RX J0848.6+4453: THE EVOLUTION OF GALAXY SIZES AND STELLAR POPULATIONS IN A z = 1.27 CLUSTER

Ground-based imaging of RX J0848.6+4453 was obtained primarily to show the performance gain provided by replacing the original E2V CCDs in GMOS-N with E2V DD CCDs. This replacement was done in 2011 October. Imaging of RX J0848.6+4453 was obtained with the original E2V CCDs in 2011 October and repeated with the E2V DD CCDs in 2011 November (Table 1). For the results presented in this paper we made use of the imaging for the mask designs for the spectroscopy and to illustrate the spectroscopic sample (Figure 1). The imaging was done in the z' filter. For the observations with the original E2V CCDs the total exposure time was 60 minutes (obtained as 12 five-minute exposures) and the co-added image had an image quality of FWHM = 052 measured from point sources in the field. For the E2V DD CCDs a total exposure time of 55 minutes was obtained and the resulting image quality was FWHM = 051. As HST/ACS imaging in two filters is available for all galaxies in the spectroscopic sample, no other use is made of the ground-based imaging.

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Table 2 summarizes the HST/ACS data for the two fields used in this paper. Data are also available for a third field, covering Lynx E. However, as none of our spectroscopic sample galaxies are within that field, these data are not used in the present paper. We also do not use the shallower imaging obtained for HST program ID 10496.

The HST/ACS data were processed as described in Chiboucas et al. (2009), using the drizzle technique (Fruchter & Hook 2002). The images were then processed with SExtractor (Bertin & Arnouts 1996). Total magnitudes z_{tot, 850} were derived from the F850LP imaging. Aperture colors (i₇₇₅ − z₈₅₀) were derived within an aperture with a diameter of 05. We used GALFIT (Peng et al. 2002) to fit r^1/4 profiles and Sérsic (1968) profiles to the galaxies in the spectroscopic sample and derive effective radii, magnitudes, and surface brightnesses. This processing was done for the observations in F850LP only. The effective radii in Table 10 are derived from the semimajor and semiminor axes as r_e = (a_e b_e)^1/2. The difference between the effective radii derived from the fits with the r^1/4 profiles and Sérsic profiles as expected correlates with the Sérsic index; see details in Appendix A. The median uncertainty on the Sérsic index is 0.1, with a few values up to 0.7 for galaxies with Best-fit indices larger than 4. As the Sérsic fits and indices in this paper are used primarily for selection of the bulge-dominated galaxies, these uncertainties do not affect our results significantly.

The photometry is calibrated to the AB system using the synthetic zero points for the filters, 25.654 for F775W, 24.862 for F850LP (Sirianni et al. 2005). Galactic reddening in the direction of the cluster is E(B − V) = 0.024 (Schlafly & Finkbeiner 2011), which gives $A_{i_{775}}=0.046$ and $A_{z_{850}}=0.034$. The photometric parameters derived using SExtractor and GALFIT are listed in Appendix A, Table 10.

The photometry was calibrated to rest-frame B band. The calibration was established using stellar population models from Bruzual & Charlot (2003) as described in Jørgensen et al. (2005). The calibration is given in Appendix A.

The spectroscopic observations were obtained in multi-object spectroscopic (MOS) mode with GMOS-N; see Table 1 for the dates of the observations. The sample selection is based on the photometry from the HST/ACS imaging. Figure 2 shows the color–magnitude (CM) relation for the field. Galaxies were selected to maximize the coverage along the red sequence from the brightest cluster galaxy (BCG) to z_{tot, 850} ≈ 24.5 mag. The triple merger (red asterisk in Figure 1), which is considered the BCG, was not included in the observations. This decision was made in part because it would eliminate another known bright cluster member from the mask and in part because the angular separation of the components is only ≈05, making it very difficult to separate them in ground-based spectroscopy obtained in natural seeing. Priority was given to galaxies within 0.1 mag of the CM relation in (i₇₇₅ − z₈₅₀) versus z_{tot, 850}. Additional space in the mask was filled with galaxies with (i₇₇₅ − z₈₅₀) > 0.5 and z_{tot, 850} in the interval from 21 mag to 25 mag. Some of these turned out to be blue cluster members. The spectroscopic sample is marked on Figures 1 and 2. Two blue stars were included in the mask in order to obtain a good correction for the telluric absorption lines. The blue stars are also marked in Figure 1.

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Table 3 gives an overview of the obtained spectroscopic observations, while Table 4 summarizes the instrument parameters for the observations. After the initial observations from program GN-2011B-DD-5, nonmembers identified from those observations were eliminated in the mask made for program GN-2013A-Q-65, and other potential members were included instead using the same selection criteria as used for the original mask.

Table 4. Gemini North Instrumentation for Spectroscopic Observations

Instrument	GMOS-N
CCDs	3 × E2V DD 2048 × 4608
r.o.n.a	(3.17,3.22,3.46) e−
gaina	(2.31,2.27,2.17) e−/ADU
Pixel scale	00727 pixel−1
Field of view	55 × 55
Grating	R400_G5305
Spectroscopic filter	OG515_G0306
Wavelength rangeb	5500–10500 Å

Notes. ^aValues for the three detectors in the array. ^bThe exact wavelength range varies from slitlet to slitlet.

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The spectroscopic observations were processed using the methods described in detail in Jørgensen & Chiboucas (2013). The only exception was the handling of the charge diffusion effect, which for the E2V DD CCDs turns out to have a spatial dependence in addition to variation with wavelength. The adopted correction is described in Appendix B.

The data processing results in one-dimensional spectra calibrated to a relative flux scale. The spectra were used to derive redshifts and, for those targets with sufficient S/N, 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 cluster were fit in the wavelength range 3750–4100 Å. Table 11 in Appendix B gives the results from the template fitting. The velocity dispersions were aperture corrected using the technique from Jørgensen et al. (1995b). Of the 52 targets observed, 24 turned out to be members of the cluster. Of these, 19 have velocity dispersion determined. The median S/N of these is 18 Å⁻¹ in the rest frame (see Table 11 for the S/N of the individual spectra). Velocity dispersions were determined for 10 nonmembers; see Table 11. We assessed the possible systematic errors on the derived velocity dispersions resulting from the determination of the instrumental resolution, the adopted telluric correction, and the sky subtraction. None of these sources cause systematic errors that affect our results significantly; see Appendix B for details.

The spectra allow determination of the following absorption-line indices: CN3883, CaHK, D4000, and Hζ_A. The indices CN3883 and CaHK are defined in Davidge & Clark (1994). For D4000 we use a shorter red passband than usually used (Gorgas et al. 1999) but calibrate our measurements to be consistent with the conventional definition of the index; see Appendix for details. For the high-order Balmer line index Hζ_A we adopt the definition from Nantais et al. (2013). All measured indices are listed in Table 12 in Appendix B.

For galaxies with detectable [O ii] emission the strength of the emission line was determined both as a (relative) flux and as an equivalent width (Table 12). As a result of the very weak continuum of some of the emission-line galaxies, the equivalent widths in some cases have very large uncertainties.

The [O ii] emission makes it possible to determine the star formation rates (SFRs), under the assumption that the line is due to star formation only. We have examined the spectra for the presence of the two neon lines [Ne v] λ3426 and [Ne iii] λ3869. The line [Ne v] λ3346 is at the cluster redshift too close to strong telluric absorption to be reliably detected. These are the only strong lines originating from active galactic nuclei (AGNs) that are in the covered wavelength region (e.g., Schmidt et al. 1998; Mignoli et al. 2013). Only ID 2063 has detectable Ne emission. We proceed to determine the SFR from the [O ii] line and flag ID 2063 in the relevant figures in the analysis of the data.

