SPECTROSCOPIC CONFIRMATION OF THE RICH z = 1.80 GALAXY CLUSTER JKCS 041 USING THE WFC3 GRISM: ENVIRONMENTAL TRENDS IN THE AGES AND STRUCTURE OF QUIESCENT GALAXIES

JKCS 041 was imaged through the F160W and F105W filters for approximately 4/3 and 2/3 orbits, respectively, using a four-point dither pattern identical to that adopted by the CANDELS survey (Koekemoer et al. 2011). After combining these deeper exposures with the grism pre-images, described below, the total exposure times were 4.5 ks in F160W and 2.7 ks in F105W. Although the calibrated frames produced using calwfc3 by the archive on-the-fly pipeline were mostly sufficient, we found it necessary to expand the pixel mask to include additional warm and hot pixels. The exposures were then registered and combined using multidrizzle with a pixel scale of 006.

In addition to the new HST imaging, JKCS 041 has been observed in the ugrizJHKs filters by the MegaCam and WIRCam instruments at the Canada–France–Hawaii Telescope (CFHT) as part of the CFHT Legacy Survey (Deep Field 1) and the WIRCam Deep Survey (Bielby et al. 2012). We also made use of Spitzer Infrared Array Camera (IRAC) observations in the 3.6 μm and 4.5 μm channels taken as part of the Spitzer Wide-Area Infrared Extragalactic Survey (SWIRE; P.I. Lonsdale).

A multi-wavelength catalog was created using SExtractor (Bertin & Arnouts 1996) with F160W as the detection band. The procedures followed those detailed in N12. All images were first aligned and drizzled onto the F160W pixel scale. Colors were then measured in apertures on images of matched resolution. To account for systematic uncertainties in zeropoints and point-spread function (PSF) matching, we added a 3% uncertainty (10% for IRAC) in quadrature to the random flux errors. For a few of the galaxies that we confirm to be members of JKCS 041 (IDs 359, 375, 376, and 281; see Section 4.2), the aperture photometry was affected by neighboring sources. In order to measure accurate colors in these cases, we used Galfit (Peng et al. 2002) to fit Sérsic profiles to all nearby sources simultaneously in each observed band.

Photometric redshifts z_phot were computed using the z_p estimator provided by EAZY (Brammer et al. 2008). Stellar population parameters were derived using a custom code for the sample of bright galaxies with strong continuum signal in the grism spectra (see Section 3.2). For fainter galaxies, we used FAST (Kriek et al. 2009) to fit Bruzual & Charlot (2003, BC03) models with exponentially declining star formation histories, dust attenuation, and a Salpeter IMF to the photometry; details of the grid can be found in N12. Finally, we use InterRest (Taylor et al. 2009) to interpolate to rest-frame colors in the Bessell (1990) UBV and Two Micron Sky Survey J filters.

A total of 14 orbits, split among 3 visits, was devoted to spectroscopy using the G102 and G141 grisms. The spacecraft orientations were spaced by 26° and 72° from the initial visit to facilitate the deblending of spectral traces. At the beginning of each sequence of grism exposures, a short undispersed exposure through the F160W (for G141) or F105W (for G102) filter was taken to register the grism images, which were then taken following the same dither pattern used for the imaging. The total integration time was 17.0 ks for each grism. In three exposures we noticed a rapidly increasing background in the final few reads; we successfully recovered data with the normal background level by masking the final reads and reprocessing the up-the-ramp readouts using calwfc3. G102 covers the wavelength range ≃ 850–1140 nm with a dispersion of 2.4 nm per pixel, whereas G141 spans ≃ 1110–1670 nm at 4.6 nm per pixel. The wide wavelength range provided by the combination of grisms proved essential to locating the Balmer/4000 Å continuum break at the redshift of JKCS 041.

The grism data were reduced using the aXe package (Kümmel et al. 2009). For each object in the catalogs described in Section 2.2 and for each visit, aXe generates a calibrated two-dimensional (2D) spectrum and an extracted spectrum, along with estimates of the noise and the flux contamination from other objects. A vertical extraction was used, with the wavelength constant perpendicular to the grism trace. Contamination from overlapping spectra was taken into account using the Gaussian emission model, which estimates the spectrum of each object by linearly interpolating the fluxes in the i, z, F105W, J, and F160W filters and distributes the flux spatially according to the Gaussian shape parameters estimated by SExtractor. We found the extracted spectra generated by aXe sufficient for deriving emission line redshifts (Section 3.1); however, we made several improvements to the extraction of the brighter sources whose continuum emission we have modeled (Section 3.2).

First, the global background subtraction performed by aXe often left significant residual trends, especially for the G102 grism. We improved upon this by fitting and subtracting a linear trend in wavelength to the background pixels in each 2D spectrum, omitting pixels in the extraction aperture and those with significant contaminating flux from other objects. The 2D spectra were created with larger dimensions than the aXe default in order to ensure they contain a significant number of blank pixels. With this improvement, the G102 and G141 spectra generally join together smoothly.

Second, aXe relies on a Gaussian approximation to the object light profile when it performs optimally weighted extraction of spectra. While adequate for many objects, this is a poor representation of the extended light profiles of large spheroidal galaxies, which include many of our primary targets. Thus, for each galaxy for which we extract a continuum spectrum, we use the F160W image to measure the light profile in the cross-dispersion direction appropriate to each visit. This profile was then used to extract a one-dimensional (1D) spectrum, including error and contamination estimates, from the 2D spectrum with improved weighting. At the same time we measure the light profile of each galaxy in the dispersion direction. In grism spectroscopy this sets the line spread function (the LSF, i.e., the spectral resolution) and so is essential for the modeling we perform in Section 3.2.

We searched for emission lines in the 1D and 2D spectra of all galaxies having H₁₆₀ < 25.5 using the plots generated by aXe2web. These include contamination estimates, which are very useful for distinguishing true emission lines from overlapping zero order images of other galaxies. We additionally verified the reality of the emission lines by comparing the three independent spectra obtained for each object at the various orientations. In total we identified 63 emission line sources. An example spectrum is shown in the left panel of Figure 1.

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Wavelengths of emission lines were measured by fitting Gaussian profiles in IRAF. We averaged the wavelengths that were measured separately in each valid spectrum (i.e., each orientation at which the spectrum fell in the field of view and was not strongly contaminated). In 35 of 63 sources unambiguous redshifts were derived through the identification of multiple lines, primarily Hα, [O ii], and [O iii]. When only a single line was identified (28 sources), it was interpreted as Hα (22 sources) or [O iii] (6 sources) depending on which was more consistent with the photometric redshift.

The rms redshift uncertainty was estimated internally from the scatter in independent measurements as σ_z = 0.003. For nine galaxies we can compare with redshifts measured at higher spectral resolution in the VIMOS-VLT Deep Survey (VVDS; Le Fèvre et al. 2013). After excluding one outlier with Δz = 0.07, the rms scatter is σ_Δz = 0.005 with no detectable systematic bias. This is 20 times smaller than the median uncertainty in the photometric redshifts of the these galaxies.

We estimate a typical 5σ line flux limit of 5 × 10⁻¹⁷ erg cm⁻² s⁻¹ in G141 data over λ ≈ 1.2–1.6 μm and in G102 over λ ≈ 0.9–1.1 μm. By simulating artificial emission lines in the extracted spectra, we verified that we would visually identify ∼80% of lines exceeding this flux limit. This limit applies to the spectra from each visit, which are the basis of our line search. These have 2–3 orbit depth, which is comparable to the 3D-HST (Brammer et al. 2012) and WISP (Atek et al. 2010) surveys, and these programs have estimated similar limits.

