THE CONTRIBUTION OF HOST GALAXIES TO THE INFRARED ENERGY OUTPUT OF z ≳ 5.0 QUASARS

Galaxies at z ∼ 2−3 are of relatively low metallicity (e.g., Cullen et al. 2014; Maier et al. 2014). Confirming the trend toward lower metallicity to z ≳ 5 is difficult with current capabilities. Recently, some groups have tried to detect the dust continua of z > 6 normal galaxies using the Atacama Large Millimeter/Sub-millimeter Array (ALMA). The unexpected failures of almost all of these efforts have led to the interpretation that these z > 6 galaxies may be scaled-up versions of local very metal-poor dwarf galaxies (e.g., Ouchi et al. 2013; Maiolino et al. 2015). As Fisher et al. (2014) pointed out, it would be almost impossible to observe the dust emission of any z > 6 galaxies with extremely low metallicity like the local dwarf galaxy 1 Zw 18. For the most luminous systems, however, the change in metallicity seems to be modest (e.g., Rawle et al. 2014). As a result, the ideal sample to draw a representative template for IR observable high-z galaxies is the moderately low metallicity galaxies in the local universe.

In addition, AGN host galaxies at z > 4 are found to be compact with typical sizes ∼1–3 kpc, from observations at rest-frame UV (Jiang et al. 2013), deep K_s-band images (Targett et al. 2012), dust continuum maps (Wang et al. 2013), submillimeter fine-structure line maps (e.g., Wang et al. 2013; Willott et al. 2013, 2015), molecular gas distributions (e.g., Walter et al. 2004, 2009; Wang et al. 2013), and SED analysis (Greve et al. 2012). Compared with extended galaxies of the same IR luminosity, they are expected to have hotter FIR SEDs owing to compact star-forming regions (Groves et al. 2008). Thus, we are motivated to search for a moderately low metallicity galaxy with a high surface density of star formation to provide an SED analogous to what we expect for the star formation in the host galaxies of high-z quasars.

Appendix A presents the procedure to derive low-metallicity galaxy templates. To summarize briefly, we began with the sample of the Dwarf Galaxy Survey (DGS; Madden et al. 2013), which includes the largest metallicity range observable in the local universe, with 12 + log(O/H) ranging from 7.14 to 8.43, and spans four orders of magnitude in star formation rates (SFRs). Combining their Herschel FIR data (Rémy-Ruyer et al. 2013) and archival Wide-field Infrared Survey Explorer (WISE) MIR photometry, we fit the broadband SEDs with an FIR modified blackbody plus an MIR power-law component and replaced the MIR fit SEDs with the corresponding Spitzer spectra. Among the 19 dwarf galaxies studied in detail, Haro 11 is the best candidate analog for high-z galaxies. Haro 11 is a moderately low metallicity (Z = 1/3 Z_⊙, James et al. 2013) dwarf (${M}_{*}={10}^{10}\;{M}_{\odot }$; Östlin et al. 2001) galaxy in the nearby universe (D = 92.1 Mpc; Bergvall et al. 2006). It shows substantial star formation activity (${\rm{SFR}}\approx 20\mbox{--}30\;{M}_{\odot }\;{{\rm{yr}}}^{-1}$; Grimes et al. 2007; see also Appendix B.2) and emits strongly in the IR (${L}_{{\rm{IR}}}\approx 2.0\times {10}^{11}\;{L}_{\odot }$; Adamo et al. 2010). Haro 11 also contains an extremely young stellar population with age  <40 Myr (Adamo et al. 2010). Some authors suggest that it is a local analog of the high-z Lyman break galaxies (LBGs) or Lyα emitters (Hayes et al. 2007; Leitet et al. 2011).

