Galaxy Populations in Massive z = 0.2–0.9 Clusters. I. Analysis of Spectroscopy

Imaging of Abell 1689, RXJ0056.2+2622, and RXJ0027.6+2616 was obtained with the Gemini Multi-Object Spectrogr-aph on Gemini North (GMOS-N), while RXJ1347.5–1145 was observed with the twin instrument GMOS-S on Gemini South. For a full description of GMOS-N and its twin, see Hook et al. (2004). All four clusters were observed using the $g^{\prime}$, $r^{\prime}$, and $i^{\prime}$ filters. The seeing for the observations varied between ≈0 5 and 1 1 . The imaging was obtained primarily to aid the sample selection and the mask design for the spectroscopic observations. The observations were processed using the Gemini IRAF package. Processing includes bias subtraction, flat-fielding, correction of signal on all three detectors to electrons, correction for fringing in $r^{\prime}$- and $i^{\prime}$-band observations, mosaicking of the detectors, and stacking of the dithered observations of each field. The stacked images were then processed with SExtractor (Bertin & Arnouts 1996), as described in Jørgensen et al. (2005). The photometric calibration for the GMOS-N data relies on the zero points and color terms established by Jørgensen (2009), while the GMOS-S data were calibrated using observations of a photometric standard star field obtained the same night as the RXJ1347.5–1145 imaging, as well as color terms from the Gemini web pages. Appendix A contains additional details on the imaging observations and processing of these data, as well as derived magnitudes and colors for the targets in the spectroscopic samples.

The cluster RXJ0056.2+2622 was also imaged with GMOS-N in the $r^{\prime}$ filter in seeing of 033–035. The observations were obtained with the purpose of determining effective radii and surface brightness of the galaxies. These data will be covered in our paper (I. Jørgensen et al. 2017, in preparation) on the two-dimensional photometry of the galaxies in the clusters. In the current paper, we use preliminary results to exclude disk-dominated galaxies from the analysis. Imaging from HST exists for the three other clusters. We will also cover these data in I. Jørgensen et al. (2017, in preparation), and we use them here only to exclude disk-dominated galaxies from the analysis. The final sample selection is described in Section 4.1.

The spectroscopic observations were obtained in multi-object spectroscopic mode with GMOS-N or GMOS-S; see Table 3 for an overview of the observations. Two fields were observed in Abell 1689, each with two masks. Two fields were observed in RXJ0056.2+2622 with one mask each. RXJ0027.6+2616 and RXJ1347.5–1145 each have one field observed with two masks. The sample selection for the spectroscopic observations was based on the photometry from the ground-based imaging. Figure 1 shows the color–magnitude relations with the selection criteria overlaid. The criteria are summarized in Table 11, in Appendix B. The selection method is similar to that used for MS0451.6–0305, RXJ0152.7–1357, and RXJ1226.9+3332 (Jørgensen & Chiboucas 2013), optimizing the inclusion of member galaxies on the red sequence, as well as covering 3–4.5 mag along the red sequence. For Abell 1689, RXJ0056.2+2622, and RXJ1347.5–1145, we also used published redshifts to optimize the inclusion of known members and exclude nonmembers. At the time of the sample selection, redshifts for Abell 1689 and RXJ0056.2+2622 were taken from the NASA/IPAC Extragalactic Database (NED), while for RXJ1347.5–1145, we used redshifts from Cohen & Kneib (2002) and Ravindranath & Ho (2002). After the inclusion of all possible targets of the highest priority (object classes 1–2, as marked in Figure 1), the remaining space in the mask was filled with fainter cluster members and/or targets on the red sequence but without redshifts (object class 3), if possible, and otherwise with bluer galaxies, some of which can be expected not to be members (object class 4). The spectroscopic samples are marked in gray-scale figures of the clusters available in Appendix A as Figures 14–17.

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Table 3.  GMOS-N and GMOS-S Spectroscopic Data

Cluster	Program ID and Dates	Exposure Time	${N}_{\exp }$	FWHM	${\sigma }_{\mathrm{inst}}$	Aperture	Slit Lengths	S/N
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Abell 1689	GN-2001B-Q-10	14,400,13,800	20	0.76, 0.80	1.492 Å, $84\,\mathrm{km}\,{{\rm{s}}}^{-1}$	0.75 × 2.0, 0.70	6.0–15.0	217
	UT 2002 Jan 11–16	+ 9960,12000
RXJ0056.2+2622	GN-2003B-Q-21	28,800+28,800	24	0.75, 0.66	1.647 Å, 110 $\mathrm{km}\,{{\rm{s}}}^{-1}$	$0.75\times 1.4$, 0.59	4.0–10.0	146
	UT 2003 Jul 27–Oct 10
RXJ0027.6+2616	GN-2003B-Q-21	28,800+28,800	24	0.66, 0.56	2.518 Å, 123 $\mathrm{km}\,{{\rm{s}}}^{-1}$	$0.75\times 1.4$, 0.59	5.0–8.1	155
	UT 2003 Aug 26–Sep 26
RXJ1347.5–1145	GS-2005A-Q-27	24,000+24,000	20	0.72, 0.90	2.476 Å, 119 $\mathrm{km}\,{{\rm{s}}}^{-1}$	$0.75\times 1.4$, 0.59	4.8–10.6	57
	UT 2005 Mar 7–May 9

Note. Column 1: galaxy cluster. Column 2: Gemini program ID and dates of observations. Program IDs starting with GN and GS were obtained with GMOS-N and GMOS-S, respectively. Column 3: exposure times in seconds. Column 4: number of useful exposures. Column 5: image quality for each mask measured as the average full-width at half-maximum (FWHM) in arcsec of the blue stars, or, for Abell 1689 and RXJ0056.2+2622 of the acquisition stars, included in the masks. The measurement was done at a wavelength corresponding to 5000 Å in the rest frame of the clusters. Column 6: median instrumental resolution derived as σ in Gaussian fits to the sky lines of the stacked spectra. The second entry is the equivalent resolution in $\mathrm{km}\,{{\rm{s}}}^{-1}$ at 4500 Å in the rest frame of the cluster. Column 7: aperture size in . The first entry is the rectangular extraction aperture (slit width × extraction length). The second entry is the radius in an equivalent circular aperture, ${r}_{\mathrm{ap}}=1.025{(\mathrm{length}\times \mathrm{width}/\pi )}^{1/2}$; cf. Jørgensen et al. (1995b). Column 8: slit lengths in . Column 9: median S/N per Å for the cluster members in the rest frame of the clusters.

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The spectroscopic observations were processed using the methods described in detail in Jørgensen et al. (2005) and Jørgensen & Chiboucas (2013). The data processing resulted in one-dimensional spectra calibrated to a relative flux scale. The spectra were used to derive redshifts, velocity dispersions, and absorption-line strengths. The spectroscopic parameters were determined using the same methods as described in Jørgensen et al. (2005). In particular, the redshifts and velocity dispersions were determined by fitting the spectra with a mix of three template stars (spectral types K0III, G1V, and B8V) using software made available by Karl Gebhardt (Gebhardt et al. 2000, 2003). The galaxies that were found to be members of the clusters were fit in the rest-frame wavelength range 3750–5500 Å. The reader is referred to Jørgensen & Chiboucas (2013) for a discussion of the use of template stars rather than (a larger number of) model spectra for the fitting of the spectra. For consistency with our previous work, we fit the spectra of the z = 0.19–0.45 galaxies using the same template stars as in Jørgensen and Chiboucas. The results from the template fitting are available in Appendix B (Table 13). The observations covered 34–72 member galaxies in the four clusters (cf. Table 1).

We determined strengths of absorption lines using the Lick/IDS definitions (Worthey et al. 1994). In addition, we determined the indices for ${\rm{H}}{\delta }_{A}$ and ${\rm{H}}{\gamma }_{A}$ as defined in Worthey & Ottaviani (1997), the ${\rm{H}}{\beta }_{G}$ index as defined in González (1993; see also Jørgensen 1997 for the index definition), CN3883 and CaHK as defined in Davidge & Clark (1994), D4000 as defined in Gorgas et al. (1999), and the high-order Balmer line index ${\rm{H}}{\zeta }_{A}$ as defined in Nantais et al. (2013). For galaxies with detectable [O ii] emission, the strength of the [O ii] λλ3726, 3729 doublet was determined as an equivalent width, EW[O ii]. In the following, we refer to the doublet as the "[O ii] line." All measured absorption-line indices and the [O ii] equivalent widths are available in Appendix B (Tables 14–15). The typical measurement uncertainties were established based on internal comparisons and are listed in Appendix B (Table 12). In our analysis, we use the Balmer line indices ${\rm{H}}{\beta }_{G}$ and $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$ ≡ −2.5 log ($1.-({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})$/(43.75+38.75)) (Kuntschner 2000) as age-sensitive indices, the iron indices Fe4383 and $\langle \mathrm{Fe}\rangle \equiv (\mathrm{Fe}5270+\mathrm{Fe}5335)/2$, and the indices Mgb, CN3883, and C4668, all of which are sensitive to the abundance ratios [α/Fe]; see Section 4.4. We also use the combination indices $[\mathrm{MgFe}]\equiv {(\mathrm{Mg}b\cdot \langle \mathrm{Fe}\rangle )}^{1/2}$ (González 1993) and $[{\rm{C}}4668\,\mathrm{Fe}4383]\equiv {\rm{C}}4668\cdot {(\mathrm{Fe}4383)}^{1/3}$ (Jørgensen & Chiboucas 2013), both constructed to be independent of [α/Fe] for the stellar population models used in the analysis; see Section 4.4.

We take the cluster catalog from Piffaretti et al. (2011) as our main source of the X-ray properties of the clusters. This catalog covers most X-ray clusters at $z\lt 1$. However, it treats RXJ0056.2+2622 and RXJ0152.7–1357 as single clusters, while the X-ray structure and the distribution of the galaxies show that they are binary clusters (e.g., Maughan et al. 2003; Barrena et al. 2007). For these clusters, we therefore use data from Mahdavi et al. (2013, 2014), who gave X-ray parameters for the two subclusters in RXJ0056.2+2622, and Ettori et al. (2004), who gave X-ray parameters for the two subclusters in RXJ0152.7–1357. We note that Ettori et al. (2009) also gave values for the RXJ0152.7–1357 subclusters, but these are significantly larger than the values in Ettori et al. (2004), and the sum of the masses as well as the sum of the luminosities are inconsistent with the values from Piffaretti et al. (2011) for the full cluster. For other clusters listed in both papers by Ettori et al., the values are consistent. It is beyond the scope of this paper to explore the reason for this apparent inconsistency. Because of the increasing evidence that the mass of RXJ1347.5–1145 initially determined from X-ray data (and adopted by Piffaretti et al.) may be too large and that the cluster is experiencing interactions with an infalling subcluster (Kreisch et al. 2016), we instead adopt the lower value from Ettori et al. (2004). These authors correct the X-ray measurements for diffuse X-ray emission southeast of the main cluster and associated with the infalling subcluster.

We have calibrated the X-ray data from Mahdavi et al. (2013, 2014) and Ettori et al. (2004) to reach consistency with Piffaretti et al. (2011) using the clusters in common. As necessary, we first convert the published X-ray parameters to M₅₀₀ using the equations from Piffaretti et al. We then determine the offset in $\mathrm{log}{M}_{500}$ to reach consistency with Piffaretti et al. When converting between radii R₅₀₀, masses M₅₀₀, and luminosities L₅₀₀, we use the relations given by Piffaretti et al. (their Equations (2) and (3)). As needed, we also adopt the following conversions from Piffaretti et al.: ${L}_{500}=0.91{L}_{\mathrm{total}}$, ${R}_{200}=1.52{R}_{500}$, and ${L}_{500}=0.96{L}_{200}$. The relation between R₂₀₀ and R₅₀₀ is equivalent to ${M}_{200}=1.40{M}_{500}$.

