ratio [α/Fe]. All fits to the models are established for ages between 2 and 15 Gyr, [M/H] from −0.33 to 0.67, and [α/Fe] from −0.3 to 0.5. The fits were established as least-squares fits with the residuals minimized in the line indices. The model fits are listed in Table 9. In addition, we use the carbon and nitrogen enhanced models to establish the dependence of the indices C4668 and CN3883 on [C/α] and [N/α]. The dependence of carbon and nitrogen enhancements is decoupled from the dependence on age, metallicity, and [α/Fe] as inclusion of [C/α] and [N/α] in the fits changes the other coefficients with negligible amounts. The other indices used in our analysis depend only very weakly on [C/α] and [N/α] (Thomas et al. 2011).

In the analysis we also use the models to estimate ages, metallicities [M/H], and abundance ratios [α/Fe]. We use Hβ_G versus [MgFe] and (Hδ_A + Hγ_A)' versus [C4668 Fe4383] to estimate ages and [M/H]. The abundance ratios [α/Fe] are derived from Mgb versus 〈Fe〉 and from CN3883 versus Fe4383. As the indices in the visible and the blue do not depend on age, [M/H], and [α/Fe] in identical ways, and the models do not perfectly model the galaxies, we expect that there will be differences between the parameters derived from the visible indices and those based on the blue indices. For example, since CN3883 in some of the galaxies appears to be weaker than expected from the Mgb measurements, given the model predictions (see Figure 6(c)), estimating [α/Fe] from CN3883 versus Fe4383 may result in lower values than when using Mgb versus 〈Fe〉. Further, the metal dependence relative to the age dependence is stronger for [C4668 Fe4383] than for [MgFe] (see Table 9), which in turn may lead to differences in both age and [M/H] estimates. However, we do not mix the parameters derived from the visible indices with those derived from the blue indices, and to a large extent we limit the analysis to using the differences between the clusters for the various parameters. Thus, these issues do not significantly affect our conclusions.

While other stellar population models are available in the literature (e.g., Vazdekis et al. 2010; Schiavon 2007), the models from Thomas et al. are widely used in the field and are readily available for fixed total metallicities, different [α/Fe] abundance ratios, and for carbon or nitrogen enhanced above the [α/Fe] abundance ratio. We tested if it would make a difference for our results if we had used the models from Schiavon (2007). We used models that treat the individual elements the same as done in the base models by Thomas et al., specifically models for which carbon, nitrogen, and sodium abundances follow [α/Fe]. For each model point, total metallicities [M/H] were derived as [M/H] = [Fe/H] + X, where X = −0.18, 0.0, 0.28, and 0.47 for the four model sets of [α/Fe] = -0.2, 0.0, 0.3, and 0.5, respectively (R. Schiavon 2012, private communication). We then fit the model index values as a function of age, [M/H], and [α/Fe] omitting the very low [M/H] and very young age models, as done for the models from Thomas et al. (2011). In general, the fits are very similar to those derived for the models from Thomas et al. with coefficients being within 10% of those listed in Table 9. Relative to the models from Thomas et al., the exceptions are as follows. (1) Mgb and 〈Fe〉 have a weaker dependence on [α/Fe] in the models from Schiavon, while Fe4383 has a stronger [α/Fe] dependence. This affects the exact location of the models in the Mgb–〈Fe〉 and CN3883–Fe4383 diagrams. However, it does not affect our results regarding [α/Fe] variations between clusters or as a function of redshift. (2) CN3883 and C4668 have a weaker dependence on [M/H] in the models from Schiavon. This would result in any measured differences in [M/H] being derived larger if we used the models from Schiavon, but it does not affect our results regarding variations between clusters or as a function of redshift. It should also be noted that the models from Schiavon reach [M/H] >0.2 only for [α/Fe] above solar and that the models do not cover the very strong C4668 indices seen for the most massive galaxies in our samples. Thus, the differences in the resulting fits may, at least in part, be caused by differences in the parameter space covered by the two sets of models.

Models for passive evolution assume that the galaxies after an initial period of star formation usually at high redshift, evolve passively without any additional star formation. The models are usually parameterized by a formation redshift z_form, which corresponds to the approximate epoch of the last major star formation episode. As the stellar populations in the observed galaxies are assumed to age passively and no other changes take place, the difference between the luminosity weighted mean ages of the stellar populations in the galaxies in each cluster and similar galaxies at the present is expected to be equal to the look-back time for that redshift. For reference, the look-back time for z = 0.89 is 7.3 Gyr with our adopted cosmology.

Thomas et al. (2005) used the properties of nearby early-type galaxies to estimate the formation redshift z_form as a function of galaxy velocity dispersion, and through an empirical relation between stellar mass and velocity dispersion as a function of stellar mass. We adopt their model for the high-density cluster environment as our base model for passive evolution and show the model predictions throughout the paper together with our data. As our relation between dynamical mass and velocity dispersion is slightly different from the stellar mass–velocity dispersion relation used by Thomas et al., we adopt our transformation in order to show the model predictions as a function of dynamical mass. For the typical low and high velocity dispersion galaxies (log σ = 2.1 and 2.35) in our sample the model from Thomas et al. implies z_form ≈ 1.4 and 2.2, respectively.

A more recent analysis by Thomas et al. (2010) used data from the SDSS to establish the formation redshift as a function of galaxy velocity dispersion and mass, covering primarily lower density environments. Using this model in place of that from Thomas et al. (2005) does not affect our results significantly. Thus, we choose to use the original high-density environment model from Thomas et al. (2005).

In our analysis, we implicitly assume that the galaxies we observe at high redshift are the progenitors to the galaxies in the low-redshift comparison sample. This may not be the case, as discussed in detail by van Dokkum & Franx (2001). We return to this issue in the discussion in Section 12.3.

We have investigated the possible evolution of sizes and velocity dispersions as a function of redshift by establishing relations with the dynamical galaxy masses. The relations and the zero points for the clusters are summarized in Table 10. The galaxies in the samples for the higher redshift clusters follow the same relations as found for the Coma cluster sample, with no significant differences in the zero points; see Figure 10. Thus, for these samples no significant evolution of size or velocity dispersion at a given dynamical mass with redshift is found. For the two highest redshift clusters treated as one sample, 3σ zero point differences would be Δlog r_e = 0.083 and Δlog σ = 0.041.

Before further addressing the issue of possible evolution of the relations with redshift, we compared our relations to relations derived based on the SDSS data as made available by Thomas et al. (2010). Using their data, taking into account the difference in adopted cosmology and limiting the sample to early-type galaxies with Mass ⩾10^10.3 M_☉, we find no significant difference in the slope of the radius–mass relation and a zero point difference of only 0.03 in log r_e. Using the SDSS data, we find a slightly steeper relation between the velocity dispersions and the masses than found from our Coma sample (a slope of 0.35 compared to 0.26 for the Coma sample). However, adopting our slope the zero point difference in log σ at 0.006 is well below the systematic errors on the velocity dispersions. Thus, we conclude that our low-redshift results are in agreement with relations based on the SDSS data.

Many authors have studied galaxy sizes as a function of redshift and found significant evolution in the sense that galaxies at a given mass are smaller at higher redshift (e.g., Trujillo et al. 2007; van Dokkum et al. 2010; Saglia et al. 2010; Newman et al. 2012). Of these studies the work by Saglia et al. most closely resembles our work, as these authors also determine dynamical masses and study galaxy clusters up to z = 1. They then derive the evolution of both sizes and velocity dispersions as a function of redshift. In Figure 10 the thin solid lines show the predicted locations of the relations for z = 0.86 (the average of the two highest redshift clusters in our sample) based on the results from Saglia et al. of r_e∝(1 + z)^−0.5 and σ∝(1 + z)^0.41. The predicted log r_e offset is equivalent to a 5σ effect in our data, while the predicted log σ offset if present would be detected in our data as an 8σ detection. Other authors find larger size evolution at a given mass as a function of redshift, though these authors use masses determined from photometry using stellar population models. For example, Newman et al., who find the same slope of the size–mass relation as we do, determine an evolution of the sizes with redshift that would lead to an offset Δlog r_e = −0.224 at z = 0.86. An offset of this size is equivalent to an 8σ detection in our data.

We note that our result and difference in conclusion with Saglia et al. (and other results showing even stronger size evolution) do not depend on our sample limit in the effective radii. Specifically, the sample used by Saglia et al. has the same limit in r_e as ours, r_e ⩾ 1 kpc. We therefore conclude that the disagreement between our results and that by Saglia et al. cannot be due to a selection effect. Previous results showing evolution of the galaxy sizes and velocity dispersions as a function of redshift were focused on field galaxies and less rich cluster environments than those of the clusters in the present paper. Further, except for two, the clusters included in Saglia et al. have cluster velocity dispersions of 300–700 km s⁻¹ (Sánchez-Blázquez et al. 2009). Thus, the difference in results may be related to the difference in cluster environment where possibly the galaxies in dense cluster environments reach the present day sizes at earlier epochs than do galaxies in less dense environments.