For all galaxies in the HST field of view brighter than H₁₆₀ < 23.3 with photometric redshifts 1.4 < z_phot < 3, we model the continuum emission in order to derive precise redshifts and stellar population properties. This flux limit corresponds to a typical signal-to-noise ratio of 5 per spectral pixel in the coadded spectra, suitable for continuum fitting, while the redshift range restricts the sample to galaxies for which the Balmer/4000 Å break is expected to fall well within the grism spectral coverage.

For each galaxy, we visually examined the spectra obtained during each of the three visits extracted using the improved weighting described in Section 2.3. The contamination model was subtracted from each spectrum. Heavily contaminated wavelength regions, often comprising an entire visit, were identified and masked. The spectra were then coadded using inverse variance weighting to produce a combined spectrum for each grism. The galaxy light profiles, measured for each visit along the dispersion direction (Section 2.3), were averaged with the same weights to estimate the LSF. The exposure times of the spectra vary significantly, since the number of visits that contribute to the stack ranges from 1 to 3. Of the 59 galaxies in the continuum sample, we were able to extract G102 and G141 spectra for 40 objects (68%). The remaining 19 sources were either heavily contaminated by neighboring sources or dispersed off the detector.

To make optimal use of the extensive data we gathered for JKCS 041, we developed a code designed to fit stellar population models jointly to spectroscopic and photometric data with flexible models and arbitrary LSFs. pyspecfit is written in Python. It is Bayesian in nature and uses MultiNest (Feroz et al. 2009), a Markov Chain Monte Carlo (MCMC) engine, to explore the parameter space and properly estimate uncertainties and degeneracies. The details of the code are described in Appendix B. An example fit is shown in the right panel of Figure 1 for a luminous red galaxy at z = 2.414. While our fits are based on the BC03 models, we note in passing that we experimented with using the 2007 models instead, but decided against this due to their uniformly poorer fits to the spectrophotometry. The poorer fits arise from excess light in the rest-frame near-infrared, which is consistent with other studies indicating that the contribution of the TP-AGB stars in these more recent models is overstated (e.g., Kriek et al. 2010; Zibetti et al. 2013).

A potential source of error in deriving redshifts from the continuum shape arises from joining spectra from the two grisms. This is of particular concern in the present sample since, as we show in Section 4, the 4000 Å break at the redshift of JKCS 041 falls near the division between the grisms. We tested for errors arising from this possible confusion by reanalyzing the spectra of the 17 continuum-selected cluster members (detailed in Section 4 below) after explicitly forcing the G102 and G141 flux levels to agree, on average, in the small wavelength range where they overlap. This process may introduce some additional noise, but it eliminates the possibility of a spurious spectral break. We found that only 2 of 17 redshifts shift by a significant amount (>2σ).⁶ Both galaxies are on the red sequence and are very likely cluster members.

Only five galaxies in the continuum sample show strong emission features; in these cases, we adopt the emission redshift. We slightly increased the noise estimates for the spectral data by 20% to obtain a median $\chi ^2_{\rm spec} / n_{\rm pixels} = 1.0$, while for the photometry we find a median $\chi ^2_{\rm phot} / n_{\rm filters} = 1.1$. This indicates that the models provide good fits and that the noise estimates are reasonable. The median random uncertainty in z_grism is $\sigma _{z_{\rm grism}}/(1+z) = 0.0025$ for the continuum-selected galaxies, which is a factor 15 improvement over their photometric redshift errors.

The redshift distribution of the emission line and continuum-selected samples in our grism survey is shown in the top panel of Figure 2. JKCS 041 is the richest structure in the field, comprising 19 galaxies, and is located at z = 1.80. The prominence of this peak is more remarkable when one considers that many of the members are red and massive systems with M_* > 10¹¹ M_☉. Since the uncertainties in the grism redshifts are σ_z ≲ 0.01, this shows that the 6.5σ overdensity of red galaxies discovered by Andreon et al. (2009) identified a dominant structure and not a blend of several poorer ones.

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Figure 3 shows the that the distribution of galaxies in the z = 1.80 cluster is clearly centered upon the diffuse X-ray emission (Andreon et al. 2009). Similar to some other high-redshift clusters (e.g., Zeimann et al. 2012), JKCS 041 does not have a single dominant galaxy located at the cluster center, which presumably reflects a lack of dynamical relaxation compared to lower-redshift systems. Nonetheless, the centroid of the spectroscopic cluster members is R.A. = 02:26:44.0 ± 6 arcsec, decl. = −04:41:36 ± 4 arcsec (red box in Figure 3), which coincides with the X-ray centroid determined by Andreon et al. to within 1σ. The cluster members are not distributed uniformly over the field; instead, all lie within R₅₀₀ of the X-ray center, and the majority are confined to a much smaller, elongated structure overlapping the X-ray emission. By considering a larger sample of red sequence candidate members extending to fainter magnitudes than our spectroscopic sample, Andreon et al. (2014) show that the red sequence galaxies follow a smoothly declining radial profile with parameters resembling those of lower-redshift clusters.

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JKCS 041 is therefore a natural identification for the source of the X-ray emission. Based on our grism data, we can now assemble a highly complete redshift catalog in the zone of the X-ray emission and verify that JKCS 041 is indeed the most likely origin. A stellar mass-selected sample is ideal for thus purpose, since it allows us to compare similar galaxy populations uniformly at different redshifts, and massive galaxies are better tracers of a deep gravitational potential. The green line in Figure 2 (middle panel) shows the limiting stellar mass for our continuum flux-selected sample, estimated as described in the caption, and demonstrates that this sample is fairly complete at masses M_* > 10^10.8 M_☉ and redshifts z = 1.4–2. At lower redshifts, since the 4000 Å break lies outside our spectral coverage, we combine our grism catalog with redshifts from the VVDS (Le Fèvre et al. 2013) and the Carnegie–Spitzer–IMACS Survey (Kelson et al. 2014). This yields a spectroscopic redshift for 83% of the mass-limited sample; for the remainder we use z_phot. To assess the association of galaxies with the X-ray emission, we consider systems that are located within the outermost contour of the X-ray emission shown in Figure 3. The bottom panel of Figure 2 shows their redshift distribution and clearly demonstrates that the z = 1.80 peak is dominant and concentrated within the X-ray emission.

Secondary peaks of the redshift distribution in the field of JKCS 041 are expected and are seen in front of other high-redshift clusters (e.g., Zeimann et al. 2012; Mantz et al. 2014). The next strongest peaks are located at z = 0.96, 1.13, and 1.48; each contains 1 or 2 massive galaxies within the zone of X-ray emission, compared to 11 in JKCS 041 (Figure 2, lower panel). Figure 4 shows the positions of galaxies in these foreground structures, with crosses marking their centroids.⁷ In addition to being more sparsely populated, the z = 0.96 and 1.13 structures are not concentrated within the X-ray emission: the z = 0.96 structure is very diffuse, and most galaxies in the z = 1.13 peak lie outside of the X-ray–emitting region. The sparse z = 1.48 structure is better aligned with the X-ray emission than the other foreground peaks, but it seems far too poor to contribute a significant fraction of the flux. Only a single galaxy is massive enough to be included in Figure 4. For comparison, the z = 1.62 group discovered by Tanaka et al. (2013a) in ultra-deep Chandra data appears to be richer, yet it exhibits diffuse X-ray flux that is still ∼15 times fainter than that observed around JKCS 041.

