Dust Temperature of Compact Star-forming Galaxies at z ∼ 1–3 in 3D-HST/CANDELS

Our sample is primarily based on data products from the 3D-HST spectroscopic survey (Brammer et al. 2012) in combination with the CANDELS program (Grogin et al. 2011; Koekemoer et al. 2011).

We use the astrometry and photometry from the 3D-HST Release v4.1 (Skelton et al. 2014) but adopt the updated physical parameters from the Data Release v4.1.5 ⁵ (Momcheva et al. 2016) to select massive galaxies with $\mathrm{log}({M}_{* }/{M}_{\odot })\gt 10$ at 1 < z < 3. Only those with use_phot = 1 in the 3D-HST catalogs are considered, i.e., galaxies with reliable photometric measurements. We adopt the "best" galaxy redshift, z_best, created by Momcheva et al. (2016). This z_best is determined by combing the grism redshift, if robust, with the spectroscopic and photometric redshifts compiled by Skelton et al. (2014). Using z_best, Momcheva et al. (2016) re-derive other auxiliary stellar population parameters, rest-frame colors, and SFRs from spectral energy modeling with FAST (Kriek et al. 2009).

Furthermore, the circularized radius, r_e, is derived using ${r}_{{\rm{e}}}={R}_{{\rm{e}}}\times \sqrt{q}$, where R_e is the effective radius along the major axis and q is the axis ratio, as measured by van der Wel et al. (2014) from CANDELS HST/WFC3 imaging mosaics with GALFIT (Peng et al. 2002). We correct them to the rest-frame optical size at 5000 Å using Equation (2) in van der Wel et al. (2014) to achieve a uniform measurement. We exclude galaxies with inaccurate or no size measurement, i.e., with Flag = 2 or 3 in the catalog of van der Wel et al. (2014).

In total, 6303 galaxies satisfy our mass and redshift cuts as well as use_phot = 1, 5700 of which have robust size measurements and would be further considered in the next section.

The four CANDELS fields used here are all covered by the PACS Evolutionary Probe (PEP; ⁶ Elbaz et al. 2011; Lutz et al. 2011; Magnelli et al. 2013) survey at 100 and 160 μm (and 70 μm in GOODS-S) and by the Herschel Multi-tiered Extragalactic Survey (HerMES; ⁷ Roseboom et al. 2010, 2012; Oliver et al. 2012) at 250, 350, and 500 μm. Our MIR to FIR photometry is retrieved from the PEP and HerMES catalogs, which were extracted at the positions of the Spitzer/MIPS 24 μm sources.

To identify AGNs in our sample, we use X-ray observations from the Chandra X-ray Observatory (Chandra; Weisskopf et al. 2000). The X-ray source catalogs for 2 Ms exposure of the Chandra Deep Field-North (Xue et al. 2016) and 7 Ms exposure of the Chandra Deep Field-South (Luo et al. 2017) are adopted for the GOODS-N and GOODS-S fields, respectively. In these two catalogs, AGNs are already identified via several X-ray-based criteria (Xue et al. 2016; Luo et al. 2017). For the COSMOS and AEGIS fields, we use the X-ray source catalogs from the Chandra COSMOS Legacy survey (Civano et al. 2016; Marchesi et al. 2016) and the AEGIS-X Deep survey (Brightman et al. 2014; Nandra et al. 2015), respectively. AGNs in these two fields are identified by either an intrinsic X-ray luminosity of L_0.5–7keV ≥ 3 × 10⁴² erg s⁻¹ or an intrinsic photon index of Γ ≤ 1.0 (obscured AGNs), which are consistent with the criteria adopted by Xue et al. (2016) and Luo et al. (2017) in the GOODS-N and GOODS-S fields, respectively. Because L_0.5–7keV is not given in the catalogs of the COSMOS and AEGIS fields, we converse the provided L_2–10keV to L_0.5–7keV via

$$\begin{eqnarray}&&{L}_{0.5\mbox{--}7\mathrm{keV}}={L}_{2\mbox{--}10\mathrm{keV}}/0.72,\end{eqnarray} \tag{ 1 }$$

assuming an intrinsic photon index of Γ = 1.8.

