INFRARED COLOR SELECTION OF MASSIVE GALAXIES AT z > 3

The GOODS-South and GOODS-North fields have been the target of some of the deepest surveys ever conducted over a broad wavelength range by space observatories and the foremost ground-based telescopes. In particular, the new HST/WFC3 near-infrared survey from CANDELS and the Spitzer/IRAC MIR survey from SEDS have significantly improved measurements of galaxy properties at $z\gt 2.$ Here we utilize the UV to MIR multi-wavelength catalogs based on detections in the HST/WFC3 F160W band from CANDELS for both GOODS-South and GOODS-North, as described by Guo et al. (2013) and G. Barro et al. (2015, in preparation), respectively. Both fields include deep photometry in the F435W, F606W, F775W, F814W, F850LP, F105W, F125W, F140W, and F160W bands from HST and 3.6, 4.5, 5.8, and 8.0 μm bands from Spitzer/IRAC (Ashby et al. 2013). The GOODS-South catalog also includes photometry in the U band from both CTIO/MOSAIC and VLT/VIMOS and Ks band imaging from the Infrared Spectrometer and Array Camera (ISAAC) and the High Acuity Wide field K-band Imager (HAWK-I) on the VLT (HUGS survey; Fontana et al. 2014). Similarly, the GOODS-North catalog includes photometry in the U band from both KPNO and LBT and Ks band imaging from both the Multi-Object Infrared Camera and Spectrograph (MOIRCS) and CFHT. Both fields reach 5σ depth of $H\sim 27.2$ mag and are 80% complete down to $H\sim 26.2.$

We also performed a systematic search for objects that are bright in the IRAC bands but are missed in the H-selected catalog, i.e., H-dropouts. We crossmatched the CANDELS H-selected catalog with an IRAC 3.6 and 4.5 μm selected catalog (Ashby et al. 2013) from the SEDS survey. The SEDS survey covers the two GOODS fields to a depth of 26 AB mag (3σ) at both 3.6 and 4.5 μm and is 80% complete down to [4.5] ∼24 mag. We first matched sources with $[4.5]\lt 24$ mag in the SEDS catalog to the H-selected catalog and identified those without H-band counterparts within a 2'' radius. This 4.5 μm magnitude cut was applied to enable sufficient color range to identify extremely red objects and to also give a complete 4.5 μm selected sample. We then visually inspected the IRAC images and excluded sources whose flux is likely contaminated by bright neighbors as well as those falling on the edge of the F160W image. We called this catalog of IRAC sources with no H-band counterparts the "H-dropout" catalog. Figure 1 shows examples of H-dropouts identified in GOODS-South. With knowledge of their positions, some of these H-dropouts are marginally detected in the H band but exhibit extended profiles and are unidentifiable as real sources without that prior knowledge. We measured aperture magnitudes in the H and K_s bands with a 1'' radius aperture at the position of their IRAC 3.6 and 4.5 μm counterparts, and then applied an aperture correction to get the total flux. For the IRAC 5.8 and 8.0 μm bands, we used a 12 radius aperture plus aperture correction, the same as that used for the IRAC 3.6 and 4.5 μm bands (directly taken from Ashby et al. 2013). Their measured flux densities across HST/WFC3 to IRAC bands are listed in Table 1.

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Table 1.  Measured Properties of all H-dropouts

R.A.a	decl.	F160W	Ks	3.6 μm	4.5 μm	5.8 μm	8.0 μm	${z}_{{\rm{phot}}}$	Notesb
J2000		(μJy)	(μJy)	(μJy)	(μJy)	(μJy)	(μJy)
GOODS-South
53.19988	−27.90455	0.32 ± 0.03	0.85 ± 0.06	3.56 ± 0.42	5.50 ± 0.53	8.55 ± 0.56	11.85 ± 0.65	4.78	24 μm
53.12757	−27.70675	0.31 ± 0.02	0.93 ± 0.06	2.83 ± 0.36	3.84 ± 0.41	4.87 ± 0.52	6.07 ± 0.58	4.62	⋯
53.04768	−27.86865	0.26 ± 0.04	0.39 ± 0.14	1.56 ± 0.23	1.96 ± 0.27	3.54 ± 1.02	3.22 ± 1.07	5.17	⋯
53.08476	−27.70800	0.05 ± 0.02	0.15 ± 0.06	1.24 ± 0.20	2.25 ± 0.29	3.27 ± 0.56	4.24 ± 0.58	5.26	X-ray
53.11912	−27.81396	0.12 ± 0.01	0.46 ± 0.04	1.18 ± 0.19	1.57 ± 0.22	1.97 ± 0.34	3.08 ± 0.36	4.16	⋯
53.06091	−27.71833	0.26 ± 0.02	0.48 ± 0.06	1.04 ± 0.16	1.47 ± 0.20	1.02 ± 0.69	2.40 ± 0.67	3.19	⋯
53.13463	−27.90748	0.04 ± 0.03	0.42 ± 0.06	1.64 ± 0.23	1.72 ± 0.24	3.14 ± 0.58	5.88 ± 0.70	4.16	⋯
53.19654	−27.75699	0.13 ± 0.02	0.62 ± 0.05	0.91 ± 0.15	1.36 ± 0.20	3.24 ± 0.44	2.63 ± 0.52	3.96	⋯
53.13270	−27.72021	0.09 ± 0.02	0.29 ± 0.06	1.03 ± 0.16	1.33 ± 0.20	0.68 ± 0.84	2.40 ± 0.65	4.68	⋯
53.02079	−27.69903	0.05 ± 0.03	0.17 ± 0.50	0.79 ± 0.14	1.19 ± 0.18	0.00 ± 0.02	2.32 ± 0.65	4.58	⋯
GOODS-North
189.30783	62.30737	0.24 ± 0.02	1.03 ± 0.26	3.60 ± 0.46	6.03 ± 0.58	8.74 ± 0.47	15.59 ± 0.54	3.99	24 μm,X-ray
189.18352	62.32741	0.25 ± 0.01	⋯	2.68 ± 0.37	4.37 ± 0.47	4.76 ± 0.75	9.67 ± 0.66	7.00	24 μm
189.42834	62.26596	0.10 ± 0.03	0.46 ± 0.19	1.27 ± 0.22	1.22 ± 0.18	2.03 ± 0.62	5.14 ± 0.55	7.00	24 μm
189.25689	62.25028	0.22 ± 0.01	0.23 ± 0.16	1.13 ± 0.19	1.14 ± 0.18	1.24 ± 0.47	2.50 ± 0.46	6.95	⋯
189.39476	62.31691	0.17 ± 0.02	0.26 ± 0.17	1.05 ± 0.18	1.20 ± 0.19	1.86 ± 0.48	2.85 ± 0.60	6.92	⋯
189.02396	62.22296	0.02 ± 0.05	0.20 ± 0.16	0.95 ± 0.17	1.28 ± 0.20	1.59 ± 0.52	2.57 ± 0.63	4.54	⋯