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While Bielby et al. (2010) considered these foreground structures as possible sources of the X-ray emission, they were unable to locate the dominant z = 1.80 cluster in a ground-based optical redshift survey. With the less biased selection and dense sampling afforded by the WFC3 grisms, we have shown that JKCS 041 is the most likely origin and is a genuine high-redshift cluster: it exhibits a spectroscopically confirmed population of massive, red galaxies that are concentrated within diffuse X-ray emission, and the observed X-ray properties are fairly consistent with expectations for a cluster with the observed richness of JKCS 041 (Andreon et al. 2014). After making a small correction to the luminosity distance, the bolometric X-ray luminosity estimated by Andreon et al. (2009) is L_X = (6.5 ± 1.5) × 10⁴⁴ erg s⁻¹ within R₅₀₀.

With the redshift of JKCS 041 established, we now construct a sample of spectroscopically confirmed member galaxies that will form the basis of the remainder of the paper. The identification of cluster members is relatively unambiguous due to the high precision of the grism redshifts. We selected as cluster members those galaxies for which >50% of the integrated probability density P(z) is located within z_clus ± 3σ_z. Here P(z) is derived from the MCMC chains for the continuum sample and is approximated as a Gaussian for the emission line sample (Section 3.1). We estimate the cluster velocity dispersion σ_v = cσ_z/(1 + z) = 800 km s⁻¹ based on the X-ray luminosity presented by Andreon et al. (2009) and the scaling relation derived by Zhang et al. (2011) for nearby clusters, which is consistent with the z ∼ 1 relation determined by Andreon et al. (2008). We began with an initial estimate of z_clus and iterate by updating z_clus with the mean redshifts of the selected members.

This procedure converged in only one iteration to yield 19 members with a mean redshift of z_clus = 1.803 ± 0.003. The selected members are precisely those in the interval z_grism = 1.803 ± 0.022, which is indicated by the vertical lines in the lower panel of Figure 2. We note that adopting the velocity window of ±2000(1 + z_clus) km s⁻¹ advocated by Eisenhardt et al. (2008) would remove only one galaxy from this sample. Among the several previously published estimates of the redshift of JKCS 041, the EAZY photometric redshifts with no corrections applied gave the true z_clus (Raichoor & Andreon 2012). Spectra, images, and P(z) distributions for the 19 confirmed members are shown in Figure 5, and their coordinates and photometric properties are listed in Table 1.

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Table 1. Redshifts and Photometric Data for Spectroscopically Confirmed Cluster Members and Red Sequence Members

ID	R.A.	Decl.	H160	z	Type	$\log M_*^{\rm auto}/{M}_{\odot }$	z − J	(U − B)r	(U − V)r	(V − J)r	UVJ	Quality
Spectroscopically confirmed cluster members
272	36.68173	−4.68934	20.63	$1.798_{-0.003}^{+0.002}$	C	11.71 ± 0.03	2.02 ± 0.04	1.20	1.84	1.15	Q	A
355	36.68644	−4.69239	20.80	$1.798_{-0.002}^{+0.002}$	C	11.52 ± 0.02	2.01 ± 0.03	1.15	1.63	1.05	Q	A
376	36.67501	−4.69286	21.20	$1.811_{-0.008}^{+0.004}$	C	11.56 ± 0.03	2.07 ± 0.05	1.34	1.90	1.14	Q	A
356	36.69423	−4.69235	21.35	$1.805_{-0.004}^{+0.003}$	C	11.36 ± 0.04	1.97 ± 0.07	1.16	1.81	1.13	Q	A
657	36.67557	−4.70257	21.61	$1.812_{-0.002}^{+0.002}$	C	11.11 ± 0.02	2.02 ± 0.05	1.20	1.77	0.92	Q	A
286	36.68790	−4.68994	21.69	$1.798_{-0.013}^{+0.068}$	C	11.47 ± 0.03	1.94 ± 0.08	1.16	1.88	1.37	Q	B
352	36.69051	−4.69215	21.88	$1.797_{-0.004}^{+0.006}$	C	11.22 ± 0.05	2.05 ± 0.08	1.23	1.87	1.08	Q	A
411	36.67382	−4.69384	22.11	$1.821_{-0.004}^{+0.004}$	C	11.15 ± 0.04	1.84 ± 0.09	1.11	1.84	1.19	Q	A
447	36.69121	−4.69487	22.12	$1.797_{-0.009}^{+0.011}$	C	10.81 ± 0.03	1.42 ± 0.09	0.82	1.34	0.64	Q	A
289	36.68965	−4.68994	22.17	$1.802_{-0.004}^{+0.003}$	C	10.89 ± 0.03	1.97 ± 0.08	1.18	1.74	0.70	Q	A
387	36.68231	−4.69296	22.36	$1.801_{-0.009}^{+0.009}$	C	11.00 ± 0.04	1.50 ± 0.11	0.94	1.51	1.49	SF	B
375	36.67488	−4.69278	22.43	$1.819_{-0.008}^{+0.008}$	C	10.88 ± 0.02	1.91 ± 0.09	1.09	1.64	1.05	Q	B
317	36.69911	−4.69091	22.45	$1.787_{-0.003}^{+0.003}$	C	10.75 ± 0.04	2.00 ± 0.11	1.14	1.61	1.11	Q	A
359	36.67696	−4.69228	22.54	$1.792_{-0.005}^{+0.004}$	C	10.67 ± 0.03	1.90 ± 0.11	1.10	1.56	0.61	Q	B
281	36.69061	−4.68944	22.77	$1.806_{-0.004}^{+0.004}$	C	10.73 ± 0.06	2.06 ± 0.17	1.12	1.75	0.98	Q	B
693	36.67771	−4.70379	22.86	$1.820_{-0.010}^{+0.019}$	C	10.51 ± 0.05	1.14 ± 0.09	0.75	1.11	0.78	SF	C
531	36.67919	−4.69839	23.12	$1.818_{-0.002}^{+0.002}$	E	9.73 ± 0.06	0.49 ± 0.11	0.27	0.46	0.16	SF	A
255	36.68793	−4.68838	23.30	$1.795_{-0.075}^{+0.004}$	C	10.53 ± 0.04	1.35 ± 0.24	0.85	1.70	0.76	Q	C
332	36.67165	−4.69125	23.83	$1.785_{-0.003}^{+0.003}$	E	9.35 ± 0.28	0.22 ± 0.21	0.11	0.21	0.82	SF	B
Candidate cluster members on red sequence (not spectroscopically confirmed), H160 < 23.3 and R < R500
772	36.67527	−4.70738	22.26	$1.81_{-0.11}^{+0.08}$	P	10.91 ± 0.28	2.00 ± 0.09	1.20	1.72	1.00	Q	...
275	36.68274	−4.68931	22.68	$1.81_{-0.19}^{+0.12}$	P	10.78 ± 0.28	1.87 ± 0.17	1.00	1.66	1.02	Q	...
404	36.68949	−4.69338	22.89	$1.59_{-0.09}^{+0.17}$	P	10.71 ± 0.28	1.86 ± 0.16	1.22	1.91	1.33	Q	...

Notes. The "r" subscript denotes colors in the rest frame. C and E types indicate continuum and emission line redshifts, whereas P denotes photometric redshifts. Q and SF refer to galaxies in the quiescent and star-forming regions of the UVJ color–color plane. For type C, M_* is derived from fits to the full spectrophotometry (Section 3.2); for types E and P, M_* is based on FAST fits to the photometry. Median random uncertainties in the rest-frame U − B, U − V, and V − J colors are 0.07, 0.03, and 0.08 mag, respectively. H₁₆₀ is F160W magnitude in the MAG_AUTO aperture, and $M_*^{\rm auto}$ is scaled here to this total flux. See Appendix A for notes on the redshift quality flags.