For each field, we use the PEP catalog as the reference one, and subsequently cross-match it with the 3D-HST catalog, the HerMES catalog, and the X-ray source catalog utilizing the method described below. Briefly, for every source in the reference catalog (i.e., the PEP catalog), we search for the nearest counterpart within an optimized matching radius. Here, we consider a range of matching radii from 01 to 5'' with a step of 01, among which the optimized one is set to the largest radius satisfying the following two criteria: (1) the fake matched fraction, defined as the ratio of the fake matched number (see below) to the successful matched number, is smaller than 5%; (2) the differential successful matched number, i.e., the new successful matched number with increasing matching radius, is larger than the differential fake matched number. To estimate the fake matched number given two catalogs, we shift one of them by 30'' in random directions 16 times and take the average of the 16 "successful" matched numbers as the fake matched number. Clearly, the optimized matching radius depends on the number densities of the matched catalogs, and thus varies between catalogs even for the same field. However, we note that most of the resulting optimized matching radii are smaller than 15.

Since both the 3D-HST catalogs and the X-ray source catalogs provide redshift information, we require that z_best from the 3D-HST catalogs and z_X (redshifts of optical counterparts of X-ray sources) from the X-ray source catalogs should be in good agreement, i.e., ∣z_best − z_X∣/z_best ≤ 0.2 (only one source was excluded by this criterion). In total, the cross-match yields a sample of 2403 galaxies with at least one Herschel measurement and a robust HST/size measurement.

Furthermore, to ensure an accurate measurement of dust temperature, we remove sources with less than three detections at rest-frame wavelength longer than 50 μm. After these selections, we obtain an MIR-to-FIR catalog including 521 galaxies, 109 of which have AGN counterparts.

We use the UVJ criteria of Williams et al. (2009) to select SFGs among our catalog of 521 galaxies, resulting in 488 FIR-detected massive SFGs with $\mathrm{log}({M}_{* }/{M}_{\odot })\gt 10$ at 1 < z < 3. To ensure a robust analysis of dust temperature, sources with catastrophic MIR-to-FIR SED fitting (see Section 3.1) are also removed from our final sample. We end up with a sample of 459 SFGs within which 95 galaxies are identified as X-ray AGN hosts. Note that approximately 64% of these galaxies have spectroscopic or grism redshift, which is key for accurate dust temperature measurements.

Finally, to identify cSFG from eSFGS, we use the compactness criteria defined by Barro et al. (2013), i.e., ${{\rm{\Sigma }}}_{1.5}=\mathrm{log}({M}_{* }{r}_{{\rm{e}}}^{-1.5}/[{M}_{\odot }\ {\mathrm{kpc}}^{-1.5}])$. Since the mass–size relation of SFGs evolves with redshift (van der Wel et al. 2014), cSFGs are identified as Σ_1.5 ≥ 10.3 at 1 < z ≤ 2 (Barro et al. 2013) and Σ_1.5 ≥ 10.45 at 2 < z < 3 (Barro et al. 2014), respectively. In total, there are 61 cSFGs.

Figure 1 shows the distributions on the UVJ and the mass–size diagrams for our final sample. We observe a higher occurrence of X-ray AGNs in cSFG than in eSFGs, i.e., 37% versus 18%, respectively. This finding is consistent with the ubiquitous AGNs in cSFGs reported by Barro et al. (2016) and Kocevski et al. (2017). More than 80% of our SFGs have V − J colors redder than 1.2, a criterion used for selecting dusty SFGs in Spitler et al. (2014). Such red V − J colors of our sample indicate that they are dust-obscured, which agrees with their Herschel detections.

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Following Casey (2012) and using the corresponding IDL code cmcirsed, we model the MIR to FIR (i.e., 24 to 500 μm) SED of our SFGs, with an MIR power law plus an FIR graybody with a single dust temperature, T_dust. The power-law component accounts for the MIR emission of small clumps associated with hot dust or for AGN radiation, while the graybody accounts for the cold dust component emission (Casey 2012; Casey et al. 2014). For galaxies lacking sufficient FIR detection, the peak of the graybody emission will be poorly constrained, resulting in an unreliable estimate on T_dust. To reduce such an effect, only galaxies with more than three data points at λ_rest > 50 μm (i.e., where the graybody emission dominates) are included in our analysis (see Section 2.2). This extra selection criteria effectively translates into having for most of our galaxies more than four bands covering their MIR to FIR emission (76% have ≥5 bands), providing us with a very accurate description of their infrared emission.