We show the comparisons of ${M}_{500}$ from Piffaretti et al. (2011) with data from Ettori et al. (2004) and Mahdavi et al. (2013, 2014) in Figure 2. The ${M}_{500}$ values from Mahdavi et al. are consistent with those from Piffaretti et al., while for the values from Ettori et al., we subtract 0.23 from $\mathrm{log}{M}_{500}$ to reach consistency with Piffaretti et al. Luminosities, ${L}_{500}$, and radii, ${R}_{500}$, are then derived from ${M}_{500}$ using the equations from Piffaretti et al.

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Figure 3 shows the adopted masses, ${M}_{500}$, versus redshifts for the full GCP cluster sample. We show typical models for the growth of cluster masses with time, based on results from van den Bosch (2002). These models are in general agreement with the newer and more detailed analysis of the results from the Millennium Simulations (Fakhouri et al. 2010). The seven z = 0.19–0.89 clusters analyzed in the present paper are all very massive and represent the most massive clusters in the GCP at a given redshift. With current models for mass evolution of clusters, their masses at $z\approx 0$ would be higher than those of the Coma and Perseus clusters and close to the masses of the two very massive local clusters Abell 2029 and Abell 2142 (also marked on Figure 3). We will in a future paper investigate those two local clusters to assess if the stellar populations of their passive galaxies are similar to those of the Coma and Perseus clusters. For now, we will assume that the bulge-dominated passive galaxies in the seven z = 0.19–0.89 clusters are viable progenitors for the bulge-dominated passive galaxies in Coma and Perseus.

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We determined the cluster redshifts and velocity dispersions for the z = 0.19–0.45 clusters using our data and the bi-weight method by Beers et al. (1990). Figure 4 shows the redshift distributions of the samples. In Jørgensen & Chiboucas (2013), we published similar results for the three higher-redshift clusters. Table 1 summarizes the redshifts and velocity dispersions for the clusters. Using Kolmogorov-Smirnov tests, we found that for all the clusters, the velocity distributions of the member galaxies are consistent with Gaussian distributions.

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In Figure 5, we show the cluster velocity dispersions versus the X-ray properties of the clusters. At a velocity dispersion of $2182\,\mathrm{km}\,{{\rm{s}}}^{-1}$, Abell 1689 deviates from the expected relations by ~7 times the uncertainty on the cluster velocity dispersion. The kinematic structure of the cluster has been studied using very large samples of redshift data. Czoske (2004) concluded based on 525 member redshifts that the central velocity dispersion is $\approx 2100\,\mathrm{km}\,{{\rm{s}}}^{-1}$ and that the central structure of the cluster is complex. Lemze et al. (2009) analyzed this data set further, confirming the high central velocity dispersion. They also determined a virial cluster mass of $\approx 1.9\cdot {10}^{15}\,{M}_{\odot }$ (for our assumed cosmology), equivalent to ${M}_{500}=1.3\cdot {10}^{15}\,{M}_{\odot }$. A similar mass estimate was found by Umetsu et al. (2015) based on lensing data. Umetsu et al., as well as Morandi et al. (2011), argued that the cluster is not spherical. Morandi et al. in particular stated that earlier mass estimates from X-data were about a factor of two too small, as spherical symmetry was assumed. Finally, Andersson & Madejski (2004) used the temperature of the X-ray gas to argue that Abell 1689 is in fact a merger, something that cannot be detected from the X-ray morphology alone. Thus, we conclude that Abell 1689 deviates from the relations shown in Figure 5 due to (1) the mass being underestimated and (2) the unrelaxed nature of the center of the cluster leading to a very high central cluster velocity dispersion.

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Barrena et al. (2007) studied the dynamical status of RXJ0056.2+2622. These authors found that the cluster consists of two structures in the plane of the sky; see also the gray-scale image with X-ray data overlaid in Figure 15 in Appendix A. Barrena et al. found a total cluster velocity dispersion of ${\sigma }_{\mathrm{cluster}}={1362}_{-108}^{+126}\,\mathrm{km}\,{{\rm{s}}}^{-1}$ and a redshift of $z=0.1929\pm 0.0005$, both in agreement with our results within the uncertainties. We attempt to determine the subcluster velocity dispersions by defining the likely members of the two subclusters from the cluster center distances. We include only galaxies that have cluster center distances to one or the other of the subcluster centers of less than half the distance between the centers. The galaxies with IDs 191 and 1654 are taken as defining the southern and northern subcluster center, respectively. We then find cluster velocity dispersions of the subclusters of ${\sigma }_{\mathrm{cluster}}=1200\mbox{--}1300\,\mathrm{km}\,{{\rm{s}}}^{-1}$; cf. Table 1, which places the subclusters above the mean relations with the X-ray properties but with rather large uncertainties on ${\sigma }_{\mathrm{cluster}}$ (see Figure 5).

Our data show that the field of RXJ0027.6+2616 contains a foreground group at z = 0.3404. Our data include nine galaxies in this group, mostly on the western edge of the observed field; see Figure 16 in Appendix A. The velocity dispersion of this group as determined from the nine galaxies is very low, $\sigma ={172}_{-47}^{+29}\,\mathrm{km}\,{{\rm{s}}}^{-1}$. These galaxies were not included in the analysis of the cluster members.

The cluster velocity dispersion for RXJ1347.5–1145 was also measured by Cohen & Kneib (2002), who found ${\sigma }_{\mathrm{cluster}}=910\pm 130\,\mathrm{km}\,{{\rm{s}}}^{-1}$ based on 47 members, and by Lu et al. (2010), who, based on additional spectroscopic observations, found ${\sigma }_{\mathrm{cluster}}=1163\pm 97\,\mathrm{km}\,{{\rm{s}}}^{-1}$ for a sample of $\approx 95$ members (sample size evaluated from Figure 2 in that paper). The result from Lu et al. is in agreement with our result of ${1259}_{-250}^{+210}\,\mathrm{km}\,{{\rm{s}}}^{-1}$. Lu et al. stated that the result from Cohen & Kneib may be in error. We confirm that this indeed seems to be the case, as we find ${\sigma }_{\mathrm{cluster}}={1256}_{-197}^{+115}\,\mathrm{km}\,{{\rm{s}}}^{-1}$ when using the Cohen & Kneib data. We caution that the results for this cluster are very sensitive to the exact choice of the upper limit for the cluster redshift. Had we, for example, excluded the three highest-redshift galaxies in our sample, we would have found ${\sigma }_{\mathrm{cluster}}={791}_{-88}^{+70}\,\mathrm{km}\,{{\rm{s}}}^{-1}$. The Lu et al. sample is significantly larger and less likely to be affected by small-number statistics. Thus, we evaluate that the joint data support a velocity dispersion of $\approx 1150\mbox{--}1250\,\mathrm{km}\,{{\rm{s}}}^{-1}$ for this cluster. When combined with the X-ray data from Ettori et al. (2004), this places the cluster on the mean relations between the cluster velocity dispersions and the X-ray properties. Cohen & Kneib proposed that the cluster may be a merger. Later investigations of the X-ray data of the cluster support this idea but for different reasons; see, e.g., Ettori et al. (2004) for a discussion of the diffuse X-ray emission southeast of the main cluster and the recent study by Kreisch et al. (2016) based on deep Chandra X-ray observations.

In summary, four of the seven clusters in our sample have evidence of nonrelaxed structures and/or deviate from the expected relations between the cluster velocity dispersions and the X-ray parameters. These clusters are Abell 1689, RXJ0056.2+2622, RXJ1347.5–1347, and RXJ0152.7–1347. RXJ0027.6+2616 has a foreground group, but this may be at a large enough distance in redshift space to not affect the cluster itself. MS0451.6–0305 and RXJ1226.9+3332 have no evident subclustering and also follow the expected relations. These complicated cluster properties should be kept in mind when we apply the fairly simple approach of using either the cluster center distances (in units of ${R}_{500}$) or the product of the cluster center distances and the radial velocities relative to the cluster redshifts as parameterization of the cluster environment for a given galaxy.

Table 4 summarizes the number of galaxies in each cluster for which we have data. The table details how many of these are bulge-dominated passive galaxies with dynamical masses ${\mathrm{Mass}}_{\mathrm{dyn}}\geqslant {10}^{10.3}\,{M}_{\odot }$ or, equivalently, $\mathrm{log}\sigma \geqslant 2.0$, and therefore the primary focus of this paper. We use $\mathrm{log}\sigma$ in place of the dynamical masses of the galaxies in our investigation of the possible primary driver of the galaxy properties. We acknowledge that the two parameters are not fully interchangeable and will return to this issue in our upcoming paper, in which we also make use of the two-dimensional photometry of all the galaxies.

Table 4.  Samples

			Bulge-dominated
Cluster	${N}_{\mathrm{members}}$	${N}_{\mathrm{disk}}$	${N}_{\mathrm{emis}}$	${N}_{\mathrm{lowmass}}$	${N}_{\mathrm{highmass}}$	${N}_{\mathrm{sample}}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)
Abell 1689	72	3a	6	15	48	48
RXJ0056.2+2622	58	4	4b	11	39	38
RXJ0027.6+2616	34	0	3c	10	21	21
RXJ1347.5–1345	43	1d	1	6	35	31
MS0451.6–0305	47	9	1	0	37	34
RXJ0152.7–1357	29	3	3	2	21	21
RXJ1226.9+3332	55	6	7	2	38	28

Notes. Column 1: galaxy cluster. Column 2: number of members with available spectroscopy. Column 3: number of disk galaxies. Column 4: number of bulge-dominated galaxies with $\mathrm{Mass}\lt {10}^{10.3}\,{M}_{\odot }$ or, equivalently, $\mathrm{log}\sigma \lt 2$; see text. The sample includes three E+A galaxies in Abell 1689 and one E+A galaxy in RXJ0056.2+2622. Column 5: number of bulge-dominated galaxies with emission with ${\mathrm{Mass}}_{\mathrm{dyn}}\lt {10}^{10.3}\,{M}_{\odot }$ or, equivalently, $\mathrm{log}\sigma \lt 2$. Column 6: number of bulge-dominated passive galaxies with ${\mathrm{Mass}}_{\mathrm{dyn}}\geqslant {10}^{10.3}\,{M}_{\odot }$ or, equivalently, $\mathrm{log}\sigma \geqslant 2$. Column 7: number of bulge-dominated passive galaxies in the final samples, which exclude E+A galaxies, galaxies in RXJ1347.5–1345 with S/N < 25 Å^–1 in the rest frame, galaxies in MS0451.6–0305 for which the spectra are contaminated by signal from neighboring objects (cf. Jørgensen & Chiboucas 2013), and galaxies in RXJ1226.9+3332 with S/N < 20.

^aIncludes IDs 972 and 752 and excludes BCG ID 584. ^bID 1296 has Hβ and [O iii] emission. The spectrum does not cover [O ii]. ^cIDs 51 and 545 have significant emission fill-in of the Hβ and are included in the emission-line galaxies. ^dID 195 based on visual inspection of imaging; see text.

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The sample selection makes use of the Sérsic index, ${n}_{\mathrm{ser}}$ (Sérsic 1968), either from our photometry (Chiboucas et al. 2009; Jørgensen & Chiboucas 2013; I. Jørgensen et al. 2017, in preparation) or for Abell 1689 from Houghton et al. (2012). We require ${n}_{\mathrm{ser}}\geqslant 1.5$ for a galaxy to be considered bulge-dominated. Galaxies for which we have no ${n}_{\mathrm{ser}}$ measurement but that appear to be spiral galaxies based on imaging data are considered disk galaxies for the purpose of the sample selection. Abell 1689 ID 584 is the brightest cluster galaxy, and we include it with the bulge-dominated galaxies, even though Houghton et al. gave a Sérsic index of 1.2. As in our previous papers, we consider galaxies with equivalent widths of EW [O ii] ≤ 5 Å passive (nonemission). This criterion matches the spectral classifications defined by Dressler et al. (1999) and used by other researchers, e.g., Sato & Martin (2006) and Saglia et al. (2010). If the [O ii] line is not included in the spectral coverage, we use the presence or absence of emission in Hβ and/or [O iii] λ5007 to evaluate if a galaxy is passive.

The galaxy RXJ0056.2+2622 ID 1170 was excluded from the analysis, as it is an E+A galaxy dominated by extremely young stellar populations. Including it in the determination of especially the scaling relation scatter would bias the determination and not give a representative view of the typical scatter of the line strengths for the cluster's galaxies. Other E+A galaxies in the sample are excluded from the analysis, as they have $\mathrm{log}\sigma \lt 2.0$.