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Although the continuum sample is strictly flux-limited (H₁₆₀ < 23.3), it forms a nearly mass-limited sample at z = 1.80. Based on the catalog of N12 that covers a much wider area, we expect 88% of galaxies at z = 1.8 with M_* > 10^10.6 M_☉ to be brighter than H₁₆₀ = 23.3. Within the WFC3 field of view surrounding JKCS 041, all galaxies above this mass threshold that are photometric candidate members (z_phot = 1.8 ± 0.2) are brighter than H₁₆₀ = 22.8, even though the imaging depth is ∼3 mag fainter. Independently, we estimate nearly the same limiting mass using the BC03 model for a solar metallicity galaxy formed in a burst at z_f = 5 (see green line in Figure 2, middle panel). Conversely, all confirmed cluster members in the continuum sample have M_* > 10^10.5 M_☉.

We thus expect the parent continuum-limited sample to be reasonably complete for stellar masses M_* > 10^10.6 M_☉. Additional incompleteness arises from those spectra that could not be extracted due to contamination from nearby sources. This affects 19 of the 59 galaxies in the continuum sample (Section 3.2). Three of these lie on the red sequence and are located at R < R₅₀₀. These are likely cluster members whose properties we list in Table 1. Three additional bluer systems located within R₅₀₀ have z_phot consistent with JKCS 041 within their 68% confidence intervals; however, the redshift uncertainties are too large to associate them with the cluster with any confidence. None of the candidate members discussed above has a stellar mass M_* > 10¹¹ M_☉. Therefore, most likely we have spectroscopically confirmed all members with M_* > 10¹¹ M_☉ and R < R₅₀₀. At lower masses M_* = 10^{10.6 − 11} M_☉, considering the three most likely photometric candidates, our estimated spectroscopic completeness is ∼75%. Given this high completeness, for the rest of the paper we focus our analysis on the spectroscopically confirmed cluster members.

Completeness for the emission line sample is less straightforward to interpret. For this reason, we confine our quantitative analysis in Sections 5 and onward to the better-defined continuum-selected sample and classify galaxies based on their colors, not on the presence of emission lines. Nonetheless, it is useful to have a rough idea of the star formation rate (SFR) corresponding to the limiting line luminosity of 3 × 10⁸ L_☉ (Section 3.1). [O ii] and [O iii] lie within our spectral coverage for JKCS 041 members. For [O ii] emission, this limit corresponds to a SFR of ≳ 30 M_☉ yr⁻¹ according to the Kewley et al. (2004) calibration with dust attenuation of A_V = 1. For galaxies with significantly subsolar metallicity, the [O ii] emission will be weaker, but [O iii] will be more visible. Limits will also be weaker for galaxies with higher dust content A_V > 1, which is expected for massive systems.

Figure 6 shows the distribution of the confirmed cluster members in the rest-frame UVJ color–color diagram. This plane is frequently used to distinguish quiescent and star-forming systems (Williams et al. 2009), and for the remainder of the paper we refer to quiescent and star-forming galaxies based on this criterion, using the specific form proposed by Whitaker et al. (2011).

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Of the 19 confirmed members, 17 arise from the continuum sample, and 15 of these fall in the quiescent region of the UVJ plane. This large number of quiescent members with spectroscopic data makes JKCS 041 an invaluable laboratory for studying environmental processes at high redshifts. None of the quiescent members shows unambiguous (>3σ) residual line emission above the continuum models, although there is a hint of [O ii] in IDs 657 and 447. Galaxy 447 is a borderline case: it falls near the edge of the quiescent selection box. It has a specific SFR of 10^−10.2 Gyr⁻¹ inferred from the spectrophotometric fitting, which is intermediate between the other 14 UVJ-quiescent members (all <10⁻¹¹ Gyr⁻¹) and the star-forming members (∼10⁻⁹ Gyr⁻¹). Of the cluster members in the star-forming region of the UVJ plane, two show emission lines (IDs 531 and 332) and have low stellar stellar masses M_* = 10^{9.4 − 9.8} M_☉, while two more massive examples having M_* = 10^{10.5 − 11} M_☉ were identified through continuum fitting (IDs 387 and 693). Note that we are able to secure redshifts of these bright blue galaxies even though they lack detectable emission lines.

Morphologically, virtually all of the quiescent confirmed members appear spheroid-dominated (see Figure 5). This visual impression is supported by a quantitative analysis of the galaxy shapes in Section 6. Of the four star-forming members, two appear compact (IDs 693 and 531), ID 332 appears diffuse and irregular, and ID 387 (located near the cluster center) appears to be an inclined disk with a red bulge.

Only one spectroscopic member is detected as an X-ray point source in the 75 ks Chandra data (Andreon et al. 2009): ID 352, a UVJ-quiescent galaxy with L_{X, 0.5 − 2 keV} = 6 × 10⁴² erg s⁻¹. To investigate the presence of obscured star formation or AGN activity in other cluster members, particularly those classified as quiescent by their UVJ colors, we measured 24 μm fluxes in the Spitzer Multiband Imaging Photometer (MIPS) data taken for the SWIRE survey.⁸ None of the quiescent members is detected at 2σ significance (>0.13 mJy), and there is no detection in a mean stack to a 2σ limit of 32 μJy.

The 2 more massive star-forming members (IDs 387 and 693) are detected with fluxes of 0.20 ± 0.06 mJy each. Based on the Wuyts et al. (2008) templates, this corresponds to a total infrared luminosity of L_IR = (1.3 ± 0.4) × 10¹² L_☉ for each source and SFRs of 140 ± 44 M_☉ yr⁻¹ for a Chabrier (2003) IMF (Bell et al. 2005). These are typical for star-forming galaxies in this mass and redshift range (e.g., Reddy et al. 2006). Thus, among the galaxies in our continuum-selected sample, we see a one-to-one correspondence between those which lie in the quiescent region of the UVJ plane and those which lack detectable 24 μm emission, albeit in fairly shallow MIPS imaging. Papovich et al. (2012) also found a good correspondence between these diagnostics in a z = 1.62 proto-cluster using deeper MIPS data, and Fumagalli et al. (2013) recently showed that UVJ-quiescent galaxies at high redshift generally lack mid-infrared emission to very deep limits. We conclude that the UVJ diagram provides reasonable classifications of cluster and field galaxies and is suitable for making differential comparisons, as we do in Sections 5 and thereafter.

In the absence of spectroscopic data, members of high-redshift clusters are frequently identified based on the red sequence. With our grism observations we can assess the purity and completeness of this method. Figure 7 shows the color–magnitude diagram for galaxies with R < R₅₀₀, where R is the distance from the X-ray centroid.

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JKCS 041 shows a clear red sequence with a mean observed color 〈z − J〉 = 1.98 ± 0.02 and a measured scatter of σ_{z − J} = 0.07. This is comparable to the rms measurement error of δ_{z − J} = 0.09, indicating that the intrinsic scatter is low (Andreon 2011). We define red sequence galaxies as those within ±2σ of the mean color to a limiting magnitude of H₁₆₀ < 23.3 (dashed in Figure 7).

The majority of the spectroscopically confirmed members in the continuum sample (13 of 17) are on the red sequence. However, in addition to the two star-forming members, two galaxies that are classified as quiescent according to their UVJ colors are bluer than the z − J red sequence (IDs 255 and 447). These are likely systems where star formation has been most recently truncated. Naturally, some galaxies located on the z − J red sequence will not be associated with the cluster. Using the grism redshifts, we identified five interlopers over the full field of view, which are indicated by boxes in Figure 3. Only two of these are located at R < R₅₀₀. Thus, a red sequence selection yields a fairly pure and complete sample (13 of 15, or 87%) of quiescent members within R < R₅₀₀, as anticipated from the high overdensity of red sequence galaxies compared to the field (Andreon & Huertas-Company 2011). At larger radii contamination is more severe.