We fix the dust emissivity to a standard reference value of 1.5 (Chapman et al. 2005; Casey et al. 2009), leaving the power-law slope (0.5 < α < 5.5) as a free parameter (Casey 2012). We first perform an automatic fitting process assuming an optically thin dust model. Then we visually inspect the best-fit SEDs for individual sources in order to ensure acceptable best-fit results. For a few cases in which the model fails to fit the data, we rerun the fit by manually adjusting (and fixing) α values. For 25 galaxies, we are able to better constrain T_dust with manual fitting, and the new best-fit results are adopted. However, there are still 29 of the original 488 FIR-detected massive SFGs that fail to achieve an acceptable fit even though manual fitting process is implemented, due to either insufficient wavelength coverage that leads the peak emission unconstrained, or the fact that the data apparently deviate a lot from the assumption of MIR power law plus FIR graybody. These galaxies with failed determination of T_dust are already excluded from our final sample (see Section 2.3).

While dust temperature can be defined in different ways, such as mass-weighted or light-weighted, the light-weighted dust temperature derived as here using the FIR peak emission is what can be best constrained observationally (Casey et al. 2014; Liang et al. 2019). These light-weighted dust temperatures reflect the condition of the ISM surrounding massive and thus luminous star-forming regions. They are also less dependent on the assumed underlying templates and allow for a direct comparison with previous works.

The SFRs in the 3D-HST catalogs are derived using rest-frame UV luminosity, L_UV, in combination with the Spitzer/MIPS 24 μm based total IR luminosities, L_IR, as described in Whitaker et al. (2014):

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{SFR} & = & {\mathrm{SFR}}_{\mathrm{UV}}+{\mathrm{SFR}}_{\mathrm{IR}},\\ & = & \ 1.09\times {10}^{-10}(2.2{L}_{\mathrm{UV}}+{L}_{\mathrm{IR}}).\end{array}\end{eqnarray} \tag{ 2 }$$

We only keep the UV-based SFRs but recalculate SFR_IR based on our MIR to FIR photometries. We make use of the total IR luminosity, L_IR, integrating the SED output by cmcirsed from the rest-frame 8 to 1000 μm, and correct AGN contribution, L_IR,AGN, with the method presented in Dai et al. (2018). Briefly, we convert the 2–10 keV luminosity of our X-ray AGNs to AGN emission at 6 μm using the well calibrated X-ray to MIR relation of Stern (2015)

$$\begin{eqnarray}&&\mathrm{log}({L}_{2\mbox{--}10\mathrm{keV}}/[\mathrm{erg}\,{{\rm{s}}}^{-1}])=40.981+1.024x-0.047{x}^{2},\end{eqnarray} \tag{ 3 }$$

where $x=\mathrm{log}(\nu {L}_{\nu }(6\,\mu {\rm{m}})/[{10}^{41}\ \mathrm{erg}\,{{\rm{s}}}^{-1}])$. L_IR,AGN is then extrapolated by multiplying νL_ν (6 μm) by a factor of 2.5, derived from the AGN template of Dai et al. (2012). We find generally small corrections for AGN contribution in our sample with a median value of L_IR,AGN/L_IR ≃ 9%. Note that for galaxies without X-ray AGN detection, the median of L_IR based on our FIR SED fitting is only larger by 0.07 dex than, and therefore broadly consistent with, that derived by Whitaker et al. (2014).

The SFR–M_* distributions for our SFGs are shown in Figure 2 along with the main sequence of SFGs from Whitaker et al. (2014). Compared to the main-sequence of SFGs, a significant number of our SFGs have enhanced star formation activity, especially in the high-redshift bin. By requiring FIR detection, our SFGs are biased to higher SFR.

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Dust temperature of SFGs is known to evolve with redshift in the sense that typical SFGs exhibit hotter dust temperature at high redshift than in the local universe, possibly due to a higher star formation efficiency or lower metallicity (Magnelli et al. 2014; Schreiber et al. 2018; Liang et al. 2019). Such an evolution cannot be neglected especially for our sample spanning a large redshift range. Therefore, Figure 3 shows the dust temperature versus redshift for both eSFGs and cSFGs compared to that of main-sequence galaxies inferred by Magnelli et al. (2014). The median dust temperatures of eSFGs and cSFGs are also summarized in Table 1. We found that the number of cSFGs relatively to the number of eSFGs significantly decreases between z ∼ 2.5 and z ∼ 1.5 (upper panel of Figure 3). This is consistent with Barro et al. (2013) in which the decrease is explained by the fact that cSFGs are continuously formed at a redshift of 2–3 and gradually fade into QGs at later times.