In the analysis we use our data for the z = 0.5–0.9 clusters published in our previous papers (Jørgensen et al. 2005; Chiboucas et al. 2009; Jørgensen & Chiboucas 2013). These papers present ground-based spectroscopy and HST/ACS imaging of MS 0451.6–0305 (z = 0.54), RX J0152.7–1357 (z = 0.83), and RX J1226.9+3332 (z = 0.89). Further, we use our data for Coma, Perseus, and A194, (Jørgensen et al. 1995a, 1995b; Jørgensen 1999; Jørgensen & Chiboucas 2013) as our z ≈ 0 comparison sample. Table 5 summarizes the cluster properties for all the clusters. The samples in all clusters are selected consistently. Except for MS 0451.6–0305, the passbands used for the determination of the effective parameters correspond roughly to rest-frame B band, as is the case for the RX J0848.6+4453 observations presented in this paper. MS 0451.6–0305 was observed in F814W, which at z = 0.54 is close to rest-frame V band. Thus, if the color gradients in the MS 0451.6–0305 galaxies are similar to those in nearby early-type galaxies, typically Δ(B − V)/Δlog r ≈ −0.04 (e.g., Saglia et al. 2000), then the effective radii derived from F814W can be expected to be about 6% smaller than if derived from a passband matching rest-frame B band for the cluster (Sparks & Jørgensen 1993).

Table 5. Cluster Properties

Cluster	Redshift	σcluster	L500	M500	R500	Nmember
		(km s−1)	(1044 erg s−1)	(1014 M☉)	(Mpc)
(1)	(2)	(3)	(4)	(5)	(6)	(7)
Perseus = A426a	0.0179	$1277_{-78}^{+95}$	6.217	6.151	1.286	63
A194a,b	0.0180	$480_{-38}^{+48}$	0.070	0.398	0.516	17
Coma = A1656a	0.0231	$1010_{-44}^{+51}$	3.456	4.285	1.138	116
MS 0451.6–0305c	0.5398 ± 0.0010	$1450_{-159}^{+105}$	15.352	7.134	1.118	47
RX J0152.7–1357d	0.8350 ± 0.0012	$1110_{-174}^{+147}$	6.291	3.222	0.763	29
RX J1226.9+3332c	0.8908 ± 0.0011	$1298_{-137}^{+122}$	11.253	4.386	0.827	55
RX J0848.6+4443e	1.2701 ± 0.0010	$733_{-85}^{+84}$	1.04	1.37	0.499	24

Notes. Column 1: Galaxy cluster; Column 2: cluster redshift; Column 3: cluster velocity dispersion; Column 4: X-ray luminosity in the 0.1–2.4 keV band within the radius R₅₀₀, from Piffaretti et al. (2011), except for RX J0848.6+4443, for which the data are from Ettori et al. (2004); Column 5: cluster mass derived from X-ray data within the radius R₅₀₀, from Piffaretti et al., except for RX J0848.6+4443, for which the data are from Ettori et al.; Column 6: radius within which the mean overdensity of the cluster is 500 times the critical density at the cluster redshift, from Piffaretti et al., except for RX J0848.6+4443, for which the data are from Ettori et al.; Column 7: number of member galaxies for which spectroscopy is used in this paper. ^aRedshift and velocity dispersion from Zabludoff et al. (1990). ^bA194 does not meet the X-ray luminosity selection criteria of the main cluster sample. ^cRedshifts and velocity dispersions from Jørgensen & Chiboucas (2013). ^dRedshift and velocity dispersion from Jørgensen et al. (2005). The velocity dispersions for the Northern and Southern subclusters are (681 ± 232) km s⁻¹ and (866 ± 266) km s⁻¹, respectively. ^eRedshift and velocity dispersion from this paper.

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Our technique for establishing the scaling relations and associated uncertainties on slopes and zero points is the same as we used in Jørgensen et al. (2005) and Jørgensen & Chiboucas (2013). In summary, we establish the scaling relations using a fitting technique that minimizes the sum of the absolute residuals perpendicular to the relation and determines the zero points as the median. The uncertainties on the slopes are derived using a boot-strap method. The technique is very robust to the effect of outliers. The random uncertainties on the zero-point differences, Δγ, between the intermediate-redshift and low-redshift samples are derived as

$$\begin{equation} \sigma _{\Delta \gamma } = \left({\rm rms}_{{\rm low-}z}^2/N_{{\rm low-}z} + {\rm rms}_{{\rm int-}z}^2/N_{{\rm int-}z} \right)^{0.5}\protect, \protect \end{equation} \tag{ 1 }$$

where subscripts "low-z" and "int-z" refer to the low-redshift sample and one of the intermediate-redshift clusters, respectively. In the presentation of the zero-point differences we show only the random uncertainties. The systematic uncertainties on the zero-point differences are expected to be dominated by the possible inconsistency in the calibration of the velocity dispersions, 0.026 in log σ (cf. Jørgensen et al. 2005), and may be estimated as 0.026 times the coefficient for log σ, or 0.052 times the coefficient for log M.

In the analysis we use spectral energy distributions (SEDs) for single stellar population (SSP) models to derive model values of the absorption-line indices that we are able to determine from the spectra of RX J0848.6+4453. We use the SEDs from Maraston & Strömbäck (2011) for a Salpeter (1955) initial mass function (IMF). In addition, we use mass-to-light (M/L) ratios for very similar models from Maraston (2005).

As in Jørgensen & Chiboucas (2013), we have derived model relations linear in the logarithm of the age and in the metallicity [M/H]. These relations are listed in Table 6 and are used to aid our analysis. In the fits presented here we include the models with age 1 Gyr as our sample includes galaxies with very young stellar populations. The fits in Jørgensen & Chiboucas (2013) were derived excluding these very young models. Thus, the M/L ratio relation in Table 6 differs slightly from the relation given by Jørgensen & Chiboucas.

The simplest models for the evolution of the stellar populations are passive evolution models. In such models it is assumed that after an initial period of star formation the galaxies evolve passively without any additional star formation. The models are usually parameterized by a formation redshift z_form, which corresponds to the approximate epoch of the last major star formation episode. In these models the age difference between galaxies at different redshifts is expected to be equal to the difference in look-back time. Thus, the relations listed in Table 6 enable us for a given z_form to derive the expected offsets for the M/L ratios and the line indices between the high-redshift clusters and our z ≈ 0 comparison sample. Alternatively, we can derive a formation redshift z_form from the measured offsets of the parameters.

The formation redshift may depend on the galaxy properties and/or the properties of the cluster environment (e.g., Thomas et al. 2005). In our analysis we use the model from Thomas et al. for the high-density environment, which prescribes a formation redshift z_form dependent on the velocity dispersion of the galaxy. We convert the velocity dispersion dependency to a mass dependency using an empirical relation between dynamical mass and velocity dispersion (see Jørgensen & Chiboucas 2013).

In our analysis, we implicitly assume that the galaxies we observe in RX J0848.6+4453 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. We return to this issue in Section 6.