Figure 8 compares the fraction f_Q of galaxies in JKCS 041 with quiescent UVJ colors to that of field galaxies in the same range of stellar mass and redshift. The comparison sample is drawn from the NEWFIRM Medium Band Survey catalogs in the AEGIS and COSMOS fields (Whitaker et al. 2011), selected from z_phot = 1.8  ±  0.2 and converted to a Salpeter IMF. Although this "field" sample includes galaxies that inhabit a range of environments, a differential comparison is still informative because JKCS 041 is a strong overdensity.⁹

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Clearly, the cluster environment has had a powerful role in determining the number of quenched systems: 88% (15 of 17) of the cluster members in the continuum sample are quiescent, whereas this fraction is less than half in the field. Roughly half of the quiescent cluster members were thus quenched by environmentally related processes. Recalling that our spectroscopic sample may be missing some cluster members with masses M_* = 10^{10.6 − 11} M_☉ due to contamination of their spectra, we have tested the effects of adding in the six unconfirmed candidate members described in Section 4.5. This would move f_Q in the lowest-mass bin only with the plotted 1σ uncertainty, resulting in a fraction that would still be elevated above the field. Using a photometric redshift selection and a statistical background subtraction, Raichoor & Andreon (2012) also estimated a high quiescent fraction f_Q ≳ 85% (1σ limit) among massive galaxies (M_* ≳ 10¹¹ M_☉) in the core of JKCS 041 (R < 0.5R₂₀₀), consistent with our spectroscopic sample.

Having determined that the efficiency of quenching in JKCS 041 is high, we now consider the ages of its quiescent members by constructing composite spectra of these galaxies. Stacking increases the signal-to-noise ratio and averages over residual contamination or background subtraction errors that may affect individual spectra. Rather than stacking the flux-calibrated spectra and photometry, we average continuum-normalized spectra covering ≃ 4000–5900 Å redward of continuum break. This technique has several advantages. First, we are able to measure the age-sensitive Balmer (Hβ, γ, δ) and Mg b absorption lines; since these are narrowband features, they are more robust against errors in the continuum shape and uncertainties in dust attenuation. Second, we avoid the rest-frame near-infrared where model uncertainties related to the TP-AGB phase can influence the derived ages around 1 Gyr. Third, we are able to make a homogeneous comparison to coeval, quiescent galaxies in the field, whose composite continuum-normalized spectrum was measured by Whitaker et al. (2013) using 3D-HST survey data.

In order to investigate mass-dependent trends, we split the sample of 15 confirmed quiescent members into a higher-mass subsample consisting of 8 galaxies with M_* > 10¹¹ M_☉, and a lower-mass subsample whose 7 members span M_* = 10^{10.5 − 11} M_☉. The continuum of each spectrum was first determined by fitting a third order polynomial to the models shown in Figure 5, excluding the strong absorption lines. Each spectrum was then divided by the continuum, shifted to the mean redshift of the cluster, and interpolated onto a grid with 48 Å pixels (17 Å in the rest frame), which is close to the native dispersion. The spectra were then combined by averaging each spectral pixel, excluding the highest and lowest measures. Uncertainties were estimated by bootstrapping. The LSFs of the galaxies entering the stack (Section 2.3) were also averaged to construct a mean LSF.

We fit the stacked spectra to simple stellar population (single-burst) models using pyspecfit, taking the redshift, age, and metallicity as free parameters. Although the actual star formation histories are possibly more complex, using the burst models enables us to make a direct comparison with other work, particular that of Whitaker et al. (2013, Section 5.3). The model spectra were continuum-normalized using the same method that was applied to the data. A broad, log-uniform prior was placed on the age. We allow the metallicity to vary to quantify the degeneracy with age. Since these galaxies are expected to evolve into the cores of present-day massive ellipticals (e.g., Bezanson et al. 2009; Hopkins et al. 2009), which are metal-enriched to [Z/H] ≈ 0.1–0.3 (e.g., Thomas et al. 2010; Conroy et al. 2014), we place a broad uniform prior on [Z/H] over the range 0–0.3.

The top left panel of Figure 9 shows the spectrum of the more massive (M_* > 10¹¹ M_☉) quiescent members of JKCS 041. The quality of the spectrum is remarkably high, with a signal-to-noise ratio of 55 per pixel, and it clearly shows several absorption lines as indicated in the figure. The model (black curve) fits the data well with an age of $1.45^{+0.24}_{-0.18}$ Gyr, marginalized over metallicity, which corresponds to a formation redshift $z_f = 3.0^{+0.4}_{-0.2}$.

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The lower left panel displays the mean spectrum of the lower-mass (M_* = 10^{10.5 − 11} M_☉) quiescent members. Although the spectrum is necessarily noisier, with a signal-to-noise ratio of 22, it is clearly different from that of the higher-mass galaxies. The clearest difference is the enhanced strength of the Balmer absorption lines: Hβ, Hγ, Hδ are all markedly deeper in the lower-mass sample. We derive a younger luminosity-weighted mean age of $0.90^{+0.19}_{-0.10}$ Gyr, corresponding to a formation redshift $z_f = 2.4^{+0.2}_{-0.1}$. The Mg b absorption in this spectrum is too deep to be matched even by a maximally old, metal-rich model; this may be due to residual non-Gaussian noise in the stack. In any case, masking Mg b shifts our age inference by only ∼1σ to 0.79 ± 0.19 Gyr (dashed lines in Figure 9).

The quiescent galaxies in JKCS 041 thus have a range of ages that follow the well-known mass-dependent trends seen in the field, in which lower-mass early-type galaxies typically have younger luminosity-weighted ages (e.g., Treu et al. 2005; Thomas et al. 2010). Although the absolute ages depend somewhat on metallicity, the right panel of Figure 9 shows that the age difference of 0.52 ± 0.26 Gyr between the two subsamples is more robust, provided that they have broadly similar metallicity. We indeed expect the mean metallicities of our mass-selected subsamples to differ by ≲ 0.1 dex, based on abundance studies at low redshift.¹⁰

Two additional pieces of data support this conclusion. First, the ages of the individual galaxies as measured from fits to their grism spectra and photometry (Section 3.2) show the same trend: the median age is 1.6 Gyr and 0.96 Gyr for the high- and low-mass subsamples, respectively, which is consistent with the ages derived from their mean continuum-normalized spectra. Second, the lower-mass galaxies have bluer colors, as shown in Figure 6. We can predict the mean color differences between the mass-selected subsamples that should arise purely from the difference in ages inferred from their absorption lines. The predicted Δ〈U − V〉 = 0.14 ± 0.08 and Δ〈V − J〉 = 0.26 ± 0.12 are consistent with the measured values of Δ〈U − V〉 = 0.20 and Δ〈V − J〉 = 0.29. Thus, the color trend can be explained by a mass-dependent trend in age, rather than metallicity or dust content.

These results should be interpreted with the usual understanding the ages are luminosity-weighted and so skew toward the most recent star formation episode. Our focus is robustly constraining the mean age as a function of mass, and some cluster members at given mass may of course be older or younger. (For example, the spectrum of ID 355, shown in Figure 5, is clearly younger than that of the first-rank cluster member.) The tightness of the red sequence led Andreon (2011) to infer that the spread in ages at a fixed mass is quite small. Their analysis, however, is sensitive to the assumed cluster redshift, which we have now revised to z = 1.80. For further details and a revised estimate of the age scatter based on our spectroscopic data, we refer to Andreon et al. (2014).