In summary, we do not detect in our data any significant evolution of sizes and velocity dispersions as a function of redshift at a given galaxy mass. Therefore, we do not to make any correction for this type of evolution in the following analysis.

Table 11 lists the fits of the FP for each of the clusters as well as the fits of the M/L ratio as a function of galaxy mass and as a function of velocity dispersion, while the zero points relative to the low-redshift best-fit relations are included in Table 10. Figures 11 and 12 show the data and the relations.

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The samples in two highest redshift clusters RXJ0152.7−0305 and RXJ1226.9+3332 were fit both separately and together. By fitting two parallel relations to the two samples we tested if there were significant zero point offsets between them and found none. Thus, for the purpose of discussing the change in slope of the relations with redshift, we will consider the fits established for the joint sample of the two clusters. The slightly larger sample of RXJ0152.7−1357 and RXJ1226.9+3332 confirms our results from Jørgensen et al. (2006, 2007) of a "steeper" FP at z = 0.86 compared to that of the Coma cluster. The MS0451.6−0305 also shows a steeper FP, but to a lesser extent.

In Figure 12, we show the model prediction from Thomas et al. (2005) for each of the cluster redshifts for models in which high-mass galaxies form the majority of their stars at high redshifts while lower mass galaxies experience later star formation. The models reproduce the general trends of the M/L–mass and M/L–velocity dispersion relations for the intermediate-redshift clusters, though the data show a larger evolution in M/L ratios that predicted by the models, especially for low-mass (low velocity dispersions) galaxies. Thus, in the case of passive evolution this would mean a lower formation redshift than z_form = 1.4, as assumed by the models for log σ = 2.1 galaxies. Using the best-fit relations for log σ versus log M/L to determine the differences in log M/L and therefore the formation redshifts we find for log σ = 2.1 (Mass = 10^10.55 M_☉) a formation redshift of z_form ≈ 1.2. At log σ = 2.35 (Mass = 10^11.36 M_☉) the difference in log M/L corresponds to z_form ≈ 2.45. Both of these estimates are based on the fits to the low-redshift sample and the joint sample of the two highest redshift clusters. The fit to the MS0451.6−0305 sample implies lower formation redshifts, ≈0.95 and 1.2 for low and high velocity dispersion galaxies, respectively.

Figure 13 shows the absorption line indices versus the velocity dispersions for the low-redshift sample together with all the intermediate-redshift samples. The relations and zero points are summarized in Table 10.

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Our data for MS0451.6−0305 allow us to compare the galaxies in this cluster directly with the low-redshift sample using the well-studied indices Hβ_G, Mgb, and 〈Fe〉. There are no significant differences in the slopes of the relations for the low-redshift sample and those for the MS0451.6−0305 sample. Using the median zero points for the cluster, we find that Hβ_G is only marginally stronger in MS0451.6−0305 than in the low-redshift sample, while both Mgb and 〈Fe〉 are weaker at the 3σ–5σ level; see Table 10. The scatter of the relations for Mgb and 〈Fe〉 are two to three times higher for MS0451.6−0305 than found for the low-redshift sample. This difference cannot be explained by higher measurement uncertainties and may indicate that the galaxies in the MS0451.6−0305 sample are more diverse than those in the low-redshift sample.

For RXJ0152.7−1357 and RXJ1226.9+3332 only indices blueward of 4700 Å are available. These indices are also available for MS0451.6−0305 and for the low-redshift samples in Perseus and A194. As for the line indices in the visible, we cannot detect any significant differences of the slopes of the relations for the different clusters. We therefore use the slopes established for the low-redshift sample and determine zero point offsets relative to these and scatter relative to the offset relations. Only the relation for the higher order Balmer lines shows a clear redshift dependence of the zero point with the intermediate-redshift clusters having stronger Balmer lines. In Jørgensen et al. (2005) we found that the RXJ0152.7−0305 galaxies have significantly weaker Fe4383 than the low-redshift sample. The other two clusters do not show significantly weaker Fe4383. All other relations for the metal lines show that the z = 0.5–0.9 clusters follow the same relations as the low-redshift sample with the zero points being within 2σ of each other. The relations for Fe4383 and C4668 show higher scatter in the intermediate-redshift clusters than found for the low-redshift sample, again indicating that the samples in these clusters may be more diverse than our low-redshift comparison sample. The samples in RXJ0152.7−1357 and RXJ1226.9+3332 contain galaxies at larger normalized cluster center distances R_cl R^-1₅₀₀ than the other clusters. We have tested if we in these samples can detect any correlation between R_cl R^-1₅₀₀ and the residuals for the relations between the line indices and the velocity dispersions. We find no significant relations. There are also no significant zero point differences between galaxies at R_cl R^-1₅₀₀ > 1 and those closer to the cluster centers. It may require larger samples in intermediate-redshift clusters, going to larger cluster center distances, to detect any correlations if these are present as they are in low-redshift clusters (Smith et al. 2006).

The model predictions for the passive evolution model from Thomas et al. (2005) are overlaid in all panels in Figure 13. For the Balmer lines, the models predict stronger lines than measured in the galaxies in the intermediate-redshift clusters. Under the assumption of passive evolution, the formation redshifts for these galaxies would have to be higher than assumed by the models. This in turn is inconsistent with the results based on the FP. For the Mgb and 〈Fe〉 indices the passive evolution models reproduce the data well, while for the blue metal indices Fe4383 and CN3883 the models predict larger zero point offsets than measured from the data. For CN3883 in particular the data show no significant zero point offsets. We return to the zero point differences as a function of redshift in the discussion of the passive evolution model in Section 12.3.

Before we discuss the physical effects, it is important to understand to what extent the results may be affected by selection effects. The spectroscopic sample selection was described in Section 3.2. Most important for the current discussion is that each cluster sample has a luminosity limit but that high-redshift samples are not complete to that limit. In addition, only galaxies with early-type morphologies and EW[O ii] ⩽5 Å are included in the sample.

We focus on how the selection effects may affect the results for the FP offset and slope. In Jørgensen et al. (2006, 2007) we presented results of a bootstrap simulation, drawing samples of the same size as the high-redshift sample from both the Coma cluster sample and the high-redshift sample, and fitting these. The results showed a significance of the slope difference at the 96%–98% level. However, one could also argue that the difference is slope may be caused by systematically missing fainter galaxies in the high-redshift sample at a given mass.

We tested this by determining if the difference in slope depends on the chosen mass limit. Due to the slope of the luminosity limit lines in the M/L–mass plane (Figure 12(a)) the effect of the limiting magnitude will decrease with increasing mass limits. The test was done using the joint sample of the galaxies in RXJ0152.7−1357 and RXJ1226.9+3332, since our analysis of the FP shows that these two samples follow the same FP. We applied lower limits in log Mass to both this sample and the Coma sample from 10.4 to 11.3 in steps of 0.1 and refit each of these subsamples. Figure 19 shows the coefficient of log M/L in the mass–M/L ratio as a function of the value of the applied mass limit. For limits of log Mass = 10.8 or smaller the difference in the slope for the intermediate-redshift sample and the Coma sample is significant approximately at the same level as for the full sample (also shown in the figure at the limit of log Mass = 10.3). In all cases the slope difference is about 0.32. If the sample is limited at log Mass = 10.9 or higher, the slope difference is about 0.16, and the uncertainties are larger due to the smaller samples. Thus, formally the slope difference is not statistically significant for limits of log Mass ⩾10.9. However, given that the slope difference is very stable for sample limits of log Mass ⩽10.8 we conclude that the result is not an effect of the selection effects due to the luminosity limits of the data.

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The mass determination used here, Mass = 5r_eσ² G⁻¹ (Bender et al. 1992), assumes homology among the galaxies. The current data set does not offer the possibility of explicitly testing the effect of possible non-homology among the galaxies. van Dokkum et al. (2010) propose that a better mass estimate may be achieved by using the Sérsic (1968) index, n, to determine the coefficient in the mass determination. Using their equation the coefficient would be 3.24 at n = 2 and 2.58 at n = 6, rather than the constant value of 5 that we have used. If we determine the masses using the equation from van Dokkum et al. (2010) and then refit the M/L–mass relation then we find for the sample of the two highest redshift clusters

$$\begin{equation} \log {M}/{L} = (0.54 \pm 0.18) \log {\rm Mass} - 3.266. \end{equation} \tag{ 9 }$$

Comparing to the M/L–mass relation for the two highest redshift clusters listed in Table 11, we conclude that this different mass estimate does not result in a significantly different slope for the relation.