Besides low metallicity, the most important two features of Haro 11 are its high SFR and compact size, indicating a very high star formation surface density. From our estimation, the SFR of Haro 11 can be as high as ∼32 M_⊙ yr⁻¹ (based on L_IR and L_FUV; see Appendix B.2), which is significantly higher than the vast majority of dwarf galaxies in the literature (Hopkins et al. 2002). Meanwhile, Haro 11 has a compact size. Its MIPS 24 μm image is perfectly diffraction limited (see Figure 1), which puts an upper limit on its IR-emitting region size (<34 or 1.2 kpc). The size of the star formation region of Haro 11 constrained from high-resolution Hα images (Östlin et al. 2009) is also small (∼1.3 kpc from measuring 50% total flux, and ∼2.7 kpc from measuring 90% total flux). The IR luminosity surface density, Σ_L(IR), of Haro 11 is $\sim {10}^{11}\;{L}_{\odot }\;{{\rm{kpc}}}^{-2},$ which approaches the values in galaxies at z ≳ 4 (e.g., GN20 has ${{\rm{\Sigma }}}_{L({\rm{IR}})}\sim {10}^{12}\;{L}_{\odot }\;{{\rm{kpc}}}^{-2}$;Hodge et al. 2015). The high SFR surface density and IR luminosity surface density of Haro 11 are exceptional among dwarf galaxies, making it the most suitable local analog to high-z quasar host galaxies.

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In Figure 2, we compare the derived Haro 11 template with a number of normal solar-metallicity SF templates in Rieke et al. (2009). Haro 11 has a larger MIR slope with α = 3.63 (${f}_{\nu }\propto {\lambda }^{\alpha }$), in contrast with normal galaxies with α ∼ 2.0 (e.g., Blain et al. 2003; Casey 2012). The derived dust temperature is T = 46.5 K with emissivity index β = 1.9. Haro 11 also presents very weak aromatic features compared with normal galaxies. All these characteristics are commonly seen for other dwarf galaxies (see Appendix A.3). Compared with typical z ∼ 2 galaxies, which can be represented by Rieke et al. (2009) SED templates with $\mathrm{log}{L}_{{\rm{IR}}}\lt 11.50$ (see Section 3.1), Haro 11 has a similar L_IR surface density but higher dust temperature. We suggest that the low metallicity of Haro 11 is the most likely reason for its warmer SED.

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Candidate AGN templates can be derived from either numerical models (e.g., Fritz et al. 2006; Hönig & Kishimoto 2010) or semianalytic models (e.g., Mullaney et al. 2011; Sajina et al. 2012). However, such models always have many free parameters, which need to be optimized to fit real AGN behavior. Hence, the starting point for determining AGN templates needs to be an accurate empirical version.

Elvis et al. (1994) built an X-ray to radio SED template for a sample of 47 well-defined optically selected quasars and subtracted the host galaxy emission in the UV/optical and NIR bands. This template has become the classic representation of Type 1 AGN SEDs in the ultraviolet, visible, NIR, and MIR. Many studies based on larger samples and modern data have closely reproduced the Elvis template (e.g., Richards et al. 2006; Shang et al. 2011; Elvis et al. 2012; Runnoe et al. 2012; Hanish et al. 2013; Scott & Stewart 2014). The remarkable similarity of these results to the Elvis template is demonstrated by the comparisons in Scott & Stewart (2014) (their Figure 5). The success of the Elvis template is also demonstrated by its broad application, for example, to study the SEDs of Type 1 AGNs in XMM-COSMOS (Elvis et al. 2012) and decompose the SEDs of intermediate-redshift quasars in Xu et al. (2015b). The template shape appears to vary little with cosmic evolution or other characteristics such as the Eddington ratio (e.g., Hao et al. 2011, 2014). In particular, this template appears to work equally well to z ∼ 6. Jiang et al. (2006) demonstrated that the rest-frame 0.15–3.5 μm SEDs of 13 z ∼ 6 quasars can be matched with the Elvis et al. (1994) template. Wang et al. (2008a) demonstrated that the average optical to NIR SED of 33 z ∼ 6 quasars is consistent with the Elvis template. Jiang et al. (2010) find that the NIR and optical–NIR colors of hundreds of quasars are virtually the same from the local epoch to z ≥ 6, i.e., they are consistent with a common SED shape, which must therefore be consistent with the Elvis template. Therefore, the Elvis template is a useful metric for testing more complex models and is currently the most suitable approach for SED decompositions involving UV-luminous Type 1 AGNs.