Whitaker et al. (2013) recently constructed composite spectra of 171 quiescent field galaxy observed in the 3D-HST grism survey. This presents an interesting opportunity to compare quenched field and clusters galaxies at the same early epoch. The Whitaker et al. data are very well suited for this comparison. In addition to being observed with the same instrument, they selected quiescent galaxies using the same UVJ color selection, and their limiting magnitude of H₁₄₀ < 22.8 (measured in the F140W filter) is similar to our limit of H₁₆₀ < 23.3. Their median stellar mass 10^11.08 M_☉, converted to a Salpeter IMF, matches the 10^11.11 M_☉ of our sample. The main difference is that the Whitaker et al. stacks combine field galaxies spanning a wide range in redshift, z = 1.4–2.2, whereas the members of JKCS 041 are obviously at a single redshift. Nonetheless, the median redshift of the galaxies in their stacks is 〈z〉 ≃ 1.6–1.7, close to JKCS 041.

Rather than subdividing their sample by stellar mass, Whitaker et al. split the quiescent selection region of the UVJ plane into two regions indicated by the dashed line in Figure 6. Among the quiescent JKCS 041 members, such a color division is very similar to a division in stellar mass: the eight quiescent members with M_* > 10¹¹ M_☉ would all fall in the redder subsample of Whitaker et al., and the seven less massive members fall in or near their bluer region. The mean color difference between the galaxies in their blue and red subsamples (Δ〈U − V〉 = 0.2, Δ〈V − J〉 = 0.3) is consistent with that described above for our mass-selected subsamples.

With this in mind, in the top left panel of Figure 9 we compare our composite spectrum of massive JKCS 041 members to the composite field spectrum of redder quiescent galaxies investigated by Whitaker et al. First, we note that the Mg b lines are nearly identical. Correspondingly, Whitaker et al. derived an age of $1.6^{+0.5}_{-0.4}$ Gyr for their redder field sample, consistent with our measurement (see right panel). Interestingly, the field stacks show faint line emission in [O iii] λλ4959, 5007 and in filling of Hβ, whereas the spectrum of the JKCS 041 members clearly lacks this emission and instead follows the stellar population model closely.¹¹

In the lower left panel of Figure 9 we compare our composite spectrum of lower-mass JKCS 041 members to the composite spectrum of bluer quiescent field galaxies. The strong Balmer lines seen in the cluster members are also evident in the field. Whitaker et al. derived a reduced age of $0.9^{+0.2}_{-0.1}$ Gyr, again consistent with our measurement for the lower-mass (M_* = 10^{10.5 − 11} M_☉) quiescent cluster members. Whitaker et al. infer [O iii] emission in their bluer subsample as well, although the signal there is more ambiguous. Our stack of lower-mass members shows no clear evidence of emission, but the lower signal-to-noise ratio makes this distinction marginal.

Comparing the ages derived in our two stacks to the Whitaker et al. measurements in the upper right panel of Figure 9, we find that the cluster and field samples span a very similar range. Quantitatively, the differences in luminosity-weighted mean stellar ages are Δt = age_JKCS041 − age_field = −0.2 ± 0.5 Gyr and $0.0^{+0.3}_{-0.1}$ Gyr for the more-massive/redder and less-massive/bluer subsamples, respectively. These results are marginalized over a range of metallicity, whereas Whitaker et al. instead fixed the metallicity to solar abundance in their analysis. If we do the same, these age differences shift to Δt = 0.2 ± 0.5 Gyr and $0.3^{+0.3}_{-0.2}$ Gyr, respectively. In this solar metallicity case, however, the age of the lower-mass cluster members is strongly influenced by the Mg b region, where we noted that the fit is poor. Masking Mg b and relying on Balmer line indictors yields $\Delta t = 0.0^{+0.2}_{-0.1}$ Gyr for the lower-mass subsample.

In each of these comparisons, we do not detect a difference between the field and cluster mean ages at the ∼1σ level, or about 0.5 Gyr and 0.3 Gyr for the more- and less-massive subsamples, respectively. Because the median redshift of the galaxies entering the Whitaker et al. stacks is slightly lower than that of JKCS 041, comparing ages is not precisely the same as comparing formation times. However, the difference in median lookback time is ∼0.3 Gyr for the massive/redder subsample and only 0.1 Gyr for less-massive/bluer examples; both are less than the statistical uncertainties. We also note that the mean ages derived above will not include any galaxies that were very recently truncated and are in transition to the quiescent region of the UVJ plane.

In summary, the mean luminosity-weighted ages of the quiescent members of JKCS 041 varies with mass, with lower-mass galaxies having younger ages. The cluster members span a remarkably similar range of ages to that seen in quiescent field galaxies near the same redshift. Intriguingly, however, the line emission seen in quiescent field samples is absent in JKCS 041, at least among its more massive members where the high quality of the spectrum permits a comparison. We discuss the physical significance of these findings in Section 7.

We used Galfit to fit 2D Sérsic profiles to the F160W images of all spectroscopically confirmed quiescent cluster members (Figure 10). The detailed procedures for PSF construction and masking or simultaneous fitting of nearby galaxies follow those described in N12. The only procedural difference is that we estimate the sky in a larger rectangular annulus around the object, with a width of 80 pixels, and mask objects more aggressively when the sky level is estimated. The derived structural parameters are listed in Table 2. Throughout this section, we refer sizes using the semi-major axis $a = R_e^{\rm maj}$ of the ellipse enclosing half of the light, and not a "circularized" effective radius $\sqrt{ab}$ that is also frequently quoted in the literature. We prefer $R_e^{\rm maj}$ because it is independent of inclination for oblate objects, which form one focus of our analysis, whereas the circularized radius is very sensitive to viewing angle for flattened systems. For the lowest-mass confirmed quiescent member (ID 255), we were unable to secure a reliable size measurement, since this galaxy is essentially unresolved. Based on our simulations, its size is likely R_h ≲ 1 pixel ≈ 0.5 kpc. Our comparison to the field is limited to galaxies having M_* > 10^10.7 M_☉, so this low-mass galaxy does not enter our analysis.

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Table 2. Sérsic Fits to Confirmed Quiescent Cluster Members

ID	$R_e^{\rm maj}$	q	n	$H_{160}^{\rm tot}$	$\log M_*^{\rm tot}/M_{\odot }$
	(kpc)
272	14.7	0.71	6.8	20.03	11.96
376	5.00	0.70	6.5	20.84	11.70
286	5.27	0.83	8.0	21.17	11.68
356	10.6	0.97	7.7	20.71	11.62
355	4.72	0.56	2.7	20.65	11.58
352	2.45	0.74	5.2	21.56	11.34
411	0.85	0.57	4.1	21.93	11.22
657	1.56	0.91	3.2	21.45	11.18
289	0.83	0.65	3.8	21.97	10.97
447	3.13	0.81	3.3	21.95	10.88
317	1.43	0.47	1.9	22.30	10.81
281	0.89	0.75	3.0	22.61	10.80
375	0.62	0.95	3.4	22.64	10.79
359	1.47	0.86	6.9	22.29	10.77
255	(unresolved—see the text)

Notes. Stellar masses in the final column are scaled to the total Sérsic magnitude and so differ from the MAG_AUTO-scaled masses in Table 1. See Section 6.1 for estimates of uncertainties.

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In this section we refer to stellar masses $M_*^{\rm tot}$ that are scaled to the total flux in the Sérsic profile fit. This is preferable when constructing the mass–radius relation, since the size and luminosity are derived consistently from the same light profile. For the largest galaxies, we note that $M_*^{\rm tot}$ can exceed the MAG_AUTO-scaled masses $M_*^{\rm AUTO}$ (Table 1) by up to 0.25 dex.