The dynamical masses of the galaxies can be determined from the velocity dispersions and effective radii as M = βr_eσ² G⁻¹, with β = 5 (Bender et al. 1992). Cappellari et al. (2006) found from integral-field-unit (IFU) data that this approximation provides a reasonable mass estimate in the absence of observational data like IFU data, which would enable more detailed modeling. These authors also tested the use of a coefficient β dependent on the Sérsic index n_ser. They derived an expression based on a spherical isotropic model

$$\begin{equation} \beta (n_{\rm ser}) = 8.87 - 0.831 n_{\rm ser} +0.0241 n_{\rm ser}^2\protect. \protect \end{equation} \tag{ 2 }$$

Their conclusion is that this expression does not improve the mass estimate over using β = 5, when comparing to the masses derived from their full modeling. Alternatively, van Dokkum et al. (2010) derived a fit to the numerical results from Ciotti (1991) and suggested the expression

$$\begin{equation} \beta (n_{\rm ser}) = 3.316 + 0.026 n_{\rm ser} -0.035 n_{\rm ser}^2 + 0.00172 n_{\rm ser}^3\protect. \protect \end{equation} \tag{ 3 }$$

We note that this expression does not reach β = 5 for any values of n_ser and therefore is not supported by the detailed modeling of IFU data done by Cappellari et al. (2006). In the following we adopt M = 5r_eσ² G⁻¹ for the mass estimates.

Traditionally determination of the SFR from the [O ii] line has been done from the equivalent width, EW[O ii], using the calibrations from Kennicutt (1992) and Gallagher et al. (1989),

$$\begin{equation} {\rm SFR} = 1.4 \times 10^{-41} L({\rm [O\,\scriptsize{II}]})\protect, \protect \end{equation} \tag{ 4 }$$

with the SFR in M_☉ yr⁻¹ and the [O ii] luminosity L([O ii]) in erg s⁻¹ derived from the equivalent width EW[O ii] as

$$\begin{equation} L ({\rm [O\,\scriptsize{II}]}) = 1.4 \times 10^{29} L_B\, {\rm EW}({\rm [O\,\scriptsize{II}]})\protect, \protect \end{equation} \tag{ 5 }$$

where L_B is the luminosity of the galaxy in rest-frame B band in solar units.

As a result of the very faint continuum of most of the star-forming galaxies in our sample, the uncertainty on EW[O ii] is dominated by the uncertainty on the continuum level and is typically 20%–25%, while the direct measurement of the relative [O ii] flux is accurate to 8%–10%. Thus, rather than use EW[O ii] and L_B to derive SFR, we instead opt to use the [O ii] flux directly. One could argue that because of the limited-size spectral aperture and the possible non-photometric conditions during some of the spectroscopic observations, we therefore underestimate the total [O ii] flux. To evaluate the size of this effect, we derived L[O ii] both from EW[O ii] and L_B and directly from the [O ii] flux. The [O ii] flux was converted to L[O ii] using a luminosity distance of the cluster of D_L = 8880.3 Mpc, which corresponds to z = 1.27 for our adopted cosmology. The L[O ii] values from the two methods are compared in Figure 5. The median offset between the two values is Δlog L[O ii] =0.1. Thus, using the [O ii] flux leads to the SFR being underestimated with a similar amount. However, this small offset is of no importance for our analysis, and since the uncertainties on L[O ii] are about half of those for L[O ii] based on the EW[O ii], we have used Equation (4) to derive the SFR.

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In Table 7 we divide the 24 members into subsamples according to available spectroscopic parameters, S/N, Sérsic index, and the strength of the [O ii] emission. Our main sample consists of subsamples 4 and 5, which are the bulge-dominated galaxies with EW[O ii] >5 Å and ≤5 Å, respectively.

For the analysis of the FP and the relations between masses, sizes, and velocity dispersions we concentrate on sample 5, the bulge-dominated galaxies with EW[O ii] ≤5 Å. Except for allowing galaxies with lower S/N spectra as part of the analysis, the selection criteria for sample 5 are the same as used in Jørgensen & Chiboucas (2013), as we will use the results presented in that paper as part of our analysis. We show the bulge-dominated galaxies with EW[O ii] >5 Å (sample 4) in the figures, but they are excluded from the determination of the zero points for the relations. In the discussion of the absorption-line strengths we show samples 4 and 5, as well as the four disk-dominated galaxies from sample 2, in the figures. We also show the disk-dominated galaxies from the z < 1 clusters. However, the relations and zero points are derived from the bulge-dominated galaxies with EW[O ii] ≤5 Å only (sample 5 in RX J0848.6+4453). In the discussion of the SFRs derived from the [O ii] emission all cluster members are included.

Before we proceed, we briefly assess possible selection effects in our RX J0848.6+4453 sample. We first note that our sample covers galaxies with effective radii r_e ≥ 1 kpc. This lower limit is similar to other studies of galaxies at z ≈ 1, in particular the study by Saglia et al. (2010), with which we will compare in our analysis of the data. Within the two HST/ACS fields of RX J0848.6+4453 there are 33 galaxies with z₈₅₀ ≤ 24.5 and within 0.1 mag of the CM relation. We have obtained spectroscopy of 20 of these. The magnitude distribution of the spectroscopically observed galaxies is not significantly different from that of all 33 galaxies as tested with the Kolmogorov–Smirnov test. It is beyond the scope of this paper to determine effective radii and surface brightnesses of all the galaxies not included in the spectroscopic sample. However, the bulge-dominated members, (samples 4 and 5) included in the analysis are distributed in the log r_e–log 〈I〉_e space similarly to our Coma Cluster sample, when the luminosity evolution of −0.769 in log 〈I〉_e is taken into account; see Figure 6. We emphasize that the purpose of this figure is not to determine the luminosity offset for RX J0848.6+4453 relative to the Coma Cluster from this projection of the FP, but only to assess the distributions in log r_e and log 〈I〉_e. In conclusion, there are no obvious selection effects related to sizes, luminosities, or surface brightnesses that may bias our results as presented in the following.

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Figure 7 shows the effective radii and velocity dispersions versus the dynamical masses. The figure shows our data for RX J0848.6+4453 together with our data for the z = 0.5–0.9 clusters and the Coma Cluster sample for effective radii derived from fits with r^1/4 profiles, panels (a) and (b). In panels (c)–(d) and (e)–(f) we show RX J0848.6+4453 together with the z = 0.5–0.9 clusters using Sérsic effective radii derived as r_e = (a_e b_e)^1/2 and r_e = (a_e + b_e)/2, respectively. In all the panels in Figure 7 the fit for the Coma Cluster sample is shown (blue lines), together with the prediction of the location of the RX J0848.6+4453 sample based on the results from Saglia et al. (2010) for dynamical masses (black lines). Table 8 summarizes the zero points for the relations for all the clusters. For RX J0848.6+4453 the zero points are derived from the eight bulge-dominated galaxies with EW[O ii] ≤ 5 Å (sample 5; see Table 7).

As described in Jørgensen & Chiboucas (2013), we found no significant evolution in effective radii or velocity dispersions at a given mass with redshift for the z = 0.5–0.9 clusters. In that paper we used effective radii from r^1/4 profiles. As the only cluster in the sample MS 0451.6–0305 was observed in a passband matching roughly rest-frame V, rather than rest-frame B. As a result of color gradients, this is expected to result in log r_e on average being 0.028 smaller than if measured from a passband matching rest-frame B (cf. Section 2.3). As the dynamical mass also depends on the effective radius, correcting for this effect would change the zero point for the size–mass relations for the cluster with an insignificant amount of −0.012.