Cappellari et al. (2006) found from the integral-field-unit (IFU) data of early-type galaxies that any non-homology is an insignificant contribution to the difference between the FP slope and the slope expected from the virial relation, thus leading these authors to conclude that the difference is due to real M/L variations. The same conclusion is reached by Bolton et al. (2007) using SDSS data to derive galaxy masses based on strong gravitational lensing. Cappellari et al. (2006) also conclude that the approximation Mass = 5r_eσ²/G provides a reasonable mass estimate when data are not available for more detailed modeling. Finally, we note that there is no significant correlation between M/L–mass relation residuals and the Sérsic index, using the relations listed in Table 11. Since the slope of the M/L–mass relation is the same using mass estimates taking the Sérsic index into account compared to using our simpler approximation, and the low-redshift IFU studies confirm that the simpler approximation is valid, we will in the following discussion assume that the galaxies in our sample form a homologous class of galaxies.

The simplest of models for galaxy evolution is passive evolution of the stellar populations over the redshift interval covered by the data. The FP (Figure 11), the M/L–mass relation and the M/L–velocity dispersion relation (Figure 12) are consistent with passive evolution with the low-mass (low velocity dispersion) galaxies being younger than those of higher mass (higher velocity dispersion). We discussed this result in detail in Jørgensen et al. (2006, 2007) for the two highest redshift clusters RXJ0152.7−1357 and RXJ1226.9+3332. The data for MS0451.6−0305 are also consistent with this interpretation. The zero point differences for the subsamples described in Section 11 implies a formation redshift for the low velocity dispersion galaxies (log σ = 2.1; Mass = 10^10.55 M_☉) of z_form = 1.24 ± 0.05. The uncertainty takes into account only the scatter of the data relative to the relations. For the high velocity dispersion galaxies (log σ = 2.35; Mass = 10^11.36 M_☉) we find z_form = 1.95^+0.30_−0.20. The result for the high velocity dispersion galaxies can directly be compared to the result from van Dokkum & van der Marel (2007) who find z_form = 2.23^+0.24_−0.18, before correcting for progenitor bias. Half of the difference between our result and that of van Dokkum & van der Marel is due to a difference in the assumed dependency of the M/L on the age of the stellar population. As such the two results agree within the uncertainties.

The other major age indicator is the strengths of the Balmer lines. The Balmer lines for the intermediate-redshift clusters are too weak compared to what is predicted by the models for passive evolution with formation redshifts as derived from the M/L ratios. We focus here on (Hδ_A + Hγ_A)', which we have measured for all the clusters. As we do not detect a change in slope of the (Hδ_A + Hγ_A)'–velocity dispersion relation with redshift, we only give the formation redshift for the full sample. For the z = 0.8–0.9 clusters we find z_form > 2.8. This is consistent with the result from Kelson et al. (2001) who finds z_form > 2.4 or >2.9 depending on which SSP model is used for the interpretation. The formation redshift for the galaxies in MS0451.6−0305 would have to be even higher; see Figure 17(f), for the galaxies to be able to passively evolve into their low-redshift counterparts.

If the offset and slope differences of the M/L–mass relation are purely due to age differences, and therefore differences in formation redshift as a function of mass, we also expect to see offsets and (to lesser extent) slope differences in the relations between the metal line indices and the velocity dispersion. As the metal lines are predicted to be weaker with younger ages, we expect the intermediate-redshift samples to show offsets to weaker metal lines. Figure 17 shows the zero points together with the model predictions from passive evolution models. The measured offsets do not allow a straightforward interpretation within the passive evolution model or a conversion of the offsets to a formation redshift. In general, the offsets are smaller than predicted from the passive evolution model from Thomas et al. (2005). In particular, all the intermediate-redshift clusters have significantly stronger CN3883 than expected from the passive evolution model. CN3883 for the z = 0.8–0.9 clusters represent 4σ deviations from the model with z_form = 4. If we were to adopt the age dependence of CN3883 from the model spectra by Maraston & Strömbäck (2011), the difference would be even larger due to the stronger age dependence predicted for CN3883; see Section 6.

Part of the difference between the formation redshifts as found from the FP and from the high-order Balmer lines (Hδ_A + Hγ_A)' may be due to different sensitivity in the two methods to progenitor bias. We found that the mean ages for the low-redshift samples are lower than expected from the passive evolution model (Figure 18) and that some of the galaxies have ages too low for them to be the progenitors of the intermediate-redshift sample galaxies. For example, roughly 40% of the low-redshift sample have ages of less than ≈7.1 Gyr, which is the look-back time corresponding to z = 0.86. We have performed a simple test for the effect of the progenitor bias, by excluding these galaxies from the estimates of the mean ages based on the blue indices. These results result in a mean age for the low-redshift sample of ≈10 Gyr, and bring the data in agreement with the passive evolution model (Figure 18). However, excluding these galaxies from the determination of the zero points for the scaling relations for M/L and (Hδ_A + Hγ_A)' versus velocity dispersion lead to only insignificant changes. It also does not bring the zero point differences between the low-redshift sample and the intermediate-redshift samples for these scaling relations into agreement with each other.

As a different way of illustrating the disagreement between the FP and the strength of (Hδ_A + Hγ_A)' we use the SSP models (Maraston 2005) to predict the stellar M/L ratios, given the ages and metallicities derived from the line indices. As the possible dependency of the M/L ratios on the abundance ratios [α/Fe] has not been modeled, we will assume that it is insignificant. In Figure 20 we show the resulting M/L ratio versus velocity dispersion. In this view there is no change in the slope with redshift. We fit the samples with a set of parallel lines as shown in the figure. The zero point differences agree with the high the formation redshift found from (Hδ_A + Hγ_A)' versus velocity dispersion. Formally we find z_form > 4. Taken at face value, Figure 20 compared with the FP (Figure 12) indicates that the stellar M/L ratios change significantly less than the dynamical M/L ratios since z ≈ 0.9. We note that Toft et al. (2012) found a similar difference in the change of M/L ratios for massive galaxies between z ≈ 2 and the present. These authors speculated that the effect may be due to a change in the dark matter content. In our view, it is premature to conclude that a change in dark matter content can lead to the effect we find for the low-mass galaxies in these intermediate-redshift clusters. However, we plan to return to this issue using our full galaxy sample in the GCP.

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Even if the difference in the formation redshift derived from the FP and from (Hδ_A + Hγ_A)' versus velocity dispersion may be consolidated by invoking a change in dark matter content, passive evolution implies that the metallicity [M/H] and the abundance ratio [α/Fe] do not vary from cluster to cluster. However, both the distributions of the estimates of [M/H] and [α/Fe] for the individual galaxies (Figure 16) and the mean values derived from the mean indices (Figure 18) show that the mean [M/H] for MS0451.6−0305 is 0.2 dex below the other clusters, while the mean [α/Fe] for RXJ0152.7−1357 is 0.3 dex above the other clusters. Both of these results contradict the model of passive evolution.

In summary, it is not possible within the current SSP models using one IMF slope (Salpeter) for all the galaxies to find a passive evolution model that agrees with the data within the measurement uncertainties. While the slope changes with redshift of the M/L–mass and M/L–velocity dispersion relations indicate a difference in formation redshift for low- and high-mass galaxies, this is not consistent with the (Hδ_A + Hγ_A)' data for the intermediate-redshift clusters. It is also inconsistent with the strong metal lines in general found for all the intermediate-redshift clusters. Further, the formation redshift implied by the M/L ratios is significantly lower than found from the higher order Balmer lines. This result does not change even if we remove all galaxies in the low-redshift sample with ages too young to have progenitors included in the intermediate-redshift samples. Future investigations may show if these two results can be consolidated by the presence of a change in the dark matter content, primarily for the low-mass galaxies, between z ≈ 0.9 and the present.

We have investigated what effect differences in the IMF as a function of galaxy mass would have on the observed evolution. For simplicity we assume that the galaxies evolve passively, but that the IMF slope depends on the galaxy mass or the velocity dispersion. This idea is based on recent results indicating that at low redshift higher mass galaxies may have steeper IMFs than the low-mass galaxies (van Dokkum & Conroy 2010, 2011; Conroy & van Dokkum 2012a, 2012b; Cappellari et al. 2012). However, an apparently contradicting result was found by van Dokkum (2008) for the evolution of the IMF, showing that a bottom-light IMF for high-mass galaxies can explain the redshift evolution of both the FP zero point and the (U − V) colors.

To investigate the effect of differences in the IMF between low- and high-mass galaxies we used the models from Vazdekis et al. (2010). Using a Kroupa (2001) "universal" IMF instead of a Salpeter IMF leads to the same age dependence on the M/L ratio, while there naturally is a zero point difference in the resulting M/L ratios for the two IMFs due to the presence of more low-mass stars in models using a Salpeter IMF than those using a Kroupa IMF. However, the evolution in the M/L ratio over the length of time probed by our data is not significantly different for the two choices of IMF.