Notes.

^aPositions are from the IRAC 3.6 and 4.5 μm selected catalogs based on the SEDS survey (Ashby et al. 2013). ^b Have X-ray or 24 μm counterparts within 2'' after crossmatching with X-ray and 24 μm catalogs. These galaxies are most likely AGNs if they are indeed at $z\gt 3.$ However, also we note that their photometric redshifts estimate with FAST is less reliable.

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The combined F160W and IRAC 4.5 μm selected catalog is not only complete to [4.5] = 24 mag but also ensures that all the H-dropouts have $H-[4.5]\gt 2.25.$ As shown by Guo et al. (2013), the agreement of the IRAC 4.5 μm photometry between the CANDELS F160W selected catalog and the SEDS 3.6 μm and 4.5 μm selected catalog is excellent for objects with $[4.5]\lt 24.5$ mag. The magnitude cut of our selection, [4.5] = 24, is much brighter than the detection limit in the SEDS survey, and therefore Eddington bias is also negligible (Guo et al. 2013).

We searched for infrared and X-ray counterparts within a 2'' radius for all the sources in both the H-selected and H-dropout catalogs based on their H band or IRAC positions. For infrared counterparts, we employed the MIPS 24 μm selected catalog of Magnelli et al. (2013), which also includes 100 μm and 160 μm photometry from the combination of PACS Evolutionary Probe (PEP; Lutz et al. 2011) and GOODS-Herschel (Elbaz et al. 2011) key programs. For X-ray counterparts, we used the 4 Ms catalog (Xue et al. 2011) for GOODS-South and the 2 Ms catalog (Alexander et al. 2003) for GOODS-North.

At $z\gt 3,$ the Balmer/4000 Å break shifts redward of the H band while the 4.5 μm band probes the rest-frame J band. Thus, both quiescent (QS) galaxies with strong Balmer/4000 Å breaks and dusty galaxies with significant UV attenuation appear red in $H-[4.5].$ Figure 2 plots the evolution of $H-[4.5]$ as a function of redshift for different sets of templates. These templates are based on BC03 models, including a non-evolving constant star formation (CSF) model computed for an age of 300 Myr and various levels of reddening (using the Calzetti et al. 2000 extinction law and solar metallicity). This figure illustrates that an $H-[4.5]\gt 2.25$ color cut can effectively select old or dusty galaxies at $z\gtrsim 3.$ On the other hand, most commonly used LBG selection techniques (e.g., Bouwens et al. 2012) are designed specifically to select young and less attenuated galaxies, with UV slope $\beta \lesssim 0$ or equivalently $E(B-V)$ ≲ 0.4–0.5 for a young SF galaxy. Therefore, the proposed red galaxy selection is complementary to the LBG selection and is crucial for a complete census of galaxy populations at $z\gtrsim 3.$ As a further illustration of this point from Figure 2, almost none of the spectroscopically confirmed $z\gt 3$ galaxies (mostly LBGs) have $H-[4.5]\gt 2.25.$ In the following sections, we refer to galaxies with $H-[4.5]\gt 2.25$ as HIEROs.

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Figure 2 also reveals that while passive or dusty galaxies at $z\gt 3$ are expected to be identified as HIEROs, extremely dust-obscured galaxies ($E(B-V)\gtrsim 0.6$) at 2 < z <3 could also enter the HIERO selection. This is similar to other red galaxy selection technique at lower redshifts. For instance, Wuyts et al. (2009) found that 15% of their distant red galaxy (DRGs, Franx et al. 2003) sample, which is intended to select galaxies at $z\gt 2,$ have spectroscopic redshifts $z\lt 2$ (also see, e.g., Grazian et al. 2007). These low-redshift DRGs are on average more obscured with A_V higher by 1.2 mag than the high-redshift DRGs. The situation is expected to be more serious in selecting galaxies at $z\gt 3$ due to the prevalence of dusty galaxies at $2\lt z\lt 3$ (see, e.g., Yan et al. 2007; Dey et al. 2008; Huang et al. 2009).