There are two issues in applying the Elvis template. The first is that it is likely to have a residual contribution in the FIR from dust heated by star formation, a possibility that has hindered its application in using the FIR to measure SFRs in quasar host galaxies (e.g., Barnett et al. 2015). However, a version of the template corrected for this effect is now available (Xu et al. 2015b). Based on the analysis of the Spitzer and IRAS data of the Elvis et al. (1994) sample, these authors found a tight correlation between the strength of the 11.3 μm aromatic feature and the IR 60–25 μm flux ratio. They concluded that star formation, as traced by the aromatic feature, boosted the IR flux ratio in the template by a factor of 1.27. A scaled Rieke et al. (2009) star-forming galaxy template (log L_IR = 11.0) was subtracted from the Elvis et al. (1994) template to remove this contribution. The second issue is that of order 10% of quasars have SEDs similar to the Elvis template in the UV and optical but that are relatively weak in the NIR and MIR, a behavior attributed to a relative lack of hot dust (Hao et al. 2010, 2011). The exact SED shape of these dust-poor quasars requires future work to address.

Leipski et al. (2013) used three components to represent the AGN SEDs for their high-redshift quasar sample: a UV/optical power law, an NIR dust emission component, and a torus model. They adjusted the relative contributions of these components to optimize their SED fits. However, all three components are implicitly embedded in the Elvis template. Any adjustments in relative strengths should only be made after it has been demonstrated that the Elvis template (or similar ones) gives an unsatisfactory fit. In this work, we use the Elvis template for our SED decomposition. When combined with the Haro 11 template, we find that its fits are of comparable quality to the relatively unconstrained fits used by Leipski et al. (2013, 2014) in the sense of chi-square tests. There is thus no advantage for our study in using those more complex and less constrained models for the quasar SEDs—they introduce additional free parameters without improving the fits correspondingly (see Section 3.3).

To compare the templates described above with observations, we used a fitting procedure that takes into account upper-limit data points where available. For n measurements of x_i with uncertainties σ_i and m nondetections with x_j < nσ_j (nth confidence level), we define the fitting chi-square as (Isobe et al. 1986)

$$\begin{eqnarray}&&{\chi }_{{\rm{total}}}^{2}=\displaystyle \sum _{i}^{n}{z}_{i}^{2}-\displaystyle \sum _{j}^{m}2\mathrm{ln}\displaystyle \frac{1+{\rm{erf}}({z}_{j}/\sqrt{2})}{2}\;,\end{eqnarray} \tag{ 1 }$$

where

$$\begin{eqnarray}&&{z}_{i}=\displaystyle \frac{{x}_{i}-{\hat{x}}_{i}(\theta )}{{\sigma }_{i}}\;,\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{\rm{erf}}(x)=\displaystyle \frac{2}{\sqrt{\pi }}{\displaystyle \int }_{0}^{x}{e}^{-{t}^{2}}{dt}\;,\end{eqnarray} \tag{ 3 }$$

which is the error function, and ${\hat{x}}_{i}(\theta )$ is the modeled value. In Equation (1), the first term on the right-hand side is the classical definition of chi-square, and the second term introduces the error function to quantify the fitting of upper limits. We use Markov Chain Monte Carlo (MCMC) methods to find the parameter set θ to minimize χ²_total; 3σ upper limits are adopted for all nondetections. To compare the fitting quality of different fitting methods, the total ${\chi }_{{\rm{total}}}^{2}$ should be normalized by the degrees of freedom, ν. In our case, $\nu =n+m-k,$ where k is the number of free parameters in the model. We will use ${\chi }_{\nu }^{2}$ to represent the reduced chi-square, i.e., ${\chi }_{\nu }^{2}={\chi }_{{\rm{total}}}^{2}/\nu .$