We then tested the difference between using a Salpeter IMF with x = 1.3 as is used in the default models and a steeper and therefore dwarf-rich IMF with a slope of x = 2.3. The result is shown in Figure 17 as the expected evolution of the M/L ratio. With the dwarf-rich IMF (x = 2.3) the M/L ratio evolves much slower for a given formation redshift. If we hypothesize that the IMF slope is x = 1.3 for the low-mass galaxies and increases slowly to x = 2.3 for the high-mass galaxies, then it would reproduce the change in slope for the M/L–mass relation (and the FP) with redshift and lead to a formation redshift of z ≈ 1.2 for all the galaxies. The high-order Balmer lines are not significantly affected by the slope of the IMF (Vazdekis et al. 2010). While we in principle can find a solution with a mass-dependent slope of the IMF that will mostly remove the age differences between low- and high-mass galaxies, the result is that their luminosity weighted mean ages are all fairly young, about 2 Gyr for the z = 0.8–0.9 galaxies and about 4 Gyr for the z = 0.54 galaxies. The model predictions for strengths of the higher order Balmer line for such young ages are in disagreement with our data, and would also predict a much larger change in the strength of these lines with redshift than seen from the data; see Figure 17(f). Thus, a simple model where the IMF slope depends on the galaxy masses (or velocity dispersions) does not seem to be viable solution to a consistent model for the observed evolution of the zero points of the M/L–mass relation and the (Hδ_A + Hγ_A)'–velocity dispersion relation, under the assumption of otherwise passive evolution. This does not rule out that there could be IMF variations as a function of galaxy masses in addition to more complex models for the galaxy evolution.

We now turn to the possible differences in metallicities and abundance ratios. The results in Sections 10 and 11 indicate that the cluster MS0451.6−0305 has [M/H] approximately 0.2 dex lower than the other clusters, while RXJ0152.7−1357 has [α/Fe] approximately 0.3 dex higher than the other clusters. The results indicate that passive evolution is too simple a model to explain the data.

It may be possible to envision that the galaxies in these clusters can evolve into their low-redshift counterparts in the time available. For MS0451.6−0305 this could happen through additional star formation to increase [M/H], as long as such new star formation does not lead to ages younger than expected at redshift zero. For RXJ0152.7−1357 a significant change in [α/Fe] may only be possible through merging of the early-type galaxies with lower [α/Fe] galaxies that are not part of the present sample. Thus, these galaxies have to be either spiral galaxies, galaxies with significant emission, or galaxies fainter than the sample limit. In the first two cases, the galaxies are expected to contain younger stellar populations than the early-type galaxies in our samples, and the merger products will therefore have younger ages than if the early-type galaxies evolved passively. Any merger scenario also has to maintain the relation between sizes and masses, as we detect no evolution in this relation; cf. Section 9.1.

Additional star formation and/or mergers in some clusters and not in others then lead to different paths of evolution for the early-type galaxies in intermediate-redshift clusters in order to reach the properties of the low-redshift counterparts and one has to ask what the underlying reason for this may be.

Of the clusters in the present sample RXJ0152.7−1357 has the clearest evidence for substructure; see Sections 2 and 7. The difference in evolutionary path may be related to the interactions of the galaxies with the intracluster gas as the two substructures interact. This idea is supported by the results from Demarco et al. (2010) who find that the details of the stellar populations appear related to the local cluster density. In particular, they find that their stacked spectrum of galaxies from low-density environment has weaker Fe4383 than the rest of the galaxies. The cluster MS0451.6−0305 is significantly more massive than the other clusters. It may be that the cluster environment in this case led to a truncated star formation history such that the resulting early-type galaxies have higher ages and lower [M/H] than expected if one just evolved RXJ1226.9+3332 passively to z = 0.54. This view is supported by the results from Moran et al. (2007a) based on their analysis of the D4000 break and presence (or rather absence) of emission lines in a very large sample of galaxies in the cluster. Moran et al. (2007a) also studied another rich intermediate-redshift cluster (CL0024+1654) and found that a different star formation history for that cluster best explained the data, indicating that cluster-to-cluster differences among rich clusters are present at z ≈ 0.4–0.5.

Even with surveys like the NOAO Fundamental Plane Survey (Smith et al. 2004, 2006; Nelan et al. 2005) our knowledge of possible cluster-to-cluster variations in rich low-redshift clusters (z ⩽ 0.1) is limited. The X-ray catalog from Piffaretti et al. (2011) contains 26 clusters at z ⩽ 0.1 with X-ray luminosities at least as high as that of the Coma cluster. Those with z ⩽ 0.067 are also included in the NOAO FPS sample. However, the published analysis of these data does not address possible cluster-to-cluster differences. Thus, it cannot be ruled out that there are cluster-to-cluster differences among the most massive galaxy clusters.

The GMOS-N photometry was calibrated to the standard SDSS system using the calibrations detailed in Jørgensen (2009). The absolute uncertainty on this calibration is 0.05 mag. The total magnitudes (mag_Best from SExtractor) and aperture colors were then compared to a selection of the available photometry of the various fields.

For MS0451.6−0305 we have compared our photometry with (1) Gunn g and r photometry (in the following denoted g_G and r_G) from the CNOC survey (Ellingson et al. 1998) and (2) VRI photometry from observations with the Subaru telescope of the field by Moran and collaborators made available through their Web site at http://www.caltech.edu/~smm/clusters/. For these comparisons, transformations between the different photometric systems are necessary. We use the transformations from Jordi et al. (2006) between the SDSS system and VRI (Table 3 in their paper). To determine the expected offsets between the CNOC photometry and ours, we use the transformations between Gunn g and r and Johnson V and R from Jørgensen (1994) together with the relevant transformations from Jordi et al.

For RXJ1226.9+3332 photometry is available from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7; Abazajian et al. 2009). For galaxies (class_star < 0.8) we adopt the SDSS magnitudes modelMag, while for stars we adopt the psfMag as the best measures of the total magnitudes.

Figures 21–23 show the comparisons. The dashed lines in the figures show the expected relations. Table 12 summarizes the offsets and scatter relative to the expected relations. Moran and collaborators determined total magnitudes using SExtractor in a very similar fashion as done for our GMOS-N data. The median offsets are 0.04 mag or smaller, indicating a very good consistency of the two data sets. The total magnitudes from the CNOC survey are measured from growth curves of aperture magnitudes with typical aperture corrections of 0.05 mag (Yee et al. 1996). Further, Ellingson et al. (1998) note that the systematic uncertainty on (g_G − r_G) is of the order 0.07 mag. Thus, our data and the CNOC data are consistent within the expected systematic error of the CNOC data. The SDSS magnitudes are expected to be total magnitudes, while the SExtractor mag_Best is expected on average to be 0.06 mag fainter than the true total magnitudes (Bertin & Arnouts 1996). Thus, the expected offset when comparing to the SDSS photometry is 0.06 mag. The average of the offsets relative to the SDSS photometry is 0.11, indicating that the two data sets are consistent within 0.05 mag, which is in agreement with the expected accuracy of the GMOS-N photometric calibration (Jørgensen 2009).

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In summary, we conclude that our GMOS-N photometry is calibrated to an absolute accuracy of 0.05 mag. Tables 14 and 13 list the standard calibrated magnitudes and colors for the spectroscopic samples of MS0451.6−0305 and RXJ1226.6+3332, respectively. The photometry in these tables is not corrected for Galactic extinction.

Total magnitudes, effective radii, and mean surface brightnesses for the spectroscopic sample in MS0451.6−0305 were derived using the fitting program GALFIT (Peng et al. 2002) and the techniques established for our project and described in detail in Chiboucas et al. (2009). Table 15 lists the resulting parameters for the fit with the r^1/4 profile and with a Sérsic (1968) profile. The magnitudes are on the AB system, using a zero point for F814W of 25.937 (Sirianni et al. 2005). The photometry has not been corrected for Galactic extinction.