Due to the strong fringing in the GMOS-S observations of RXJ1347.5–1145 and its effect on the sky subtraction, we conservatively exclude galaxies with S/N < 25 from the analysis. This removes IDs 444, 513, 657, and 919 from our analysis. The measurements are still listed in the tables, but we caution that, in particular, the line index measurements are expected to have larger uncertainties than otherwise adopted for the cluster. In addition, we remove RXJ1347.5–1145 IDs 743 and 1011 from the analysis. The GMOS-S imaging shows ID 743 as double; there is no HST imaging covering this galaxy. The galaxy also has $\mathrm{log}\sigma \lt 2.0$. The spectrum of ID 1011 appears to be a BL Lac object with a featureless optical continuum superimposed on a spectrum of an old stellar population. Thus, the effect is that all the line indices are weaker than otherwise expected from an old stellar population. The object is within 8 of a point source in the Chandra X-ray catalog (Evans et al. 2010).

In the analysis, we focus on the bulge-dominated passive galaxies with dynamical masses $\mathrm{Mass}\geqslant {10}^{10.3}\,{M}_{\odot }$ or $\mathrm{log}\sigma \geqslant 2.0$. The lower limit is set by both the available local reference sample and the available data for the intermediate-redshift clusters. The number of bulge-dominated galaxies with low masses (or velocity dispersions) is listed in Column (5) in Table 4. Column (7) in Table 4 gives the number of galaxies in each cluster that meet all criteria for being included in the analysis. The sample selection for Coma, Perseus, Abell 194, MS0451.6–0305, RXJ0152.7–1357, and RXJ1226.9+3332 is identical to the selection used in Jørgensen & Chiboucas (2013). In samples for the two highest-redshift clusters, we reach cluster center distances of ${R}_{\mathrm{cl}}\approx 1.8{R}_{500}$, while all other cluster samples only reach ${R}_{\mathrm{cl}}/{R}_{500}=0.8\mbox{--}1.0$. For galaxies in the two double clusters RXJ0056.2+2622 and RXJ0152.7–1157, we use ${R}_{\mathrm{cl}}/{R}_{500}$ derived relative to the subcluster center closest to the galaxy.

In addition to the measurements for the individual galaxies, we construct composite spectra with higher S/Ns by coadding the spectra. The spectra are coadded by velocity dispersion. When possible, given the number of observed galaxies, we use bins of 0.05 in $\mathrm{log}\sigma$. When this results in less than three galaxies in a bin and/or low S/N, we use bins of 0.1 in $\mathrm{log}\sigma$. The velocity dispersion bin with $\mathrm{log}\sigma \lt 2.0$ contains galaxies that we otherwise omit from the analysis of the individual measurements; see Section 4.1. Our analysis in Section 6 focuses on the blue indices measured from the composites. These measurements and the average velocity dispersions of the galaxies included in each composite are available in Table 16 in Appendix C. We do not attempt to measure the velocity dispersions directly from the composites.

For our local reference sample in Perseus, we use luminosity-weighted average parameters for subsamples of galaxies using the same binning as described above for the higher-redshift galaxies. The average parameters for the Perseus subsamples are also listed in Table 16 in Appendix C.

We adopt the empirical scaling relations and zero points for the local reference sample and the $z=0.5\mbox{--}0.9$ clusters from Jørgensen & Chiboucas (2013). These relations were established using a fitting technique that is very robust to outliers. It minimizes the sum of the absolute residuals perpendicular to the relation and determines the zero points as the median and uncertainties on the slopes using a bootstrap method; see Jørgensen et al. (2005) and Jørgensen & Chiboucas (2013) for details. As in those papers, we then determine the random uncertainties on the zero-point differences, ${\rm{\Delta }}\gamma$, between the intermediate-redshift and local reference samples as

$$\begin{eqnarray}&&{\sigma }_{{\rm{\Delta }}\gamma }={({\mathrm{rms}}_{\mathrm{low} \mbox{-} z}^{2}/{N}_{\mathrm{low} \mbox{-} z}+{\mathrm{rms}}_{\mathrm{int} \mbox{-} z}^{2}/{N}_{\mathrm{int} \mbox{-} z})}^{0.5}.\end{eqnarray} \tag{ 1 }$$

Subscripts "low-z" and "int-z" refer to the local reference sample and one of the intermediate-redshift clusters, respectively. Only the random uncertainties are shown in the figures in the following. We expect the systematic uncertainties on the zero-point differences to be dominated by the possible inconsistency in the calibration of the velocity dispersions, 0.026 in $\mathrm{log}\sigma$, and may be estimated as 0.026 times the coefficient for $\mathrm{log}\sigma$; see also Jørgensen et al. (2005).

We use single stellar population (SSP) models in the interpretation of the data. In Jørgensen & Chiboucas (2013), we discussed the differences and similarities of the models from Thomas et al. (2011) and Schiavon (2007). Since then, new models taking into account variations in abundance ratios have been published by Vazdekis et al. (2015). Vazdekis et al. assumed that at fixed metallicity, non-α-elements, including C, N, and Na, decrease in abundance when [α/Fe] increases. Magnesium is used as a proxy for all α-elements. Thomas et al., in contrast, assumed that the elements C, N, and Na track the α-elements in abundance ratios.

We used the model spectral energy distributions (SEDs) available for the Vazdekis models to test whether these models for $[\alpha /\mathrm{Fe}]\gt 0$ can reproduce the line strengths found in our cluster galaxy samples. Our test shows that the models fail to reproduce the strong CN3883 and C4668 indices present in the galaxies that also have strong Mgb indices. Thus, the underlying assumption of a decrease in C and N with increasing Mg abundances appears to not be supported by the data. We therefore proceed as in Jørgensen & Chiboucas (2013), using the models from Thomas et al.

In Jørgensen & Chiboucas (2013), we established an empirical relation between CN₂ and CN3883 (Equation (4) in that paper): $\mathrm{CN}3883=(0.84\pm 0.13){\mathrm{CN}}_{2}+0.146$. We have confirmed that this relation is also valid for the full sample used in the present paper. As in Jørgensen & Chiboucas (2013), we use the relation to transform the Thomas et al. (2011) model predictions for CN₂ to predictions for CN3883. We use the models for a Salpeter (1955) initial mass function. In Jørgensen & Chiboucas (2013), we derived model relations linear in the logarithm of the age, metallicity [M/H], and abundance [α/Fe]. We use these relations (Table 9 in that paper) to aid our analysis in the following. While traditionally, one may have considered the various indices as primarily tracking one of the quantities of age, [M/H], or [α/Fe], as shown by the relations and first described by Worthey (1994) and Worthey & Ottaviani (1997) (see also Tripicco & Bell 1995), all the line indices depend on all three physical quantities. The Balmer line strengths decrease with increasing ages, while all the metal-line strengths increase. The metal-line strengths increase with increasing [M/H], while the Balmer line strengths decrease. The dependence on [α/Fe] is more complicated, with the iron line strengths decreasing with increasing [α/Fe] and all other metal-line strengths increasing. The Balmer line strengths also increase with [α/Fe] but generally less so than the metal-line strengths.

Having established which set of SSP models we use, we next turn to models for the star formation history. We evaluate models that assume passive evolution over the time period covered by the redshifts of the observed clusters. For our adopted cosmology, the look-back time to z = 0.89, the highest redshift covered by our data, is 7.3 Gyr. Thus, we assume that following the initial period of star formation, the bulge-dominated passive galaxies in our samples evolve passively, without any further star formation. As is common practice, we parameterize these models using a formation redshift ${z}_{\mathrm{form}}$, which should be understood to be the approximate epoch of the last major star formation episode.

In our analysis, we also use the results from Thomas et al. (2005, 2010) on the relations between the velocity dispersions, ages, metallicities [M/H], and abundance ratios [α/Fe]. In particular, as a consequence of the relation between velocity dispersions and ages at $z\approx 0$, the formation redshift ${z}_{\mathrm{form}}$ must depend on the galaxy velocity dispersion. With that prediction, we can then derive predictions for ages and line indices as a function of redshift and galaxy velocity dispersion. We show those predictions in relevant figures in the following.

Our analysis implicitly assumes that the galaxies we observe in the higher-redshift clusters can be considered progenitors to the galaxies in the clusters at lower redshifts. As discussed in detail by van Dokkum & Franx (2001), this may not be a valid assumption. In Section 7, we return to this issue of progenitor bias.

Figure 8 shows the measured scatter, as well as the intrinsic scatter, in the relations as a function of redshift. We derive the intrinsic scatter from the measured scatter by subtracting in quadrature the adopted typical measurement uncertainties for the line indices. The uncertainties are given in Appendix B(Table 12) for the z = 0.19–0.45 clusters and in Jørgensen & Chiboucas (2013) for the higher-redshift clusters. For the local reference sample, we adopt as a typical measurement uncertainty for each line index the median of the individual uncertainties. As shown in Figure 8, in a few cases, the resulting intrinsic scatter in a relation is zero. This is likely due to overestimated measurement uncertainties.

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From Figure 8, we conclude that all of the relations have intrinsic scatter. The scatter in a given relation is similar for all clusters, except for the scatter in the Fe4383–velocity dispersion relation for RXJ0152.7–1357 at z = 0.83. In Jørgensen et al. (2005), we found this cluster to have very high average abundance ratio [α/Fe] due to galaxies with low Fe4383 indices. These are the galaxies causing the high scatter in the Fe4383–velocity dispersion relation. We used Kendall's τ rank-order tests to evaluate if correlations may be present between the intrinsic scatter in any of the relations and the redshifts of the clusters. We omitted from the tests any measurements with an intrinsic scatter found to be zero, as well as the very low scatter measurement for the MS0451.6–0305 C4668–velocity dispersion relation. We find possible correlations with redshift for the scatter in $\langle \mathrm{Fe}\rangle$ and C4668, for which the probability of no correlation being present is 0.5% and 1.5%, respectively. It requires data for significantly more clusters to firmly establish these possible correlations. In all other cases, no significant correlations were found.

The intrinsic scatter in the relations can, in principle, be used to set limits on the scatter in ages and/or metallicities and abundance ratios of the stellar populations in the galaxies. In doing so, we use the model relationships between line index strengths, age, metallicity, and abundance ratios established in Jørgensen & Chiboucas (2013). If we assume that only the ages vary at a given velocity dispersion, then the scatter in the $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$–velocity dispersion relation of 0.015 translates to an age scatter of only 0.12 dex. Similarly, the scatter in the ${\rm{H}}{\beta }_{G}$–velocity dispersion relation of 0.045 gives an age scatter of 0.20 dex. These results point toward a very large degree of synchronization of the star formation history for passive galaxies at a given velocity dispersion. The scatter in the Mgb and Fe4383 relations implies similarly low age scatter. However, the larger scatter in the other three metal-line relations ($\langle \mathrm{Fe}\rangle$, C4668, and CN3883), combined with their dependence on age, implies an age scatter of 0.45–0.55 dex. The dependence on metallicity for these three indices is a factor of 2–4 stronger than their dependence on age (cf. Jørgensen & Chiboucas 2013). Thus, the larger scatter in the relations for these indices may be due to scatter in metallicities, as well as ages, at a given velocity dispersion.

We have investigated the possible cluster environment dependency of the scaling relations. We use both the cluster center distances, ${R}_{\mathrm{cl}}/{R}_{500}$, and the radial velocity of the galaxies relative to the clusters, ${v}_{| | }/{\sigma }_{\mathrm{cl}}$, in this test. In particular, as shown by Haines et al. (2012, 2015) in their analysis of clusters extracted from the Millennium Simulations (Springel et al. 2005), the phase-space parameter $| {v}_{| | }| /{\sigma }_{\mathrm{cl}}\cdot {R}_{\mathrm{cl}}/{R}_{500}$ provides a one-dimensional measure within the phase-space diagram expected to be directly related to the accretion epoch of a galaxy onto the cluster.