To deal with the trade-off between the goodness of fit and the complexity of the model, we use the corrected Akaike Information Criterion (AICc) test (Sugiura 1978), which is defined by

$$\begin{eqnarray}&&{\rm{AICc}}=-2\mathrm{ln}{{ \mathcal L }}_{{\rm{max}}}+2k+\displaystyle \frac{2k(k+1)}{N-k-1}\;,\end{eqnarray} \tag{ 4 }$$

where ${{ \mathcal L }}_{{\rm{max}}}$ is the maximum likelihood achievable by the model and N is the number of data points used in the fit, $N=n+m.$ The likelihood of a model to fit data satisfies

$$\begin{eqnarray}&&-2\mathrm{ln}{{ \mathcal L }}_{{\rm{max}}}={\chi }_{{\rm{total}}}^{2}+C\;,\end{eqnarray} \tag{ 5 }$$

where the constant C is related to the errors, σ_i, and the binning, Δx_i, of the data points, which are fixed at the time of observations. We can ignore C when comparing different models to fit the same observations, and finally we have

$$\begin{eqnarray}&&{\rm{AICc}}={\chi }_{{\rm{total}}}^{2}+2k+\displaystyle \frac{2k(k+1)}{n+m-k-1}\;.\end{eqnarray} \tag{ 6 }$$

We now discuss alternative SF template candidates to be used at high z. Rieke et al. (2009) derived templates for local normal star-forming galaxies with different IR luminosities (L_IR). Although carefully calibrated in the local universe, these templates may not apply at high redshift. The star formation in luminous galaxies at high z has been found to be more physically extended than that in local galaxies with similar L_IR (local LIRGs and ULIRGs are sub-kpc, whereas high-z DSFGs are kpc in size; see Rujopakarn et al. 2011). Rujopakarn et al. (2011, 2013) found that the Rieke et al. (2009) $\mathrm{log}{L}_{{\rm{IR}}}$ = 11.00–11.50 SED templates are representative of galaxies found at 0.4 < z < 2.7 owing to their similar L_IR surface densities. This argument is supported by the consistency between the empirical average SED of z ∼ 2 galaxies derived in Kirkpatrick et al. (2012) and the $\mathrm{log}{L}_{{\rm{IR}}}$ = 11.00–11.50 SED templates from Rieke et al. (2009) (Figure 3). In fact, Figure 3 shows the progressively poorer correspondence of the Rieke et al. (2009) templates with the empirical one with increasing L_IR. It is also consistent with the finding of a shift toward colder FIR SEDs at high redshift by Symeonidis et al. (2009, 2013). Greve et al. (2012) found evidence of extended structures in DSFGs out to redshift z ∼ 4.0, based on analysis of their IR SEDs. With this evidence, we focus on Rieke et al. (2009) SED templates with luminosity $\mathrm{log}{L}_{{\rm{IR}}}\lt 11.50$ in the following comparisons. These normal SF templates represent galaxies that are almost certainly more metal-rich than is appropriate for z > 4. We will therefore compare them with fits using a template derived from Haro 11.

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We test the Rieke et al. (2009) and Haro 11 template fittings to extremely high-z galaxies, as examples of potential host galaxies for high-redshift quasars. Owing to the lack of data available for star-forming galaxies at z > 5, we extend our redshift range down to z = 4. We find eight galaxies (see Table 1) with multiple constraints on their rest-frame IR SEDs, suitable for comparison with these templates. By selection, these highest-z DSFGs are limited to a handful of submillimeter galaxies (SMGs), which were originally discovered in the submillimeter and are relatively bright in the FIR. The identification technique of SMGs could bias their SEDs to be relatively cold compared with high-z galaxies selected in other ways (Le Floc'h et al. 2004), whereas the SEDs of low-metallicity galaxies tend to be relatively hot (e.g., Rémy-Ruyer et al. 2013). As a result, the high-z galaxy examples studied here might be biased against typical low-metallicity galaxies, which, as in the case of Haro 11, tend to have SEDs dropping rapidly toward the submillimeter.