Table 15. MS0451.6−0305: Photometric Parameters from HST/ACS Data in F814W

ID	mtot, dev	log re, dev	〈μ〉e, dev	mtot, ser	log re, ser	〈μ〉e, ser	nser	P.A.
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
12	19.53	0.299	23.02	19.70	0.135	22.38	2.32	−53.1	0.72
153	20.19	−0.275	20.81	20.19	−0.275	20.81	4.00	9.1	0.41
220	20.20	0.188	23.14	20.64	−0.148	21.90	1.41	40.9	0.12
234	20.57	−0.190	21.61	20.94	−0.470	20.58	1.40	71.3	0.34
258	20.82	−0.185	21.89	21.20	−0.465	20.87	1.23	7.8	0.49
299	18.54	0.151	21.30	18.56	0.136	21.24	3.88	52.9	0.12
309	21.17	−0.254	21.90	21.21	−0.286	21.78	3.70	−14.5	0.19
323	19.94	−0.370	20.09	19.77	−0.230	20.62	5.61	74.3	0.26
386	22.27	−0.508	21.73	22.33	−0.557	21.55	3.50	27.1	0.14
468	21.82	−0.220	22.72	22.03	−0.384	22.11	2.38	42.0	0.23
554	20.81	−0.383	20.89	20.96	−0.497	20.47	2.64	−10.2	0.10
600	21.13	−0.446	20.89	21.04	−0.376	21.15	4.59	53.8	0.26
606	20.59	−0.664	19.26	20.53	−0.616	19.44	4.86	−36.6	0.59
684	20.49	−0.191	21.53	20.65	−0.311	21.09	2.80	−26.0	0.34
716	20.55	−0.102	22.03	20.71	−0.227	21.57	2.87	−84.7	0.24
722	21.41	0.086	23.83	22.08	−0.407	22.04	0.60	−24.4	0.40
833	22.74	−0.608	21.70	22.74	−0.602	21.72	4.14	−1.9	0.15
836	20.45	0.149	23.19	21.13	−0.324	21.50	0.82	43.0	0.53
897	20.48	−0.526	19.84	20.52	−0.559	19.72	3.49	−17.2	0.72
901	20.94	−0.767	19.10	20.60	−0.458	20.31	8.85	63.6	0.16
921	19.48	−0.143	20.77	19.53	−0.177	20.64	3.68	69.1	0.20
971	19.01	0.137	21.69	19.12	0.052	21.37	3.42	12.3	0.21
1002	20.10	0.146	22.82	20.31	−0.005	22.28	2.89	−54.1	0.28
1082	19.79	−0.224	20.67	19.76	−0.200	20.76	4.24	0.2	0.20
1156	20.28	−0.173	21.41	20.46	−0.305	20.92	2.73	−4.8	0.61
1204	20.08	−0.308	20.53	20.06	−0.289	20.60	4.20	13.6	0.34
1331	20.38	−0.198	21.39	20.52	−0.317	20.93	2.54	53.5	0.65
1491	21.46	−0.836	19.27	21.54	−0.893	19.07	2.84	82.7	0.54
1497	19.95	−0.429	19.80	19.87	−0.373	20.00	4.69	−8.2	0.45
1500	19.60	0.018	21.69	19.88	−0.190	20.93	2.50	−75.5	0.09
1507	20.39	−0.551	19.63	20.40	−0.556	19.61	3.93	13.1	0.35
1584	22.48	−0.582	21.56	22.47	−0.575	21.59	4.08	19.3	0.42
1594	19.87	−0.237	20.68	19.75	−0.141	21.05	4.92	−34.9	0.19
1638	20.12	−0.172	21.26	19.95	−0.022	21.83	5.40	40.8	0.07
1720	18.47	0.367	22.29	18.12	0.588	23.06	5.28	−70.1	0.30
1723	18.98	0.017	21.06	19.27	−0.194	20.29	1.51	76.1	0.80
1753	20.16	−0.298	20.66	19.83	−0.020	21.73	6.37	−61.7	0.30
1823	19.98	−0.353	20.21	19.89	−0.278	20.50	4.84	−70.2	0.29
1904	20.35	−0.408	20.30	20.32	−0.389	20.37	4.22	−38.8	0.29
1931	20.11	−0.266	20.78	20.20	−0.333	20.53	3.31	−57.1	0.31
1952	19.88	−0.247	20.64	19.89	−0.255	20.61	3.82	−41.6	0.16
2031	20.41	−0.553	19.64	20.38	−0.527	19.74	4.34	−70.5	0.51
2032	21.01	−0.675	19.63	21.03	−0.778	19.13	1.10	60.3	0.16
2127	19.36	0.244	22.57	19.91	−0.162	21.09	0.89	−71.2	0.51
2166	20.07	−0.015	21.99	20.04	−0.022	21.92	1.11	−67.1	0.41
2223	20.89	−0.401	20.88	20.71	−0.387	20.77	2.77	10.3	0.34
2230	21.60	−0.344	21.88	21.54	−0.289	22.09	4.51	−6.2	0.12
2240	21.60	−0.581	20.70	21.75	−0.680	20.34	2.40	85.9	0.62
2491	21.43	−0.316	21.85	21.43	−0.354	21.66	2.54	−58.2	0.15
2561	22.17	−0.379	22.27	22.06	−0.282	22.65	4.96	−85.5	0.46
2563	19.40	0.262	22.70	19.37	0.267	22.70	3.86	−28.9	0.12
2645	19.01	0.335	22.68	19.43	0.020	21.52	1.45	77.5	0.47
2657	19.25	0.419	23.34	19.91	−0.058	21.62	0.78	−48.7	0.13
2689	20.39	−0.598	19.39	20.41	−0.616	19.33	3.71	−47.4	0.68
2788	20.57	−0.309	21.01	20.40	−0.275	21.02	2.77	74.5	0.13
2913	19.79	−0.315	20.21	19.78	−0.305	20.26	4.16	−2.1	0.19
2945	20.58	−0.445	20.36	20.67	−0.518	20.08	2.73	28.2	0.38
3005	21.18	−0.192	22.22	21.38	−0.348	21.64	2.69	−32.3	0.21
3124	20.07	−0.114	21.50	20.23	−0.234	21.05	2.90	−28.3	0.58
3260	21.27	−0.752	19.50	21.17	−0.679	19.77	5.43	36.4	0.69
3521	19.75	0.019	21.84	19.95	−0.132	21.28	2.68	38.8	0.25
3610	20.54	0.159	23.33	21.22	−0.362	21.41	0.39	−57.7	0.80
3625	21.54	−0.388	21.60	21.36	−0.238	22.17	5.36	−62.9	0.13
3635	22.34	−0.430	22.18	22.13	−0.434	21.95	3.75	69.4	0.73
3697	22.16	−0.632	20.99	22.47	−0.846	20.24	1.32	48.3	0.15
3724	20.93	−0.492	20.47	20.87	−0.442	20.66	4.59	−50.8	0.15
3749	20.90	−0.283	21.48	20.77	−0.180	21.87	5.06	82.4	0.18
3792	21.39	0.161	24.18	22.05	−0.344	22.32	0.50	18.5	0.48
3857	20.84	−0.408	20.79	20.87	−0.436	20.69	3.68	−34.4	0.46
3906	22.51	−0.375	22.63	22.57	−0.420	22.46	3.61	81.1	0.14

Notes. Column 1: galaxy ID; Column 2: total magnitude from fit with r^1/4 profile; Column 3: logarithm of the effective radius in arcseconds from fit with r^1/4 profile; Column 4: mean surface brightness in mag arcsec⁻² within the effective radius, from fit with r^1/4 profile; Columns 5–7: total magnitude, logarithm of the effective radius, and the mean surface brightness, from fit with a Sérsic profile; Column 8: Sérsic index; Column 9: position angle of the major axis measured from north through east; Column 10: ellipticity.

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We have compared our GALFIT results with data from S. Moran (2011, private communication) who also used GALFIT to process the HST/ACS data, but with a different PSF model. Figure 24 and Table 16 summarize the comparison. As the errors in the total magnitude and the effective radii are correlated (e.g., Jørgensen et al. 1995a) we also show the comparison as the difference in magnitude versus the difference in effective radius. The four galaxies deviating from the correlation are labeled. Two of these (ID = 2166 and 2645) are spirals or irregulars possibly causing the large difference between the two sets of data. The other two (ID = 1720 and 2563) have close neighbors. The detailed handling of these when running GALFIT is likely to affect the resulting parameters and could be the cause of the large differences between the two sets of data. We also note that for ID = 2563 the GALFIT magnitude from Moran deviates with more than 1 mag from the Subaru ground based data made available at Moran's Web site http://www.astro.caltech.edu/~smm/clusters/. The photometry from Moran is on the Vega system with an F814W zero point of 25.501. Thus, the expected offset is 0.436 mag. Excluding the four outliers marked in the figure, we determine the offset between the two data sets by fitting a line to the data shown in Figure 24(c). The intersect between the fit and the y-axis gives an offset of 0.401 mag. This method of determining the offset between the magnitudes is more robust than a direct comparison as it eliminates the effect of the correlated errors. Thus, our magnitudes are 0.035 mag brighter than those determined by Moran. This difference is most likely due to difference in the PSFs used in our work and that by Moran; see Chiboucas et al. (2009).

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For the purpose of calibrating the HST/ACS photometry to the rest frame, we have chosen first to calibrate the F775W (RXJ0152.7−1357) and F814W (MS0451.6−0305 and RXJ1226.9+3332) AB magnitudes to i' magnitudes. We use the synthetic transformations from Sirianni et al. (2005) listed in their Table 3 together with transformations from Jordi et al. (2006) in order to transform from I_c to i' (I_c = i' − 0.245(r' − i') − 0.387). While one could argue that a more direct calibration would be preferable, we judge that our method do not add significantly to the systematic effects on the data as these are dominated by the underlying assumptions of the spectral energy distributions. When applying the transformation, we use the (r' − i') colors from our GMOS photometry.

