EARLY-TYPE GALAXIES AT INTERMEDIATE REDSHIFT OBSERVED WITH HUBBLE SPACE TELESCOPE WFC3: PERSPECTIVES ON RECENT STAR FORMATION

The mean rest-frame optical (g' − r')_rcolors and optical ($M_r^{\prime }$) absolute magnitudes measured for the majority (>75%) of ETGs in Rutkowski et al. (2012) are in general agreement with the optical colors observed for low-redshift red-sequence galaxies, provided a small (∼0.2 mag) color correction is applied to correct for the passive evolution of the stellar population to the redshift range we considered. This suggests that the stellar mass budgets of the ETGs are likely dominated by relatively old, low-mass stellar objects. The traditional paradigm of ETG formation predicts that these stellar populations formed in a short (t ≲ 1 Gyr), massive burst of star formation at high redshift (z  ≳  3; see Kaviraj et al. 2013b). As a result, we expect that the optical-IR SEDs—the wavelength regime in which stellar light from t ≫ 1 Gyr populations dominates the spectrum of old galaxies—should be well-described by stellar population synthesis models that assume a comparable star formation history (SFH).

We produced a library of stellar population models composed of Bruzual & Charlot (2003, hereafter, BC03) population synthesis templates to use for characterizing the old stellar populations in these ETGs. Star formation in these models was defined by a single-burst, exponentially declining SFH with the star formation rate, ψ, characterized by ψ(t)∝e^−t/τ. We calculated models for N = 16 values of τ, the decay of the star formation history, defined with a logarithmic stepsize of

$$\begin{equation} \Delta ({\rm log}(\tau [{\rm Gyr}]))=\frac{{\rm max}({\rm log}(\tau))-{\rm min}({\rm log}(\tau))}{(N-1)}=0.28, \end{equation} \tag{ 1 }$$

over the range −2.0 < log(τ[Gyr])  <  2.0. The model ages were defined over the range 1× 10⁸  <  t(yr) <13.7 × 10⁹ with a logarithmic step-size of log(Δt[yr])  ≃  0.02. A Salpeter stellar initial mass function was assumed (see van Dokkum & Conroy 2010) and the metallicity was fixed at solar. We applied the Calzetti et al. (2000) prescription for dust extinction, assuming 0 ≲ E(B − V) ≲ 1 mag characteristic of low-redshift ETG and spheroidal galaxies (Kaviraj et al. 2011).

We fit these models to the broadband observed optical-IR (F435W, F606W, F775W, F850LP, F098M, F125W, F160W) SEDs of each ETG, measuring the best-fit model parameters by minimizing the goodness-of-fit $\chi ^2_{\nu }$ statistic for each ETG's observed SED, following the standard formalism of Papovich et al. (2001). Old, low-mass (M ∼ M_☉) stellar populations emit predominantly at optical–near-IR wavelengths observed with this filter set, thus (temporarily) excluding the UV ensures that our one-component fitting is largely insensitive to any RSF. In the fitting process, we fix the redshift of each ETG to its spectroscopic redshift (Table 1; Rutkowski et al. 2012). The age of the universe at this redshift was used to set the maximum allowable stellar age in the library of models considered in the analysis of ETGs' SED. In Figure 1, we present the best-fit mass and age parameter measured from these one-component SED fits. The SEDs of the majority of ETGs in this sample are dominated by a massive, (M  ≳  10¹⁰ M_☉), relatively dust-free, old (t >2–3 ×10⁹ Gyr) stellar population—in agreement with the traditional paradigm of galaxy assembly for ETGs.

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Table 1. Measured Characteristics of Catalog ETGs