Table 1.  Comparisons of Galaxy Templates Used to Fit z > 4 Galaxies

Source	z	${\chi }_{\nu ,{\rm{Haro11}}}^{2}$	R09 Best	${\chi }_{\nu ,{\rm{R09}}}^{2}$	References
(1)	(2)	(3)	(4)	(5)	(6)
HFLS 3	6.34	13.1	11.50	30.9	(1)
AzTEC 3	5.30	1.5	11.50	2.3	(2), (3)
HLS J0918+5142	5.24	18.1	11.50	18.4	(3)
AzTEC 1	4.64	6.9	11.50	2.0	(3)
Capak4.55	4.55	0.6	11.50	2.1	(3)
ID 141	4.24	5.7	11.50	17.9	(5)
GN10	4.05	3.2	11.50	1.5	(3)
GN20	4.05	23.1	11.25	0.2	(3)

Note. Column (1): source names sorted by their redshifts. Column (3): ${\chi }_{\nu }^{2}$ of Haro 11 template fitting. Column (4): the Rieke et al. (2009) template that has the minimum ${\chi }_{\nu }^{2}$. Column (5): minimum ${\chi }_{\nu }^{2}$ among tested Rieke et al. (2009) templates. Column (6): references for photometric data.

References. (1) Riechers et al. 2013; (2) Dwek et al. 2011; (3) Huang et al. 2014; (4) Rawle et al. 2014; (5) Cox et al. 2011.

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Table 1 summarizes the fitting results for the z > 4 galaxies. We limit the fits to rest-frame 8–1000 μm, where the emission is purely from dust. Although a few examples, e.g., GN20, have a cold FIR SED matched better by the Rieke et al. (2009) templates, in general the fits with the Haro 11 SED are at least as good. We conclude that it is as good as the local higher-metallicity templates in fitting the SEDs of these extreme z > 4 SMGs. That is, even given the selection bias against it, the Haro-11-based template can be used without a substantial loss of accuracy.

The Elvis et al. (1994) template has been shown to match Type 1 quasar SEDs for redshifts up to z ∼ 3 and for wavelengths λ ≲ 24 μm (Hao et al. 2014; Xu et al. 2015b). An issue in applying it, or the similar template of Richards et al. (2006), in the FIR is the uncertain contribution of host galaxy star formation (e.g., Barnett et al. 2015). However, Xu et al. (2015b) were able to correct for this effect. In Figure 4, we compare this corrected template with the stacked SEDs from Leipski et al. (2014). While the UV–optical parts of all three SEDs are well matched with the AGN continuum template, differences emerge in the IR. The stacked SED of quasars detected in at least three Herschel bands has a substantial excess over the AGN template in the FIR, which we attribute to host galaxy star formation (see Section 5.1). The stacked SED of quasars not detected with Herschel is not matched as well in the IR, although the reduced chi-square is still acceptable. This behavior could be due to the unsuitability of a classical AGN template to represent the hot-dust-free (Jiang et al. 2010) or hot-dust-poor (Hao et al. 2010, 2011) quasars (hereafter hot-dust-deficient [HDD] quasars), as pointed out by Leipski et al. (2014). The fit to the Herschel partly detected (detected in only one to two Herschel bands) stacked SED is virtually perfect over the entire wavelength range. The agreement of the template with both the Herschel-undetected and Herschel partly detected stacked SEDs suggests that the star-formation-corrected Elvis SED is a good choice to fit the high-redshift AGN continua. More discussion will be provided in Section 5.

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To test further whether the Haro 11 template and the AGN (modified Elvis et al. 1994) template are reasonable choices to decompose z ≳ 5 quasar SEDs, we focus on five quasars with the most complete IR SEDs. Besides SDSS J1204−0021, the SEDs of all the other quasars were studied in Leipski et al. (2013).¹ We model the observed rest-frame 1–1000 μm SED as a linear combination of the Haro 11 template and the AGN template with two free normalizing factors. These two templates are taken to be independent. To compare the Haro 11 template with the normal SF templates, we replace the Haro 11 template by the normal SF templates in Rieke et al. (2009) and redo the fit. We also apply the Leipski et al. (2013) model to the UV–IR SED of these quasars and compare the fits of the IR SED with those from our two-component models.