To enable a cleaner selection of $z\gt 3$ galaxies, we use an additional J − H color to separate $z\gt 3$ galaxies from low-redshift contaminants, following the color track of theoretical templates. As shown in Figure 3, although a heavily attenuated galaxy ($E(B-V)\gtrsim 0.4$) at $z\lt 3$ could have a similar $H-[4.5]$ color as normal massive SF galaxies at $z\gt 3,$ the Balmer/4000 Å break falling between the J and H bands at $z\sim 2$–3 leads to a much redder J − H (and also $J-{K}_{s}$) color than for galaxies at $z\gt 3.$ Similarly, passive galaxies at $z\gt 3$ also have redder J − H colors due to much redder rest UV slopes than SF galaxies. Therefore, an additional J − H color criterion separates these different populations and approaches a pure selection of $z\gt 3$ massive (SF) galaxies. Based on the color tracks of theoretical models and the photometric redshifts of HIEROs (details of photometric redshift determinations are discussed in Section 3), we separate $z\gtrsim 3.5$ SF galaxies (${JH}-\mathrm{blue}$ HIEROs) from z ∼ 2−3 contaminants (${JH}-\mathrm{red}$ HIEROs) as

$$\begin{eqnarray}&&{JH}-\mathrm{blue}\;(\mathrm{high}-z):H-[4.5]\gt 2\times (J-H)+1.45\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{JH}-\mathrm{red}\;(\mathrm{low}-z):H-[4.5]\leqslant 2\times (J-H)+1.45.\end{eqnarray} \tag{ 2 }$$

Because both $H-[4.5]$ and J − H are poorly constrained for H-dropouts, we classify all the H-dropouts as ${JH}-\mathrm{blue}$ HIEROs (the redder $H-[4.5]$ color of H-dropouts suggests that they are in general at higher redshift). In total, we identify 359 HIEROs (116 ${JH}-\mathrm{blue}$ and 243 ${JH}-\mathrm{red}$) in the 2 GOODS fields, 18 of which are H-dropouts. After examining the reliability of the color measurements of independent sources with an approach described in Section 3.2, our final sample includes 285 (80% of the original sample) HIEROs. We list respective fractions of the two categories of HIEROs in Table 2.

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Table 2.  Number Counts of HIEROs

Sample	Number	Number	Number	Number	Number	Number
	(H-detected)	(H-detected, cleana)	(H-dropouts)	(final sample)	(${F}_{24\mu {\rm{m}}}\gt 30$ μJy)	(X-rayb)
${JH}-\mathrm{red}$	243	206	⋯	206	123	39
${JH}-\mathrm{blue}$	116	61	18	79	18	14
All	359	267	18	285	141	53

Notes.

^aSee Section 3.2. ^bDetected at 0.5–8 keV.

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Caputi et al. (2012) studied a sample of extremely red galaxies with $H-[4.5]\gt 4$ in UDS. Only 15 galaxies in our sample present such extremely red colors. While nearly all of these 15 galaxies have ${z}_{{\rm{phot}}}\gt 3,$ the majority of the massive $z\gt 3$ galaxies will be missed by this extreme criterion. (A more extreme color cut leads to fewer contaminants at lower redshifts but also to a lower completeness in selecting high-redshift galaxies.) Similarly, Wang et al. (2012b) studied a sample of K- and IRAC-selected extremely red objects (KIEROs, ${K}_{s}-[4.5]\gt 1.6$) in GOODS-North, aiming to identify specifically dusty galaxies at $z\gt 2.$ They showed that the majority of KIEROs are at $z\sim 2$–3.5. Of our HIERO sample, 46% satisfy the color criterion of KIEROs. Compared to both previous studies, the advantage of our color selection is a more complete sample of massive (including both passive and SF) galaxies at $z\gt 3$ because our selection was specifically designed to complement the LBG selection. This allows us to perform a complete census of massive galaxy evolution at $z\gtrsim 3.$ Moreover, with the proposed $H-[4.5]$ and J − H diagram, we are able to distinguish high-redshift galaxies from low-redshift contaminants, enabling a much cleaner (and also complete) selection of massive galaxies compared to previous studies.

The HIEROs are extremely faint at observed UV and visible wavelengths. Even though the GOODS fields have been extensively covered by spectroscopic observations, only 11 HIEROs have spectroscopic redshifts (Kajisawa et al. 2010; Dahlen et al. 2013; Hsu et al. 2014, and references therein). Therefore, we use photometric redshifts to gain insight into their nature. The unique features of these galaxies, e.g., many of them are consistent with being extremely dusty with A_V exceeding 3–4, lead to concerns that they may not be represented in the templates used by most photometric redshift methods. Hence, we used galaxy templates spanning a larger parameter space particularly a larger range of A_V to determine their photometric redshifts. To this aim, we employed FAST (Kriek et al. 2009) to fit the full U band to 8.0 μm photometry for all galaxies in the HIERO sample. FAST also provides self-consistent estimates of stellar masses. We constructed stellar templates from the Bruzual & Charlot (2003; BC03, hereafter) stellar population synthesis model with a Chabrier (2003) initial mass function and solar metallicity, assuming exponentially declining star formation histories (SFHs) with e-folding times $\tau =0.1$–10 Gyr. We allowed the galaxies to be attenuated with $0\leqslant {A}_{V}\leqslant$ 6 mag with reddening following the Calzetti et al. (2000) law. To avoid strong influence on the fitting from one single band (in some cases due to an emission line or bad photometry), we restricted the maximum signal-to-noise ratio (S/N) in the photometry to be 20. Examples of the fitting are shown in Figure 4.