Using the r^1/4 effective radii, the offsets for the RX J0848.6+4453 subsample of bulge-dominated EW[O ii] ≤ 5 Å galaxies relative to the Coma Cluster relations are about a third of what is expected based on the results from Saglia et al. Further, the offsets are significant only at the 1σ level. If we use the effective radii from the Sérsic profiles, the offsets relative to the z = 0.5–0.9 clusters are slightly larger, though still only significant at the 1- to 1.5-sigma level. We note that Saglia et al. used effective radii derived as r_e = (a_e + b_e)/2. However, we find no significant difference between using r_e = (a_e b_e)^1/2 and r_e = (a_e + b_e)/2 for our samples.

Concentrating on the results based on the r^1/4 effective radii, we convert the median offsets in radii and velocity dispersions to an estimate of the median change of the dynamical mass, using M = 5r_eσ² G⁻¹. This indicates an insignificant mass change, Δlog M = 0.01 ± 0.11. Taking the uncertainty into account, we can interpret this as an upper limit on the mass increase of ≈23%.

The five bulge-dominated emission-line galaxies (sample 4 in Table 7) show no offsets in effective radii or velocity dispersion relative to the Coma Cluster relations (Figure 7) when using r^1/4 effective radii and also no offsets relative to the z = 0.5–0.9 clusters when using the effective radii based on Sérsic profiles.

Figure 8 shows the FP edge-on for the RX J0848.6+4453 samples 4 and 5 (Table 7), together with our samples for z = 0.5–0.9 clusters and the Coma Cluster samples. In Figure 9 we show the FP as the M/L ratios versus the dynamical masses and the velocity dispersions. Tables 8 and 9 summarize the derived relations and zero points. All results in these two tables relating to only the z = 0.5–0.9 clusters and the Coma Cluster samples are adopted from Jørgensen & Chiboucas (2013) and reproduced here to aid the discussion of the results for the RX J0848.6+4453 sample.

The RX J0848.6+4453 sample appears to follow a steep relation in M/L versus mass and M/L versus velocity dispersion, as is the case for the two highest-redshift clusters RX J0152.7–1357 and RX J1226.9+3332 from Jørgensen & Chiboucas. However, because the sample contains only eight galaxies, it is not possible to determine the slopes of the relations or the coefficients in the FP by fitting only this sample. Instead, we have determined the best-fit relations by fitting parallel relations to the three clusters. Thus, the assumption is that only the zero point varies between these clusters. Table 9 summarizes the derived relations. As the zero points for RX J0152.7–1357 and RX J1226.9+3332 are not significantly different from each other (cf. Jørgensen & Chiboucas 2013), we use their common zero point. We then derive the zero-point difference for RX J0848.6+4453 relative to that, and from there we derive the formation redshift z_form required for the galaxies in RX J0848.6+4453 to evolve passively to the location of the M/L versus mass relation for RX J0152.7–1357 and RX J1226.9+3332. However, the zero-point difference is so small that z_form = ∞ is needed. Thus, we conclude that the location of the M/L versus mass relation for RX J0152.7–1357 and RX J1226.9+3332 cannot be the result of passive evolution of a higher-redshift sample like the RX J0848.6+4453 sample.

The zero-point offset for RX J0848.6+4453 (sample 5) relative to the Coma Cluster sample is consistent with passive evolution and a formation redshift of $z_{\rm form}= 1.95^{+0.22}_{-0.15}$. All eight galaxies in this sample have log M < 11.1. The higher-mass galaxies in the cluster have stronger emission lines and show a much larger scatter around the M/L versus mass relation. We note that the z = 0.5–0.9 clusters contain low-mass galaxies with z_form significantly below 1.95. We return to the discussion of this in Section 6.

In Figure 10 we show the available absorption-line indices versus the velocity dispersions. The figure includes the disk-dominated galaxies from all the clusters. For RX J0848.6+4453 these are the galaxies listed in Table 7 as sample 2. Table 8 lists the relations shown in the figure. The correlation between the Hζ_A indices and the velocity dispersions is only significant for the sample of galaxies in MS 0451.6–0305, for which a Kendall's τ rank-order test gives a probability of 0.7% of no correlation being present. For all the other cluster samples, the probabilities are 22% or larger that there is no correlation. We have therefore established the slope of the relation fitting only the MS 0451.6–0305 sample. For this relation the residuals were minimized in the direction of Hζ_A. The zero points for all the samples were then derived using the slope established from the MS 0451.6–0305 sample.

The correlation between the D4000 indices and the velocity dispersions for the individual clusters is weak. However, a Kendall's τ rank order test for the joint sample of all the galaxies in the z < 1 samples yields a probability of 0.4% of no correlation being present. Thus, we determine the slope by fitting the full sample. After this, we determine the cluster-specific zero points relative to this relation.

The main results we derive from Figure 10 and the relations in Table 8 are (1) the presence of very strong Hζ lines in the RX J0848.6+4453 galaxies compared to the lower-redshift samples, (2) the RX J0848.6+4453 galaxies have significantly weaker CN3883 than found for the lower-redshift samples, and (3) the RX J0848.6+4453 galaxies are not significantly offset in D4000 or CaHK relative to the lower-redshift samples, though the scatter in these indices may be somewhat larger than for the lower-redshift samples. It should be noted that except for CN3883 being weaker in the RX J0848.6+4453 galaxies than in the lower-redshift samples, none of the offsets in D4000, CaHK, and CN3883 between the z = 0.5–1.3 clusters and the low-redshift comparison sample are significant. We return to this in Section 6.

We then investigate whether it is possible to use a combination of indices to estimate ages and metallicities of the galaxies in RX J0848.6+4453. Figure 11 shows the strength of Hζ_A versus CN3883, CaHK, and D4000. The figure also shows model predictions based on the SSP SEDs from Maraston & Strömbäck (2011). These predictions are degenerate in metallicity and age. Thus, we can only approximately estimate the ages of the stellar populations from the indices. The metallicities cannot be constrained beyond noting that owing to the strength of CaHK and CN3883 the metallicities of the RX J0848.6+4453 galaxies must be similar to those of the lower-redshift galaxies, i.e., solar or above solar. The best age estimates come from using Hζ_A versus CN3883. The area in this diagram populated by the RX J0848.6+4453 galaxies (see Figure 11(a)) can only be reached if the stellar population ages are 1–2 Gyr. Only a handful of the z = 0.5–0.9 bulge-dominated galaxies populate the same part of the diagram.

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Figure 12 shows the SFRs derived from the [O ii] emission and the strength of the Hζ line versus the cluster center distance, R_cluster, and versus the dynamical mass. As not all galaxies have determination of the dynamical mass, Figure 12(b) contains fewer points than Figure 12(a). Figures 12(c) and (d) show only galaxies with measurements of Hζ_A, which in particular excludes the three low-mass (M <10^10.5 M_☉) galaxies that are included in Figure 12(b). From Figures 12(a) and (c) we conclude that star-forming galaxies and galaxies with strong Hζ_A are present throughout the cluster. There is no trend in SFR or Hζ_A with R_cluster, and also no radius within which star formation is absent. Figures 12(b) and (d) show that star formation and strong Hζ_A are present in the most massive of the bulge-dominated galaxies. However, the SFR is well below that of galaxies on the star formation "main sequence" (e.g., Wuyts et al. 2011).