In Figure 5, we present the SED decomposition results. In general, the Haro 11 template fits have smaller residuals (≲0.3 dex) compared with the best-fit² normal SF template. In particular, the Haro 11 template yields much better fits in representing the warm dust component from the two-component decomposition. We comment on the two-component fits (left and middle columns of Figure 5) for each SED below.

J0338+0021 (or SDSS J033829.31+002156.3; we use JHHMM ± DDMM for brevity). The Haro 11 template is better than the best normal SF template in decomposing the SED. Fitting the MIR at <10 μm and the FIR drop beyond 100 μm results in the normal SF template model underestimating the flux at 10–100 μm. We note an excess between ∼10 and ∼40 μm over the normal SF template-fitting model SED, which could be the warm excess seen in relatively low z AGN SEDs reported by Xu et al. (2015b). In contrast, such an excess is not strong in the Haro 11 template fits.

J0756+4104. Judging from the fit ${\chi }_{\nu }^{2},$ the normal SF template seems better. However, ∼50% of the χ_ν² of the Haro 11 template fit is contributed by the data point at the longest wavelength (${\lambda }_{{\rm{rest}}}=139\mu {\rm{m}}$), whereas the ${\chi }_{\nu }^{2}$ contribution of the same data point in the normal SF template fitting is minimal. Again, the normal SF template fitting underestimates the SED at ∼10–40 μm. We conclude that the normal SF template and the Haro 11 template yield fits of similar quality.

J0927+2001. The Haro 11 template is much better than the normal SF template in reproducing the observed SED. The maximum deviation of the dwarf galaxy model and observed SEDs is less than 0.3 dex. In the case of this quasar, the normal SF template underestimates the SED at ∼10–100 μm.

J1148+5251. For this well-studied quasar, the Haro 11 template fitting is almost the same as the best normal SF template fitting when comparing ${\chi }_{\nu }^{2}.$ Interestingly, our estimation of the host contribution of this quasar is consistent with result based on the theoretical analysis by Schneider et al. (2015) .

J1204–0021. This is the only case where the Haro 11 template fitting has one data point with fitting residual (slightly) greater than 0.3 dex. Both two-component fits underestimate the observed 10–100 μm flux. However, the residual from the Haro 11 template fitting is much smaller than the normal SF one.

 For the Leipski et al. (2013) model (right column of Figure 5), we only apply the fit to the detected data points in the UV to IR, in the same fashion as Leipski et al. (2013), and compute the ${\chi }_{\nu }^{2}$ for the detected data points at rest frame 1–1000 μm. Since it has more components, especially a torus component selected from a large model library, small details of the observed SED can be reproduced. Thus, the residuals are generally smaller. However, our two-parameter fit has similar reduced chi-square compared with the Leipski et al. (2013) model, despite its simplicity. To judge which fit is preferred, we have used the AICc test (see Section 2.3). Since the slope of the power-law component is not useful in fitting the IR data, we have assumed that the Leipski et al. (2013) fits had six free parameters over 1–1000 μm. As shown in Table 2, the value of AICc is lower in all five cases for the two-parameter fits, indicating that they are indeed preferred. That is, even for these quasars with the maximum number of measurements, the Leipski et al. (2013) model overfits the data compared with our two-parameter one.