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For the few galaxies with spectroscopic redshifts in our sample, Figure 5 shows the comparison between spectroscopic and photometric redshifts. Our photometric redshift estimates in general agree with spectroscopic redshifts with the normalized median absolute deviation (Brammer et al. 2008) ${\sigma }_{{\rm{NMAD}}}\sim 0.06.$ (The significant outlier at ${z}_{{\rm{spec}}}=1.2$ is a type 1 AGN.) However, the spectroscopic sample is significantly biased, with 9 of 11 objects detected in X-rays and a median H-band magnitude $\langle H\rangle \approx 22.3$ (compared to $\langle H\rangle \approx 23.9$ for the total sample). Hence, larger and deeper spectroscopic samples are needed to verify the accuracy of the photometric redshifts. On the other hand, based on photometric redshift estimates from CANDELS (see, e.g., Dahlen et al. 2013), we derive ${\sigma }_{{\rm{NMAD}}}\sim 0.11.$ Specifically, for HIEROs at $z\lesssim 3,$ the photometric redshifts from CANDELS are systematically higher by $\sim 0.2$–0.3, likely due to the absence of highly attenuated galaxy templates in the CANDELS photometric redshift codes, (favoring a high-redshift solution to account for the red color actually due to attenuation). This trend is also confirmed based on the photometric comparisons between ours and from CANDELS for the whole HIERO sample.

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While the majority of HIEROs yield a good fit, a substantial number of galaxies cannot be well fitted with FAST and the BC03 models. We checked in detail their SEDs and F160W and IRAC images and found that most of them have bright stars or galaxies within a few arcseconds, hence their photometry is likely unreliable. This is particularly a problem in the IRAC bands due to their larger PSFs. To explore whether this is the origin of the problem, we re-fit the SEDs with the same set of templates but excluding the IRAC photometry. A better fit (much smaller ${\chi }^{2}$) was achieved for many sources with a significantly different redshift solution. Figure 6 presents two such examples. This illustrates that indeed the IRAC photometry for these sources is problematic (in most cases boosted) due to contamination by close neighbors. As a result, the true $H-[4.5]$ color of these sources is likely much bluer (as can also be seen from their best-fitted SED in the second fit).

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Although in principle we can simply reject all sources with a bad fit in the first run to clean our sample, it will introduce a bias toward the choice of SED-fitting methods and templates, i.e., some sources with a bad fit may be due to the wrong templates instead of bad photometry. To be conservative, we borrow the "clean index" concept in dealing with the source confusion at far-infrared wavelengths (Elbaz et al. 2011) to identify sources whose IRAC fluxes are reliable. We define a source as "clean" only if it satisfies at least one of the following two criteria: (1) it has no neighbor within 2'' (rougly the size of the FWHM of the IRAC PSF) and a good SED (photometric redshift)-fitting result (${\chi }^{2}\lt 4,$ corresponding roughly to the one-tailed (right-tail) probability > 0.95) when including IRAC photometry; (2) similar redshift solutions are achieved during the two SED-fitting runs, i.e., $| {z}_{{\rm{phot}}}(\mathrm{no}\;\mathrm{IRAC})-{z}_{{\rm{phot}}}(\mathrm{IRAC})| /{z}_{{\rm{phot}}}(\mathrm{IRAC})\lt 30\%.$ (For sources that only satisfy the second criterion, it is unclear whether or not their IRAC photometry is contaminated: the bad fit could be because there are no perfect templates in the library or because the data quality is not good enough.) This leaves us 285 clean HIEROs including the 18 H-dropouts (Table 2). Among these 285 HIEROs, 223 of them (78%) have a good fit with ${\chi }^{2}\lt 4$ when including the IRAC photometry.

Figure 7 shows the photometric redshift distribution for the final clean samples. Our classification based on J − H and $H-[4.5]$ colors successfully separates galaxies at $z\gtrsim 3.5$ from those at relatively lower redshifts, i.e., $2\lt z\lt 3$. The median redshifts for ${JH}-\mathrm{blue}$ and ${JH}-\mathrm{red}$ HIEROs are $\langle z\rangle \sim 4.4$ and $\langle z\rangle \sim 2.5,$ respectively. Among the 79 ${JH}-\mathrm{blue}$ HIEROs, only 14 (18%) have photometric redshifts ${z}_{{\rm{phot}}}\lt 3.$ Most of these 14 are detected at MIPS 24 μm, in contrast to the $z\gt 3$ ${JH}-\mathrm{blue}$ HIEROs. On the other hand, 52 out of 206 (28%) of ${JH}-\mathrm{red}$ HIEROs are at $z\gt 3$ with the majority (30 out of 52) being at $3\lt z\lt 3.5.$ Figure 7 also compares the distribution of the two populations of HIEROs in the $H-[4.5]$ versus $[4.5]$ color–magnitude diagram. As expected, the ${JH}-\mathrm{blue}$ HIEROs are, in general, fainter at 4.5 μm as well as redder in $H-[4.5].$