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In our study of the massive z = 0.5–0.9 clusters also included in this paper we found no indication of evolution with redshift in sizes or velocity dispersions of the passive bulge-dominated galaxies (Jørgensen & Chiboucas 2013). Our results on RX J0848.6+4453 presented here indicate a very small (1σ) difference between the sizes and velocity dispersions of galaxies at a given mass in this cluster compared to those at z ≈ 0. A similar conclusion regarding the size evolution was reached for 16 galaxies in RX J0848.6+4453 by Saracco et al. (2014), who, using stellar masses, put an upper limit on the size evolution of r_e∝(1 + z)^−0.1 equivalent to ≈8% from z = 1.27 to the present.

Recent studies have addressed the question of the possible environmental dependence of the size and velocity dispersion evolution of galaxies. Several authors have directly compared sizes of passive galaxies in high-density and low-density environments. Lani et al. (2013) find that at z > 1 galaxies in high-density environments are ≈50% larger than those in low-density environments. Delaye et al. (2014) reach a similar conclusion. Converting the Delaye et al. result on size dependences on redshift in the field and in clusters to a difference in sizes at z ≈ 1.3 gives a size difference of ≈30%, with the cluster galaxies being larger. Specifically for clusters Delaye et al. find r_e∝(1 + z)^−0.53 using stellar masses, which is in agreement with the result from Saglia et al. (2010) using dynamical masses for the clusters in the EDisCS survey. At z ≈ 0 any differences in sizes between field and cluster galaxies appear to have disappeared, or at least become undetectable; see Huertas-Company et al. (2013).

In a study of a z ≈ 1.8 cluster, Newman et al. (2014), on the other hand, find no difference between the sizes of the galaxies in that cluster and field galaxies at similar redshifts, thus contradicting the above results and arguing that these other results are due to differences in the morphological mixture of the samples studied.

Of these results, only Saglia et al. (2010) use dynamical masses, and their result is therefore most directly comparable to our result and also the only study that makes it possible to directly compare to our results for the evolution of the velocity dispersion. In Figure 13 we summarize the results as the median offset for each of the z = 0.5–1.3 clusters relative to the location of the Coma Cluster relations. The dashed lines in this figure show the results from Saglia et al. for dynamical masses. The size and velocity dispersion evolution required to bring our RX J0848.6+4453 to the z ≈ 0 location of the relations with mass is only about a third of that found by Saglia et al. Formally the zero-point differences relative to the Coma Cluster sample are only significant at the 1σ level.

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The result from Saglia at al. is corrected for progenitor bias using a method adopted from Valentinuzzi et al. (2010). We have chosen to assess the effect of progenitor bias on our result in an empirical fashion using the information about the Hβ line strength for our Coma Cluster sample to evaluate the ages of galaxies in this sample. Using the model relation between the Hβ line strength, age, metallicity [M/H], and abundance ratio [α/Fe] based on stellar population models from Thomas et al. (2005) and established in Jørgensen & Chiboucas (2013), we can remove galaxies from the Coma Cluster sample too young to have progenitors in our RX J0848.6+4453 sample. The difference in look-back time between the two clusters is 8.3 Gyr for our adopted cosmology. With [M/H] =0.3 and [α/Fe] = 0.3 as typical average values for galaxies in the Coma Cluster sample (see Jørgensen & Chiboucas 2013), we then require log Hβ_G ≤ 0.29 in order for the galaxies to be older than about 8.3 Gyr. Doing so reduces the zero-point difference between the Coma Cluster sample and our sample in RX J0848.6+4453 for the size–mass relation to zero, while the offset for the velocity dispersion–mass relation is 0.011 in log space. These values are shown in Figure 13 as open circles. Thus, the correction for progenitor bias decreases the possible evolution in size and velocity dispersions, as also found by Saglia et al.

Our result for RX J0848.6+4453, combined with our previous results for the massive z = 0.5–0.9 clusters (Jørgensen & Chiboucas 2013; also shown in Figure 13), indicates an even larger difference between the evolution in dense environments and in the field than found by, e.g., Delaye et al. (2014). However, we note that the clusters in our z < 1 sample are significantly more massive than those in the EDisCS sample. Based on models for cluster mass evolution (van den Bosch 2002; see Figure 4), RX J0848.6+4453 is expected to evolve to a similarly massive cluster by the present time. Of the above studies, we can only confirm that Delaye et al. include some similarly massive clusters. Further, our galaxy samples in the clusters are selected consistently based on both morphology n_ser > 1.5 and spectroscopic properties (passive galaxies with EW[O ii] ≤ 5 Å). Therefore, our result cannot be explained as due to a mix-up of sample selections.

We conclude that with homogeneous selection of samples in very massive clusters and use of dynamical galaxy masses, we find a size and velocity dispersion evolution from z ≈ 1.3 to the present of ≈16% and ≈7%, respectively. Both differences are significant only at the 1σ level. Further, the evolution is likely to have completed by z ≈ 0.9. We put an upper limit of 23% on the increase in mass associated with this evolution (see Section 5.1).

Figure 14 summarizes the changes in the M/L ratios and the absorption-line strengths as the zero-point offsets of the z = 0.5–1.3 cluster samples relative to the low-redshift samples. All clusters are shown in these figures. Results for the z = 0.5–0.9 clusters for M/L and CN3883 are adopted from Jørgensen & Chiboucas (2013).

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We compare the zero point for the M/L–mass relation for the RX J0848.6+4453 bulge-dominated galaxies with EW[O ii] ≤5 Å to that of the Coma Cluster sample. The difference is consistent with passive evolution and a formation redshift of $z_{\rm form}=1.95^{+0.22}_{-0.15}$. This is higher than for the z = 0.5–0.9 clusters (Jørgensen & Chiboucas 2013; see also Figure 14(a)), for which we found z_form ≈ 1.4. The difference becomes even larger, when considering that the eight passive galaxies in our RX J0848.6+4453 all have masses below 10^11.1 M_☉. For similar low-mass galaxies in the z = 0.5–0.9 clusters the formation redshift is ≈1.2 (blue points in Figure 14(a)).

We speculate that the reason for this difference is that a large fraction of the low-mass galaxies in z = 0.5–0.9 clusters have entered the passive bulge-dominated population more recently than z ≈ 1.3. Thus, the difference is due to a progenitor bias. The RX J0848.6+4453 sample does not include the progenitors of those young bulge-dominated galaxies in the z = 0.5–0.9 clusters, as such progenitors observed at z ≈ 1.3 would have very strong star formation and may also not yet be bulge dominated. This conclusion is similar to that reached by Sánchez-Blázquez et al. (2009), who argue that 50% of the low-mass galaxies on the red sequence at low redshift have entered the red sequence recently.

Turning to the strength of the Hζ line, our results support the idea that RX J0848.6+4453 experienced a major episode of star formation 1–2 Gyr prior, consistent with z_form = 1.95. The strengths of Hζ seen in the RX J0848.6+4453 galaxies can, according to stellar population models, only be achieved for such young stellar populations (see Figure 11(a)). Within the uncertainty, this is also consistent with the zero-point offset of the Hζ_A–velocity dispersion relation for RX J0848.6+4453 relative to the low-redshift sample (Figure 14(b)). The occurrence of such a star formation episode is further supported by the fact that the most massive bulge-dominated galaxies in the cluster all have significant [O ii] emission.