GOODS ID	Stellar Characteristics			Spatial Characteristics
	tYC[Gyr]	fYC/100%	$\chi ^2_{\nu }$	n	Re	B/A	θ	mF160W	$\chi ^2_{\nu }$
J033202.71-274310.8	0.641$_{0.000}^{0.078}$	0.580$_{0.240}^{0.420}$	7.84	5.78 ± 0.007	10.24 ± 0.023	0.79 ± 0.000	−69.3 ± 0.07	17.18 ± 0.00	1.020
J033203.29-274511.4	0.143$_{0.053}^{0.059}$	0.050$_{0.024}^{0.030}$	1.08	Failed Fcrit
J033205.09-274514.0	0.114$_{0.023}^{0.047}$	0.058$_{0.022}^{0.082}$	0.96	2.42 ± 0.086	1.45 ± 0.018	0.92 ± 0.011	27.8 ± 5.62	22.48 ± 0.01	0.441
J033205.13-274351.0	0.114$_{0.023}^{0.029}$	0.094$_{0.038}^{0.186}$	1.21	2.58 ± 0.130	1.08 ± 0.021	0.86 ± 0.007	34.9 ± 2.83	23.61 ± 0.03	0.355
J033206.27-274536.7	0.571$_{0.443}^{1.929}$	0.009$_{0.008}^{0.290}$	1.10	2.55 ± 0.023	2.69 ± 0.008	0.29 ± 0.000	−89.1 ± 0.05	21.95 ± 0.01	0.443
J033206.48-274403.6	0.047$_{0.047}^{0.208}$	0.000$_{0.000}^{0.006}$	0.83	1.25 ± 0.027	2.85 ± 0.017	0.81 ± 0.004	27.6 ± 0.88	21.94 ± 0.01	0.468
J033206.81-274524.3	0.003$_{0.002}^{0.014}$	0.000$_{0.000}^{0.000}$	2.35	2.88 ± 0.148	1.99 ± 0.033	0.34 ± 0.004	−34.0 ± 0.27	22.98 ± 0.03	0.401
J033207.55-274356.6	0.404$_{0.349}^{0.402}$	0.030$_{0.029}^{0.970}$	0.88	4.15 ± 0.064	3.31 ± 0.051	0.85 ± 0.005	−72.6 ± 1.35	21.31 ± 0.01	0.400
J033207.95-274212.1	0.181$_{0.109}^{0.141}$	0.009$_{0.006}^{0.020}$	0.56	3.01 ± 0.098	0.79 ± 0.008	0.55 ± 0.007	68.5 ± 0.67	22.29 ± 0.00	0.526
J033208.41-274231.3	0.404$_{0.177}^{0.236}$	0.016$_{0.010}^{0.022}$	0.34	6.82 ± 0.083	0.60 ± 0.002	0.91 ± 0.003	−17.0 ± 1.33	20.42 ± 0.00	0.721
J033208.45-274145.9	0.003$_{0.002}^{0.042}$	0.000$_{0.000}^{0.000}$	1.04	5.92 ± 0.059	2.15 ± 0.020	0.86 ± 0.003	74.3 ± 0.75	20.21 ± 0.00	0.596
J033208.53-274217.7	0.072$_{0.050}^{0.089}$	0.001$_{0.001}^{0.003}$	1.95	2.87 ± 0.029	3.28 ± 0.012	0.66 ± 0.001	−87.3 ± 0.16	22.03 ± 0.01	0.817
J033208.55-274231.1	0.003$_{0.002}^{0.078}$	0.000$_{0.000}^{0.002}$	1.08	4.26 ± 0.323	3.62 ± 0.264	0.90 ± 0.016	43.8 ± 7.56	24.60 ± 0.05	0.671
J033208.65-274501.8	1.015$_{0.110}^{0.419}$	0.260$_{0.120}^{0.740}$	1.19	1.29 ± 0.016	2.02 ± 0.006	0.63 ± 0.001	−55.7 ± 0.18	21.35 ± 0.01	0.603
J033208.90-274344.3	0.286$_{0.031}^{0.074}$	0.340$_{0.180}^{0.660}$	1.09	1.65 ± 0.058	1.63 ± 0.012	0.62 ± 0.006	−23.8 ± 0.74	24.70 ± 0.01	0.377
J033209.09-274510.8	0.114$_{0.033}^{0.047}$	0.072$_{0.024}^{0.068}$	1.31	1.84 ± 0.255	0.51 ± 0.013	0.40 ± 0.027	17.0 ± 1.964	23.79 ± 0.01	0.368
J033209.19-274225.6	0.571$_{0.368}^{1.329}$	0.022$_{0.018}^{0.338}$	1.02	1.63 ± 0.018	2.82 ± 0.009	0.62 ± 0.001	−34.4 ± 0.18	22.46 ± 0.01	0.551
J033210.04-274333.1	0.001$_{0.000}^{0.089}$	0.000$_{0.000}^{0.000}$	0.86	7.16 ± 0.031	4.25 ± 0.033	0.85 ± 0.002	−76.6 ± 0.38	19.71 ± 0.00	0.556
J033210.12-274333.3	0.227$_{0.226}^{1.573}$	0.002$_{0.002}^{0.277}$	1.42	4.34 ± 0.059	1.41 ± 0.011	0.54 ± 0.003	51.2 ± 0.27	21.26 ± 0.01
J033210.16-274334.3	0.001$_{0.000}^{1.699}$	0.000$_{0.000}^{0.089}$	0.82	5.17 ± 0.046	2.00 ± 0.017	0.93 ± 0.003	87.6 ± 1.44	20.68 ± 0.01
J033210.76-274234.6	0.360$_{0.105}^{0.044}$	0.012$_{0.007}^{0.006}$	0.59	1.76 ± 0.002	4.11 ± 0.005	0.73 ± 0.000	77.8 ± 0.10	20.85 ± 0.00	3.786
J033210.86-274441.2	0.143$_{0.112}^{0.143}$	0.007$_{0.005}^{0.012}$	0.24	3.68 ± 0.201	0.94 ± 0.024	0.47 ± 0.007	−73.0 ± 0.69	23.86 ± 0.06	0.442
J033211.21-274533.4	0.052$_{0.048}^{0.108}$	0.000$_{0.000}^{0.002}$	3.67	2.25 ± 0.060	1.34 ± 0.021	0.46 ± 0.002	−30.6 ± 0.15	24.93 ± 0.46	0.439
J033211.61-274554.1	0.023$_{0.022}^{0.158}$	0.000$_{0.000}^{0.002}$	1.77	5.01 ± 0.071	2.40 ± 0.021	0.37 ± 0.002	−55.1 ± 0.15	24.11 ± 0.05	0.407
J033212.20-274530.1	0.360$_{0.074}^{0.093}$	0.024$_{0.010}^{0.018}$	1.06	3.38 ± 0.047	2.81 ± 0.034	0.63 ± 0.004	−26.6 ± 0.43	19.89 ± 0.01	8.33
J033212.31-274527.4	0.360$_{0.133}^{0.149}$	0.026$_{0.014}^{0.026}$	1.28	Fail to Converge
J033212.47-274224.2	0.453$_{0.167}^{0.451}$	0.032$_{0.016}^{0.088}$	0.75	0.45 ± 0.019	1.97 ± 0.020	0.85 ± 0.007	−14.4 ± 2.16	21.78 ± 0.00	0.637
J033214.26-274254.2	0.181$_{0.090}^{0.074}$	0.028$_{0.018}^{0.038}$	2.37	Failed Fcrit
J033214.45-274456.6	0.005$_{0.004}^{0.250}$	0.000$_{0.000}^{0.013}$	1.30	1.81 ± 0.052	3.55 ± 0.055	0.66 ± 0.005	−50.9 ± 0.85	22.09 ± 0.01	0.426
J033214.65-274136.6	0.001$_{0.000}^{0.019}$	0.000$_{0.000}^{0.000}$	0.97	5.73 ± 0.213	4.11 ± 0.101	0.88 ± 0.006	−32.2 ± 2.24	23.00 ± 0.02	0.449
J033214.68-274337.1	0.161$_{0.047}^{0.066}$	0.054$_{0.030}^{0.086}$	2.84	2.64 ± 0.080	1.43 ± 0.013	0.40 ± 0.007	−29.2 ± 0.43	22.31 ± 0.01	0.401
J033214.73-274153.3	0.404$_{0.118}^{0.236}$	0.042$_{0.018}^{0.058}$	0.31	5.40 ± 0.127	0.84 ± 0.010	0.56 ± 0.006	83.2 ± 0.54	21.44 ± 0.00	0.647
J033214.78-274433.1	0.025$_{0.024}^{0.296}$	0.000$_{0.000}^{0.011}$	1.21	1.05 ± 0.030	1.78 ± 0.012	0.70 ± 0.002	−82.2 ± 0.53	23.168 ± 0.02	0.425
J033214.83-274157.1	0.404$_{0.118}^{0.167}$	0.046$_{0.022}^{0.054}$	0.21	0.69 ± 0.017	2.40 ± 0.015	0.88 ± 0.005	−27.2 ± 1.70	22.055 ± 0.00	0.531
J033215.98-274422.9	0.404$_{0.083}^{0.049}$	0.078$_{0.036}^{0.062}$	1.06	3.45 ± 0.057	4.46 ± 0.030	0.55 ± 0.002	64.0 ± 0.19	23.704 ± 0.03	0.413
J033216.19-274423.1	0.286$_{0.106}^{0.118}$	0.024$_{0.012}^{0.022}$	0.39	4.43 ± 0.757	4.11 ± 0.535	0.81 ± 0.033	48.6 ± 6.00	22.920 ± 0.05	4.375
J033217.11-274220.9	0.020$_{0.016}^{0.006}$	1.000$_{0.996}^{0.000}$	3.78	Failed Fcrit
J033217.12-274407.7	0.453$_{0.251}^{0.562}$	0.024$_{0.017}^{0.116}$	0.25	2.97 ± 0.109	1.07 ± 0.013	0.31 ± 0.005	−2.6 ± 0.37	23.43 ± 0.03	0.386
J033217.14-274303.3	0.286$_{0.031}^{0.035}$	0.040$_{0.014}^{0.018}$	0.59	4.07 ± 0.019	0.94 ± 0.001	0.87 ± 0.001	−49.8 ± 0.40	19.72 ± 0.00	0.533
J033217.49-274436.7	0.360$_{0.133}^{0.093}$	0.044$_{0.026}^{0.032}$	1.09	8.94 ± 0.100	6.50 ± 0.148	0.99 ± 0.003	−31.1 ± 113.40	20.14 ± 0.01	0.387
J033217.91-274122.7	0.013$_{0.012}^{0.077}$	0.000$_{0.000}^{0.000}$	1.51	2.56 ± 0.041	2.64 ± 0.016	0.93 ± 0.002	−59.3 ± 1.72	22.82 ± 0.01	0.439
J033218.31-274233.5	0.255$_{0.074}^{0.066}$	0.009$_{0.004}^{0.008}$	3.84	5.25 ± 0.014	3.43 ± 0.010	0.48 ± 0.000	−10.9 ± 0.04	19.09 ± 0.00	0.665
J033218.64-274144.4	0.001$_{0.000}^{0.003}$	0.000$_{0.000}^{0.000}$	1.51	3.55 ± 0.605	0.87 ± 0.054	0.76 ± 0.023	−15.1 ± 5.11	23.53 ± 0.04	0.419
J033218.74-274415.8	0.321$_{0.094}^{0.132}$	0.014$_{0.007}^{0.014}$	0.67	2.97 ± 0.029	2.72 ± 0.010	0.58 ± 0.001	61.4 ± 0.12	22.59 ± 0.01	0.450
J033219.02-274242.7	0.072$_{0.070}^{0.214}$	0.001$_{0.001}^{0.010}$	1.50	2.21 ± 0.044	6.06 ± 0.099	0.59 ± 0.005	17.5 ± 0.55	22.87 ± 0.01	0.930
J033219.48-274216.8	0.321$_{0.118}^{0.132}$	0.016$_{0.009}^{0.012}$	0.65	7.93 ± 0.038	2.44 ± 0.015	0.71 ± 0.001	−82.7 ± 0.14	19.29 ± 0.00	0.560
J033219.59-274303.8	0.404$_{0.083}^{0.105}$	0.036$_{0.016}^{0.028}$	1.23	7.64 ± 0.226	2.89 ± 0.039	0.92 ± 0.003	−36.4 ± 1.33	22.05 ± 0.03	0.681
J033219.77-274204.0	0.509$_{0.505}^{0.925}$	0.034$_{0.033}^{0.966}$	0.50	Failed Fcrit
J033220.02-274104.2	0.005$_{0.004}^{0.198}$	0.000$_{0.000}^{0.003}$	1.30	9.06 ± 0.130	2.70 ± 0.053	0.89 ± 0.003	−31.4 ± 1.09	20.11 ± 0.01	0.612