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Our analysis on photometric redshifts (both from our own estimates based on FAST and those from CANDELS) confirms that the selection criterion of ${JH}-\mathrm{blue}$ HIEROs yields a clean selection of z > 3 galaxies. Remaining low-redshift contaminants can be removed based on SED modeling or on their strong 24 μm detections (with a median ${F}_{24\mu {\rm{m}}}\sim 98$ μJy). The F160W images of these $z\lt 2$ contaminants show that most of them are either extremely faint or likely mergers, leading to uncertain J − H colors or unusual extinction properties, which explains why they enter our selection.

The advantage of using FAST to derive photometric redshifts is that it also gives self-consistent estimates of stellar masses. Figure 8 shows the stellar mass estimates of ${JH}-\mathrm{blue}$ HIEROs. The modeling assumptions are described in Section 3, i.e., the BC03 stellar library, Calzetti et al. (2000) extinction law with 0 $\leqslant \;{A}_{V}\leqslant 6$, and exponentially declining star formation histories (single τ model) with e-folding times ranging from 0.1 to 10 Gyr. Delayed τ models give nearly identical estimates of stellar masses. Our mass estimates imply that the ${JH}-\mathrm{blue}$ HIEROs are massive SF galaxies at $z\gtrsim 3.5$ with a median $\langle {M}_{*}\rangle \approx {10}^{10.6}$ ${M}_{\odot }$.

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The best-fit ages for ${JH}-\mathrm{blue}$ HIEROs from single τ models range from t = 0.1 to t = 1.6 Gyr with a median $\langle t\rangle \approx 1\;{\rm{Gyr}}$ for galaxies at $z\gt 3$ and $\langle t\rangle \approx 0.1\;{\rm{Gyr}}$ for galaxies a $z\leqslant 3.$ The median attenuation is $\langle E(B-V)\rangle =0.33,$ with galaxies at $z\lt 3$ much dustier than those at $z\gt 3$ ($\langle E(B-V)\rangle =0.83$ versus $\langle E(B-V)\rangle =0.25$). These best-fit stellar properties do not change significantly by using delayed τ models. These results suggest that most ${JH}-\mathrm{blue}$ HIEROs are massive, dusty SF galaxies which have already assembled relatively old stellar populations. Their red $H-[4.5]$ colors thus appear to be caused by a combination of moderately old stellar populations (strong 4000 Å break) and dust attenuation. The few $z\lt 3$ contaminants tend to be less massive, younger, and also much dustier, suggesting that the red $H-[4.5]$ colors are mostly caused by severe dust attenuation.

As discussed in Sections 2.2 and 3, ${JH}-\mathrm{red}$ HIEROs include in general two populations, $z\sim 2$–3 dusty SF galaxies and passive galaxies at $z\sim 3$–4. As illustrated in Figure 3, it is possible to distinguish between the two populations based on their different behaviors in the observed near-infrared to MIR colors. Here we propose to separate the two populations with the observed J − K versus $K-[4.5]$ color–color diagram, which for $z\sim 3$ resembles the rest-frame U − V versus V − J diagram (Williams et al. 2009). Figure 9 shows the distribution of ${JH}-\mathrm{red}$ HIEROs in this diagram. Galaxies with the lower sSFR (from SED fitting) population in the upper left region while galaxies with higher sSFR are located in the lower right region. As independent evidence, most 24 μm detections fall in the SF region, consistent with SF galaxies at $z\lt 3.$ Based on the distribution of galaxies with different sSFRs and the direction of reddening from the Calzetti et al. (2000) law, we define the criteria for QS galaxies as: $J-K\gt (K-[4.5])+1.2,$ $J-K\gt 2.2,$ and $K-[4.5]\lt 1.6.$ The remaining galaxies are classified as SF. This diagram is not only limited to classifications of HIEROs but also provides an efficient way to identify QS galaxies at $z\gtrsim 3$ in general.

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As shown in Figure 9, roughly 10% (21 out of 206) of the ${JH}-\mathrm{red}$ HIEROs are classified as QS galaxies. The median redshift of these is $\langle z\rangle \approx 3.4,$ suggesting that they are among the earliest quenched systems in the universe. Among these 21 QS ${JH}-\mathrm{red}$ HIEROs, 15 are at ${z}_{{\rm{phot}}}\gt 3$ out of 52 z > 3 ${JH}-\mathrm{red}$ HIEROs altogether.

The ${JH}-\mathrm{red}$ HIEROs are also primarily massive galaxies (the right panel of Figure 8) with a $\langle {M}_{*}\rangle \approx {10}^{10.7}$ ${M}_{\odot }$ for both QS and SF subpopulations. The median best-fit age and attenuation for QS galaxies are $\langle t\rangle \;=$ 1.0 Gyr and $\langle E(B-V)\rangle \;=$ 0.17 while for SF galaxies $\langle t\rangle \;=$ 0.7 Gyr and $\langle E(B-V)\rangle \;=$ 0.6, respectively. These results are consistent with the classifications based on the observed J − K versus K − [4.5] diagram. The high attenuation value for SF galaxies in this ${JH}-\mathrm{red}$ HIERO population is also consistent with their high 24 μm flux densities with $\langle {F}_{24\mu {\rm{m}}}\rangle \approx 90$ μJy, which corresponds roughly to a total infrared luminosity ${L}_{{\rm{TIR}}}\sim {10}^{12}$ $\;{L}_{\odot }$ at $z\sim 2.5$.