It is worth noting that all the bulge-dominated galaxies show young stellar populations through the strength of the Hζ line, the presence of [O ii] emission, or both. These galaxies are distributed throughout the cluster (see Figure 12). Thus, there is no indication that the star formation has yet been quenched in the center of the cluster. This is different from results for the more massive clusters RDCS J1252.9–2927 (z = 1.24) and XMMU J2235.3–2557 (z = 1.4) at similar redshifts. Both of these clusters show an absence of star-forming galaxies in the very center of the clusters (Nantais et al. 2013; Grützbauch et al. 2012). We speculate that the difference is related to the mass of the clusters, as the two latter clusters have M₅₀₀ = 6.1 × 10¹⁴ M_☉ (Stott et al. 2010) and M₅₀₀ = 4.4 × 10¹⁴ M_☉ (Rosati et al. 2009; see also Stott et al. 2010), respectively, thus masses that are a factor of 3–4.5 larger than the mass of RX J0848.6+4453. Lynx E, which is located in the same supercluster as RX J0848.6/4453/Lynx W and is similarly massive as RDCS J1252.9–2927 and XMMU J2235.3–2557 (M₅₀₀ = 4.7 × 10¹⁴ M_☉; Stott et al. 2010), has not yet been studied in the same detail.

Two studies of z ≈ 2 clusters find similar results regarding the presence of star formation in massive cluster galaxies as we find for RX J0848.6+4453. Strazzullo et al. (2013) find in their study of J1449+0856 (z = 2.0) that the cluster hosts massive star-forming as well as passive galaxies in the core. This cluster has an estimated mass of M₅₀₀ = 3.4 × 10¹³ M_☉ (Gobat et al. 2011, with the conversion M₂₀₀ ≈ 1.54 M₅₀₀ from Brodwin et al. 2011). Thus, the cluster is significantly less massive than RX J0848.6+4453, but based on the models for cluster mass evolution with redshift (see Figure 4), it is expected to evolve into a cluster mass similar to that of RX J0848.6+4453 at z ≈ 1.3.

Tanaka et al. (2013) investigated the cluster galaxies around the radio source PKS 1138–262 (z = 2.16) and conclude that this cluster also contains a mix of massive star-forming and passive galaxies, as if the cluster is in the process of quenching the star formation. Shimakawa et al. (2014) derived the velocity dispersion of Hα and Lyα emitters that they consider part of the virialized core of the cluster. They find σ_cluster = 683 km s⁻¹, from which they derive M₂₀₀ = 1.71 × 10¹⁴ M_☉, or M₅₀₀ = 1.1 × 10¹⁴ M_☉ with the conversion from Brodwin et al. This cluster mass represents an upper limit as even the core may not yet be virialized. However, it appears that the cluster may already have a mass comparable to that of RX J0848.6+4453 and therefore will be expected to evolve into a significantly more massive cluster than RX J0848.6+4453 at later epochs.

The difference in look-back time between z ≈ 2 and z ≈ 1.3 is about 1.5 Gyr with our adopted cosmology. Thus, it is plausible that we are in fact seeing J1449+0856, PKS 1138–262, and RX J0848.6+4553 at slightly different epochs during the quenching of the star formation as the galaxies fall into the dense cluster environment. We speculate that this process takes place earlier (or faster) in more massive clusters like RDCS J1252.9–2927 and XMMU J2235.3–2557. Detailed spectroscopic observations of both those two clusters and higher-redshift progenitors of such massive clusters are needed to resolve this question. Based on its mass estimate, PKS 1138–262 may be such a progenitor.

The results for the M/L ratios, Hζ line strength, and [O ii] emission appear to give a consistent picture of the stellar populations in the bulge-dominated RX J0848.6+4453 galaxies and an epoch of the period of the last star formation of z_form = 1.95. However, the strengths of the metal lines CN3883 and CaHK, as well as the D4000 strength, appear in contradiction with these results. These three indices are all stronger than expected for 1–2 Gyr old stellar populations with metallicities of [M/H] = 0–0.3, based on the predictions from SEDs from Maraston & Strömbäck (2011). This is shown in Figures 14(c)–(e), where we show the zero-point offsets for these three indices relative to our low-redshift sample. The figure also shows the results for the z = 0.5–0.9 clusters from Jørgensen & Chiboucas (2013). As our RX J0848.6+4453 sample is the first sample of z > 1 galaxies with measured metal absorption-line indices, we cannot compare this result to any prior results. We do caution that the stellar population models may not correctly model these blue indices. In Jørgensen & Chiboucas (2013) we showed that the SEDs from Maraston & Strömbäck predict CN3883 too strong for a given CN₂ index. Because of that, the prediction of the age dependency for CN3883 based on these SEDs is also significantly stronger than if we adopt the dependency derived from the CN₂ index as we did in Jørgensen & Chiboucas (2013). In Figure 14(c) we show the latter prediction as well for z_form = 1.8. From this it is clear that it is yet not straightforward to interpret the strength of this blue metal index within the framework of the SSP models. Thus, to make progress on the interpretation of the metal indices, further progress is needed on the modeling. This is beyond the scope of this paper. Additional data for z > 1 cluster galaxies are also needed to confirm the presence of these strong metal lines in galaxies at these redshifts.

The spectroscopic reductions were done using the same techniques as described for the nod-and-shuffle data used in Jørgensen & Chiboucas (2013). The only difference is that size and behavior of the charge diffusion effect (CDE) of the GMOS-N E2V DD CCDs compared to that of the original GMOS-N E2V CCDs. Briefly, the CDE becomes stronger at longer wavelengths and is seen as charge diffused from each individual pixel into all neighboring pixels; see also Abraham et al. (2004) for a description and Jørgensen & Chiboucas (2013) for a figure that shows how the CDE affects spectroscopic data. As explained in the latter paper, in the absence of a correction the CDE leads to oversubtraction of the sky signal at long wavelengths.

We attempted to use the same technique to correct for the CDE for the E2V DD CCDs as used in Jørgensen & Chiboucas (2013). However, it turns out that the effect for these CCDs depends not only on the wavelength but also on the physical location on the array. We therefore obtained custom calibrations to enable the correction. These calibrations consist of quartz-halogen flat fields taken through the MOS masks. The flat fields are shuffled on the detector the same way as the science observations are obtained. However, in order to avoid saturating the array, only one shuffle cycle was used for the shuffled flat fields. At the same time we obtained conventional quartz-halogen flat fields. Using the two types of flat fields together makes it possible to derive a correction image that can be used to correct the flat fields taken with the science observations at night, such that after the correction the flat fields will include the multiplicative effect of the CDE. Owing to the small flexure effect, as well as the fact that the science data are taken with deliberate small offsets in the detector translation stage between exposures, flat fielding for pixel-to-pixel variations should be done with flat fields taken with the science data, rather than simply using the shuffled flat fields obtained after the fact.

The determination of the correction image is done with the following steps.

• 1.  
  Bias correct of both shuffled and conventional flat field.
• 2.  
  Fit both flat fields with cubic splines row by row and detector by detector.
• 3.  
  Normalize the smooth fits for each slitlet with the fit in the central row of each slitlet. This is also done detector by detector.
• 4.  
  For both flat fields, mosaic the images from the three arrays in GMOS-N.
• 5.  
  Cut each flat field into slitlets.
• 6.  
  Ratio the conventional flat field with the shuffled flat field in original position. This will show the CDE affecting the lower part of the lower image of the slitlets.
• 7.  
  Repeat the steps mosaic, cut, and ratio, but with the conventional flat-field offset to match the upper image of the flat field in the shuffled flat field. The resulting ratio image will show the CDE affecting the upper part of the upper image of the slitlets.
• 8.  
  Fit the effect row by row with a cubic spline in order to suppress pixel-to-pixel noise in the correction image.
• 9.  
  Reformat the correction image to match the flat fields, which have six extensions matching the six read-out amplifiers on the array.