J033220.09-274106.7	0.001$_{0.000}^{0.056}$	0.000$_{0.000}^{0.000}$	2.64	9.17 ± 0.147	5.05 ± 0.128	0.62 ± 0.003	−66.0 ± 0.33	20.16 ± 0.01	0.686
J033220.67-274446.4	0.102$_{0.063}^{0.079}$	0.003$_{0.002}^{0.004}$	3.62	3.91 ± 0.026	2.33 ± 0.011	0.60 ± 0.001	−87.8 ± 0.17	20.39 ± 0.00	0.670
J033221.28-274435.6	0.509$_{0.105}^{0.132}$	0.022$_{0.010}^{0.024}$	1.76	0.64 ± 0.004	6.31 ± 0.014	0.49 ± 0.001	−35.1 ± 0.12	20.36 ± 0.00	13.968
J033222.33-274226.5	5.000$_{4.999}^{1.000}$	0.030$_{0.030}^{0.970}$	1.14	3.63 ± 0.050	2.02 ± 0.013	0.43 ± 0.003	60.8 ± 0.20	21.28 ± 0.00	0.421
J033222.58-274141.2	0.571$_{0.250}^{1.129}$	0.036$_{0.022}^{0.444}$	0.20	2.15 ± 0.032	2.53 ± 0.013	0.88 ± 0.003	−85.5 ± 0.93	21.49 ± 0.00	0.666
J033222.58-274152.1	0.255$_{0.052}^{0.031}$	0.740$_{0.520}^{0.260}$	0.84	Failed Fcrit
J033223.01-274331.5	0.806$_{0.520}^{1.094}$	0.076$_{0.064}^{0.924}$	0.97	6.13 ± 0.084	2.28 ± 0.031	0.84 ± 0.004	−74.3 ± 0.88	20.84 ± 0.01	0.426
J033224.36-274315.2	0.019$_{0.014}^{0.003}$	1.000$_{0.988}^{0.000}$	9.69	Failed Fcrit
J033224.98-274101.5	0.102$_{0.044}^{0.042}$	0.006$_{0.003}^{0.003}$	1.80	6.05 ± 0.035	1.82 ± 0.009	0.82 ± 0.001	44.6 ± 0.32	20.03 ± 0.00	0.506
J033225.11-274425.6	0.031$_{0.026}^{0.016}$	0.009$_{0.009}^{0.012}$	2.11	Failed Fcrit
J033225.29-274224.2	0.404$_{0.044}^{0.049}$	0.920$_{0.480}^{0.080}$	2.71	Failed Fcrit
J033225.47-274327.6	0.404$_{0.202}^{0.167}$	0.009$_{0.007}^{0.014}$	3.52	3.74 ± 0.017	5.95 ± 0.022	0.87 ± 0.001	71.2 ± 0.30	21.49 ± 0.00	0.538
J033225.85-274246.1	0.014$_{0.013}^{0.041}$	0.000$_{0.000}^{0.001}$	1.40	Failed Fcrit
J033225.97-274312.5	0.453$_{0.452}^{2.297}$	0.009$_{0.009}^{0.990}$	0.36	2.40 ± 0.131	0.82 ± 0.011	0.57 ± 0.011	−33.9 ± 1.22	22.77 ± 0.01	0.443
J033225.98-274318.9	0.006$_{0.005}^{0.058}$	0.000$_{0.000}^{0.000}$	1.48	6.08 ± 0.129	1.59 ± 0.026	0.44 ± 0.005	−45.2 ± 0.34	21.46 ± 0.01	0.518
J033226.05-274236.5	5.000$_{0.750}^{0.000}$	1.000$_{0.400}^{0.000}$	2.76	2.31 ± 0.093	2.02 ± 0.029	0.24 ± 0.002	−9.1 ± 0.19	23.05 ± 0.03	0.445
J033226.71-274340.2	0.321$_{0.118}^{0.132}$	0.012$_{0.006}^{0.012}$	0.36	3.65 ± 0.063	1.35 ± 0.011	0.58 ± 0.002	42.9 ± 0.27	22.65 ± 0.01	0.467
J033227.18-274416.5	0.571$_{0.062}^{0.000}$	0.120$_{0.054}^{0.040}$	3.69	4.81 ± 0.028	4.17 ± 0.010	0.56 ± 0.000	29.0 ± 0.05	21.16 ± 0.01	1.034
J033227.62-274144.9	0.203$_{0.042}^{0.052}$	0.018$_{0.006}^{0.014}$	2.75	1.81 ± 0.028	1.85 ± 0.008	0.68 ± 0.002	−44.8 ± 0.28	21.66 ± 0.01	0.640
J033227.70-274043.7	1.015$_{0.375}^{0.885}$	0.120$_{0.084}^{0.880}$	1.34	4.03 ± 0.078	2.46 ± 0.020	0.33 ± 0.001	−77.0 ± 0.10	22.17 ± 0.02	0.478
J033227.84-274136.8	0.050$_{0.047}^{0.153}$	0.001$_{0.000}^{0.007}$	1.83	6.75 ± 0.075	10.16 ± 0.21	60.61 ± 0.002	52.7 ± 0.27	20.30 ± 0.01	0.492
J033227.86-274313.6	0.019$_{0.016}^{0.062}$	0.000$_{0.000}^{0.005}$	1.43	Failed Fcrit
J033228.88-274129.3	0.203$_{0.164}^{0.202}$	0.003$_{0.003}^{0.010}$	0.64	2.75 ± 0.017	3.28 ± 0.007	0.91 ± 0.001	−56.4 ± 0.59	21.88 ± 0.01	0.542
J033229.04-274432.2	5.000$_{4.999}^{0.000}$	1.000$_{1.000}^{0.000}$	0.58	2.20 ± 0.096	1.32 ± 0.016	0.20 ± 0.010	−51.3 ± 0.42	22.34 ± 0.00	0.922
J033229.30-274244.8	0.072$_{0.052}^{0.089}$	0.004$_{0.003}^{0.009}$	0.89	1.25 ± 0.058	2.16 ± 0.022	0.55 ± 0.005	82.7 ± 0.58	22.45 ± 0.01	0.503
J033229.64-274030.3	0.102$_{0.062}^{0.101}$	0.009$_{0.006}^{0.026}$	2.08	1.32 ± 0.036	2.02 ± 0.013	0.43 ± 0.005	87.3 ± 0.40	22.39 ± 0.00	0.449
J033230.56-274145.7	0.143$_{0.042}^{0.059}$	0.042$_{0.020}^{0.046}$	1.82	0.95 ± 0.012	1.63 ± 0.005	0.58 ± 0.002	78.4 ± 0.26	21.64 ± 0.00	0.361
J033231.84-274329.4	0.002$_{0.001}^{0.225}$	0.000$_{0.000}^{0.009}$	0.58	7.66 ± 0.272	3.38 ± 0.164	0.90 ± 0.011	−78.4 ± 3.61	21.71 ± 0.02	0.393
J033232.34-274345.8	0.114$_{0.050}^{0.029}$	0.040$_{0.024}^{0.056}$	1.58	Failed Fcrit
J033232.57-274133.8	0.001$_{0.000}^{0.001}$	0.002$_{0.000}^{0.000}$	2.37	Not Fit
J033232.96-274106.8	0.143$_{0.016}^{0.037}$	0.048$_{0.014}^{0.026}$	0.57	0.78 ± 0.015	1.15 ± 0.005	0.89 ± 0.002	69.8 ± 1.37	23.30 ± 0.02	0.480
J033233.28-274236.0	5.000$_{4.999}^{0.000}$	0.180$_{0.180}^{0.820}$	0.10	2.59 ± 0.169	1.18 ± 0.023	0.39 ± 0.014	38.6 ± 0.92	23.03 ± 0.01	0.464
J033233.40-274138.9	0.203$_{0.089}^{0.084}$	0.016$_{0.010}^{0.026}$	2.20	1.87 ± 0.023	2.25 ± 0.007	0.82 ± 0.002	−21.0 ± 0.48	23.37 ± 0.03	0.388
J033233.87-274357.6	0.005$_{0.004}^{0.250}$	0.000$_{0.000}^{0.007}$	1.48	3.62 ± 0.070	1.13 ± 0.008	0.91 ± 0.005	53.1 ± 2.57	21.53 ± 0.00	0.458
J033234.34-274350.1	0.161$_{0.059}^{0.094}$	0.009$_{0.004}^{0.010}$	3.56	9.73 ± 0.086	5.43 ± 0.093	0.84 ± 0.002	28.7 ± 0.51	19.77 ± 0.01	0.430
J033235.10-274410.7	0.052$_{0.026}^{0.028}$	0.012$_{0.006}^{0.010}$	8.73	4.86 ± 0.128	3.17 ± 0.094	0.83 ± 0.009	35.9 ± 1.91	21.44 ± 0.01	0.392
J033235.63-274310.2	0.001$_{0.000}^{0.025}$	0.000$_{0.000}^{0.000}$	1.16	4.53 ± 0.095	4.08 ± 0.037	0.54 ± 0.002	−24.8 ± 0.22	22.43 ± 0.01	0.439
J033236.72-274406.4	0.143$_{0.063}^{0.059}$	0.009$_{0.005}^{0.006}$	0.67	3.79 ± 0.086	4.87 ± 0.065	0.54 ± 0.003	23.9 ± 0.28	22.96 ± 0.02	0.403
J033237.32-274334.3	0.114$_{0.079}^{0.113}$	0.004$_{0.003}^{0.005}$	1.15	1.73 ± 0.020	4.37 ± 0.043	0.87 ± 0.005	−86.8 ± 1.58	21.34 ± 0.01	0.493
J033237.38-274126.2	0.404$_{0.149}^{0.167}$	0.007$_{0.005}^{0.012}$	1.72	Fail to Converge
J033238.06-274128.4	0.128$_{0.127}^{0.232}$	0.001$_{0.001}^{0.006}$	2.32	5.80 ± 0.032	4.76 ± 0.037	0.58 ± 0.001	40.0 ± 0.12	19.67 ± 0.00	0.535
J033238.36-274128.4	0.286$_{0.125}^{0.223}$	0.050$_{0.034}^{0.290}$	6.48	3.35 ± 0.060	1.21 ± 0.008	0.90 ± 0.004	46.2 ± 2.49	24.37 ± 0.05	0.475
J033238.44-274019.6	0.026$_{0.025}^{0.117}$	0.000$_{0.000}^{0.002}$	1.14	6.01 ± 0.074	3.09 ± 0.042	0.72 ± 0.003	−80.6 ± 0.45	20.71 ± 0.01	0.442
J033238.48-274313.8	0.255$_{0.052}^{0.066}$	0.160$_{0.078}^{0.360}$	1.66	Failed Fcrit
J033239.17-274026.5	0.321$_{0.066}^{0.083}$	0.032$_{0.014}^{0.030}$	1.02	2.41 ± 0.026	3.83 ± 0.014	0.65 ± 0.001	−28.7 ± 0.21	22.85 ± 0.01	0.448
J033239.17-274257.7	0.571$_{0.211}^{0.236}$	0.032$_{0.018}^{0.040}$	0.54	5.59 ± 0.022	5.30 ± 0.019	0.89 ± 0.000	20.8 ± 0.24	20.47 ± 0.00	0.562
J033239.18-274329.0	0.003$_{0.002}^{0.224}$	0.000$_{0.000}^{0.006}$	0.44	5.85 ± 0.149	2.55 ± 0.065	0.87 ± 0.008	25.1 ± 2.21	21.81 ± 0.01	0.360
J033239.52-274117.4	0.052$_{0.052}^{0.203}$	0.000$_{0.000}^{0.005}$	1.42	1.41 ± 0.022	3.57 ± 0.019	0.63 ± 0.003	4.7 ± 0.33	22.26 ± 0.01	0.457
J033240.38-274338.3	0.025$_{0.022}^{0.047}$	0.000$_{0.000}^{0.001}$	0.65	4.30 ± 0.048	5.68 ± 0.083	0.64 ± 0.003	26.2 ± 0.37	20.90 ± 0.01	0.376
J033241.63-274151.5	0.038$_{0.034}^{0.052}$	0.000$_{0.000}^{0.001}$	4.30	1.99 ± 0.036	3.70 ± 0.020	0.94 ± 0.004	9.3 ± 2.85	22.70 ± 0.01	0.474
J033242.36-274238.0	0.509$_{0.149}^{0.132}$	0.018$_{0.010}^{0.018}$	1.51	8.65 ± 0.048	5.77 ± 0.056	0.46 ± 0.000	74.4 ± 0.06	18.79 ± 0.00	0.977
J033243.93-274232.4	0.001$_{0.000}^{0.063}$	0.000$_{0.000}^{0.000}$	3.03	3.54 ± 0.056	4.84 ± 0.039	0.59 ± 0.001	28.6 ± 0.25	22.49 ± 0.01	0.478
J033244.97-274309.1	0.009$_{0.008}^{0.171}$	0.000$_{0.000}^{0.002}$	4.93	Failed Fcrit