Figure 25 and Table 17 summarize the comparison of our GMOS-N photometry (derived with SExtractor) and the HST/ACS photometry (derived with GALFIT) calibrated to the i' band. The expected offset between the magnitudes is 0.06 mag, due to the systematically missed flux in the best magnitudes from SExtractor (Bertin & Arnouts 1996). For RXJ0152.7−1357 and RXJ1226.9+3332 the magnitudes agree within the uncertainties, while the median offset for MS0451.6−0305 deviates with 0.08 mag from the expectations, roughly a 3σ difference given the scatter in the comparison. We take this as the upper limit on systematic errors affecting the photometry.

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We have derived total magnitudes in the rest-frame B band from the observed i' magnitudes and colors, using calibrations established based on Bruzual & Charlot (2003) stellar population models spanning the observed color range; see Jørgensen et al. (2005) for details. For MS0451.6−0305 we use (r' − i') in the calibration, while for the two higher redshift clusters (i' − z') was used. Table 18 lists the calibration to the rest-frame B magnitudes, B_rest, for each of the three clusters at the cluster redshifts, as well as the distance modulus, DM(z), for our adopted cosmology. The absolute B-band magnitude, M_B, is then derived as

$$\begin{equation} M_{\rm B} = B_{\rm rest} - {\rm DM}(z). \end{equation} \tag{ A1 }$$

Techniques for how to calibrate to a "fixed-frame" photometric system are described in detail by Blanton et al. (2003).

The GCP spectroscopic data for MS0451.6−0305 were obtained in a similar fashion as the RXJ0152.7−1357 and were reduced using the same techniques; see Jørgensen et al. (2005). The observations were obtained in individual exposures with exposure time of 2700 s. The slit lengths were between 41 and 135. Longer slits were used for larger galaxies to facilitate better sky subtraction. A few of the slits also contained two objects. The two masks used for the field cover a total of 70 galaxies and two blue stars. Three M-stars were included in the mask by mistake due to limitations in the star-galaxy separation. The blue stars are used for telluric absorption line correction, as described in detail in Jørgensen et al. (2005). The faintest objects were included in both masks. About half the data were taken with a central wavelength set at 7330 Å, the other half with 7410 Å. This facilitates full wavelength coverage across the gaps between the GMOS-N CCDs. Between each observation the telescope was nodded along the slit. Three different positions were used: 0'' and ±125. This was done to improve the sky subtraction, though in retrospect it did not do so, and in some cases it complicated the sky subtraction as the spectra were very close to the ends of the slits.

The GCP spectroscopic data for RXJ1226.9+3332 were obtained using the GMOS-N in nod-and-shuffle mode. Glazebrook & Bland-Hawthorn (2001) describe the principles of the nod-and-shuffle technique, while Abraham et al. (2004) show illustrations and give a detailed description of GMOS-N nod-and-shuffle data obtained in a fashion very similar to what was used for the GCP observations. In the following sections we describe the reduction of the nod-and-shuffle data obtained for RXJ1226.9+3332, while we refer to Jørgensen et al. (2005) for those steps in the reduction not specific to the nod-and-shuffle mode. Figure 26 shows a subframe of observations through one of the masks at different steps in the data reduction process. We refer to each of these steps in the following description.

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The data for RXJ1226.9+3332 were obtained in individual exposures with exposure times of 1800 s. We used a slit length of 275 and a shuffle distance of 38 pixels. The sub-exposure time was 60 s. The telescope nod along the slit was 125. This places the two images of the object 0625 from the center of the slit and 075 from the ends of the slit. Two masks were used for RXJ1226.9+3332 covering a total of 49 galaxies and two blue stars. The blue stars are used for correction for the telluric absorption lines in the spectra. The faintest objects were included in both masks. About half the data were taken with the central wavelength set at 8150 Å and the other half at 8200 Å in order to obtain full spectral coverage across the gaps between the CCDs.

As described in Abraham et al. (2004), the GMOS-N CCDs have charge traps that show up as short pairs of elevated signal in the dispersion direction, separated by the shuffle distance. The areas affected by the charge traps are one unbinned pixel in the spatial direction and 6–60 unbinned pixels in the dispersion direction. Figure 26(a) of the raw data shows some of these charge traps. Due to the geometry of the charge traps, it is recommended to obtain nod-and-shuffle data unbinned in the Y-direction. Partial correction for the charge traps is achieved by subtraction of nod-and-shuffle dark exposures. These exposures were taken with the shutter closed, and the same exposure time and shuffle configuration as used for the science data. For RXJ1226.9+3332 we obtained 15 darks. The dark exposures are stacked and cleaned for cosmic-ray-events as if they were bias images. They are used in place of the bias images in the basic reduction of the data. The signal in the charge traps changes slowly with time, thus it is recommended to use nod-and-shuffle darks obtained as close as possible in time to the science data, while still using a sufficient number to get a high S/N combined dark frame. Our data for RXJ1226.9+3332 had only one set of nod-and-shuffle darks, so some charge traps are still visible after the dark subtraction. Figure 26(b) shows the data after subtraction of the nod-and-shuffle dark (and flat fielding).

To further eliminate the effect of the charge traps, the science data are taken at three different detector positions in the spatial direction. This is achieved by moving the detector translation assembly (DTA) in steps corresponding to integer unbinned pixels. Data were obtained at DTA positions corresponding to positions on the detector of 0 (home position), –6 and +6 pixels. The stacking of the individual exposures is done after the flat-field correction and is described in Appendix B.4.

The GMOS-N CCDs show a wavelength-dependent charge diffusion effect (CDE). The effect becomes stronger at longer wavelengths and is seen as charge diffused from each individual pixel into all neighboring pixels. The effect is described in Abraham et al. (2004). Figure 27 illustrates how the CDE affects the GCP spectroscopic data in the spatial direction. The effect on the science spectra depends on the exact configuration of the observations. For the GCP data, and the data described in Abraham et al., the CDE will lead to an oversubtraction of the sky signal at long wavelengths if no correction is applied for the effect. The approach used here to correct for the CDE is to model the size of the effect from a Quartz–Halogen flat field, and then use the model to correct otherwise normalized flat fields such that the CDE is corrected for in the flat fielding of the data. The model contains no correction for the CDE in the dispersion direction. The CDE in the dispersion direction will lead to a slightly degraded spectral resolution at long wavelengths. However, the measurements of the spectral resolution as a function of wavelength show that the variation is insignificant for the spectral parameters measured in this work.

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The details in the modeling of the CDE are as follows. First, the Quartz–Halogen flat field is bias subtracted and normalized slit-by-slit (the normal procedure is to normalize row by row). It is known from twilight flat fields that the illumination from Quartz–Halogen lamp in the Gemini calibration unit can be considered flat on scales of 275. Thus, any variation in signal along the slits in this normalized flat field is assumed to be due to the charge diffusion. The flat field is then wavelength calibrated using a matching arc exposure. The flat field is mosaicked and the slitlets are cut out using the standard tasks from the Gemini IRAF gmos package (gmosaic and gscut). All the slitlets are combined using the wavelength information to obtain one flat-field spectrum covering the full wavelength range of all the slitlets. This combined spectrum shows the effect of the CDE as a variation along the slit, the size of which increases with increasing wavelength and decreases with distance Δy from the slit end. The variation is fitted by a smooth function taking both of these variables into account. The best-fitting function is

$$\begin{equation} \rm {CDE} = 1 \,-\, exp(\psi \,+\, (-8.367 \times 10^{-5} \,-\, 8.692\, \times\, 10^{-5} \psi) \lambda), \end{equation} \tag{ B1 }$$

where

$$\begin{equation} \psi = -11.80 - 1.829 \Delta y. \end{equation} \tag{ B2 }$$

Here, λ is the wavelength in Å and Δy is the distance from the slit end in unbinned pixels. The CDE is a multiplicative effect. The normalized flat fields are corrected for the effect by multiplying these with the function in Equation (B1). The function does not depend on the grating or wavelength setting of the grating. The CDE is present in all GMOS-N data. The size of the CDE for a specific data set depends on the object positions within the slitlets and the extraction aperture. Figure 27 illustrates the size of the CDE for the configuration used for the GCP data. The figure also compares the correction used by Abraham et al. (2004) (D. Crampton 2004, private communication) with the correction resulting from Equation (B1) for the configuration of slit lengths, object positions, and apertures used by Abraham et al. Due to the shorter slitlets used by Abraham et al. the CDE is slightly larger for those data than for our data. For nod-and-shuffled data with the configurations used for our observations the effect becomes larger than 0.2% redward of 8930 Å. Just redward of this wavelength the typical signal from galaxy i' = 22.5 mag galaxy in our sample is only ≈2% of the signal in the strong skylines. Thus, uncorrected CDE would lead to systematic sky subtraction errors of 10%. Equation (B1) can be used to correct all GMOS-N spectroscopic data taken with the E2V detector array for the CDE. Alternatively, for spectroscopic data obtained without nod-and-shuffle can be sky-subtracted fitting a second-order polynomial to the sky signal along the spatial direction of the spectra, as done in Jørgensen et al. (2005), in which case no correction for the CDE is needed.