We use Spearman rank-order tests to test for correlations between the residuals for all the scaling relations and both measures of the cluster environment. The test is performed for both the full samples and samples limited to ${R}_{\mathrm{cl}}/{R}_{500}\leqslant 1.0$ and to $| {v}_{| | }| /{\sigma }_{\mathrm{cl}}\cdot {R}_{\mathrm{cl}}/{R}_{500}\leqslant 2$ or ≤1. This is done to ensure that the results are not driven by the relatively few galaxies at values above 1 in either environment parameter. Figure 9 shows the residuals of the scaling relations for $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$ and C4668 versus the cluster center distances, ${R}_{\mathrm{cl}}/{R}_{500}$, and versus $| {v}_{| | }| /{\sigma }_{\mathrm{cl}}\cdot {R}_{\mathrm{cl}}/{R}_{500}$. The panels are labeled with the probabilities that no correlations are present. The best-fit relations are shown. In addition to the correlations shown in the figure, we also found similar shallow but significant correlations for the residuals in Mgb. No other correlations were significant. In the cases of correlations between the residuals and environment parameters, the contribution to the intrinsic scatter in the relations originating from the environment is very small, as these relations are very shallow. For example, taking into account the correlation with environment for the C4668–velocity dispersion relation reduces the scatter in the relation by only 2%. Thus, in our presentation of the results regarding the zero points (Section 5.3), we do not take into account these very weak dependences on the environment.

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In Figure 10, we show the median zero-point differences of the scaling relations for each cluster relative to the local reference sample. The zero-point differences shown here for MS0451.6–0305, RXJ0152.7–1357, and RXJ1226.9+3332 are from Jørgensen & Chiboucas (2013). The zero-point differences for the four other clusters (Abell 1689, RXJ0056.2+2622, RXJ0027.6+2616, and RXJ1347.5–1137) are based on the new data presented in the current paper. The zero points are listed in Table 5. There are no significant zero-point differences between the two subclusters in RXJ0056.2+2622 or RXJ0152.7–1357. Thus, each of these clusters is treated as one cluster for the purpose of showing the zero-point differences. Predictions of the zero-point differences based on passive evolution models with formation redshifts between z = 1.2 and 4 and SSP models from Thomas et al. (2011) are overlaid on the figure. At fixed metallicity and abundance ratio for a given velocity dispersion, these predictions have no significant dependence on the assumed metallicity or abundance ratio, as shown by the linear parameterization of the models that we derived in Jørgensen & Chiboucas (2013). In the passive evolution models, the Balmer line indices, ${\rm{H}}{\beta }_{G}$ and $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$, are expected to be stronger at higher redshift, reflecting the younger stellar populations, while all of the metal indices are expected to be weaker at higher redshift than at present (cf. Section 4.4).

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The zero-point differences for the higher-order Balmer lines $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$ follow the passive evolution model. A ${\chi }^{2}$ fit gives the best fit of ${z}_{\mathrm{form}}=6.5$ with a 1σ lower limit of ${z}_{\mathrm{form}}=3.1$ (Figure 10(d)). No upper limit can be established. However, the zero-point differences for the ${\rm{H}}{\beta }_{G}$–velocity dispersion relation are significantly smaller than expected for the passive evolution models (Figure 10(a)). Equivalently, the ${\rm{H}}{\beta }_{G}$ indices for the $z=0.19\mbox{--}0.54$ clusters are weaker than expected. This may be due to partial emission fill-in, as explored by Concas et al. (2017) for galaxies in the Sloan Digital Sky Survey (SDSS). Due to this evidence, in the following, we will focus on the higher-order Balmer lines when discussing the age differences.

The scaling relations for the metal-line indices have zero-point differences that are less straightforward to interpret. The indices $\langle \mathrm{Fe}\rangle$, C4668, and Fe4383 are generally weaker at higher redshift than at present, though the zero-point differences for the scaling relations (Figures 10(c), (e), and (f)) show significantly higher scatter relative to any given passive evolution model than is the case for $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$. The data give 1σ lower limits on ${z}_{\mathrm{form}}$ of 2.0 and 4.3 for $\langle \mathrm{Fe}\rangle$ and Fe4383, respectively, consistent with the result based on $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$. The best-fit result for C4668 is ${z}_{\mathrm{form}}={1.4}_{-0.3}^{+0.8}$, marginally inconsistent with the result based on $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$. However, the result is to a large extent driven by the large zero-point difference found for MS0451.6–0305, for which the scaling relation also has a rather low scatter. The Mgb and CN3883 indices are significantly stronger than expected for the majority of the $z\geqslant 0.19$ clusters based on the passive evolution models (Figures 10(b) and (g)). Thus, these indices cannot be used to constrain ${z}_{\mathrm{form}}$ but instead may be an indicator of the limitations of the models. Part of the difference in behavior of the metal-line indices relative to the $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$ index may also be due to cluster-to-cluster variations in the metallicities and abundance ratios. We return to this question in Section 6.3.

In this investigation, we use the line indices derived from the composite spectra for the z = 0.19–0.89 clusters and the luminosity-weighted average line indices for the local reference sample (cf. Section 4.2). This is done primarily to gain S/N, as even with our fairly high S/N individual spectra, ages, [M/H], and [α/Fe] for the individual galaxies would have uncertainties as large as 0.3 dex. When we use the indices from the composite spectra and the luminosity-weighted average indices, the resulting uncertainties on the ages, [M/H], and [α/Fe] are typically 0.06 dex.

We limit our analysis to determinations based on indices in the blue wavelength region ($({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$, [C4668Fe4383], Fe4383, CN3883), as these are available for all z = 0.19–0.89 clusters in our sample. Figure 11 shows the indices versus each other in the relevant combinations and with SSP models from Thomas et al. (2011) overlaid. As in Jørgensen & Chiboucas (2013), we use the higher-order Balmer lines versus the combination index [C4668Fe4383] to determine ages and [M/H], as the combination index is constructed to be independent of [α/Fe]. We use the model grid for [α/Fe] = 0.3 for this determination. To determine [α/Fe], we use CN3883 versus Fe4383. We first fit the $[\alpha /\mathrm{Fe}]=0.3$ models with a second-order polynomial. Then, the abundance ratios are determined from the distance between a given data point and this polynomial, measured along the direction of the [α/Fe] dependency (shown as purple arrows in the figure). To estimate the uncertainties, we add and subtract the adopted uncertainties on the line indices and derive age, [M/H], and [α/Fe] at these extreme points in the parameter spaces. The maximum absolute difference between results from the extreme points and the result from the measured indices is used as the uncertainty on a given parameter. See Jørgensen & Chiboucas (2013) for details.

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In the following sections, we investigate how the derived ages, metallicities, and abundance ratios change with velocity dispersion and redshift.

In Figure 12, we show the derived ages, metallicities [M/H], and abundance ratios [α/Fe] versus the mean velocity dispersion of the spectra making up each composite spectrum or entering into the luminosity-weighted average line indices. The best least-squares fits to the data are shown as blue solid lines. The relations are summarized in Table 6. The fit to ages versus velocity dispersion was established as a set of parallel lines, allowing the zero points for the clusters to be different for each cluster. The fit is shown for the average zero point for the $z\leqslant 0.19$ clusters (Perseus, Abell 1689, and RXJ0056.2+2622). Correlations are present for [M/H] and [α/Fe], while the ages are consistent with no correlation with the velocity dispersion.

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Table 6.  Relations for Ages, Metallicities, and Abundance Ratios

Relation	${\mathrm{rms}}_{\mathrm{meas}}$	${\mathrm{rms}}_{\mathrm{int}}$
(1)	(2)	(3)
$\mathrm{log}\,\mathrm{age}=(0.10\pm 0.09)\,\mathrm{log}\sigma +0.65$ a	0.10	0.08
$[{\rm{M}}/{\rm{H}}]=(0.69\pm 0.09)\,\mathrm{log}\sigma -1.35$	0.13	0.12
$[\alpha /\mathrm{Fe}]=(0.86\pm 0.16)\,\mathrm{log}\sigma -1.65$	0.17	0.15

Note. Column 1: best-fit relation. Column 2: scatter of the relation as rms in the Y-direction. Column 3: estimated intrinsic scatter.

^aRelation fit as parallel lines allowing different zero points for each cluster. The table lists the average zero point for the $z\leqslant 0.19$ clusters (Perseus, Abell 1689, and RXJ0056.2+2622).

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We used the Thomas et al. (2005) relations between age and velocity dispersion at $z\approx 0$ to derive predictions for the stellar population ages as a function of velocity dispersion and redshift, under the assumption of passive evolution. The predictions are shown in Figure 12(a), color-coded to match the clusters at $z\approx 0.0$, 0.2, 0.5, and 0.9. The predictions are generally consistent with the ages, though our results are also consistent with flat relations offset from each other as a function of the cluster redshifts. We have also shown predictions using the steeper age–velocity dispersion relation at $z\approx 0$ from Thomas et al. (2010; thin dot-dashed lines). This relation results in much steeper relations at higher redshift, in disagreement with the data at $z\gt 0.5$. In Section 7, we address the possible reasons for this disagreement. The intrinsic scatter in the age–velocity dispersion relations corresponds to a scatter in age of 0.08 dex (cf. Table 6).

The relation between the metallicities [M/H] and the velocity dispersions is almost identical to the one found by Thomas et al. (2005, 2010). The relation for the abundance ratios [α/Fe] is marginally steeper than that found by Thomas et al. The steeper slope is almost exclusively driven by a few of the measurements at low velocity dispersions. The scatter relative to the relations listed in Table 6 implies intrinsic scatter of [M/H] and [α/Fe] at fixed velocity dispersions of 0.12 and 0.15 dex, respectively. The scatter should be taken as a lower limit, since it is based on determinations from composite spectra (or luminosity-weighted average line indices), the construction of which may have eliminated some of the intrinsic scatter present for the individual galaxies. Even so, we conclude that the [M/H]–velocity dispersion and [α/Fe]–velocity dispersion relations are steep and tight at all redshifts covered by our sample. Neither relation depends on the redshift.

Next, we investigate the redshift dependency of ages, metallicities [M/H], and abundance ratios [α/Fe]. Figure 13 summarizes the determinations based on the composite spectra and the index values at $\mathrm{log}\sigma =2.24$ on the scaling relations for the clusters. Thus, the figure shows both representative median values for each cluster based on the scaling relations and the typical scatter in the parameters, primarily due to the dependence on the velocity dispersions as reflected in the symbol sizes. In panel (a), we show the predictions from passive evolution models with formation redshifts ${z}_{\mathrm{form}}=1.2\mbox{--}4.0$. As expected, the dominating trend is the change in age with redshift. A best fit to the median points for the clusters gives a formation redshift of ${z}_{\mathrm{form}}={1.96}_{-0.19}^{+0.24}$, shown as the dashed black line in panel (a). This formation redshift is lower than that found from the zero-point differences of the $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$–velocity dispersion relation (see Figure 10(d)), for which we find ${z}_{\mathrm{form}}\geqslant 3.1$ as the 1σ lower limit. However, it is also clear that the local reference sample contains galaxies that are too young to be the descendants of the galaxies in the high-redshift clusters if only passive evolution is at work. We discuss this in more detail in Section 7.1.

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The median value of the metallicities [M/H] (Figure 13(b)) is 0.24, marked with a dashed line. However, as noted in Jørgensen & Chiboucas (2013), MS0451.6–0305 at z = 0.54 has significantly lower metallicity at [M/H] ≈ 0.1.

The median value of the abundance ratios [α/Fe] (panel (c)) is 0.3, marked with a dashed line. RXJ0152.7–1357 at z = 0.83 has a significantly higher abundance ratio of $[\alpha /\mathrm{Fe}]\approx 0.55$ (see also Jørgensen et al. 2005). RXJ1347.5–1347 at z = 0.45 and the local reference sample (Perseus and Abell 194) have $[\alpha /\mathrm{Fe}]=0.14$. Additional observations to confirm or refute these results would be very valuable.