Notes. We present spatial and stellar characteristics measured for the ETGs in Sections 3.2 and 4, respectively. Columns 2–4 provide characteristics of the best-fit young stellar population. Uncertainties associated with these parameters represent the 68% confidence interval. Columns 5–10 provide quantitative characteristics of the ETGs morphology. Row values associated with the spatial parameters in these columns are defined as follows: "Failed F_crit" = galaxies that failed the criterion for identifying well-resolved galaxies were not fit (see Section 4.1); "Not Fit" = galaxies were not fit because the light-profiles of the ETG were strongly blended with bright neighbors; "Fail to Converge" = one or more parameters could not be well-fit by GALFIT. The $\chi ^2_{\nu }$ values of ETGs in Column 10 are provided in bold for the ETGs that were better fit with a two-component spatial model (i.e., PSF and Sérsic model, see Section 4.1).

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By design, the single-component SED analysis in the previous section is sensitive to the majority (by mass) old stellar populations in these ETGs. Here, we aim to better constrain the complete SFH, modeling the SEDs by including synthetic stellar templates that describe both the old and young stellar populations. Well-studied lines and broad absorption complexes (e.g., Hα; Ca H and K, Balmer breaks) at optical wavelengths cannot be used here because only broadband imaging was publicly available for the majority of these ETGs. Enabled by the UV sensitivity of the HST we can instead use broadband UV diagnostics to characterize recent (t ≲ 1 Gyr) star formation in these ETGs.

Before characterizing any young stellar population in the ETGs, we must first confirm that the UV emission does not likely arise from old, low-mass (M ≲ 1 M_☉) stellar populations. Such hot (T > 25, 000 K) stellar populations (e.g., extreme horizontal branch (EHB) stars, see O'Connell 1999) can produce a "UV Upturn" (UVX). The evolution of the EHB progenitors is not fully understood, but it is believed to be a metallicity-dependent mass-loss effect in old (t > 10 Gyr) stars (Yi et al. 1998, 1999).

We apply the UV–optical color–color criteria defined by Yi et al. (2011) to differentiate between UVX-dominated and recently star-forming ETGs. None of the ETGs in our sample are found to be dominated at UV–optical wavelengths by the emission from an EHB population. This agrees with the expectation from the theory of the evolution of low-mass stars to the EHB (see Yi et al., 2003), that at z  ≳  0.3 the UVX will be negligible because the stars in galaxies at this redshift are too young (see Kaviraj et al. 2007). We cannot exclude the possibility of an EHB population, but—if they are present (see Han et al. 2007)—this is a minority stellar population in low-redshift ETGs (≪1% of the total stellar mass, Yi et al. 2011). Where they exist, the blue rest-frame UV–optical colors measured in Rutkowski et al. (2012) likely indicate the presence of a relatively young (t ≲ 1 Gyr) population of massive stars.

The characteristics of any minor, young stellar population in these optically red ETGs will not be well-constrained if the SFHs are modeled with a library of stellar population templates that assumes (Section 3.1) the star formation rate is well-described by a single, exponentially declining starburst event from high (z > 3–4) redshift. We extend our analysis of the SFHs to include two-component stellar template models, in which the SFH is defined by two independent bursts of star formation of varying mass fractions and ages.