For nod-and-shuffle data, the flat fields are derived by first bias correcting and normalizing the flat fields row-by-row. Because the flat fields are taken without nod-and-shuffle they are then "doubled" by shifting the flat field by the shuffle distance, and combining the un-shifted and shifted flat field such that the resulting flat field contains the resulting flat-field correction at both shuffle positions. The CDE correction is only applied to the "outer" sections of a pair of spectra, since as shown in Figure 27(a) the effect cancels out on the "inner" sections.

After the dark subtraction and flat fielding (processing with the task gsreduce) the frames are sky subtracted using the task gnsskysub. This task makes a shifted copy of each frame and subtracts it off the original frame, such that the two shuffled images of a given slitlet is differenced. The result is a sky subtracted image with the object appearing positive from one nod position and negative from the other nod position, see Figure 26(c). With the knowledge of the DTA positions, all exposures obtained at the same wavelength are then stacked, shifted to the DTA zero position. In the process cosmic-ray events and any remaining signal from the charge traps is rejected. The frames are given weight according to their signal as determined from the two blue stars included in the mask. A custom version of the task gnscombine was used to accomplish all of these processing steps. The clean stack is shown in Figure 26(d). There are separate stacks for different wavelength settings and different masks.

The wavelength calibrations are established in the standard way from CuAr lamp exposures. The stacked science frames are cut into slitlets and each slitlet is wavelength calibrated. The cutting is done using the task gscut which automatically finds the edges of the slitlets based on a matching flat-field frame. The wavelength calibration is applied using the task gstransform. The resulting frames have one science extension per slitlet. Figure 26(e) shows the result for two objects.

The subframe shown in Figure 26 contains one of the gaps between the CCDs. This is seen as the dark vertical area in panels (a) and (b) and the light gray vertical area in panels (c)–(e). At this point the two wavelength settings are combined and at the same time the positive and negative nod positions are combined. This is done using a custom script gscombine which handles all the offsets as well as weights the input relative to the signal in these. The resulting frames have one science extension per slitlet (Figure 26(f)) with the full signal in the center of the extension. The outer edges in the spatial direction still shows the negative object signal from the nodding. Because of exposures being taken at two wavelength settings, the resulting spectra have no gaps in the wavelength coverage, though of course the S/N is slightly lower where only signal from one wavelength setting contributes.

The spectra are then traced and extracted to 1D spectra in a standard way using the tasks gsextract. We use an aperture size of 085. The spectra are corrected for the telluric absorption lines using the blue stars in the masks and a relative flux calibration is applied using the task gscalibrate, see Jørgensen et al. (2005) for details. Figure 26(g) shows the extractions of the wavelength regions of the targets shown throughout the figure.

The observations for the GSA data did not make use of the GMOS nod-and-shuffle mode. We therefore reduced the data using the methods described in Jørgensen et al. (2005). However, many of the objects were close to the ends of the slits, presumably to make it possible to cover more objects with a single MOS masks. This led to significantly larger systematic sky subtraction errors than for the GCP data. The systematic errors in the sky subtraction make the spectra unreliable at wavelengths longer than ≈8500 Å. This corresponds to 4500 Å in the rest frame of RXJ1226.9+3332. In this paper, the data are not used beyond ≈8500 Å in the observed frame.

The GSA data include no blue stars in the masks suitable for deriving the telluric correction. We therefore used the telluric correction spectrum from the GCP data, convolved to the resolution of the GSA data, and scaled to optimize the correction.

The instrumental resolution for each spectrum was derived from the skylines of spectra stacked in the same way as the science spectra; see Jørgensen et al. (2005) for details. The median resolution for each data set is listed in Table 5. The GSA data have lower spectral resolution (≈3.9 Å) than the GCP data (≈3.1 Å). This is due to the wider slits used for the GSA data. There are small differences in the spectral resolution for the various data sets taken through the same nominal slit widths. In particular, the average difference between the RXJ1226.9+3332 data and the MS0451.6−0305 data is about 3%, which is equivalent to 20 μm difference in slit width at the focal plane of GMOS-N. This difference may be caused by a small difference in the focus setting for the laser cutter. Further, as was seen for the RXJ0152.7−1357 data (Jørgensen et al. 2005), the resolution was found to vary with X-position on the array, while there is no dependency on the Y-position on the array. The range of the variations is approximately ±8%. As noted in Jørgensen et al. (2005), it is not known why this dependency is present, though it is possible that it is due to a small tilt of the mask in the laser cutter during the cutting, such that effectively the laser is slightly out of focus on one side of the mask. Independent of the cause, it makes it necessary to ensure that the individual values for the instrumental resolution are used when deriving the velocity dispersions of the galaxies.

The redshifts and the velocity dispersions were determined by fitting a mix of three template stars to the spectra. As in Jørgensen et al. (2005), we used software made available by Karl Gebhardt (Gebhardt et al. 2000, 2003) and three template stars of spectral types K0III, G1V, and B8V. The velocity dispersions have been corrected for the aperture size using the technique from Jørgensen et al. (1995b). Tables 21 and 23 in Appendix B summarize results from the template fitting. Measured velocity dispersions as well as aperture corrected velocity dispersions are listed for the cluster members. The velocity dispersions for galaxies in MS0451.6−0305 were also corrected for the systematic errors due to the lower resolution of these spectra. The correction is described in detail in the next section. For galaxies that are not members of the clusters, we give the redshift. The detailed data for these galaxies will be discussed in a future paper. The wavelength intervals used for the fits are 3750–5600 Å and 3750–4650 Å for MS0451.6−0305 and RXJ1226.9+3332, respectively. In the tables we include a measure of the goodness of the fit derived as

$$\begin{equation} \chi ^2 = N^{-1} \, \sum [(S_{\rm obs,i} - S_{\rm fit,i}) / N_{\rm obs,i}]^2, \end{equation} \tag{ B3 }$$

where S_{obs, i} is the observed spectrum, S_{fit, i} is the best fit, N_{obs, i} is the noise, the sum is over the spectral pixels inside the fitting wavelength range, and N is the number of spectra pixels. The mean χ² for the galaxies included in the analysis is 4.2 and 4.4 for MS0451.6−0305 and RXJ1226.9+3332, respectively. The χ² values are generally large than one due to a combination of slight template mismatch and underestimated uncertainties due to sky subtraction noise at the strong skylines. In Figure 28 we show three sample spectra from each cluster with the best fit overplotted. The main purpose of using a set of template stars is to span the range of stellar populations represented in the spectra. The figure demonstrates that three template stars successfully accomplish this, except for a slight template mismatch at the strong magnesium lines at 5170 Å. Such a mismatch is also seen if we use the SSP model spectra from Maraston & Strömbäck (2011). Further, using these model spectra result is similar quality of fits as measured by χ² as using the three template stars. Thus, for consistency with previously published results, we choose to continue to use the template stars for the kinematics fits.

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The large wavelength range of the MS0451.6−0307 spectra allow us to test if excluding the calcium H and K lines from the fit leads to significantly different velocity dispersions. We find that not to be the case, the mean difference in log σ is 0.020 ± 0.010 with and rms scatter of 0.066. The difference is within the expected systematic differences between data sets of 0.026 and also only significant at the 2σ level. The wavelength coverage for RXJ1226.9+3332 does not allow a similar test. For consistency we include the calcium H and K lines in all the kinematics fits.

The Lick/IDS absorption line indices CN₁, CN₂, G4300, Fe4383, C4668 (Worthey et al. 1994), as well as the higher order Balmer line indices Hδ_A and Hγ_A (Worthey & Ottaviani 1997) were derived for both clusters. We have also determined the D4000 index (Bruzual 1983; Gorgas et al. 1999), and the blue indices CN3883 and CaHK (Davidge & Clark 1994). For MS0451.6−0305 the wavelength coverage allowed determination of the Lick/IDS absorption line indices Hβ, Mgb, Fe5270, and Fe5335, as well as Hβ_G (see González 1993; Jørgensen 1997). Because of the lower relative uncertainties on Hβ_G compared to Hβ, Hβ_G is used in the analysis. A transformation between the two indices can be found in Jørgensen (1997). The indices have been corrected for the aperture size and for the effect of the velocity dispersions as described in Jørgensen et al. (2005); see also Jørgensen et al. (1995b).