The zero-point differences of the relations between the galaxy velocity dispersions and the line indices support a high formation redshift. The best fit of the zero-point differences for the $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$–velocity dispersion relation gives ${z}_{\mathrm{form}}=6.5$ and a 1σ lower limit of ${z}_{\mathrm{form}}\geqslant 3.1$ (cf. Figure 10). However, if we use the ages derived from the composite spectra, we find ${z}_{\mathrm{form}}={1.96}_{-0.19}^{+0.24}$ (cf. Figure 13). The two results can be reconciled by realizing that the zero-point differences are strongly affected by the fact that the local reference sample of galaxies in the Perseus cluster contains galaxies that are too young to have their progenitors included in the higher-redshift samples, i.e., by progenitor bias in the samples. See van Dokkum & Franx (2001) for one of the earliest discussions of progenitor bias. The difference in look-back time between the two high-redshift clusters (RXJ0152.7–1357 and RXJ1226.9+3332 at an average redshift z = 0.86) and Perseus (z = 0.018) is 6.9 Gyr for our adopted cosmology. To be included in the passive galaxy sample at any redshift, a galaxy would most likely have to contain stellar populations at least 1 Gyr old, on average, since at younger ages we expect emission lines strong enough that our criteria on EW[O ii] would exclude such galaxies from the sample. Thus, as a test, we remove from the local reference sample the 34 galaxies for which $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$ versus [C4668Fe4383] indicates ages less than 8 Gyr. The zero point of the $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$–velocity dispersion relation for the remaining 31 galaxies is 0.005 lower than that found from the full sample. This in turn affects the zero-point differences for the two high-redshift clusters. If we adjust the zero-point differences for just those two clusters, realizing that the differences for the other clusters also ought to be offset but with smaller amounts, then we find a best-fit 1σ lower limit of ${z}_{\mathrm{form}}\geqslant 2.0$. Thus, the difference between the determination of ${z}_{\mathrm{form}}$ from the scaling relations and the formation redshift derived from the ages may be fully explained as an effect of progenitor bias. In addition, the median age of the galaxies in the local reference sample older than 8 Gyr is 10 Gyr, placing the median value exactly on the best fit of ${z}_{\mathrm{form}}$ from the ages based on the blue indices, see Figure 13. We also note that the ages of the galaxies in the local reference sample indicate that about half of such passive cluster galaxies at $z\approx 0$ have become passive since $z\approx 0.9$. This is similar to the conclusion reached by Sánchez-Blázquez et al. (2009) in their analysis of the line indices of the EDisCS sample of passive galaxies. It is possible that the main stellar mass of such apparently young galaxies was formed earlier, and that the measured low ages are caused by later star formation episodes involving a small fraction of the mass (see discussion by, e.g., Serra & Trager 2007).

The zero-point differences of the scaling relations involving the iron indices ($\langle \mathrm{Fe}\rangle$ and Fe4383) give formation redshifts consistent with the scaling relation for $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$, while the scaling relation for C4668 gives a marginally lower formation redshift. We note that some of the largest outliers relative to the expected zero-point differences for passive evolution are clusters that are also outliers relative to the median metallicity [M/H] and abundance ratio [α/Fe] of the clusters. Specifically, RXJ0152.7–1357 (z = 0.83), which we found to have very high [α/Fe], is offset to weaker Fe4383 and stronger C4668 than expected from ${z}_{\mathrm{form}}\approx 2$ (Figures 10(e) and (f)). RXJ0027.6+2616 (z = 0.37) and MS0451.6–0305 (z = 0.54), which we found to have lower than median [M/H], is offset to weaker Mgb, $\langle \mathrm{Fe}\rangle$, and/or C4668 than expected.

In the following, we adopt ${z}_{\mathrm{form}}={1.96}_{-0.19}^{+0.24}$ as our best estimate of a common formation redshift for the galaxies, under the assumption of passive evolution. In Jørgensen & Chiboucas (2013), we determined the formation redshift from the fundamental plane (FP) for the three highest-redshift clusters and found ${z}_{\mathrm{form}}={1.95}_{-0.2}^{+0.3}$ for the massive galaxies and a lower ${z}_{\mathrm{form}}=1.24\pm 0.05$ for the less massive galaxies. Our results based on direct age estimates are in agreement with these results, though we cannot put tight constraints on a possible mass (or velocity dispersion) dependency on ${z}_{\mathrm{form}}$, as done from the FP. Other studies of the FP for clusters up to $z\approx 1$ give similar results for the massive galaxies (see van Dokkum & van der Marel 2007 and references therein).

We found that the residuals relative to the Mgb–velocity dispersion and C4668–velocity dispersion relations correlate with the cluster center distances and phase-space parameter $| {v}_{| | }| /{\sigma }_{\mathrm{cl}}\cdot {R}_{\mathrm{cl}}/{R}_{500}$. A weaker correlation may also be present for the residuals of the scaling relation for $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$. However, the slopes of the relations are very shallow, and the correlations can only explain a very small fraction of the intrinsic scatter in the relations. None of the other scaling relations show significant dependences on the cluster environment. We caution that our coverage in cluster center distances is fairly limited, reaching to only R₅₀₀ for the majority of the clusters and $1.8{R}_{500}$ for the two highest-redshift clusters in the sample. In addition, the clusters were purposely chosen to be very massive and thus limit any effect of cluster environment on our results. Our results are in agreement with the study of four nearby clusters by Smith et al. (2006). These authors also found that the Mgb–velocity dispersion and C4668–velocity dispersion relations depend on the cluster center distances, while the scaling relations for the iron lines do not. They found weaker dependencies on cluster center distances for the Balmer line–velocity dispersion relations, also in general agreement with our results. Their study reaches cluster center distances of $1.5{R}_{500}$. Harrison et al. (2011), in their study of four nearby clusters, commented that the only difference they found between the outskirts and the cores of these clusters was that the relations between the velocity dispersions and age, [M/H], and [α/Fe] were weaker in the outskirts than in the cores. This study reaches 10 times the virial radius, or $\approx 15\,{R}_{500}$. In contrast, McDermid et al. (2015), in their study of the ATLAS-3D sample, found the Virgo cluster galaxies to be older and have higher [α/Fe] abundance ratios than the field galaxies.

We do find a few significant cluster-to-cluster differences in the average metallicities [M/H] and abundance ratios [α/Fe]. We cannot tie these differences to specific properties of these clusters. RXJ0152.7–1357 is a double cluster, probably in the process of merging (e.g., Girardi et al. 2005), and the high [α/Fe] may be related to this event. However, RXJ0056.9+2622 is also a double cluster, presumably in the process of merging (Barrena et al. 2007), but its [M/H] and [α/Fe] agree with the sample-wide values. The cluster with a lower than average [M/H], MS0451.6–0305, has an X-ray structure consistent with a relaxed cluster with no substructure. Thus, there are no obvious reasons that the metallicity should be different from the average and no obvious pathway to increasing the metallicity to be similar to that of our local reference sample. We speculate that these cluster-to-cluster differences are stochastic. They may have been established in substructures that later merged to form the larger clusters. Moran et al. (2007), in their study of the two clusters MS0451.6–0305 and CL0024+17, found evidence of cluster-wide differences in the star formation history of the galaxies but no clear trace of what caused the differences. More in-depth studies of massive intermediate-redshift clusters are obviously needed to quantify the frequency of such differences between clusters and maybe understand their origin.

Many authors have found ages, metallicities, and abundance ratios of bulge-dominated passive galaxies to be correlated with the velocity dispersions of the galaxies. Harrison et al. (2011) provided an overview of determinations prior to the publication of that paper, including the results from Thomas et al. (2005, 2010). Harrison et al. also presented new results for galaxies in four nearby clusters. McDermid et al. (2015) gave results based on the ATLAS-3D sample of nearby bulge-dominated galaxies. In Section 6, we use the results from Thomas et al. (2005, 2010) as representative of the many results in the literature (see references in Harrison et al.). In general, the studies agree on an [α/Fe] dependency on the velocity dispersion with a slope of $\approx 0.3\mbox{--}0.35$ with a median value of 0.33. The slopes for [M/H] vary in the interval 0.2–0.8, with a median value of ≈0.6. The slopes for the ages vary between 0.24 (Thomas et al. 2005) and very steep slopes of ≈1 (Bernardi et al. 2006; McDermid et al. 2015). The median value is ≈0.4. It is beyond the scope of the present paper to investigate all of the possible reasons for the disagreement between these studies. However, it is clear that authors who find a very steep slope for the age dependency on the velocity dispersion include nearby young galaxies (ages less than ≈5 Gyr) whose progenitors would not be in our $z\gt 0.5$ samples, as they are not expected to be passive galaxies at those redshifts.

Based on ages, [M/H], and [α/Fe] derived from our composite spectra, we find steep and tight relations between [M/H] and velocity dispersions and between [α/Fe] and velocity dispersions. However, the relation between ages and velocity dispersions is very shallow, with the slope not being significantly different from zero. As shallow slopes are also found for the higher-redshift clusters in the sample, this result significantly constrains the slope of the relation at low redshift to be no steeper than that found by Thomas et al. (2005).

From the scatter in the relations between ages, [M/H] and [α/Fe], and velocity dispersions, we find the intrinsic scatter of the three parameters to be 0.08, 0.12, and 0.15 dex, respectively. The scatter should in all cases be understood as lower limits because of our use of composite spectra or luminosity-weighted average indices in the determination. Both Harrison et al. (2011) and McDermid et al. (2015) found the intrinsic scatter in the ages to be significantly higher at 0.20 dex. Presumably, this apparent disagreement is due to a combination of our use of composite spectra and the inclusion of many very young galaxies in the samples of Harrison et al. and McDermid et al. Both studies find the intrinsic scatter in [M/H] and [α/Fe] to be slightly lower than that of our results, 0.10 and 0.07, respectively. We here quote the McDermid et al. values from line indices calibrated to half an effective radius as comparable to our measurements. The main conclusion from all these results is that the velocity dispersion and the properties of the stellar populations are tightly correlated. The star formation history of a bulge-dominated galaxy must to a high degree be determined by the velocity dispersion of the galaxy. This is to a large extent in agreement with the results presented by Muzzin et al. (2012), who, based on a study of cluster galaxies at $z=0.8\mbox{--}1.2$, concluded that the properties of passive bulge-dominated galaxies are determined by their mass (rather than their environment). We caution that mass and velocity dispersion cannot be assumed to be fully equivalent, though they are tightly correlated.

Table 7 summarizes the GMOS-N and GMOS-S imaging of the z = 0.19–0.45 clusters. The derived photometric parameters (total magnitudes and colors) are listed in Table 8. Colors were derived as total colors based on the total magnitudes and as aperture colors. We used both the image quality of the data and the expected sizes of the galaxies to optimize the choice of aperture size. Specifically, the aperture diameter in arcsec was derived as

$$\begin{eqnarray}&&{D}_{\mathrm{app}}=2\cdot 2.355{({(\mathrm{FWMM}/2.355)}^{2}+{r}_{\mathrm{galaxy}}^{2})}^{0.5},\end{eqnarray} \tag{ 2 }$$

where ${r}_{\mathrm{galaxy}}$ is the angular size of a member galaxy with a size (effective radius) of 2.5 kpc. The resulting apertures sizes for Abell 1689, RXJ0056.2+2622, and RXJ0027.6+2616 are similar in the three filters. Thus, we used the same aperture size for all three filters: ${D}_{\mathrm{app}}=4\buildrel{\prime\prime}\over{.} 35$, 418, and 2 66 for the three clusters. For RXJ1347.5–1145, we used ${D}_{\mathrm{app}}=3.09$ for the $g^{\prime}$ band and 2 51 for the $r^{\prime}$ and $i^{\prime}$ bands.