In this analysis we follow the same methodology defined in Jeong et al. (2007). We fit a two-component synthesized stellar populations model simultaneously to the observed ERS photometry, minimizing the $\chi ^2_{\nu }$ of the model fit to measure the best-fit model to each ETG's ten-filter SED. As in Jeong et al. (2007), we applied a template library of stellar population models for which the old stellar population is modeled by the Y² models that include EHB stars (Yi et al. 2003), assuming an initial burst of star formation at z  ≃  3 (Rutkowski et al. 2012; Kaviraj et al. 2013b). The second component is designed to represent any possible young stellar components and is derived from the BC03 templates assuming a fixed solar metallicity for all models. When fitting the complete UV–optical near-IR SED, only the mass of the old stellar population models was variable. In contrast, both the age (hereafter, t_YC) and the mass fraction (f_YC = (M_young/M_total) × 100%) of the younger stellar component were variable—10⁻³ < t_YC[Gyr] < 5 and 10⁻⁴ < f_YC[%] < 100. Both stellar populations components could be derived from the BC03 models in principle because the color–color measurements demonstrate that the contribution from UV-bright, old stellar populations is likely to be negligible.

If the characteristics of the young and old stellar populations are derived from an SED analysis that uses a library of two-component synthesized stellar population templates derived exclusively from the BC03 templates, the derived age and mass fraction of the young stellar populations are in good agreement (∼90% of the ETGs agree, to within the measurement uncertainties) with those measured using synthesized BC03+Y² libraries as discussed previously. For the few ETGs, where they exist, we can attribute discrepancies between the best-fit age and mass fraction measured using these two libraries to degeneracies in the fitting arising from the large photometric uncertainties in one or more of the bands that assess rest-frame UV emission (i.e., these ETGs have a signal-to-noise ratio in the UV ≲ 1).¹²

For ease of comparison of these results with similar measurements of the RSF in ETGs at lower redshift, we chose to define the two-component synthesis models used here as identical to Jeong et al. (2007). Note that in this two-component SED analysis we did not apply an explicit correction for dust. Dust preferentially attenuates the SED at UV wavelengths, thus the fraction of ETGs that are found to have experienced a minor, recent star formation event is a lower limit to the true fraction.

A representative two-component model fit SED is shown in Figure 2 for ETG J033212.20−274530.1. In Table 1, we present the best-fit parameters from our two-component SED analysis, with upper and lower uncertainties on the measurement of each free parameter indicating the 68% confidence level. Where they exist, large young stellar population parameter uncertainties can be primarily attributed to the photometric uncertainties associated with the WFC3 UVIS data. The ERS program is a medium-depth survey that observed these UV-faint (F225W  ≳  23 mag) ETGs to a signal-to-noise ratio in the range 1 ≲ S/N ≲ 20 (see Table 1 in Rutkowski et al. 2012). These photometric uncertainties are markedly lower¹³ than those measured in previous surveys of comparable galaxies at this intermediate redshift range (e.g., Ferreras & Silk 2000). Although $\chi ^2_{\nu }$ values of the best-fit models are generally small ($\chi ^2_{\nu }$ ≲ 1–2), we caution that the uncertainty in the measurement t_YC & f_YC is not correspondingly small, due to the implicit degeneracies in fitting these models to SEDs with large photometric uncertainties. Furthermore, distinguishing between a massive old stellar population and a relatively low-mass young (t ≲ 50 Myr) starburst—in which the UV-light can be strongly attenuated by the young stellar population dusty birth cloud—using broadband photometry alone is difficult (see, e.g., Kaviraj et al. 2007). These systematic effects are more pronounced at the high redshift (z > 1), a range in which the observed ERS filters are insensitive to rest-frame wavelengths greater than ∼1 μm, where old stellar populations dominate the SED.

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Throughout the text, we will define ETGs to have evidence for recent star formation when the characteristics of the best-fit young stellar population from this two-component SED analysis is in the range of 1 <f_YC[%] <10 and 0.1 <t_YC[Gyr] <1. Applying this criteria, we conservatively measure at least ∼40% of ETGs to have experienced a recent, minor burst of star formation in a sample of 77 total ETGs well-fit (i.e., $\chi _{\nu }^2$) with this two-component analysis. The mean age and mass fraction of the best-fit young stellar population component for the sample equals t_YC = 360 ± 160 Myr and f_YC = 3.7 ± 2%. At low redshift (z ≲ 0.1), Kaviraj et al. (2007) observed ∼30% of ETGs to have UV colors consistent with recent star formation, with the average age of the young stellar component of ∼300–500 Myr. At higher redshift (1 <z <3), Kaviraj et al. (2013a) found that ∼60% of massive spheroidal galaxies have evidence of recent star formation and have a redshift of formation z_f  ≃  3–4. Considering only the magnitude of the observed fraction of ETGs with RSF suggests that star formation in ETGs generally declines with decreasing redshift.

Each of these previous measurements of the fraction of ETGs with RSF is a lower limit to the total fraction at a given redshift, as the measurements are subject to the photometric completeness in each survey, particularly at the UV wavelengths most sensitive to recent star formation in these optically red ETGs. This completeness can vary considerably between surveys. For example, the GALEX Medium Imaging Survey (MIS)—which was used in the measurement of the low-redshift fraction of ETGs with RSF in Kaviraj et al. (2008)—is complete to NUV < 23; our ERS data probes UV magnitudes that are 2.5 mag fainter. We measure a fraction of ETGs with RSF that is approximately equal to 30% (11/38 ETGs) and consistent with the measurement in the local universe, if only ETGs with $M_{r^{\prime }}<-21.3$ (see Table 5; Rutkowski et al. 2012) are considered (i.e., including only those galaxies as bright as those considered in the sample of Kaviraj et al. 2008).

In Figure 3 we provide the (FUV–V)_r and (NUV–V)_r colors of the ETGs measured from the two-component analysis, plotted with respect to their spectroscopic redshifts. Here, ETGs measured with recent star formation (as defined by the conservative criteria above) are indicated as large, filled colored points, with an inset color scheme corresponding to the best-fit young stellar component. In addition, we include those ETGs (smaller, red filled points) with measurement uncertainties of the age and stellar mass fraction of young stars consistent (i.e., <1 dex, see Table 1) with recent star formation. Black, unfilled circles in the figure indicate ETGs whose best-fit young stellar parameters are consistent with a quiescent star formation history. In addition to these measured data, we incorporate additional data for a subset of ETGs from the catalogs presented in Rutkowski et al. (2012). We overplot X-ray/Radio sources as filled star symbols, and recently star-forming ETGs with UV–optical colors previously reported as upper limits are overplotted with a small, down(red)ward-pointing arrow. We also overplot (vertical lines) the offset between the UV–optical color reported in Rutkowski et al. (2012) and those measured from the best-fit two-component model. For clarity, we only show the color offset when the difference between the rest-frame colors derived from the broadband transformation in Rutkowski et al. (2012) and the model colors is greater than 0.2 mag. Few (∼15%) ETGs show large offsets—this confirms that the generalized transformation of the observed broadband UV-optical colors to the rest-frame GALEX UV–optical colors is reasonable for the majority of intermediate redshift ETGs.

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In Figure 3, in particular for the (FUV–V)_r colors, there appears to be an evolution from high to low redshift toward relatively bluer colors. This contradicts the initial conclusion that the sample is consistent with a general decline, or potentially constant, in the fraction of ETGs experiencing recent star formation from 2 < z < 3 to z ∼ 0. The trend does not likely represent a cosmological effect. Rather, the eye is strongly biased by the few extremely red (FUV–V   ≳   7) ETGs at z  ≳  1, whose colors were derived from the two-component SED analysis. In this analysis these ETGs are marked by downward-pointing arrows, indicating that these ETGs were non-detected in the rest-frame FUV. Additionally, these galaxies are relatively faint (m_F606W  ∼  26) at optical wavelengths. Uncertainties in the measurement of the best-fit model from which these UV-optical colors are derived are further compounded by the fact that at high redshift (z > 1) the reddest ERS filter (F160W) is sensitive to rest-frame optical (λ < 8000 Å) emission. As a result, at z  ≳  1 the stellar mass in old stars becomes increasingly difficult to constrain without the near-IR rest-frame data available for the ETGs at lower redshifts. Similarly, the young stellar mass fraction relative to the total old stellar mass becomes increasingly difficult to constrain. Thus, for these ETGs—which were measured to have a mass fraction consistent with zero—the derived UV–optical colors will be very red, not for physical reasons but as a result of these compounding photometric and modeling uncertainties. The initial conclusion that the fraction of star-forming ETGs declines or remains constant, as a function of decreasing redshift, remains tenable. We note that the addition of deeper UV photometry and IR rest-frame photometry could improve the uncertainties associated with the higher redshift ETGs' rest-frame UV-optical measured photometry and stellar population fitting (although existing archival data is at significantly lower spatial resolution).