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Table 1. The Source Number, Dust Temperature, and Dust Mass for eSFGs, cSFGs, and SFGs Hosting AGNs in Two Redshift Bins

Sample	N	Tdust/K	$\mathrm{log}({M}_{\mathrm{dust}}/{M}_{\odot })$
1 < z ≤ 2
eSFGs	337	31.6 ± 0.5	8.1 ± 0.1
cSFGs	34	31.8 ± 1.8	8.4 ± 0.1
AGNs	67	33.3 ± 1.2	8.3 ± 0.1
2 < z < 3
eSFGs	62	38.3 ± 1.9	8.5 ± 0.1
cSFGs	26	38.8 ± 2.9	8.7 ± 0.1
AGNs	28	38.7 ± 2.4	8.7 ± 0.1

Note. For T_dust and M_dust, the median is provided, together with uncertainties estimated via the bootstrapping method.

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It is clear that both eSFGs and cSFGs generally follow the T_dust − z evolutionary track defined by the main-sequence SFGs presented in Magnelli et al. (2014), especially for galaxies at z ≲ 2. From z ∼ 2.5 to ∼1.5, the dust temperature of cSFGs drops by 7.0 ± 3.4 K. In the same redshift range, the dust temperature of eSFGs drops by 6.7 ± 2.0 K. The redshift evolution of dust temperatures for cSFGs and eSFGs are thus fully consistent within the uncertainties.

In the higher redshift bin, T_dust of both cSFGs and eSFGs are about 5 K higher than that inferred by Magnelli et al. (2014). This trend can, however, be explained by their higher SFRs as revealed in Figure 2.

Similarly, T_dust for AGN-hosting SFGs are also uniformly distributed around the T_dust–z track of main-sequence SFGs (see the open circle in Figure 3 and Table 1). No AGN effect on the temperature of the cold dust is observed for our sample. However, further interpretation is limited by both the small sample size and the large uncertainty involved during the T_dust calculation.

Based on our FIR SED fits, we also infer dust masses (M_dust) by extrapolating the rest-frame 850 μm emission of our galaxies and assuming a dust absorption coefficient of κ₈₅₀ = 0.15 m² kg⁻¹ (Casey 2012). The resulting M_dust is given in Table 1. It can be seen that a huge amount of dust is enclosed in our SFGs, which is expected from their FIR detections. Though cSFGs might have more dust compared to eSFGs, it should be treated with caution since the reliability of M_dust measurement is limited by the lack of data at longer wavelengths. Our measurement is consistent with those of high-redshift dusty SFGs or submillimeter galaxies with T_dust ≈ 20–50 K and $\mathrm{log}({M}_{\mathrm{dust}}/{M}_{\odot })\approx 8\mbox{--}9.3$ (Kovács et al. 2006; Casey 2012; Casey et al. 2014). Furthermore, the huge amount of dust in cSFGs also directly confirms the observations of Barro et al. (2014) that SFGs become more compact before they lose their gas and dust.

To reveal the role of compactness in dust heating, we plot the Σ_1.5–T_dust relation, color-coded by specific star formation rates (sSFR ≡ SFR/M_*), in Figure 4. Obviously, there is no significant trend between Σ_1.5 and T_dust in both redshift bins, while the Pearson linear (or Spearman rank) correlation coefficients are close to zero for both subsamples. This result suggests a similar dust temperature for cSFGs and eSFGs, which is consistent with Gómez-Guijarro et al. (2019) in which the authors found that the ISM properties of cSFGs are similar to those of eSFGs located slightly above the main sequence. Moreover, no significant feature of sSFR on the Σ_1.5–T_dust plane is observed in both redshift bins, although we will show in Section 4.2 that cSFGs tends to have smaller sSFR compared to eSFGs at 2 < z < 3.

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In this section, we focus on the effect of star formation activities on dust, with both the sSFRs and the SFR surface densities (Σ_SFR = $\mathrm{SFR}/2\pi {r}_{{\rm{e}}}^{2}$). ⁸

Dust temperature has been found to correlate with sSFR, better than other quantities like SFRs or L_IR (Magnelli et al. 2014). In Figure 5 we show the relation between T_dust and sSFR, color-coded by their compactness (Σ_1.5). The whole sample is divided into two redshift bins (1 < z ≤ 2 and 2 < z < 3). The running medians of T_dust for two subsamples are shown with green solid lines, while the uncertainties of the running medians estimated via the bootstrapping method (green hatched shadows) and the running standard deviations (yellow shadows) are also plotted in Figure 5.