Based on X-ray luminosity estimates, ∼20% of ${JH}-\mathrm{red}$ HIEROs are classified as X-ray AGNs (${L}_{0.5-8\mathrm{keV}}\gt {10}^{42}$ erg s⁻¹), consistent with the X-ray AGN fraction in massive galaxies at $z\sim 2$. The ${JH}-\mathrm{blue}$ HIEROs have similar AGN fraction, $\sim 18\%.$ These results indicate that our selection criteria are not particularly biased toward AGNs compared to non-AGN massive galaxies.

By selection, the HIEROs are faint in their rest-frame UV despite their high stellar masses. Specifically, the ${JH}-\mathrm{blue}$ HIEROs are generally massive SF galaxies at $z\gt 3.$ Previous studies of LBGs at these redshifts reveal a tight correlation between stellar mass and UV luminosity (see, e.g., González et al. 2011). This allows the UV luminosity function to translate directly to the stellar mass function, as is commonly adopted in studying high-redshift stellar mass functions. It is therefore interesting to compare HIERO and LBG stellar masses at similar redshifts and UV luminosities to explore how the HIEROs affect the stellar mass estimate.

We selected a sample of $z\sim 4$ LBGs (B-dropouts) that are on average at similar redshifts as the ${JH}-\mathrm{blue}$ HIERO population in the two GOODS fields using the same criteria as Bouwens et al. (2012). The rest-frame UV luminosities (M₁₆₀₀) were derived using EaZY (Brammer et al. 2008) at fixed redshifts from CANDELS. Figure 10 compares the M_*–${L}_{{\rm{UV}}}$ relations. (The HIERO rest-frame UV luminosities came from the best-fit SED templates at fixed redshifts estimated by FAST.) Compared to LBGs at similar masses, the HIEROs are generally 2–3 magnitudes fainter in the rest-frame UV. The existence of these galaxies suggests that using a simple M_*–${L}_{{\rm{UV}}}$ relation (or using only UV-selected samples) to determine the stellar mass function underestimates the massive end. We will illustrate this point further in Section 7.

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The general faintness of HIEROs in the UV suggests that most of their star formation is hidden by dust. The amount of this hidden star formation can be inferred through infrared emission, which originates from the thermal reradiation by dust of their absorbed ultraviolet light. Therefore, understanding the SEDs in the infrared is essential to get a complete view of star formation in HIEROs. Alternatively, we could use dust-unbiased tracers of star formation, e.g., radio continuum, to measure the total SFR. However, although both the far-infrared and radio surveys in the GOODS fields are among the deepest ever conducted, only a few HIEROs are individually detected. Moreover, most of the detected ones are ${JH}-\mathrm{red}$ HIEROs. For instance, crossmatching with the VLA 1.4 GHz catalog in GOODS-North (Morrison et al. 2010), 33 out of 142 HIEROs are detected at 1.4 GHz with ${F}_{\text{1.4 GHz}}\gt 20$ uJy, but only 6 out of 33 are classified as ${JH}-\mathrm{blue}$ HIEROs. This is likely caused by the high redshifts of the ${JH}-\mathrm{blue}$ HIERO population and that most of them are not extreme starbursts (contrary to bright submillimeter galaxies). To probe lower SFRs that are typical of HIEROs, a stacking approach is required.

For the ${JH}-\mathrm{blue}$ HIERO population, we excluded contaminants at low redshifts by applying a redshift cut of $z\gt 3,$ which leaves us 66 galaxies. For the ${JH}-\mathrm{red}$ HIERO population, we separately stacked SF and QS galaxies. The exquisite multi-wavelength data in GOODS allow us to perform stacking across the whole infrared wavelength range, including the 16 and 24 $\mu {\rm{m}}$ bands from Spitzer, 100, 160, 250, 350, and 500 $\mu {\rm{m}}$ from Herschel, 850 μm from SCUBA, 870 $\mu {\rm{m}}$ from LABOCA, and 1.1 mm from AzTEC. This permits a comprehensive understanding of their infrared SEDs. Moreover, the combination of stacked far-infrared and submillimeter colors provides an independent and complementary estimate of their redshift from the position of their peak far-infrared emission (Hughes et al. 2002; Daddi et al. 2009).

To avoid contamination from a few relatively bright members, we conducted a median stacking in the infrared and submillimeter bands (16 μm–1.1 mm) using the IAS stacking code library (Béthermin et al. 2010). (Using mean stacking would leave the main results unchanged, likely because the fraction of bright members is small.) We retrieved flux densities by PSF-fitting the stacked images. A correction factor ranging from 0.92 at 250 μm to 0.75 at 500 μm was applied to account for clustering, which does not change much with redshift and stellar mass of the galaxies (Béthermin et al. 2012; Schreiber et al. 2015). We determine uncertainties on the flux densities with bootstrapping.