These ETGs were identified in Rutkowski et al. (2012) by visual selection based on their similarity with the classical morphology of ETGs: a high degree of rotational symmetry and smoothly varying stellar light-profile. Such light-profiles can be well described with relatively few parameters, for example, the Sérsic profile defined as:

$$\begin{equation} I(r)=I(0)\times \,\exp [-b_n(r/r_e)^{1/n}], \end{equation} \tag{ 2 }$$

where I(0) is the intensity at radius r = 0, r_e is the half-light radius, n is the Sérsic index, and b_n is a normalization constant that is a function of the Sérsic index and ensures that the radius r_e encloses half of the total galaxy light. Generally, disk-dominated galaxies are described by a Sérsic profile with n  ≃  1; bulge-dominated, spheroidal galaxies are best-fit by Sérsic profile with n  ≃  4. However, a large dispersion for spheroidals is observed. At low redshift, Kormendy et al. (2009) measured a mean Sérsic index of n  ≃  3.8 (N = 37 ETGs) with a large spread (>35% of the ETGs were measured n > 4; 60% of those were measured with n > 7). Krajnovic et al. (2013) measured disk-like Sérsic profiles (n ≲ 2) for the majority of the SAURON sample of local ellipticals (de Zeeuw et al. 2002). High-redshift compact, quiescent ETGs also are found to have a large dispersion in measured Sérsic indices—van der Wel et al. (2011) and Ryan et al. (2012) report n ≲ 2 for 30%–60% of compact (r_e ≲ 1 kpc) massive (log(M[M_☉])  ≳  11) quiescent ETGs, whereas Cassata et al. (2013) and Williams et al. (2014) report large (n > 2.5) indices for ∼90% of ETGs. Considering the wide range of observed morphologies of ETGs, we can reasonably expect to find a similar diversity in this sample of visually selected ETGs, especially as our sample selection includes S0s/Lenticulars and compact ETGs (see Table 2 in Rutkowski et al. 2012).

A quantitative assessment of the ETGs morphologies may reveal unique clues to the assembly histories of the ETGs. For example, in simulations of gas-rich major mergers at high redshift, Wuyts et al. (2010) found that the ETG descendants of such mergers have surface brightness profiles best characterized by large Sérsic indices (n ≲ 10), with a core, young component associated with the final coalescence of the merger. In our sample, a visual inspection of the rest-frame UV morphologies (see Figure 1 in Rutkowski et al. 2012) reveals that for the ∼30% of the ETGs that show appreciable UV emission, this light appears to be dominated by core emission. The combination of the blue UV–optical colors in these ETGs and core-dominated UV light-profiles could, in light of this Wuyts et al. result (and others, see Hopkins et al. 2008, 2009), provide clues about the formation and evolution of the ETGs.

We used GALFIT (Peng et al. 2002) to first measure the best-fit Sérsic profile for each ETG in 200 kpc×200 kpc postage stamp images extracted from the ERS F160W mosaics. We implemented GALFIT via the IDL software wrapper iGALFIT¹⁴, which is useful for iterative batch processing. This software requires the user to provide an image and weight map in the same units (counts s⁻¹), ensuring that the uncertainty ($\chi ^2_{\nu }$) of each profile fit in GALFIT is properly normalized.

We prepared large (250–500 square pixels) postage stamps for each ETG for analysis with GALFIT. We masked a large (20 ≲ N ≲ 50) number of regions in each postage stamp that contained neighboring galaxies or noisy pixels (e.g., at WFC3 chip and mosaic gaps). It was never necessary to mask more than ∼10% of the total image area, but this masking is necessary. GALFIT calculates the sky brightness locally within each image, and fits the model light-profile assuming that all flux within the region of interest is associated with the ETG. Identifying and removing the contaminating sources (e.g., foreground and background objects) ensures a more accurate measurement of the light-profile.

In Table 2 of Rutkowski et al. (2012), 15 galaxies were noted for their compact morphologies, so it is also necessary to exclude ETGs that may be only marginally spatially resolved. We identify which marginally resolved ETGs to exclude by fitting all ETGs with a Sérsic profile and an empirical PSF (defined by stacking known stars in the ERS field, see Windhorst et al. 2011). We then calculated the fractional χ² difference, F_crit, equal to:

$$\begin{equation} F_{{\rm crit}}=\frac{\left(\chi^{2}_{PSF}-\chi^{2}_{{\rm S\acute{e}rsic}}\right)}{\chi^{2}_{{\rm S\acute{e}rsic}}}, \end{equation} \tag{ 3 }$$

where χ² is measured from the two model fits (Bond et al. 2009). Ryan et al. (2012) determined that for ERS ETGs observed in F160W, F_crit  ≃  0.01 can generally distinguish point-sources from well-resolved galaxies. Thirteen galaxies were measured to have F_crit < 0.01 and are designated "Failed F_crit" in Table 1. Nine of these ETGs were originally noted for their compact morphology in Rutkowski et al. 2012, and a visual inspection of publicly available spectra¹⁵ confirmed that ∼50% (7/13) of those ETGs were identified with [O ii]3727 Å, or an unknown emission line, in their spectrum, potentially indicating the presence of a central star cluster or weak AGN. If the stellar light-profiles of these ETGs were relatively faint in comparison to a bright, spatially unresolved point source, this could explain the poor Sérsic profile fit. We exclude these galaxies from the subsequent analysis. At this stage, we also exclude one additional ETG because the light-profile of this galaxy was inextricably blended with a nearby galaxy and no accurate mask model could be determined. This ETG is indicated "Not Fit" in Table 1.

Next, we inspected the residual images produced by GALFIT by differencing the best-fit Sérsic model light-profile and the original input image. We found that ∼20% ETGs that were not excluded by the above criteria were still poorly fit by a single Sérsic profile.¹⁶ These images typically showed an irregular, patchy, or "ring"-like structure (a bright core, bounded by an oversubtracted region) in their residual map. This structure may indicate the presence of an additional component, either in the core (a "cuspy" core or centrally concentrated star-forming region, see, e.g., Suh et al. 2010) or wings (possibly indicating an extended core stellar-disk component).

To improve our Sérsic model fit, we re-measured the light-profiles using a two-component model composed of a combined Sérsic model and the empirically defined PSF. We repeated our fitting of the light profiles with this model, measuring the best-fit model (M) that satisfied the criteria that (1) GALFIT parameter solution converged for each model, and (2) $M=\min \lbrace \chi ^2_{\rm{S\acute{e}rsic}},\chi ^2_{\rm{S\acute{e}rsic}+PSF}\rbrace$, where the χ² was reported by GALFIT. In Table 1, ETGs whose light profiles were better modeled with this two-component spatial model are designated with $\chi ^2_{\nu }$ in a boldface font. No solution could be found for two ETGs with either the one- (Sérsic only) or two- (Sérsic +empirical PSF) component model. Rather than attempt a fit with additional components, we designate the row value for these ETGs as "Fail to Converge" in Table 1, and do not consider these ETGs in the following discussion. In summary, 86 of 102 ETGs were well-fit ($\langle \chi ^2_{\nu }\rangle$ = 0.54) with either the one- or two-component Sérsic model.