Our field comparison sample is drawn from four of the CANDELS survey fields. We have augmented the UDS and GOODS-S catalogs in N12 by adding data in COSMOS and GOODS-N, where we make use of the NMBS and MOIRCS Deep Survey (Kajisawa et al. 2011) photometry. In each field, photometric redshifts, stellar masses, and rest-frame colors were estimated using the same procedures described in Section 2.2, based throughout on the BC03 models and a Salpeter IMF. Sérsic profiles were fit to the CANDELS F160W images using the same methods applied to JKCS 041. Our field comparison sample consists of 225 galaxies with M_* > 10^10.7 M_☉ in the redshift interval z = 1.8 ± 0.3 that are classified as quiescent according to their UVJ colors. Galaxies within 1 Mpc of the known z = 1.62 cluster at the edge of the UDS field (Papovich et al. 2010; Tanaka et al. 2010; see Section 7) were removed. For 17 galaxies in the field sample (7.5%) and 1 of the cluster members, the Sérsic index reached the maximum value n = 8 allowed in our fits. Since the radii derived in such cases are often unreliable (see N12, Raichoor et al. 2012), we indicate these galaxies separately in our plots and omit the n = 8 field galaxies when fitting the mass–radius relation.

To validate our fitting method, we inserted hundreds of simulated galaxies with Sérsic profiles into the UDS and JKCS 041 images with a distribution of parameters similar to that in our sample. We found that n, R_h, and the total flux are recovered with negligible biases, i.e., less than a few percent. The typical 1σ uncertainties in R_h are $\sigma _{R_h} = 10\%$ for the majority of systems having R_h < 05, increasing to 17% for larger galaxies. In about 7% of cases, R_h differs from the true value by more than factor of 1.5. The Sérsic index n is recovered with errors of σ_n = 0.4 when n < 5, increasing to σ_n = 0.9 for more extended profiles having n = 5–7. Total fluxes are recovered with a scatter of σ_mag ≃ 0.1 mag. These estimates can be applied to the measurements in Table 2.

We begin our structural comparison of quiescent field and cluster galaxies by considering their shapes. Figure 11 compares the projected axis ratios q = b/a of the two samples. The top panel shows that the field sample spans a wide range of shapes that extends to highly flattened systems with low q. This suggests that many quiescent field galaxies at z ∼ 1.8 harbor a significant disk component. A visual inspection of images of the systems having q ≲ 0.5 supports this conclusion. Other authors have noted evidence of significant disk-like structures in quiescent galaxies at z > 1, even at the highest stellar masses, based on both their projected axis ratio distribution (van der Wel et al. 2011; Weinzirl et al. 2011; Buitrago et al. 2013; Chang et al. 2013a, 2013b) and on results from two-component bulge/disk decompositions (Stockton et al. 2008; McGrath et al. 2008; Bruce et al. 2012; Papovich et al. 2012)

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Turning to the JKCS 041 members in the lower panel of Figure 11, there appear to be fewer flattened galaxies: only one, for example, has q < 0.5. Quantitatively, the difference in mean projected axis ratios is 〈q_JKCS〉 − 〈q_field〉 = 0.11 ± 0.04, and we derive a p-value of 0.03 from a permutation test that indicates this difference is moderately significant.¹² This suggests a probable difference in the underlying morphological composition of the cluster and field galaxies.

More physical insight can be gained from the q distribution using a model for the distribution of intrinsic galaxy shapes. Chang et al. (2013b) have shown that the q distribution of quiescent galaxies can be understood as arising from a two-component population viewed at random angles. One component consists of mildly triaxial galaxies that are nearly spherical, and the other consists of a highly flattened, oblate population. In the following, we refer to these as the spheroid and disk-like components, respectively, although it should be kept in mind that the quiescent disk-like galaxies are likely composite objects containing significant bulges (Bruce et al. 2012) and may be related to the lenticular population at lower redshift; we note that these passive disk-like galaxies appear to span a range of Sérsic indices n ≈ 1–5. This decomposition of the q distribution is not unique, but it is motivated by more detailed photometric and kinematic classifications at lower redshift and serves as a useful starting point for understanding the z > 1 population. Chang et al. showed that the fraction f_obl of quiescent systems belonging to the disk-like population appears to be roughly independent of mass over the range of masses and redshifts relevant for the present paper. In support of this, we see no trend in 〈q〉 with mass in Figure 11.

Overlaid on the histograms in Figure 11 are fits based on this two population model.¹³ Figure 12 shows the inferred fraction f_obl of disk-like galaxies. We find that about half (f_obl = 0.52 ± 0.08) of the z ∼ 1.8 field sample belongs to the disk-like population, consistent with Chang et al., whereas in JKCS 041 the q distribution is best fit with a pure spheroid population (f_obl = 0), with f_obl < 0.28 at 68% confidence. Comparing the two samples, we find that f_obl is lower in the cluster at 90% confidence.

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The stellar mass–radius relations for the quiescent field galaxies and the quiescent JKCS 041 members are shown in Figure 13. As a first step toward comparing the two, we fit a linear relation with Gaussian scatter $\mathcal {N}(\sigma)$ to the field sample:

$$\begin{eqnarray} \log R_e^{\rm maj} / {\rm kpc} &=& \alpha + \beta \log {M}_*^{\rm tot} / 10^{11} {M}_{\odot } \nonumber \\ && - 0.26\,(z-1.8) + \mathcal {N}(\sigma), \end{eqnarray} \tag{ 1 }$$

where β = 0.61 ± 0.07, α = 0.22 ± 0.02, and σ = 0.23 ± 0.01. Here we have taken into account the mild redshift evolution ∂log R/∂z = −0.26 expected within field sample based on the results by N12. This fit is shown by the blue line. Comparing the JKCS 041 members to the mean field relation, there is no evidence for a systematic difference between the two: $\langle \Delta \log R_e^{\rm maj} \rangle = 0.01 \pm 0.09$.¹⁴ There is a hint, however, of a mass-dependent trend: the five most massive galaxies are all displaced above the mean field relation, by an average $\langle \Delta \log R_e^{\rm maj} \rangle = 0.21 \pm 0.12$.

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Since the axis ratio distribution suggests that the morphological mix of quiescent galaxies may be different in JKCS 041 and the field (Section 6.2), it is important to consider what effect this may have on a comparison of sizes. If the morphological compositions indeed differ, then a simple comparison of radii—such as that performed above—will conflate the sizes of spheroids and disks, rather than isolating the effect of the environment on galaxies of comparable morphologies. While nearly edge-on disk-like galaxies are easily identified, it is not easy to locate the same systems viewed at lower inclination. A division in Sérsic index is not very effective, since flatted (q ≲ 0.4) quiescent galaxies are seen in the field over a wide range of n ≈ 1–5. Therefore, rather than attempting to morphologically classify the individual galaxies in the distant field sample, we proceed from the model of the underlying shape distribution discussed in Section 6.2 and follow its implications for the mass–radius relation.

The lower panel of Figure 13 demonstrates that the flattened quiescent field galaxies having q < 0.4 (green symbols) appear to follow a different mass–radius relation: they have smaller $R_e^{\rm maj}$ than the bulk field sample (black symbols), and increasingly so at higher masses.¹⁵ We expect the q < 0.4 galaxies to be a fairly pure (f_obl = 0.89, according to the decomposition in Section 6.2) but incomplete sample of the disk-like population. Since $R_e^{\rm maj}$ is independent of inclination for transparent, oblate objects, those galaxies in the disk-like population that are viewed more nearly face-on, i.e., with higher q, should follow the same mass–radius relation. Assuming that a fraction f_obl = 0.52 ± 0.08 of quiescent field galaxies—of all inclinations—belong to this disk-like population, it is then straightforward to estimate the mass–radius relation for the spheroids. Specifically, at each mass we consider the mean $\langle \log R_e^{\rm maj} \rangle$ as a weighted average: $f_{\rm obl} \langle \log R_{e,{\rm obl}}^{\rm maj} \rangle + (1 - f_{\rm obl}) \langle \log R_{e,{\rm sph}}^{\rm maj} \rangle$.