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In each redshift bin, T_dust of our sample is roughly consistent with that of the main-sequence galaxies at similar redshift (magenta dashed line; Magnelli et al. 2014) within the large scatters. At 1 < z ≤ 2, a weak positive correlation with a linear correlation coefficient of r = 0.34 ± 0.06 between sSFR and T_dust is found, which supports that active star formation heats dust intensively. However, at 2 < z < 3, due to the lack of small-T_dust SFGs in the low-sSFR regime, such a relation is more ambiguous, and T_dust seems to show no correlation with sSFR (r = 0.16 ± 0.09). The lack of small-T_dust SFGs with relatively low sSFR at 2 < z < 3 might be due to the selection effect, i.e., our FIR selection bias to galaxies with more intense star formation compared to the main-sequence SFGs at similar redshift (Whitaker et al. 2014), as suggested by the right panel of Figure 2 and the large void region below the Magnelli et al. (2014) relation at z ∼ 2.5 in Figure 3.

In the low-redshift bin, SFGs with different compactness are well mixed, which is supported by the similar distributions of sSFR for eSFGs and cSFGs given in Figure 5. However, both the distribution of individual galaxies and the comparison of the sSFR distributions between the eSFG and cSFG subsamples imply that more compact SFGs (redder color in Figure 5) seem to possess lower sSFR at 2 < z < 3, which might be a signature of suppression of star formation. However, as shown in the right panel of Figure 2, our FIR selected galaxies form an SFR detection limit of ∼100 M_⊙ yr⁻¹, which bias our sample to more star-bursting galaxies at low-M_* end. Given that eSFGs in this subsample tend to be less massive than cSFGs, ⁹ eSFGs thus might be more star-bursting (higher sSFR) than cSFGs. In other words, the observed lower sSFR of cSFGs at 2 < z < 3 might result from the FIR selection combining with the lack of cSFGs at the low-M_* end. Further M_*-controlled comparison reveals that cSFGs and eSFGs have similar sSFR within the same M_* bins, supporting that the apparently lower sSFR of cSFGs might be just a selection effect.

High-redshift cSFGs also seem to have slightly hotter dust than that predicted by the main-sequence SFGs (Magnelli et al. 2014). This might suggest differences in the ISM conditions of these compact objects with respect to typical SFGs with similar sSFR. However, considering the low number statistic and the aforementioned selection effect, this result should be treated with caution.

Similar plots for the T_dust–Σ_SFR relation are also shown in Figure 5. SFGs with greater compactness (gray to red points) have significantly larger Σ_SFR than eSFGs, suggesting that size shrinkage is more dramatic than SFR changes. The linear correlation coefficients between T_dust and Σ_SFR are 0.30 ± 0.06 and 0.24 ± 0.08 for the 1 < z ≤ 2 and 2 < z < 3 subsamples, respectively, indicating a weak relation in both redshift bins.

From Figures 5, we find that AGN hosts are distributed in a similar way as those without AGNs. The two populations share the same dependence of T_dust on star formation activities, in terms of sSFR and Σ_SFR. Star formation thus might be the main heating source of dust in these galaxies.

In short, at 1 < z ≤ z, cSFGs seem to be indistinguishable from eSFGs except for their compact stellar morphology, while an apparent suppression of star formation is observed for cSFGs at 2 < z < 3; however, this might be a selection effect.

Given the current data, we only observed an apparent suppression of star formation for our selected cSFGs compared to eSFGs at 2 < z < 3. The role of these cSFGs in the picture of galaxy evolution is still unclear.

Elbaz et al. (2018) compiled a sample of z ∼ 2 Herschel-selected galaxies, which resemble the massive end (M_* ≳ 10¹¹ M_⊙) of our high-redshift subsample, ¹⁰ and found that galaxies located within the scatter of the main sequence tend to have compact star formation and short depletion timescales. The authors argued that these galaxies could be at the last step of star formation. Although we do not have measurement of star formation-related size for our sample, the most massive galaxies at 2 < z < 3 located within the scatter of the main sequence also tend to have compact stellar morphology (see Figure 2), possibly suggesting similar properties to those galaxies hidden in the main sequence in the Elbaz et al. (2018) sample.

Furthermore, based on observations of galaxies at 0.5 < z < 3, Gómez-Guijarro et al. (2019) reported that cSFGs and eSFGs exhibit similar star formation efficiencies, while the ISM properties (e.g., CO excitation and local physical conditions of the neutral gas) of cSFGs are also similar to those of eSFGs located slightly above the main sequence. Besides the above ISM properties, our results (i.e., Table 1 and Figure 4) provide the further supplement related to dust that no significant differences in T_dust and M_dust are observed between cSFGs and eSFGs for both redshift subsamples.

Therefore, for cSFGs in both redshift bins, because of their similarity to eSFGs, it is possible that these galaxies form their compact stellar cores via slow secular evolution rather than a rapid compaction process, as suggested by Gómez-Guijarro et al. (2019).