In Figure 4, we plot the best-fit half-light radii (converted to a physical scale of kiloparsecs, assuming the spectroscopic distance) against the measured Sérsic index, with the symbol colors indicating the age of the young stellar population, t_YC. The mean Sérsic index 〈n〉 equals 3.7 ± 2.1 and the mean half-light radius of 〈r_e〉 equals 2.9 ± 1.88 kpc. In the top panel of Figure 4, we plot a log-normal function fit to the distribution of n, where 〈n〉 = 2.1, σ = 1.2 and skewness, γ, equals 1.6. In the right panel of Figure 4, we plot a log-normal function fit to the distribution of r_e, with a best-fit mean, variance (in kpc), and skewness equal to 1.4, 1.3, and 2.0, respectively. In general, there is no strong correlation observed between characteristics of the young stellar populations identified from the analysis of Section 3 and the morphology of these ETGs, i.e., recent star formation is observed for ETGs with both disk (n < 2.5) and bulge-like (n > 2.5) morphologies. We note that the mean Sérsicindex for high-mass ETGs (M > 10^10.5 M_☉) equals 〈n〉 = 4.2 (σ = 2.2); the mean index measured for low-mass ETGs equals 〈n〉 = 2.2 (σ = 1.2). For a discussion of the possible implications of these results for the evolution of ETGs at intermediate redshift, we refer the reader to Section 5.

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Mergers of companions with massive ETGs are implicated in theory and observation to explain the recent star formation observed in the latter. The space density of major (μ = (M_comp/M_ETG)  ∼  1, i.e., equal mass) mergers is not high enough to account for the observed star formation in intermediate to high-redshift ETGs (e.g., López-Sanjuan 2010, 2012; Kaviraj et al. 2013b). Minor (μ ⩾ 1:4) mergers occur more frequently than major mergers, and as a result are a more viable mechanism for introducing gas into ETGs (Kaviraj et al. 2013a). Due to the relatively short destruction timescales of companions in minor mergers (Peirani et al. 2010), catching such mergers "in the act" in order to directly correlate recent mergers with the incidence of recent star formation is not feasible with this small sample. Instead, the presence of companion galaxies can be used as a proxy for future mergers, as the infall times are markedly longer (≫1 Gyr; Tal et al. 2013). In the following sections, we outline (Section 4.2.1) and apply (Section 4.2.2) a method for measuring the number of likely companions for each ETG.

4.2.1. Likely Companions to ETGs: Method

4.2.2. Likely Companions to ETGs: Results

Applying the López-Sanjuan formalism we find that the total number of likely companions (N_c, defined as the sum of the individual system contributions, ν_k, as outlined in the Appendix) is only greater than one if the galaxies within the volume of interest are measured with a spectroscopic redshift. Conversely, no ETGs were measured with N_c  ≳  1 if all possible companions had only measured photometric redshifts. For systems—with possible companions measured only with photometric redshifts—to contribute ν_k  ≃  1, the uncertainty in the companions' redshift must be quite small. Only in the idealized case where the photometric redshift of the possible companion equals the spectroscopic redshift of the ETG, will a Gaussian PF with σ_z ≲ 10⁻³ (or, equivalently an uncertainty in velocity equal to σ_v ≲ 10² km s⁻¹) contribute $N_{c}^{j}\sim$ 1. No possible companions with photometric redshifts and such narrow PFs met the selection criteria (Section 4.2.1). In practice, the PFs associated with photometric redshifts for possible companions were measured with σ_z  ≃  10⁻¹. Uncertainties of this magnitude imply contributions to the total number of likely companions in these pairs of ≲10⁻². The total number of galaxies with only photometric redshifts (i.e., no companions considered had spectroscopic redshifts) was never greater than seven in the search region. Thus, the cumulative contribution of these system was never greater than N_c  ≃  0.1. Increasing the search volume could increase the number of possible companions considered. Doing so will also decrease the likelihood for a merger by z ∼ 0 below ∼50% based on the results of Tal et al. 2013. We cannot expect that the PFs of the possible companions will be appreciably improved by the use of more broad or medium band filters. In the zCOSMOS survey, for example, Knobel et al. (2012) used imaging in 30 medium- and broadband filters to measure photometric redshifts, and found even this extensive coverage to be insufficient for identifying individual pairs and groups for galaxies at z ≲ 1.

We have measured more than one likely companion for ∼20% (16/102) of the ETGs where the companions' redshifts were spectroscopically confirmed. As such, this measurement is a strong lower limit on the frequency of companions to ETGs. In Table 2, we present a list of these ETGs. We include 1σ uncertainties associated with N_c, measured with an empirical jackknife technique following Efron (1982), where:

$$\begin{equation} \sigma ^2=(N-1)\sum \limits _{j=1}^N \frac{(N_c^i - N_c)^2}{N}, \end{equation} \tag{ 4 }$$

here $N_c^i$ is the total number of galaxies excluding the contribution from the ith system, N_c is the total number of likely companions, N equals the total number of galaxies, and the sum is measured over the set of j possible companions. In Table 2, we also include the number of possible companions with photometric (Column 3) and spectroscopic (Column 4) redshifts that contributed to the measurement of N_c.

Table 2. Number of Likely Companions

GOODS ID	Nc	nspec	nphot
J033205.09-274514.0	3.03 ± 1.64	7	3
J033206.27-274536.7	1.01 ± 0.82	2	1
J033207.55-274356.6	1.02 ± 0.90	4	1
J033208.53-274217.7	1.01 ± 0.87	3	1
J033210.04-274333.1	1.01 ± 0.77	3	1
J033210.12-274333.3	1.02 ± 0.91	5	1
J033211.21-274533.4	1.01 ± 0.87	3	1
J033211.61-274554.1	1.01 ± 0.82	2	1
J033212.20-274530.1	1.01 ± 0.82	2	1
J033212.31-274527.4	1.02 ± 0.87	3	1
J033214.45-274456.6	1.01 ± 0.89	4	1
J033219.02-274242.7	1.01 ± 0.87	3	1
J033226.71-274340.2	1.01 ± 0.93	6	1
J033231.84-274329.4	1.02 ± 0.90	4	1
J033233.40-274138.9	2.01 ± 1.22	2	2
J033235.10-274410.7	1.00 ± 0.82	2	1

Notes. Column 2: number of likely companions, with 1σ uncertainties measured from an empirical jackknife technique (Section 4.2.2). Columns 3 and 4: number of photometric and spectroscopic possible companions.

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We measure the average characteristics for galaxies with and without companions for the subset of ETGs (N = 33) measured with recent star formation (1 <f_YC[%] < 10; 0.1 <t_YC[Gyr] < 1) in Section 3.2 and with morphological parameters that were well fit ($\chi ^2_{\nu }<$ 2). For ETGs with N_c < 1 (N = 26), the mean Sérsic index, mass, and sizes equal 〈 n, M[M_☉], r_e[kpc] 〉  ≃  (3.6 ± 2.5, 10.5 ± 0.59, 2.6 ± 1.7), with 1σ dispersion reported on each mean value. The mean age and mass fraction of young stars for this subset equals 〈 t_YC[Myr], f_YC[%]〉 ≃ (325 ± 185, 3 ± 2). For the subsample of ETGs with N_C ⩾ 1 (N = 6), 〈 n, M[M_☉], r_e[kpc]〉 ≃ (3.9 ± 1.5, 10.7 ± 0.52, 2.3 ± 1.9). The mean age and mass fraction of young stars for this subset equals 〈 t_YC[Myr], f_YC[%]〉 ≃ (260 ± 130, 2 ± 1.9). If these data are normally distributed in each sample, a two-sample t-test shows that the mean parameters presented for ETGs with, and without, companions are not statistically significant. Whether these measurements are in fact normally distributed is difficult to determine given the small sample sizes, but we conclude that the measured properties of ETGs with and without companions are indistinguishable.

In Figure 5, we plot the half-light radii of the ETGs (Section 4.1) against the stellar masses derived from the optical–IR SED fits (Section 3.1). Here, we only plot ETGs that were well-fit ($\chi ^2_{\nu }<$ 2) in the analyses of all sections. For reference, we plot the mean uncertainties in half-light radius and stellar mass for an ETG with an average size and mass. We overplot three empirical size–mass relationships observed for local ETGs and late-type galaxies (dotted and solid black curves, respectively; reproduced from Shen et al. 2003) and intermediate redshift (1.0 <z < 1.5) ETGs (dashed line; from Williams et al. 2010)—these relationships are not fits to the data. We indicate ETGs with likely (N_c  ≳  1) companions within Δv = 750 km s⁻¹ with an “×” symbol. ETGs that were best-fit (Section 3.2) with a minor component of young (1% <f_YC[%] <10% and 0.1. < t[Gyr] <1) stars are plotted as filled points with a color defined by the key in the figure. ETGs not meeting these additional criteria are plotted as small, filled circles.