The blue band in Figure 13 shows the resulting constraint on the relation for quiescent field spheroids. If the cluster galaxies are indeed dominated by spheroids, as suggested by their axis ratio distribution, it is clear that any difference between the field and cluster relations at high masses is much reduced. Quantitatively, the sizes of the five most massive cluster members do not differ systematically ($\langle \Delta \log R_e^{\rm maj} \rangle = -0.06 \pm 0.19$) from the field spheroid relation, although the uncertainties are necessarily increased, and when considering the full range of masses, the cluster members are slightly smaller but still consistent with the field spheroids ($\langle \Delta \log R_e^{\rm maj} \rangle = -0.14 \pm 0.10$). We regard our morphological separation of the mass–radius relation of quiescent galaxies as a first approximation, since it relies on a very simple model for the underlying distribution of shapes (Section 6.2; Chang et al. 2013b) and its apparent invariance with mass at z ∼ 2. More data is needed to test this model and its implication that the fraction of massive, quiescent galaxies with significant disk components increases with redshift. However, it is clear that a difference in the morphological mixtures of the field and cluster samples could significantly affect comparisons of their mass–radius relations.

In summary, there is no significant difference overall between the mass–radius relation defined by the quiescent JKCS 041 members and that defined by our coeval field sample. There is a weak hint of a mass-dependent trend in which the most massive cluster members are offset to larger radii, if all color-selected quiescent galaxies are considered irrespective of morphology. However, a closer inspection reveals that this may arise because the cluster population is richer in spheroids, and spheroids are "larger" than quiescent disk-like galaxies. Figure 14 supports this conclusion via a direct comparison the surface mass density profiles of the JKCS 041 members to the field galaxies. Here we consider only field galaxies with q > 0.45 to better match the cluster sample. The HST PSF was deconvolved from the observed F160W light profile using the technique proposed by Szomoru et al. (2010), and the resulting light profile was converted to a stellar mass profile using a constant M_*/L for each galaxy. There is no clear difference in the mass profiles in the field and JKCS 041 samples.

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Several recent studies of the environmental dependence of galaxy sizes at high redshifts are compared in Figure 15. The references in the upper left legend refer to individual clusters, for which we have compiled published structural measurements of their quiescent or early-type members. In Section 7 we review the bulk physical properties of the z > 1.6 clusters themselves; our focus here on the mass–radius relation. To synthesize these published results into a quantity that can be compared as directly as possible, given the diversity of samples and methods (see Appendix C for details), we compute the mean offset $\langle \Delta \log R_e^{\rm maj} \rangle$ between the quiescent members of each cluster and the field relation in Equation (1). We regard Figure 15 as a first step toward synthesizing results from various high-z studies, but caution that systematic differences in measurement techniques may affect a comparison of our field sample with other authors' cluster data; some of these are discussed in Appendix C.

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Considering the z > 1.6 clusters first, Papovich et al. (2012; see also Bassett et al. 2013), Zirm et al. (2012), and Strazzullo et al. (2013) have all remarked on evidence for larger sizes among the quiescent members of the clusters they studied. (We note that many of these members are actually photometric candidates, whereas the members of JKCS 041 are confirmed by grism redshifts.) Based on Figure 15, we regard the present evidence for a variation in the mass–size relation in the cores of these most distant clusters and proto-clusters as very marginal. On the other hand, present sample sizes are too small to rule out a modest size enhancement of ∼0.05 dex. Moving to lower redshifts, Delaye et al. (2014) studied nine clusters at z = 0.8–1.4 along with a field sample selected and analyzed in a homogeneous way. They found significant evidence for an offset in the mass–radius relation by Δlog R_e ≃ 0.1 dex. In the two z ∼ 1.2 clusters studied by Rettura et al. (2010) and Raichoor et al. (2012), however, we find no significant offset.

Bassett et al. (2013) noticed that the slight trend for the quiescent candidate members of the cluster they studied (IRC-0218A, z = 1.62) to have larger R_e and smaller n was mostly driven by a population of disk galaxies located at large cluster-centric radii R ≈ 1–1.5 Mpc.¹⁶ Although their remark that differences in morphology can influence comparisons of the mass–radius relation is similar to our findings, we note that that the nearly pure disks they discuss (n ∼ 1) have larger R_e than the mean quiescent galaxy—consistent with faded spirals that have been starved of gas during infall—whereas the disk-like quiescent field population discussed in Section 6.3 is offset to smaller R_e and exhibits a wide range of n indicating a significant build-up of bulges (see a similar trend in Huertas-Company et al. 2013b). Altogether, this points to a complex mixture of morphologies varying from the field to the cluster outskirts and core.

In addition to these cluster studies, two recent studies have examined the dependence of the mass–radius relation on local density in blank field surveys, where the densest regions are typically groups or low-mass clusters. These results are distinguished with dashed error bars in Figure 15. Cooper et al. (2012) found a size enhancement of Δlog R_e ≃ 0.1 dex among early-type galaxies in the densest regions in the DEEP3 survey fields. In the UDS field, Lani et al. (2013) detected a similar enhancement that was dominated by the most massive and highest-redshift galaxies. This is the regime where we found that differences in the morphological mix could affect our interpretation of JKCS 041. Lani et al. considered such a possibility and tested it by cutting their sample in Sérsic index n. Although this is a reasonable first approach, we find the connection between the oblate, disk-like quiescent population and Sérsic index to be loose (Section 6.3). Additionally, while the M_*–$R_e^{\rm maj}$ relation likely varies with q (Figure 13), we find no such dependence on n for quiescent galaxies. In future work, it would be useful to consider the q distributions of samples whose mass–radius relations are being compared.¹⁷

In contrast to these z ≳ 1 studies, there appears to be no dependence at z ∼ 0 of the size of early-type galaxies on local density, halo mass, or position within the halo (Weinmann et al. 2009; Guo et al. 2009; Nair et al. 2010; Huertas-Company et al. 2013a). These z ∼ 0 results, however, have been challenged by Valentinuzzi et al. (2010), who claim an excess of compact massive galaxies in local clusters; interestingly, these compact galaxies show a tendency to have S0 morphologies. The only clear point of agreement is that the brightest cluster galaxies (BCGs) in very massive clusters are exceptionally large (e.g., Bernardi et al. 2007).

In summary, the evidence for environmental variation in the mass–radius relation in the most distant z > 1.6 clusters is still limited by small samples. At z ∼ 1 there is good evidence for an offset to larger sizes in the cluster sample studied by Delaye et al. (2014), as well as in group-scale overdensities (Cooper et al. 2012; Lani et al. 2013). At z ∼ 0, most evidence points toward a remarkable independence of early-type galaxy structure on environment. There are contrary indications for many secondary trends that might shed light on an underlying physical picture: are galaxy sizes enhanced primarily in distant clusters' cores (Delaye et al.) or their outskirts (Bassett et al. 2013)? Is the enhancement stronger for higher (Lani et al.) or lower-mass (Delaye et al.) galaxies? Furthermore, the evolutionary connection between z ≳ 1 results and the precise constraints available at z ∼ 0 remains unclear.