The stacked flux densities for all populations are listed in Table 3. For ${JH}-\mathrm{blue}$ HIEROs, significant detections are revealed except at 16 and 70 μm due to shallower depths. For ${JH}-\mathrm{red}$ SF HIEROs, significant detections are found at all wavelengths while there are no detections with ${\rm{S}}/{\rm{N}}\gt 3$ in any infrared bands for ${JH}-\mathrm{red}$ QS HIEROs. This provides independent evidence that our approach successfully separates the QS and SF populations. Moreover, the peak of the infrared SED for ${JH}-\mathrm{blue}$ and ${JH}-\mathrm{red}$ SF HIEROs falls, respectively, at $\sim 500$ μm and ∼350 μm, lending evidence that they are most likely at $z\sim 4$ and $z\sim 2.5,$ consistent with our photometric redshifts.

Table 3.  Stacked Infrared Flux Densities of HIEROs

Sample	16 μm	24 μm	70 μm	100 μm	160 μm	250 μm	350 μm	500 μm	870 μm	1.1 mm
	(μJy)	(μJy)	(μJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)
${JH}-\mathrm{blue}$ HIEROs	5.8 ± 3.7	14.6 ± 3.8	184 ± 260	0.22 ± 0.05	0.90 ± 0.20	3.09 ± 0.54	3.67 ± 0.83	4.60 ± 0.62	1.15 ± 0.19	0.92 ± 0.22
${JH}-\mathrm{red}$ HIEROs(SF)	28.6 ± 5.9	74.4 ± 7.4	177.7 ± 27.2	0.63 ± 0.04	2.01 ± 0.16	6.21 ± 0.55	7.22 ± 0.64	5.61 ± 0.49	1.09 ± 0.14	0.72 ± 0.15
${JH}-\mathrm{red}$ HIEROs(QS)	5.7 ± 5.6	6.3 ± 3.4	84.3 ± 40	0.1 ± 0.05	0.2 ± 0.1	0.3 ± 0.3	0.3 ± 0.5	2 ± 0.7	−0.06 ± 0.1	−0.4 ± 0.1

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Figure 11 shows the median SEDs of the two populations of HIEROs. With the well-constrained SED shape, their total infrared luminosities (TIR) constrain their SFRs. We fit the stacked 160 μm−1.1 mm (to avoid rest-frame $\lt 40$ μm wavelengths, which may suffer from AGN contamination) SEDs using a suite of infrared templates, including the 105 template SEDs from Chary & Elbaz (2001; CE01, hereafter). During the fitting, we fixed the redshift at the median value of the sample and left the template normalizations as free parameters. The best-fit model is the template that minimizes ${\chi }^{2}.$ The total infrared luminosity for ${JH}-\mathrm{red}$ and ${JH}-\mathrm{blue}$ HIEROs are $1.2\times {10}^{12}{L}_{\odot }$ and $2.4\times {10}^{12}{L}_{\odot },$ respectively. We also fit the full-band SED from UV to far-IR for HIEROs using the code CIGALE (Noll et al. 2009; Serra et al. 2011) using BC03 models in the UV-to-NIR and Draine & Li (2007) models in the infrared. This gives a consistent measurement of L_TIR as shown in Figure 11.

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To derive realistic uncertainties on SFRs and specific SFRs, we bootstraped galaxies simultaneously in all the infrared bands, i.e., bootstrapping SEDs. Each time we randomly selected a subsample of the galaxies, performed median stacking in all the bands, and determined the SFR and sSFRs from the TIR and median stellar mass of the subsample. We repeated this process 50 times and determined the dispersion of SFR and sSFR. This method avoids the drawback that the uncertainties in different bands as derived from bootstrapping galaxies in a single band are likely correlated, e.g., galaxies that are fainter in the shorter wavelength may tend to be brighter in the larger wavelength due to the variations in dust temperature and/or redshifts.

A tight correlation between ${L}_{{\rm{IR}}}/{L}_{{\rm{UV}}}$ and UV continuum slope β exists for UV-selected L* SF galaxies in the local universe and up to $z\sim 2.5$ (Meurer et al. 1999; Kong et al. 2004; Reddy et al. 2012). At higher redshifts, it becomes more difficult to directly measure both ${L}_{{\rm{IR}}}$ and β. Based on infrared stacking analysis, Lee et al. (2012) derived IR luminosities for a statistical sample of $L\gt \gt {L}^{*},$ $z\sim 4$ LBGs and showed that they are consistent with the IRX–β relation presented by Meurer et al. (1999). For HIEROs, because most of them are relatively faint in the rest-frame UV, we first performed a median stacking across the observed-frame HST/ACS F435W to HST/WFC3 F160W bands for ${JH}-\mathrm{blue}$ HIEROs and ${JH}-\mathrm{red}$ HIEROs, respectively, and then measured their flux densities based on the stacked images. We then used the measurements for rest-frame 1400–2800 Å to derive β. This process is illustrated in Figure 12. The strong break between the observed-frame B₄₃₅, V₆₀₆, and I₇₇₅ bands for ${JH}-\mathrm{blue}$ HIEROs provides additional independent evidence that most HIEROs should be at similar redshifts as B-dropouts and V-dropouts, i.e., $z\sim 4$–5.