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A few trends appear in Figure 5 that may provide some insight into the mechanism(s) inducing RSF in intermediate redshift ETGs. First, there does not appear to be a mass dependency in the distribution of ETGs that have experienced recent star formation (t <1 Gyr). Although many of the low-mass galaxies (M < 10^10.5) are likely to have experienced a minor burst of RSF in the previous ∼1 Gyr, RSF is also observed in high-mass ETGs. Second, we note that high-mass (M > 10^10.5 M_☉) ETGs with RSF and those (albeit few) ETGs with likely companions (N_c ⩾ 1) appear to occupy unique sectors in the size–mass parameter space. Recently, star-forming ETGs appear to be distributed on or near the Shen et al. (2003) low-redshift size–mass relation. In contrast, quiescent ETGs—in particular, ETGs with companions—appear on or near the intermediate-redshift size–mass relationship for ETGs. The tight apparent clusters, at M ≃ 10.5 and 11 M_☉, within the broader mass–size distributions are populated by ETGs over a wide redshift range (0.6 <z < 1.4), although we reiterate the important note from Section 3.2 that these ERS data are most sensitive to recent star formation at the lower (z ≲ 1) redshift range of our samples.

We confirm with a two-sample t-test that the means of each of these distributions are distinguishable (i.e., the null hypothesis is rejected at ≳  95%, if the data are normally distributed). To better illustrate this apparent clustering, we collapse the bivariate size–mass distributions of these two populations of ETGs along a preferred vector that is approximately parallel to the empirical size–mass relationships for high-mass ETGs (Williams et al. 2010). This vector—a non-unique bisection that was estimated from a visual inspection of the distributions of these two populations—is overplotted (indicated $\skew3\overrightarrow{\rm A}$ in Figure 5) for reference in Figure 5 as a thin-line arrow originating at log(M, r_e)  ≃  10.5, 0.1. For each of the ETGs with RSF and with likely companions we measure the magnitude of the perpendicular distance, $\skew8\overrightarrow{\rm dA}$ from the preferred vector $\skew3\overrightarrow{\rm A}$. A histogram of these distances is plotted in black (N_c ⩾ 1) and red (RSF), respectively, in Figure 6. Additionally in Figure 6, the best-fit Gaussian function to each distribution is overplotted in the same color. Here, the mean for all quiescent high-mass ETGs is distinguishable (null hypothesis is rejected at >99.5% level) from ETGs with recent star formation, with the median distinguished at 5σ. If the ETGs with RSF (ETGs with N_c ⩾ 1) that lie above (below) the vector $\skew3\overrightarrow{\rm A}$ are removed for the purposes of refining the fit of the Gaussian to each distribution, the means of the two distributions can be distinguished at 7σ.

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The observed diversity in the colors and SFHs of our ETGs is difficult to reconcile with models that would predict more uniformly passive characteristics for such galaxies. For example, Peng et al. (2010) presented a model in which massive (M  ≳  10¹⁰ M_☉) galaxies reside in a "mass-quenching" regime, in which these galaxies' evolution is dominated by internal feedback, in contrast to environmental factors. This model predicts that 65%–80% of massive ETGs in our sample will reside on the red sequence. We do not observe such a mass-dependency for star formation in our sample.

The lack of a strong mass-dependent trend of observed RSF may be interpreted as support for star formation in ETGs as a stochastic process (e.g., RSF is related to the environment). Although the number of ETGs with companions is small (N = 10), the distinction in the distributions may still be instructive of the process(es) driving recent star formation or transforming the sizes of massive ETGs. We note that the companion galaxies to the ∼20% of ETGs identified with companions (Section 4.2.2) are bright (m_F606W ≲ 23 mag) and therefore massive,¹⁹ and have blue UV–optical rest-frame colors (〈(NUV − V)_r〉 ≃ 2.5 mag). This suggests that these companions are relatively gas-rich. From simulations, these companions will likely merge (  ≳  50%) by z ∼0 (Tal et al. 2013). If these companions do not consume their cold-gas reserves in advance of a future merger, then some degree of new star formation should be expected in the ETGs.

Alternatively, the measured size–mass distribution and the observed characteristics of ETGs with RSF could be interpreted as evidence for a progenitor bias. In effect, in our sample we may have caught recently quenched galaxies "in the act" as they transitioned toward the red sequence. For a comparison with high (z  ∼  1.5) redshift studies, consider the recent results of Bedregal et al. (2013, hereafter "B13"), which selected ∼40 passive galaxies from the HST WFC3 IR grism pure-parallel WISP survey (PI: M. Malkan). Differences in the selection of galaxies between the B13 sample and our own makes a direct comparison difficult—B13 used rest-frame optical color and mass to select relatively more massive (〈 M 〉 ≃ 10¹¹ M_☉) passive galaxies for study, whereas our selection is primarily morphological and does not by design preclude minor recent star formation — but the B13 results are germane to this discussion. First, BC10 also observe a diversity in the average ages of the stellar populations in massive, quenched galaxies, with approximately 30% of the galaxies residing off the passive, red sequence. They interpret the homogeneous spread in the mass of the quenched galaxies on and off of the red-sequence as evidence that multiple mechanisms are responsible for the quenching of star formation in high mass galaxies, and the authors emphasize that the spectra of these galaxies imply that they are transitioning from a former period of intense star formation at high (z ≫2) redshift. B13 also predict that the massive galaxies in their sample would join the red sequence by z ∼1, implying that young stellar populations in quenched intermediate redshift ETGs could still be directly detectable in our broadband UV data.

Furthermore, at low-redshift (z ≲ 0.1), Wyder et al. (2007) have suggested that a continuum of young and old transitioning galaxies populate the UV–optical low-redshift (z ≲ 0.1) green valley. In our sample, among massive (>10^10.5 M_☉) recently star-forming ETGs we do find disk-like (n < 2.5) ETGs, which supports an interpretation that the observed RSF could be associated with the quenching of star formation in higher redshift progenitors of local ETGs. We note, however, that the mean Sérsic index measured for these high-mass ETGs (see Section 4.1) is large (〈 n〉 ≃ 4.2), and is similarly large for both the sample of recently star-forming and quiescent high-mass ETGs (〈 n〉 ≃ 4.5). It is important to note that the high mean Sérsicdoes not necessarily imply that the histories of massive galaxies have followed a relatively quiescent evolution. Carollo et al. (2013), in the study of thousands of z ∼ 1 ETGs, found that ∼90% of high mass (M > 10^10.5 M_☉) star-forming disk galaxies are bulge-dominated in their light-profiles.

We observe (1) the association of companions with ETGs, albeit a small fraction of the total number of ETGs in the catalog; (2) the presence of bulge-dominated profiles in both compact, quiescent, and recently star-forming ETGs; (3) recent star formation independent of ETG stellar masses; and (4) a distinction between the size–mass distributions of ETGs with RSF and ETGs with likely companions. Considered jointly, these observations imply that both the introduction of quenched galaxies and mergers both likely play a non-negligible role in the formation of young stars and size-mass evolution of intermediate redshift ETGs.

This conclusion is most severely limited by the relatively small number of ETGs identified with possible companions that have spectroscopic redshifts. We have obtained spectroscopic observations of an additional ∼100 intermediate redshift ETGs and possible companions in the COSMOS field with MMT Hectospec in order to expand the sample size of ETGs and their possible companions at 0.35 ≲ z ≲ 1.5. This survey program specifically targeted both previously unobserved bright (F160W <21 mag) ETGs, as well as their bright companions. Repeating the companion analysis presented in Section 4 with the increased spectroscopic redshift statistics–combined with deep U-band observations (<27.5 mag) we obtained at the Large Binocular Telescope—will improve the observational constraints of the role of relatively gas-rich minor mergers in the mass-size evolution and stellar mass-assembly of ETGs.