We refer the reader to Table 13 in Jørgensen et al. (2005) for the coefficients adopted for the aperture corrections for the velocity dispersions and the line indices. The aperture corrections are the largest for the highest redshift clusters. For RXJ1226.9+3332 the typical correction for the velocity dispersion and the metal lines measured as an equivalent width is 0.025 on the logarithm of the measurement. The correction on CN3883 is of a similar size. The Balmer lines have insignificant aperture corrections. The coefficients given in Jørgensen et al. (2005) are based on radial profiles of nearby galaxies. While one could argue that we do not know that radial profiles of intermediate-redshift galaxies are similar, no better information exists at this point. We also note that the luminosity profiles for the intermediate-redshift galaxies are similar to those found for low-redshift samples (well modeled by Sérsic profiles with an index of roughly 2–6), lending support to the assumption that line index profiles are also similar. In the extreme one could use the size of the aperture corrections as a limit on the consistency between the data sets.

We have estimated the uncertainties on the line indices using two methods: (1) uncertainties derived from the local S/N in the passbands following the method described in Cardiel et al. (1998) and (2) from internal comparisons of indices derived from stacking subsets of the frames available for each cluster.

We first note that method (1) leads to slightly larger uncertainties than the method use in Jørgensen et al. (2005). We have therefore rederived the uncertainties for the RXJ0152.7−1357 galaxies. The effect on the uncertainties on Hδ_A and Hγ_A is negligible. The uncertainties on Fe4383, C4668, and CN3883 are ≈40% larger than those listed in Jørgensen et al. (2005).

The internal comparisons of line indices are based on galaxies included in both masks for each of the clusters and for RXJ1226.9+3332 also on line indices derived from each of the two stacks of data for the two wavelength settings. Figure 29 and Table 19 summarize the comparisons. Only galaxies for which the S/N per Å in the rest frame is above 20 in the sub-stacks are included. We use the scatter in the comparisons to estimate the uncertainties on the indices. Column 5 in Table 19 lists the adopted uncertainties. For the indices used in the analysis these are a factor of 1.5–3 larger than the uncertainties based on the local S/N of the spectra. The larger uncertainties resulting from this method are most likely due to increased noise in the sky subtraction around the strong skylines. However, there is no indication of general over- or under-subtraction of the sky signal blueward of 9290 Å. In the analysis we adopt the uncertainties listed in Table 19 for the line indices and show these as typical error bars on all relevant figures.

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At wavelengths longer than 9290 Å systematic errors in the sky subtraction of the GCP data become evident. This is the wavelength at which very strong OH bands start affecting the data. Even with nod-and-shuffle and the correction for the CDE it is clear from our data that systematic errors dominate redward of this wavelength. Therefore only line indices that fall at shorter wavelengths than 9290 Å in the observed frame are considered reliable and included in the tables and the analysis. For RXJ1226.9+3332 this wavelength corresponds to 4910 Å in the rest frame, while for MS0451.6−0305 it is 6032 Å. Figure 36 shows the RXJ1226.9+3332 spectra to 5200 Å in the rest frame to make it possible to assess the presence of emission in Hβ as well as the [O iii] lines at 4949 Å and 5007 Å. Line index measurements considered unreliable due to systematic errors in the sky subtraction are not listed in the tables.

The systematic sky subtraction errors for the GSA data are larger than those of the GCP data due to the poorer sky subtraction. Figure 30 shows representative spectra from the GSA data with S/N ≈ 20, 30, and S/N > 50, together with the higher S/N spectra of the same galaxies from the GCP data. The plot shows the consistency of the wavelength calibrations, also confirmed from redshift comparisons and the consistency of the relative flux calibration which is important for consistent determination of the line indices. Based on inspection of the spectra and the corresponding sky spectra, we conclude that in the observed wavelength intervals 7700–8035 Å and 8268–8475 Å, which contain very strong skylines, the weak or narrow metal line indices (CN₁, CN₂, Fe4383) and the Balmer line indices can be significantly affected by the systematic errors. We use the S/N per Å in the rest frame for the full spectrum to determine if the indices are reliable. For indices to be reliable in the observed wavelength interval 7700–8035 Å we require S/N ⩾ 30, while the requirement for indices in the interval 8268–8475 Å is S/N ⩾ 50. For spectra with S/N < 10, only the redshifts have listed in Table 23 as both the velocity dispersions and the indices have very large uncertainties.

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Finally, we compare the GCP and the GSA data to ensure consistency and in order to provide better estimates of the uncertainties on the line indices from GSA data than those resulting from estimates based on the local S/N of the spectra. There are 23 galaxies in common between the GCP data and the GSA data for RXJ1226.9+3332. Our approach is to calibrate the GSA data to consistency with the GCP data, since the latter has higher S/N and better resolution. Figure 31 shows the comparison of the redshifts, velocity dispersions and CN3883 for these two data sets. Table 20 summarizes the comparisons. The velocity dispersions derived from the GSA data are systematically 0.022 smaller in log σ than found from the GCP data. Even though this is below the 0.026 possible systematic errors in the low-redshift comparison samples (cf. Jørgensen et al. 2005), we have chosen to correct the GSA data for the offset. The scatter for the comparison of the velocity dispersions is within the expected scatter based on the uncertainties as derived from the kinematics fits. None of the offsets for the line indices are significant. As for the GCP data, we use the scatter to estimate the uncertainties. We use the adopted uncertainties for the GCP data (Table 19). The resulting uncertainties listed in Table 20 are a factor of two to three larger than the uncertainties on the GCP data. The higher order Balmer lines are not included in the table as none of the GSA spectra result in measurements if these indices used in the analysis.

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For galaxies with detectable emission from [O ii] we determined the equivalent width of the [O ii]λλ3726,3729 doublet. With an instrumental resolution of σ ≈ 3 Å (FWHM ≈7 Å), the doublet is not resolved in our spectra and we refer to it simply as the "[O ii] line."

In Jørgensen et al. (2005) we used simulated spectra to determine how the input S/N and the galaxy velocity dispersion relative to the instrumental resolution affected the determined velocity dispersions. Those simulations are also applicable to the RXJ1226.9+3332 data obtained for the GCP, as these have similar instrumental resolution and S/N as the RXJ0152.7−1357 data in Jørgensen et al. The instrumental resolution of the GCP data for RXJ1226.9+3332 and RXJ0152.7−1357 is about 120 km s⁻¹. However, both the RXJ1226.9+3332 GSA data and the MS0451.6−0305 GCP data have worse instrumental resolutions, both equivalent to about 145 km s⁻¹ at 4300 Å in the rest frame of the galaxies in the clusters. Further, the GSA data in general have lower S/N than the GCP data and are subject to larger effects from systematic sky subtraction errors. To estimate the effect of the worse instrumental resolution we ran simulations in a similar fashion as described in Jørgensen et al., using the observed noise spectrum and the instrumental resolution relevant for the data set. We then simulated spectra with S/N between 10 and 50 Å⁻¹ in the rest frame, and input velocity dispersions between 50 and 300 km s⁻¹. For these simulations we used a mix of the G1V and K0III template stars each contributing half the flux to the simulated spectrum. Each combination of S/N and input velocity dispersion was realized 100 times. We use the median of the output velocity dispersion in the following assessment.

Figure 32 shows the result of the two sets of simulations. The main difference between the simulations for the two high-redshift clusters and for MS0451.6−0305 is difference in the length of the wavelength interval used for the kinematic fitting. The simulations matching the RXJ1226.9+3332 GSA data set (Figures 32(a)–(c)) show a similar dependence on the input velocity dispersions as found for our previous simulations for RXJ0152.7−1257. The thin solid line in Figure 32(a) shows the simulations for RXJ0152.7−1257 from Jørgensen et al. Since the dependence on the input velocity dispersion is approximately is the same for the two sets of simulations, any difference between velocity dispersions derived from the GCP data and the GSA data is expected to be small, as was found in the previous section.

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The simulations matching the MS0451.6−0305 data set (Figures 32(d)–(f)) show that velocity dispersions are systematically derived too small, and that the systematic error increases with decreasing input velocity dispersion. For input velocity dispersion log σ > 1.9 we establish a correction function:

$$\begin{eqnarray} \log \sigma _{\rm corrected} &=& \log \sigma _{\rm output} +0.0424 - 0.2138(\log \sigma _{\rm output}-2.1)\nonumber\\ &&+ 0.5426(\log \sigma _{\rm output}-2.1)^2. \end{eqnarray} \tag{ B4 }$$

The function is shown as the solid line in Figure 32(f). Since the size of this correction is similar to or larger than typical inconsistencies between different data sets, we have chosen to apply the correction to the measured velocity dispersions for MS0451.6−0305 galaxies. The correction is applied to the value in column log σ_cor (together with the aperture correction) in Table 21, while the column log σ lists the raw measure values.

Tables 21–24 list the results from the template fitting and the derived line indices. For RXJ1226.9+3332 galaxies included in both the GCP and the GSA data, only the values from the GCP data are listed. The GSA velocity dispersions are calibrated to consistency with the GCP data as explained in Appendix B.7.