Table 7.  GMOS-N and GMOS-S Imaging Data

Cluster	Program IDa	Dates	Filter	Exposure Time	FWHMb	Sky Brightness	Anc
		(UT)		(s)	(arcsec)	(mag arcsec−2)	(mag)
Abell 1689 F1d	GN-2003B-DD-3	2003 Dec 24	$g^{\prime}$	4 × 180	0.54	21.55	0.089
	GN-2001B-Q-10	2001 Dec 24	$r^{\prime}$	5 × 300	1.05	20.32	0.062
	GN-2001B-Q-10	2001 Dec 25	$i^{\prime}$	3 × 300	1.04	19.49	0.046
Abell 1689 F2d	GN-2003B-DD-3	2003 Dec 24	$g^{\prime}$	4 × 180	0.57	21.54	0.089
	GN-2001B-Q-10	2001 Dec 24	$r^{\prime}$	6 × 300	1.05	19.80	0.062
	GN-2001B-Q-10	2001 Dec 25	$i^{\prime}$	3 × 300	0.81	19.51	0.046
RXJ0056.2+2622 F1e	GN-2003B-Q-21	2003 Jul 2	$g^{\prime}$	4 × 120	0.79	21.94	0.192
	GN-2003B-Q-21	2003 Jul 2	$r^{\prime}$	4 × 120	0.70	21.24	0.133
	GN-2003B-Q-21	2003 Jul 2	$i^{\prime}$	4 × 120	0.62	20.34	0.099
RXJ0056.2+2622 F2e	GN-2003B-Q-21	2003 Jul 30	$g^{\prime}$	4 × 120	1.04	22.06	0.192
	GN-2003B-Q-21	2003 Jul 30	$r^{\prime}$	4 × 120	0.85	21.20	0.133
	GN-2003B-Q-21	2003 Jul 30	$i^{\prime}$	5 × 120	1.05	19.98	0.099
RXJ0027.6+2616	GN-2003B-Q-21	2003 Jul 1 to 2003 Jul 2	$g^{\prime}$	4 × 360	0.60	21.97	0.134
	GN-2003B-Q-21	2003 Jul 1 to 2003 Jul 2	$r^{\prime}$	4 × 300	0.47	21.22	0.099
	GN-2002B-SV-90	2002 Sep 30
	GN-2003B-Q-21	2003 Jul 1	$i^{\prime}$	32 × 120	0.65	20.02	0.069
RXJ1347.5–1145	GS-2005A-Q-27	2005 Apr 13	$g^{\prime}$	4 × 450	1.16	22.16	0.204
	GS-2005A-Q-27f	2005 Jan 11	$g^{\prime}$	1 × 450	0.99	19.58	0.204
	GS-2005A-Q-27	2005 Jan 11	$r^{\prime}$	4 × 300	0.72	20.94	0.141
	GS-2005A-Q-27	2005 Jan 11	$i^{\prime}$	4 × 300	0.73	20.39	0.105

Notes.

^aObservations with program IDs starting with GN and GS were executed with GMOS-N and GMOS-S, respectively. ^bImage quality measured as the average FWHM of 7–10 stars in the field from the final stacked images. ^cGalactic extinction at cluster center (Schlafly & Finkbeiner 2011), as provided by the NASA/IPAC Extragalactic Database. ^dF1 pointing eastern field (R.A., decl.) ${}_{{\rm{J}}2000}$ = (13 11 37.0, –1 20 29), F2 pointing western field (R.A., decl.) ${}_{{\rm{J}}2000}$ = (13 11 23.5, –1 20 29). ^eF1 pointing southern field (R.A., decl.) ${}_{{\rm{J}}2000}$ = (0 55 59.0, 26 20 30), F2 pointing northern field (R.A.,decl.) ${}_{{\rm{J}}2000}$ = (0 56 00.5, 26 25 10). ^fObservation obtained in twilight, used for photometric calibration only.

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Table 8.  GMOS Photometric Data for the Spectroscopic Samples

Cluster	ID	R.A. (J2000)	Decl. (J2000)	${g}_{\mathrm{total}}^{{\prime} }$	${r}_{\mathrm{total}}^{{\prime} }$	$i{{\prime} }_{\mathrm{total}}$	${(g^{\prime} -r^{\prime} )}_{\mathrm{total}}$	${(r^{\prime} -i^{\prime} )}_{\mathrm{total}}$	${(g^{\prime} -r^{\prime} )}_{\mathrm{aper}}$	${(r^{\prime} -i^{\prime} )}_{\mathrm{aper}}$	${n}_{\mathrm{ser}}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
A1689	14	13 11 13.54	−1 22 23.9	20.52	19.15	18.76	1.372	0.387	1.314	0.410	⋯
A1689	15	13 11 13.54	−1 19 35.1	18.77	17.72	17.17	1.057	0.541	1.178	0.493	⋯
A1689	30	13 11 14.44	−1 21 55.4	19.72	18.47	18.07	1.251	0.394	1.219	0.432	⋯
A1689	45	13 11 14.95	−1 19 19.0	21.09	20.00	19.57	1.097	0.423	1.098	0.422	⋯
A1689	70	13 11 15.94	−1 19 10.1	20.11	18.91	18.56	1.207	0.352	1.191	0.406	⋯
A1689	74	13 11 15.97	−1 19 04.4	19.83	18.56	18.17	1.273	0.384	1.259	0.451	⋯
A1689	91	13 11 16.88	−1 20 00.5	20.46	19.39	18.84	1.067	0.551	1.157	0.540	⋯
A1689	135	13 11 18.17	−1 18 13.0	20.74	19.61	19.24	1.128	0.371	1.158	0.418	⋯
A1689	152	13 11 18.80	−1 19 03.9	20.50	19.21	18.76	1.296	0.448	1.309	0.440	⋯
A1689	160	13 11 19.06	−1 21 28.8	20.05	19.53	19.27	0.516	0.264	0.477	0.257	⋯

Note. Column 1: galaxy cluster. Column 2: object ID. Columns 3–4: R.A. in hours, minutes, and seconds, decl. in degrees, arcminutes, and arcsec. Positions are consistent with USNO (Monet et al. 1998), with an rms scatter of $\approx 0\buildrel{\prime\prime}\over{.} 5$. Columns 5–7: total magnitudes in $g^{\prime}$, $r^{\prime}$, and $i^{\prime}$. Columns 8–9: colors derived from the total magnitudes. Columns 10–11: colors derived from aperture magnitudes. Column 12: adopted Sérsic indices from Houghton et al. (2012) used for sample selection (see text).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 8 includes only the spectroscopic samples. Photometry used for the sample selection described in Section 4.1 covers to $g^{\prime} \approx 25$ mag in Abell 1689 and RXJ0056.6+2622 and $r^{\prime} \approx 25.5$ mag in RXJ0027.6+2616 and RXJ1347.5–1145. Figures 14–17 show the spectroscopic samples overlaid on gray-scale images of the clusters and with X-ray contours overlaid.

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The photometry from GMOS-N was calibrated using the magnitude zero points and color terms from Jørgensen (2009), while the calibration of the GMOS-S photometry is based on observations of a standard field on the night of the science observations combined with the color terms from the Gemini web page. To achieve internal consistency between the two fields observed in RXJ0056.2+2622, an offset of 0.095 mag was added to the $i^{\prime}$-band magnitudes for galaxies in field 1 (F1 in Table 7). In addition, we used SDSS DR12 for external comparison and, in some cases, calibration of our magnitude zero points. This was done consistently for the full GCP sample of 14 clusters (and one field that is not a cluster). Based on this comparison, the Abell 1689 $r^{\prime}$- and $i^{\prime}$-band magnitudes were offset with −0.147 and −0.117, respectively. We will describe the calibration of the full GCP sample in detail in I. Jørgensen et al. (2017, in preparation).

The GMOS-N data of Abell 1689 were also processed by Houghton et al. (2012). We compared our photometry in $g^{\prime}$ and $r^{\prime}$ for Abell 1689 with that from Houghton et al. These authors used slightly different zero points than those used in this paper and may not have used any color terms in their calibration. They did not publish photometry in the $i^{\prime}$ band. While Houghton et al. used the same spectroscopic ID numbering as we do (the numbering originates from our original mask design), there is some confusion in both the published tables and the VizieR catalog version of Houghton et al.'s data. It also appears that for the slitlet containing both ID 584 and ID 615, Houghton et al. extracted only ID 615 but by mistake assigned the spectrum to ID 584. In Table 9, we list our unique IDs, together with the Houghton et al. photometry IDs and the coordinates for the galaxies in question. We take the correct numbering into account in our comparisons.

Figure 18 and Table 10 summarize the comparisons of the $r^{\prime}$-band total magnitudes and the aperture colors $(g^{\prime} -r^{\prime} )$ with the data from Houghton et al. The majority of the galaxies with absolute differences larger than 0.5 mag are located in the center of the cluster. Omitting these galaxies from the comparisons reduces the scatter but does not significantly affect the median differences (see Table 10). Only two of those galaxies are in the spectroscopic sample: ID 636 and ID 655. An offset in the total magnitudes of −0.07 is expected due to the difference in adopted zero points for the standard calibration. An offset in $(g^{\prime} -r^{\prime} )$ of 0.17 is expected due to the difference in adopted zero points and the use of a color term in our calibration. The remainder of the offset may be due to the difference in the aperture sizes. We use an aperture size of 435, while Houghton et al. used 29. However, we do not convolve the $g^{\prime}$ band to the $r^{\prime}$-band resolution, since our main color determination comes from the total magnitudes.

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Table 10.  Abell 1689: Comparison with Houghton et al.

Parameter	Δ	rms	N
$r^{\prime}$	−0.05	0.41	471
$r^{\prime}$ a	−0.05	0.14	434
$(g^{\prime} -r^{\prime} )$	0.24	0.21	471
$(g^{\prime} -r^{\prime} )$ a	0.25	0.16	434
Redshift	−0.0001	0.0001	71
$\mathrm{log}\sigma$	−0.047	0.160	71
$\mathrm{log}\sigma$ b	−0.051	0.061	64

Notes. Median differences Δ = "our data"—"Houghton et al."

^aExcluding galaxies for which the $r^{\prime}$-band magnitudes from Houghton et al. deviate more than 0.5 mag from our determination. ^bExcluding galaxies for which Houghton et al. found velocity dispersions less than $75\,\mathrm{km}\,{{\rm{s}}}^{-1}$.

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The selection criteria for the spectroscopic samples are summarized in Table 11. The spectroscopic data were processed using the same techniques as described for the MS0451.6–0306 data in Jørgensen & Chiboucas (2013). The processing produces one-dimensional spectra fully calibrated and on a relative flux scale.

Table 11.  Selection Criteria for Spectroscopic Samples in the $z=0.18\mbox{--}0.45$ Clusters

Cluster	Obj. Class	Selection Criteria
Abell 1689	1	Confirmed member based on redshift $\wedge \,17\leqslant g^{\prime} \leqslant 21.2\,\wedge \,0.9\leqslant (g^{\prime} -r^{\prime} )\leqslant 1.5\,\wedge \,0.25\leqslant (r^{\prime} -i^{\prime} )\leqslant 0.6$
	2	No redshift $\wedge \,17\leqslant g^{\prime} \leqslant 21.2\,\wedge \,0.9\leqslant (g^{\prime} -r^{\prime} )\leqslant 1.5\,\wedge \,0.25\leqslant (r^{\prime} -i^{\prime} )\leqslant 0.6$
	3	$21.1\lt g^{\prime} \leqslant 22.2\,\wedge \,0.9\leqslant (g^{\prime} -r^{\prime} )\leqslant 1.5\,\wedge \,0.25\leqslant (r^{\prime} -i^{\prime} )\leqslant 0.6$
	4	$18\leqslant g^{\prime} \leqslant 22.2\,\wedge \,0.0\leqslant (g^{\prime} -r^{\prime} )\lt 0.9$
RXJ0056.2+2622	1	Confirmed member based on redshift $\wedge \,17\leqslant g^{\prime} \leqslant 21.2\,\wedge \,0.8\leqslant (g^{\prime} -r^{\prime} )\leqslant 1.4\,\wedge \,0.2\leqslant (r^{\prime} -i^{\prime} )\leqslant 0.55$
	2	No redshift $\wedge \,17\leqslant g^{\prime} \leqslant 21.2\,\wedge \,0.8\leqslant (g^{\prime} -r^{\prime} )\leqslant 1.4\,\wedge \,0.2\leqslant (r^{\prime} -i^{\prime} )\leqslant 0.55$
	3	$21.1\lt g^{\prime} \leqslant 22.2\,\wedge \,0.8\leqslant (g^{\prime} -r^{\prime} )\leqslant 1.4\,\wedge \,0.2\leqslant (r^{\prime} -i^{\prime} )\leqslant 0.55$
	4	$20\leqslant g^{\prime} \leqslant 22.2\,\wedge \,0.0\leqslant (g^{\prime} -r^{\prime} )\lt 0.8$
RXJ0027.6+2616	1	$18\leqslant r^{\prime} \leqslant 20.1\,\wedge \,0.4\leqslant (r^{\prime} -i^{\prime} )\leqslant 0.8\,\wedge \,1.5\leqslant (g^{\prime} -r^{\prime} )\leqslant 1.9$
	2	$20.1\lt r^{\prime} \leqslant 20.7\,\wedge \,0.4\leqslant (r^{\prime} -i^{\prime} )\leqslant 0.8\,\wedge \,1.5\leqslant (g^{\prime} -r^{\prime} )\leqslant 1.9$
	3	$20.7\lt r^{\prime} \leqslant 21.5\,\wedge \,0.4\leqslant (r^{\prime} -i^{\prime} )\leqslant 0.8\,\wedge \,1.5\leqslant (g^{\prime} -r^{\prime} )\leqslant 1.9$
	4	$18\lt r^{\prime} \leqslant 21.5\,\wedge \,0.1\leqslant (r^{\prime} -i^{\prime} )\lt 0.4$
RXJ1347.5–1145a	1	Confirmed member based on redshift $\,\wedge 18\leqslant r^{\prime} \leqslant 21\,\wedge \,0.6\leqslant (r^{\prime} -i^{\prime} )\leqslant 0.9$
	2	Confirmed member based on redshift $\,\wedge 21\lt r^{\prime} \leqslant 22.4\,\wedge \,0.6\leqslant (r^{\prime} -i^{\prime} )\leqslant 0.9$
	3	No redshift $\,\wedge 18\leqslant r^{\prime} \leqslant 22.4\wedge \,0.6\leqslant (r^{\prime} -i^{\prime} )\leqslant 0.9$
	4	$19\leqslant i^{\prime} \lt 22.4\,\wedge \,0.2\leqslant (r^{\prime} -i^{\prime} )\lt 0.6$