The calibration was repeated for each of the two wavelength settings used for the science observations and for each of the two MOS masks. Thus, in total four calibration images were used. We repeated the determination several times over a period of a few weeks to ensure that the calibration did not change in time. No significant time dependence was found. Figure 17 shows a subimage of the two-dimensional correction image together with examples of the size of the correction as it affects the science data. The size of the correction depends on the geometry of the slitlets, the placement of the objects in the slitlets, and the extraction aperture. The correction effect shown in Figure 17 matches the configuration used for our data. The CDE calibration is critical for MOS nod-and-shuffle observations using slits as short as done here (25) and attempting to obtain observations redward of ≈8000 Å.

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Following the CDE correction, the remaining spectroscopic reduction steps are identical to those described in Jørgensen & Chiboucas (2013). The results of the spectroscopic reductions are one-dimensional extracted spectra calibrated to a relative flux scale. The spectra were median filtered and resampled to just better than critical sampling (cf. Jørgensen & Chiboucas). The instrumental resolution was derived from sky spectra processed exactly the same way as the science spectra. The instrumental resolution for all slitlets is between 2.90 and 3.14 Å measured as sigma in a Gaussian fit to the sky lines.

The calibrated spectra were fit with stellar templates as described in Jørgensen & Chiboucas (2013). This results in determination of the redshifts and the velocity dispersions. 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. Spectra of member galaxies were fit in the wavelength range 3750–4100 Å. The software fits the spectra in pixel space. The template stars are convolved to the instrumental resolution of the science spectra. Individual values for each slit are used as these are not identical. As in Jørgensen & Chiboucas (2013), we determine the instrumental resolution from stacked sky spectra processed in the same way as the science spectra. The software determines the line-of-sight velocity distribution (LOSVD) from the science spectra, and then the velocity dispersion is derived from the LOSVD through both a Gauss–Hermite polynomial fit and a Gaussian fit. For the 19 member galaxies with velocity dispersion determined the offset in log space between the two measurements is −0.036, with the Gauss–Hermite polynomial fits giving the smaller velocity dispersions. One may argue that using Gaussian fits is a suitable choice for the RX J0848.6+4453 data owing to the relatively short wavelength range and a median S/N of 18 Å⁻¹, making the uncertainties on the higher-order terms of the Gauss–Hermite polynomial fit large. However, for consistency with previous work, we use the velocity dispersions derived from the Gauss–Hermite polynomial fits to the LOSVD.

Because the software determines the fits in pixel space, it is straightforward to mask wavelength ranges not to be included in the fit. We used this to flag areas of strong residuals from the sky subtraction, and for ID 2772 also to mask Balmer emission lines in the fitted wavelength range. None of the other galaxies have significant emission lines within the wavelength range 3750–4100 Å. As in Jørgensen & Chiboucas, we use three template stars with spectral types K0III, G1V, and B8V. Figure 18 shows the normalized spectra, fits, and residuals in the wavelength region covered by the fits. The purpose of the set of template stars is to span the stellar populations in the galaxies. From Figure 18 we conclude that use of these three stars accomplishes this. Further, we choose to use the same template stars as in our previous work to ensure consistency with our previous publications. Aperture correction of the velocity dispersions was performed using the technique from Jørgensen et al. (1995b).

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The uncertainties, σ_log σ, on the velocity dispersions are derived by the fitting software using a bootstrap method. In Figure 19 we show the resulting uncertainties versus the S/N of the spectra. The uncertainties scale approximately with S/N as σ_log σ ≈ 1.2 × S/N⁻¹. This relation is shown in the figure.

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We have assessed possible systematic errors on the derived velocity dispersions resulting from (1) incorrect instrumental resolution, (2) incorrect telluric correction, and (3) incorrect sky subtraction.

The instrumental resolution varies from slit to slit, with the total range being approximately ±4.5%. The formal uncertainties on the derived instrumental resolutions as estimated from the rms scatter of measurements of individual skylines in each slit are 1%–3%. We estimated the systematics that may be introduced in the velocity dispersion measurements from incorrect determination of the instrumental resolution by refitting all spectra adopting instrumental resolutions of 10% larger and 10% smaller than measured. The median offsets relative to the velocity dispersions listed in Table 11 are less than 0.005 in log σ. As this is a factor of five less than the intrinsic consistency of 0.026 of our low-redshift sample (Jørgensen et al. 2005), we conclude that systematic errors from incorrect determination of the instrumental resolution do not affect our results significantly.

The telluric correction was derived from spectra of two blue stars included in the masks. Thus, the calibration spectra were obtained with identical airmass and water vapor as the science spectra and processed in the same way as the science spectra. The combined spectrum of the two blue stars was normalized. We then cleaned the spectrum for noise and stellar features outside the known bands of atmospheric absorption. At wavelengths longer than 8500 Å we used an ATRAN model spectrum of the atmospheric absorption (Lord 1992) to guide this cleaning process. Figure 20 shows the normalized spectrum before cleaning, the ATRAN model, and the adopted telluric correction. The wavelength interval for the kinematics fitting is shown in the observed frame. The long-wavelength limit of this fitting interval was set to avoid the strong telluric absorption bands redward of ≈9300 Å. As the spectra used to determine the telluric correction are obtained simultaneously with the science, there can be no mismatch in airmass or water vapor. Nevertheless, we tested the effect of the telluric correction being systematically wrong with 10% by correcting the spectra with the telluric correction test spectrum derived from the measured telluric correction spectrum as

$$\begin{equation} {\rm telluric_{\rm test}} = 1 - X (1-{\rm telluric_{\rm measured}})\protect, \protect \end{equation} \tag{ B1 }$$

with X = 0.9 and 1.1, respectively. The spectra were then flux calibrated, resampled, normalized, and processed with the kinematics fitting software. The resulting velocity dispersions are in both cases consistent with those presented in Table 11 with median zero-point offsets of <0.003 for the two cases and rms scatter of 0.04 in log σ for the 19 member galaxies with measured velocity dispersions.

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Finally, we assessed the systematic effects on the velocity dispersions from a possible incorrect sky subtraction. The data are obtained in nod-and-shuffle mode to limit such sky subtraction errors. Within the wavelength fitting interval (3750–4100 Å in the rest frame) even for the brightest cluster member observed, ID 1763, the signal from the galaxy is only 2.6% of the average sky signal. Figure 20 illustrates this by showing the spectrum of ID 1763 in counts together with the matching sky spectrum scaled down with a factor of 100. We tested the effect of the sky subtraction being over- or undersubtracted with 0.1%. An error in the sky subtraction of this size causes visible systematic residuals in the resulting spectra within the wavelength region used for the kinematics fitting. We therefore view this as the upper limit on the possible systematic error in the sky subtraction. The spectra were then processed through the remainder of the processing steps and velocity dispersions derived. Comparing the resulting velocity dispersions to those presented in Table 11 for the 19 member galaxies with measured velocity dispersions, we find median offsets in log σ of <0.015 in the two cases. The rms scatter in log σ for over- and undersubtraction of the sky is 0.13 and 0.05, respectively. If limiting the comparison to the 13 bulge-dominated galaxies with S/N ≥10, the scatter decreases to 0.08 and 0.03, respectively. These 13 galaxies are the galaxies included in our analysis of the size and velocity dispersion evolution, as well as in the FP analysis.

We conclude that systematic errors on the measured velocity dispersions due to the determination of the instrumental resolution, the adopted telluric correction, or the sky subtraction do not affect our results significantly.