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The right panel of Figure 12 compares the relation between ${L}_{{\rm{IR}}}/{L}_{{\rm{UV}}}$ and β for both HIEROs and LBGs. The HIEROs have significantly redder UV slopes ($\beta \sim 0$) than the brightest/most massive LBGs ($\beta \sim -1.9$) at similar redshifts. On the other hand, the effective dust attenuation, ${L}_{\mathrm{IR}}/{L}_{\mathrm{UV}},$ is extremely high for HIEROs, reaching ∼1000 for both ${JH}-\mathrm{blue}$ HIEROs and ${JH}-\mathrm{red}$ HIEROs. The ${JH}-\mathrm{red}$ HIEROs fall on the Meurer relation within uncertainties while ${JH}-\mathrm{blue}$ HIEROs tend to be above the Meurer relation, which is consistent with the results on a K_s-selected massive galaxy sample at $z\sim 3.3$ by Pannella et al. (2015). This is at odds with recent findings on UV-selected samples at $z\sim 5,$ which are systematically below the Meurer relation (Capak et al. 2015). This may be caused by UV selection tending to select less massive and less dusty galaxies, leading to a biased view of galaxy populations at high redshift.

Using a Kennicutt (1998) conversion of SFR [${M}_{\odot }$ yr⁻¹] = ${L}_{{\rm{IR}}}[{L}_{\odot }]/{10}^{10}$ (Chabrier 2003, IMF), the SFR for ${JH}-\mathrm{red}$ and ${JH}-\mathrm{blue}$ HIEROs are 120 ${M}_{\odot }$ yr⁻¹ and 240 ${M}_{\odot }$ yr⁻¹, respectively. These and other properties are listed in Table 4. Figure 13 shows the sSFR for ${JH}-\mathrm{blue}$ and ${JH}-\mathrm{red}$ SF HIEROs. The sSFR for ${JH}-\mathrm{blue}$ HIEROs, 4.2 Gyr⁻¹, is twice as high as that for similarly massive galaxies at $z\sim 2$ (Schreiber et al. 2015). This suggests that the sSFR of massive galaxies continues to increase at $z\gt 2.5$ and up to z ∼ 4. However, the growth rate at $z\gtrsim 2.5$ is slower than that at $z\sim 0$–2. For instance, Sargent et al. (2014) found that the evolution of sSFR at $z\lesssim 2.5$ roughly follows ${(1+z)}^{2.8},$ which predicts sSFR ∼7 Gyr⁻¹, much higher than we observed here at $z\sim 4.$ Based on simple analytic arguments on the accretion rates into halos and the accretion of baryons into galaxies, Dekel & Mandelker (2014) showed the evolution of sSFR for typical galaxies should follow $\mathrm{sSFR}\sim {(1+z)}^{2.5},$ which also predicts a higher sSFR at $z\sim 4$ than observed for HIEROs. Several recent studies report similar slow evolution of sSFR at $z\gtrsim 2.5$ but for less massive or for UV-selected galaxies (e.g., González et al. 2014; Tasca et al. 2015). Our finding suggests that the slow evolution of sSFR at $z\gtrsim 2.5$ (or the fast evolution of sSFR at $z\lt 2.5$) is likely a universal behavior for all masses of galaxies.

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Table 4.  Measured Physical Properties of HIEROs

Number	n	${z}_{{\rm{phot}}}$	log M*	log (LIR)	UV slope (β)	SFR	sSFR
	(arcmin−2)	(median)	(mean, ${M}_{\odot }$)	(${L}_{\odot }$)		(${M}_{\odot }$ yr−1)	(Gyr−1)
${JH}-\mathrm{blue}$ HIEROs 66	0.2	4.43	10.78	12.38	−0.05	240	${4.2}_{-0.8}^{+0.6}$
${JH}-\mathrm{red}$ HIEROs (SF) 185	0.54	2.51	10.77	12.10	1.12	120	${1.9}_{-0.2}^{+0.2}$
${JH}-\mathrm{red}$ HIEROs (QS) 21	0.06	3.42	10.7	<11.65	⋯	$\lt 45$	$\lt 0.9$

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Most previous studies on the cosmic SFR densities at $z\gtrsim 4$ contain only contributions from LBGs. The cosmic SFRD contributed by HIEROs needs to be added to have a complete view of cosmic SFR densities at high redshift. Using a total area of 340 arcmin² and assuming that individual HIEROs have the same sSFR as derived from stacking, the total SFRD contributed by HIEROs is $\sim 6\times {10}^{-3}$ ${M}_{\odot }$ yr⁻¹ Mpc⁻³ at $z\sim 3.7$ and $\sim 8\times {10}^{-3}$ ${M}_{\odot }$ yr⁻¹ Mpc⁻³ at $z\sim 4.7.$ By comparison, recent studies showed that the total SFRD of LBGs is ∼0.049 and ∼0.036 ${M}_{\odot }$ yr⁻¹ Mpc⁻³ at $z\sim 4$ and $z\sim 5,$ respectively (Bouwens et al. 2014). Thus, despite the small number of HIEROs, they contribute 15%–25% to the SFRD at $z\sim 4$–5, not taken into account in previous studies based on UV-selected samples. (There is essentially no overlap between the HIERO and LBG selections.) Figure 13 plots the SFRD from HIEROs identified in this work and from LBGs in previous work (Bouwens et al. 2014; Finkelstein et al. 2015).