Notes.

^aAt the time of sample selection, only imaging in $r^{\prime}$ and $i^{\prime}$ was available.

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The masks for Abell 1689 contained slits tilted to be aligned with the major axis of the galaxies. As we want to subtract the sky signal before we interpolate the spectra, the tilted slits in the Abell 1689 data were first semi-rectified by oversampling the spectra by a factor of five and then shifting the spectra by integer rows in the oversampled spectra. The sky signal was then subtracted and the rows shifted back to their original position before processing the data through the remainder of the steps. See Barr et al. (2005) for details on this process.

The observations of Abell 1689 were obtained with the detectors unbinned, while all other observations used binning in the spectral direction. These unbinned observations unnecessarily oversample the spectra. Thus, after basic processing and extraction, the Abell 1689 observations were rebinned to match the binning of the other observations.

For RXJ0027.6+2616 and RXJ1347.5–1145, two blue stars were included in the mask in order to obtain a good correction for the telluric absorption lines. The masks for Abell 1689 and RXJ0056.2+2622 did not include blue stars. Instead, the telluric correction was established from a stack of all of the spectra in each mask. This is the same technique used by Barr et al. (2005) for the GCP cluster RXJ0142.0+2131.

The observations of RXJ1347.5–1145 were obtained with GMOS-S with the E2V CCDs. These detectors have fairly strong fringing in the red. Therefore, the observations were obtained in pairs of exposures with dithers along the slit. We used these to determine the fringe correction in a similar way as for RXJ0152.7–1157 (see Jørgensen et al. 2005). Two frames were excluded from further processing at this point, as the fringes were too strong to allow a useful correction and the stack of better-reduced frames gave sufficient S/N for our purpose.

All flux-calibrated one-dimensional spectra were median-filtered with a 5-pixel filter in the spectral direction to limit the effect of residuals from the sky subtraction. The filtering was taken into account in the determination of the instrumental resolution.

The calibrated spectra were fit with stellar templates as described in Jørgensen & Chiboucas (2013). This results in determination of the redshifts and velocity dispersions. As in Jørgensen and Chiboucas, we used three template stars with spectral types K0III, G1V, and B8V. The fits were performed with the kinematics fitting software made available by Karl Gebhardt; see Gebhardt et al. (2000, 2003) for a description of the software. The software performs the fitting in pixel space. Thus, it is straightforward to mask wavelength intervals affected by either emission lines or strong residuals from the sky subtraction. In particular, the residuals from the strong sky line at 5577 Å were masked in all cases. For all four clusters, the fits were done for the wavelength region 3750–5500 Å in the rest frame of the clusters. Aperture correction of the velocity dispersions was performed using the technique from Jørgensen et al. (1995b).

The strengths of the absorption lines were measured using the definitions of the Lick/IDS indices (Worthey et al. 1994), as well as the higher-order Balmer line indices ${\rm{H}}{\delta }_{A}$ and ${\rm{H}}{\gamma }_{A}$ (Worthey & Ottaviani 1997). We measured the ${\rm{H}}{\beta }_{G}$ index as described in Jørgensen (1999). The original passband definition for this index is from González (1993). The indices CN3883 and CaHK were measured using the passband definitions from Davidge & Clark (1994). The definition of the D4000 index is from Bruzual (1983) and Gorgas et al. (1999). We have adopted the passband definition for the higher-order Balmer line ${\rm{H}}{\zeta }_{A}$ from Nantais et al. (2013).

The line indices were aperture-corrected and corrected for the velocity dispersions of the galaxies using the techniques and corrections detailed in Jørgensen et al. (2005; see also Jørgensen & Chiboucas 2013). As in Jørgensen et al. (2014), we assume that ${\rm{H}}{\zeta }_{A}$ has no aperture correction.

The residuals from the strong sky line at 5577 Å in some cases affect the determination of the line indices. Where such effects are significant, the line index determinations have been removed from the tables of our measurements. The details are as follows. For members of Abell 1689 and RXJ0056.2+2622, the 5577 Å sky line falls within the passbands of C4668. The passbands of this index are fairly wide. We have therefore evaluated whether the C4668 measurements are affected by the 5577 Å residuals by interpolating across the wavelength region that may be affected (5565–5589 Å) and repeating the line measurement on the interpolated spectra. For those galaxies where the difference in C4668 derived from the spectra before interpolation and after is larger than 0.065 in log space (approximately twice the typical measurement uncertainty), we have deemed the index unreliable and omitted the measurements from the tables and analysis.

For members of RXJ0027.6+2616, the sky line falls within the passbands of the ${\rm{H}}{\delta }_{A}$ index. As the line is fairly weak and the passbands narrow, we have chosen not to attempt to measure this line. Since we want to use the combination index $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$ ≡ −2.5 log ($1.-({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})$/(43.75+38.75))(Kuntschner 2000) in the analysis, we solve this problem by deriving an empirical relation between fully corrected measurements of ${\rm{H}}{\delta }_{A}$ and ${\rm{H}}{\gamma }_{A}$ based on the data for the 94 members of the clusters MS0451.6–0305, RXJ0152.7–1357, and RXJ1226.9+2226. We find ${\rm{H}}{\delta }_{A,\mathrm{cor}}=(0.689\pm 0.045){\rm{H}}{\gamma }_{A,\mathrm{cor}}+2.707$ with an rms scatter of 1 Å. We then use that relation to derive ${\rm{H}}{\delta }_{A}$ for the RXJ0027.6+2616 galaxies and subsequently use those values together with the ${\rm{H}}{\gamma }_{A}$ measurements to derive $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$. This, in effect, means that $({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$ for this cluster is based on ${\rm{H}}{\gamma }_{A}$ only.

For members of RXJ1347.5+1145, the indices ${\rm{H}}{\zeta }_{A}$, CN3883, and D4000 may be affected by the residuals from the 5577 Å sky line. As ${\rm{H}}{\zeta }_{A}$ is a fairly weak index and the passbands are narrow, we have chosen not to attempt to measure this line if the 5577 Å line is within 3 Å of any of the passbands for the individual galaxy redshift. For CN3883 and D4000, we take the same approach as used for C4668 for the Abell 1689 and RXJ0056.2+2622 members. We use limits of 0.025 and 0.035 for changes in CN3883 and D4000, respectively. Thus, these indices are only listed for galaxies for which the measurements are not significantly affected by the sky residuals.

The formal uncertainties on the indices were determined based on the S/N following Cardiel et al. (1998). However, as in Jørgensen & Chiboucas (2013) for the $z=0.54\mbox{--}0.89$ clusters, we also performed substacking of the frames to evaluate the uncertainties (see Appendix B.4 and Table 12).

Table 12.  Internal Comparison

Parameter	A1689					RXJ0027.6+2616					RXJ1347.5–1145
	N	rms	Ratio	${\sigma }_{\mathrm{median}}$	${\sigma }_{\mathrm{adopt}}$	N	rms	Ratio	${\sigma }_{\mathrm{median}}$	${\sigma }_{\mathrm{adopt}}$	N	rms	Ratio	${\sigma }_{\mathrm{median}}$	${\sigma }_{\mathrm{adopt}}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)
$\mathrm{log}\sigma$	19	0.064	1.5	0.014	0.020	17	0.064	1.4	0.024	0.035	15	0.072	1.2	0.030	0.036
CN3883	15	0.048	4.4	0.006	0.028	15	0.033	1.9	0.008	0.016	11	0.065	3.5	0.010	0.036
$({\rm{H}}{\delta }_{A}+{\rm{H}}{\gamma }_{A})^{\prime}$	19	0.013	4.0	0.001	0.006	16	0.018	4.0	0.001	0.006	15	0.031	3.7	0.004	0.016
$\mathrm{logFe}4383$	17	0.117	3.7	0.010	0.036	15	0.089	2.7	0.014	0.038	12	0.233	2.7	0.033	0.090
$\mathrm{logC}4668$	8	0.188	6.4	0.006	0.036	15	0.092	3.5	0.008	0.030	11	0.275	4.6	0.023	0.105
CN2	19	0.025	5.9	0.003	0.016	16	0.029	4.9	0.003	0.017	15	0.051	4.1	0.007	0.029
$\mathrm{logCaHK}$	17	0.060	4.6	0.004	0.020	17	0.074	4.2	0.006	0.027	15	0.083	2.7	0.013	0.034
D4000	14	0.064	9.7	0.004	0.037	14	0.065	6.7	0.005	0.032	10	0.091	7.9	0.007	0.054
$\mathrm{logG}4300$	18	0.063	3.4	0.006	0.020	15	0.063	3.3	0.008	0.028	13	0.184	3.3	0.019	0.061
log ${{\rm{H}}}_{\beta }$	17	0.066	7.1	0.004	0.030	14	0.098	7.9	0.005	0.042	12	0.071	2.5	0.014	0.035
log Mgb	18	0.040	4.4	0.004	0.016	16	0.051	4.1	0.004	0.018	13	0.108	2.7	0.016	0.043
log $\langle \mathrm{Fe}\rangle$	17	0.122	10.5	0.004	0.040	16	0.080	4.9	0.006	0.031	12	0.125	2.9	0.014	0.041

Note. Column 1: parameter. Columns 2–6: for Abell 1689, number of galaxies in comparison, rms scatter of comparison, ratio between the rms scatter and the expected scatter based on nominal individual uncertainties, median of nominal individual uncertainties for all cluster members included in the analysis, and adopted uncertainty on the parameter (except for the velocity dispersion, we use the individual uncertainties from the kinematics fitting). Columns 7–11: same information for RXJ0027.6+2616. Columns 12–16: same information for RXJ1347.5–1145.

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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 $\sigma =1.5\mbox{--}2.5\,\mathring{\rm A}$ (FWHM = 3.5–5.8 Å) and galaxy velocity dispersions typically $\geqslant 100\,\mathrm{km}\,{{\rm{s}}}^{-1}$, the doublet is not resolved in our spectra, and we refer to it simply as the "[O ii] line."

Table 13 lists the results from the template fitting (redshifts and velocity dispersions), while Table 14 gives the derived absorption-line strengths. The emission-line equivalent widths are listed in Table 15.