Our ability to determine line indices from the spectra is limited by the sky subtraction errors, which in turn to a large extent are a result of the imperfect correction for the CDE. While the spectra cover wavelengths to 4400 Å in the rest frame, the sky subtraction errors limit the range for which the spectra can be used for determination of absorption-line indices to ≈4075 Å in the rest frame (9250 Å observed). We have derived the following indices: CN3883, CaHK, D4000, and Hζ_A. We have adopted the bandpass definition for the higher-order Balmer line Hζ from Nantais et al. (2013). The index is named H6_A in Nantais et al., while we opt to name it after the name of the Balmer line it is measuring.

The red bandpass of the original definition of the D4000 index (Gorgas et al. 1999) is in our spectra severely affected by the sky subtraction errors. We have therefore defined a shorter red bandpass in order to be able to measure the equivalent of the D4000 index. We call this index D4000_short and define it as

$$\begin{eqnarray} {\rm D4000_{\rm short}} &=& 1.2107 \,(200/75) \, \left(\int _{4000(1+z)}^{4075(1+z)} f_{\lambda } d\lambda \right)\nonumber \\ &&\times\left(\int _{3750(1+z)}^{3950(1+z)} f_{\lambda } d\lambda \right)^{-1} - 0.092\protect. \protect \end{eqnarray} \tag{ B2 }$$

The definition ensures that on average ${\rm D4000_{\rm short} = D4000}$. The factor (200/75) reflects the difference in the length of the two passbands in the definition, as the original D4000 index has identical length passbands. Figure 21(a) shows the two indices versus each other for our sample of member galaxies in Perseus, A194, MS 0451–0305, RX J0152.7–1357, and RX J1226.9+3332. The figure also shows the indices determined from the model SEDs from Maraston & Strömbäck (2011). The rms scatter of the data points relative to the one-to-one relation is 0.046. In Jørgensen & Chiboucas we estimated that the measurement uncertainty on D4000 for our z = 0.5 and z = 0.9 data is 0.051 and 0.033, respectively. Thus, the internal scatter of the relation between D4000 and D4000_short is insignificant, and we will assume that D4000_short has an uncertainty similar to that of D4000.

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Our data for RX J0848.6+4453 do not allow us to stack the frames in subsets for the full data set in order to derive better estimate uncertainties on the spectroscopic parameters. However, in the wavelength region 3750–4100 Å the median S/N of the data is similar to that of our spectra for MS 0451.6–0305 (Jørgensen & Chiboucas 2013). We therefore adopt the uncertainties for CN3883, log CaHK, and D4000 from that paper (Table 19 in that paper). The values are 0.035, 0.060, and 0.051 for CN3883, log CaHK, and D4000, respectively. The uncertainty on Hζ_A depends too strongly on the strength of the index to be adequately represented by one value. Thus, we show individual error bars on figures using this index, except for the low-redshift sample, for which we for clarity show the median uncertainty. The low-redshift sample spectra have fairly low S/N in the wavelength region of Hζ. That, combined with the weak strength of the line for these galaxies, leads to a high relative uncertainty, typically 0.26 on log Hζ_A. The line indices have been aperture corrected and corrected for velocity dispersion as described in Jørgensen et al. (2005); see Jørgensen & Chiboucas (2013) for a discussion of the method applied to intermediate-redshift galaxies. As for the lower-order Balmer lines, we assume that Hζ_A has no aperture correction.

As Hζ_A is the only Balmer line index measurable from our RX J0848.6+4453 data, we have used the data for the three z < 1 clusters and model SEDs from Maraston & Strömbäck (2011) to evaluate to what extent this index is suitable for estimating ages. In Figure 21(b) we show the indices for the high-order Balmer lines versus each other for the low-redshift sample and three z < 1 clusters. Model predictions based on the model SEDs from Maraston & Strömbäck are overplotted. Hζ_A is useful as an indicator of very young stellar populations, ages of 2 Gyr or less. The ages of the older stellar populations are difficult to measure using Hζ_A owing to the uncertainties affecting our data.

The mix of the three template stars in our best-fit models from the kinematics fitting as expected correlates with the Hζ_A and CaHK indices in the sense that the B8V fraction in the best-fit model increases with increasing Hζ_A, while the sum of the G1V and K0III fractions increases with increasing CaHK. However, because stellar population models already exist to assist the interpretation of the index strengths and no such modeling exists for the template stars, we will use only the indices in our analysis of the data.

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

Tables 11 and 12 list the results from the template fitting and the derived line strengths.

Table 12. RX J0848.6+4453: Line Indices and [O ii] for Cluster Members

ID	CN3883	σCN3883	CaHK	σCaHK	D4000a	σD4000	HζA	$\sigma _{\rm H\zeta _A}$	EW [O ii]	$\sigma _{\rm EW[{\rm O\,\scriptsize{II}}]}$	flux([O ii])b	$\sigma _{\rm flux([{\rm O\,\scriptsize{II}}]}$
240	0.097	0.013	26.60	0.65	2.169	0.015	7.85	0.24	5.0	2.0	1.23	0.19
654	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	183.5	102.9	4.10	0.40
807	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	44.1	2.5	6.43	0.15
1123	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	155.7	123.5	5.97	0.32
1264	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	2.139	0.019	⋅⋅⋅	⋅⋅⋅	2.9	0.6	0.57	0.11
1362	0.179	0.013	18.37	0.73	1.962	0.014	3.32	0.34	15.6	2.7	3.57	0.14
1533	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	25.9	8.3	2.93	0.17
1644	⋅⋅⋅	⋅⋅⋅	14.00	1.59	2.115	0.030	12.68	0.37	9.9	2.6	1.77	0.20
1748	0.122	0.009	22.59	0.50	2.291	0.011	2.90	0.25	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅
1763	0.202	0.008	22.41	0.40	2.366	0.010	3.06	0.23	17.0	0.5	8.36	0.16
1809	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	24.2	9.9	2.10	0.14
1888	0.158	0.007	19.19	0.34	2.164	0.007	2.09	0.20	9.1	0.3	5.36	0.17
2015	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	3.154	0.042	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅
2063	0.070	0.010	13.85	0.62	1.893	0.010	3.65	0.25	14.6	2.2	4.63	0.14
2111	0.113	0.021	11.41	1.24	1.704	0.019	4.62	0.51	8.0	1.0	1.81	0.15
2369	0.099	0.030	20.23	1.63	2.103	0.033	6.64	0.58	29.6	8.4	1.88	0.16
2417	0.116	0.023	⋅⋅⋅	⋅⋅⋅	1.544	0.021	4.69	0.48	40.8	6.5	7.29	0.30
2702	0.156	0.026	27.68	1.49	2.136	0.031	4.29	0.62	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅
2735	0.089	0.016	14.51	1.04	1.853	0.017	1.99	0.40	3.5	0.9	0.91	0.11
2772	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	1.568	0.009	⋅⋅⋅	⋅⋅⋅	32.3	1.4	10.29	0.15
2943	0.188	0.014	19.82	0.77	2.081	0.015	2.60	0.39	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅
2989	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	2.165	0.012	⋅⋅⋅	⋅⋅⋅	1.9	0.3	0.67	0.11
3090	0.174	0.005	19.99	0.27	2.065	0.006	4.17	0.14	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅

Notes. The indices have been corrected for galaxy velocity dispersion and aperture corrected. ^aMeasured as D4000_short; cf. Equation (B2). ^bRelative flux in 10⁻¹⁵ erg cm⁻² s⁻¹ Å⁻¹ measured within the spectral aperture.

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