Table 13.  Results from Template Fitting

Cluster	ID	Redshift	Membera	$\mathrm{log}\,\sigma$	$\mathrm{log}\,{\sigma }_{\mathrm{cor}}$ b	${\sigma }_{\mathrm{log}\sigma }$	Template Fractions			${\chi }^{2}$	S/Nc
							B8V	G1V	K0III
A1689	14	0.1894	1	2.003	1.956	0.001	0.00	0.57	0.43	3.5	142
A1689	15	0.1791	1	2.264	2.247	0.014	0.00	0.41	0.59	18.8	247
A1689	30	0.1893	1	2.112	2.078	0.028	0.00	0.76	0.24	10.7	264
A1689	45	0.1841	1	1.994	1.945	0.003	0.00	0.68	0.32	7.1	130
A1689	70	0.1886	1	2.074	2.036	0.040	0.00	0.48	0.52	5.9	197
A1689	74	0.1929	1	2.167	2.139	0.029	0.00	0.62	0.38	13.7	180
A1689	91	0.1943	1	2.127	2.095	0.011	0.00	0.76	0.24	6.1	82
A1689	135	0.1867	1	1.994	1.946	0.029	0.00	0.58	0.42	3.7	126
A1689	152	0.1879	1	2.068	2.029	0.030	0.00	0.44	0.56	11.3	215
A1689	160	0.0817	0	⋯	⋯	⋯	⋯	⋯	⋯	⋯	56

Note.

^aAdopted membership. 1: galaxy is a member of the cluster. 0: galaxy is not a member of the cluster. ^bVelocity dispersions corrected to a standard size aperture equivalent to a circular aperture with diameter of 3 4 at the distance of the Coma cluster and corrected for systematic effects using Equation (3). ^cS/N per Å in the rest frame of the galaxy. The wavelength interval 4100–5500 Å was used for all galaxies.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 14.  Line Indices for Cluster Members

Cluster/ID	H${\zeta }_{A}$	CN3883	CaHK	D4000	H${\delta }_{A}$	CN1	CN2	G4300	H${\gamma }_{A}$	Fe4383	C4668	Hβ	H${\beta }_{{\rm{G}}}$	Mgb	Fe5270	Fe5335
A1689:
14	⋯	⋯	⋯	⋯	3.17	⋯	⋯	4.95	−4.14	4.48	7.04	⋯	⋯	3.43	3.54	2.65
14	⋯	⋯	⋯	⋯	0.13	⋯	⋯	0.10	0.11	0.13	0.12	⋯	⋯	0.05	0.05	0.05
15	0.72	0.269	23.42	2.084	−2.49	0.126	0.149	5.70	−6.24	4.39	6.02	1.75	1.92	4.59	2.55	3.25
15	0.13	0.005	0.20	0.003	0.08	0.002	0.002	0.06	0.07	0.08	0.07	0.03	0.02	0.03	0.03	0.03
30	⋯	⋯	⋯	⋯	−0.12	⋯	0.030	4.98	−4.37	4.39	⋯	2.06	2.22	3.62	3.00	2.28
30	⋯	⋯	⋯	⋯	0.07	⋯	0.002	0.05	0.06	0.07	⋯	0.03	0.02	0.03	0.03	0.03
45	0.72	0.151	16.27	1.630	−0.83	0.046	0.069	4.82	−4.73	2.74	4.90	0.77	0.83	3.33	2.10	2.90
45	0.19	0.007	0.39	0.004	0.15	0.004	0.005	0.12	0.13	0.16	0.14	0.05	0.04	0.05	0.05	0.06
70	3.00	0.238	26.56	2.124	−1.48	0.083	0.107	5.20	−4.49	4.90	6.02	2.21	2.66	3.91	3.36	2.78
70	0.15	0.007	0.26	0.004	0.11	0.003	0.003	0.08	0.08	0.09	0.09	0.03	0.02	0.03	0.04	0.04
74	2.57	0.238	23.37	2.316	−0.83	0.050	0.098	5.60	−5.90	5.12	6.00	2.18	2.29	4.80	3.06	2.67
74	0.19	0.008	0.33	0.006	0.13	0.003	0.004	0.08	0.09	0.11	0.10	0.04	0.02	0.04	0.04	0.04
91	3.22	0.109	22.30	2.244	−0.62	0.023	0.060	5.72	−6.25	5.28	6.06	1.74	1.78	3.92	3.51	2.35
91	0.33	0.016	0.63	0.011	0.24	0.006	0.007	0.19	0.21	0.24	0.22	0.08	0.05	0.08	0.08	0.09
135	1.27	0.120	21.00	1.878	−1.04	0.021	0.043	5.51	−4.75	4.35	5.52	1.97	2.34	3.96	2.34	3.32
135	0.22	0.009	0.42	0.005	0.16	0.004	0.004	0.11	0.12	0.14	0.13	0.05	0.03	0.05	0.05	0.06
152	1.28	0.219	21.18	1.757	−1.99	0.078	0.105	6.31	−5.33	4.84	⋯	1.76	2.05	4.30	3.25	2.67
152	0.14	0.005	0.26	0.003	0.11	0.003	0.003	0.07	0.08	0.09	⋯	0.03	0.02	0.03	0.03	0.04
217	1.15	0.217	22.64	2.207	−1.65	0.039	0.070	5.89	−6.21	3.95	6.41	1.79	2.01	4.51	2.54	2.47
217	0.13	0.005	0.20	0.003	0.08	0.002	0.002	0.06	0.07	0.08	0.07	0.03	0.02	0.03	0.03	0.03

Note. The indices have been corrected for galaxy velocity dispersion and aperture-corrected. Table 14 is published in its entirety in the machine-readable format. In the portion shown here for guidance regarding its form and content, the lines are wrapped such that the second line for each galaxy lists the uncertainties.

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Table 15.  Equivalent Widths of [O ii] for Cluster Members

Cluster	ID	EW [O ii]	${\sigma }_{\mathrm{EW}[{\rm{O}}{\rm{II}}]}$
A1689	368	6.6	1.1
A1689	508	10.6	2.3
A1689	724	24.1	2.2
A1689	752	6.3	1.2
A1689	814	5.8	0.4
A1689	906	7.6	1.7
A1689	972	6.2	0.3
A1689	1013	36.1	0.7
RXJ0056.2+2622	323	8.7	1.2
RXJ0056.2+2622	1054	30.9	1.5
RXJ0056.2+2622	1256	29.6	4.8
RXJ0056.2+2622	1391	91.5	12.3
RXJ0027.6+2616	1	8.2	0.4
RXJ0027.6+2616	760	3.9	0.4
RXJ0027.6+2616	841	30.6	3.7
RXJ0027.6+2616	1081	5.4	0.8
RXJ1347.5–1145	195	4.7	0.4
RXJ1347.5–1145	436	103.4	3.4

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As in Jørgensen & Chiboucas (2013), we performed simulations to evaluate any systematic effects on the derived velocity dispersions. Model spectra were constructed using the average of the K0III and G1V template stars. Random noise was then added using information from the real noise spectra. We made 100 realizations of each of the combinations covering velocity dispersions from 50 to $300\,\mathrm{km}\,{{\rm{s}}}^{-1}$ and S/N per Å in the rest frame from 10 to 50. The S/Ns of our data are generally higher than 50, but it turns out that only for the very low S/N is the S/N a factor in recovering the velocity dispersion. We then fit the model spectra and compared the recovered velocity dispersions with the input values. The simulations are summarized in Figure 19. Simulations were run for all four clusters, as the locations of the higher noise wavelength intervals due to sky lines depend on the redshift of the cluster. As can be seen from the figure, in all cases, there is a small systematic offset to higher velocity dispersion. We correct for this by fitting a first-order polynomial to the difference as a function of output velocity dispersion, constraining the fits to $\mathrm{log}\sigma \gt 1.9$. The simulations for Abell 1689 and RXJ0056.2+2622 are nearly identical. Thus, we fit those simulations together and derive

$$\begin{eqnarray}&&\mathrm{log}{\sigma }_{\mathrm{corrected}}=\mathrm{log}{\sigma }_{\mathrm{out}}-0.0519+0.1142(\mathrm{log}{\sigma }_{\mathrm{out}}-2.1).\end{eqnarray} \tag{ 3 }$$

The simulations for RXJ0027.6+2616 and RXJ1347.5–1145 are different with at most 0.003 for $\mathrm{log}\sigma \geqslant 2.0$. Thus, we also fit these simulations together and derive

$$\begin{eqnarray}&&\mathrm{log}{\sigma }_{\mathrm{corrected}}=\mathrm{log}{\sigma }_{\mathrm{out}}-0.0690+0.2407(\mathrm{log}{\sigma }_{\mathrm{out}}-2.1).\end{eqnarray} \tag{ 4 }$$

The fits were derived for input velocity dispersions of $\mathrm{log}\sigma \gt 1.9$. Deviations from the fits for velocity dispersions smaller than this limit are of the order 0.01–0.05 on $\mathrm{log}\sigma$.

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As the size of the systematic effects in the determination of the velocity dispersions is the same or larger than the systematic errors expected between different data sets, we choose to correct the derived velocity dispersions using the formulae in Equations (3) and (4). The velocity dispersions listed in Table 13 as $\mathrm{log}{\sigma }_{\mathrm{cor}}$ have been corrected for this effect, as well as aperture-corrected. The raw measurements are listed in the tables as $\mathrm{log}\sigma$.

The mask designs for Abell 1689, RXJ0027.6+2616, and RXJ1347.5–1145 are such that for each cluster, 15–19 of the galaxies were observed in two masks, each with sufficient S/N to derive velocity dispersions and line indices. Thus, we effectively have repeat observations of these galaxies and use them for internal comparisons of the parameters and to assess the uncertainties. Figure 20 and Table 12 summarize the comparisons. In general, the uncertainties on the velocity dispersions from the kinematics fitting are in good agreement with the internal comparisons. For the line indices, the uncertainties derived from the S/N of the spectra are underestimated, most likely due to systematics from the sky subtraction, as we also noted in Jørgensen & Chiboucas (2013). The ratios of the scatter in the comparisons and the expected scatter based on the uncertainties range between 2 and 10. We therefore adopt global uncertainties on the line indices. The adopted uncertainties are listed in Table 12 and shown in the figures of these parameters as typical error bars. The uncertainties for the RXJ0056.2+2622 measurements are assumed to be the same as those for the Abell 1689 measurements, as the two clusters have similar redshifts and were observed with identical instrument configurations and to similar S/N.

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In this section, we compare our redshifts and velocity dispersions to those published by Houghton et al. (2012). We converted the relative radial velocities published by Houghton et al. to redshift using the cluster redshift of 0.183 assumed by Houghton et al. Figure 21 and Table 10 summarize the comparisons. The very small difference in redshifts may originate from the accuracy of the cluster redshift stated by Houghton et al. and is, in any case, of no importance for our results. The offset between the velocity dispersions is −0.05 in $\mathrm{log}\sigma$, with our measurements being smaller. Houghton et al. used a 1 4 extraction aperture, while we use 2 0. However, adopting the aperture correction from Jørgensen et al. (1995b) would only explain an offset of 0.003 in $\mathrm{log}\sigma$. Houghton et al. used the arc spectra for determining the instrumental resolution and stated this as $\approx 75\,\mathrm{km}\,{{\rm{s}}}^{-1}$ at 5000 Å (equivalent to $\approx 70\,\mathrm{km}\,{{\rm{s}}}^{-1}$ at 4500 Å in the rest frame of the cluster). We measure the instrumental resolution from sky spectra stacked the same way as the galaxy spectra and find $\approx 85\,\mathrm{km}\,{{\rm{s}}}^{-1}$ at 4500 Å in the rest frame of the cluster. Thus, a systematic difference is expected of −0.03 to −0.01 on $\mathrm{log}\sigma$ for galaxies with $\sigma =100\,$ and $200\,\mathrm{km}\,{{\rm{s}}}^{-1}$, respectively. The remainder of the difference between the two sets of measurements is most likely due to differences in the choice of template spectra. The scatter in the comparison confirms our estimates of the random measurement uncertainties on $\mathrm{log}\sigma$ of 0.02 for the highest velocity dispersion galaxies, rising to 0.04 for the lower velocity dispersion galaxies.

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