Table 2.  SED Decomposition Results for Five z ≳ 5 Quasars with Well-measured SEDs

Source	Redshift	LIR/1013L⊙	${f}_{{\rm{host,}}{\rm{IR}}}$	${\chi }_{\nu }^{2}$	AICc	R09 Best	${\chi }_{\nu ,{\rm{R09}}}^{2}$	${\chi }_{\nu ,{\rm{L13,IR}}}^{2}$	AICcL13
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
SDSS J0338+0021	5.03	4.01	0.57	5.03	45.95	11.50	11.70	2.25	49.00
SDSS J0756+4104	5.11	3.77	0.69	2.44	25.26	11.50	1.95	2.07	48.28
SDSS J0927+2001	5.77	3.21	0.64	1.96	21.39	11.50	4.51	3.03	52.12
SDSS J1148+5251	6.43	5.31	0.34	3.09	33.31	11.50	3.00	3.63	51.10
SDSS J1204−0021	5.03	3.79	0.46	6.92	54.44	11.50	14.91	18.78	110.34

Note. Results of full IR fits. Upper-limit data points are included in the evaluation process. Column (3): the total IR luminosity (8–1000 μm) estimated from the "Haro 11 + AGN" two-component SED fit. Column (4): the fraction of luminosity of host template contribution to the whole fit SED, based on the result from the "Haro 11 + AGN" decomposition. Column (5): reduced chi-square from the "Haro 11 + AGN" decomposition. Column (6): the AICc test value of the "Haro 11 + AGN" two-component model. Column (7): log L_IR of the Rieke et al. (2009) template, which has the minimum ${\chi }_{\nu }^{2}$. Column (8): the minimum ${\chi }_{\nu }^{2}$ of the "normal SF galaxy + AGN" decomposition with all tested Rieke et al. (2009) templates. Column (9): reduced chi-square from the Leipski et al. (2013) model, only counting data points at rest frame 1–1000 μm. Column (10): the AICc test value of the Leipski et al. (2013) model, assuming six free parameters.

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In summary, we find that the Haro 11 galaxy template and the modified Elvis AGN template are at least as good at fitting the overall high-z quasar SEDs as the fits using templates for local star-forming galaxies of solar metallicity. The Haro 11 template fits better in the rest-frame MIR but may be slightly worse in the FIR range. Though the Leipski et al. (2013) model could reproduce more details of the observed SED, our two-component model yields fits of comparable overall quality and is preferred in model selection owing to its simplicity.

To study the host galaxies of high-z quasars from IR SEDs, the heating sources of the IR-emitting dust and the contribution from the host star formation should be examined first. Previously, a number of papers made the assumption that the heating process for the FIR-emitting warm dust is dominated by host star formation (e.g., Leipski et al. 2014), or assumed some conservative fraction of host star formation heating (e.g., Wang et al. 2011b). From a theoretical point of view, Li et al. (2008) and Schneider et al. (2015) studied the heating of the observed SED of J1148+5251, an archetypal high-luminosity, high-redshift quasar. They argued that the heating of the dust in the host galaxy could be dominated by processes related to the central engine, rather than the host star formation. This field is quite controversial.

As shown in Figure 6, the AGN template from Xu et al. (2015b) is not sufficient to reproduce the FIR SED of many z ≳ 5 quasars with rest-frame FIR detections. To investigate the average IR properties of these quasars, we fit the three stacked SEDs in Leipski et al. (2014), shown in Figure 4. For the FIR-detected SED (from objects detected in at least three Herschel bands), we can see a clear contribution in the FIR from the host galaxy. For the partly detected SED (from objects with significant PACS 100 μm and/or 160 μm flux), the AGN template alone is enough to reproduce the SED. For the objects without any Herschel detections, there are some HDD quasars with SEDs deviating from normal AGNs, as indicated by the low ratio of rest 24 μm to optical. The stacked SEDs for the 14 partly Herschel detected and the 33 nondetected systems show no evidence for significant FIR output over that of typical quasar templates. It would be difficult to understand why just 10 systems from this sample had strong heating of the host galaxy interstellar medium (ISM) by the quasar. A plausible explanation is that these 10 Herschel-detected systems have high levels of star formation, while for the other quasars the star formation is weak.

At very high redshift, cosmic microwave background (CMB) is also a source for dust heating (da Cunha et al. 2013). However, since the dust temperatures in high-z quasar host galaxies are typically ∼35–50 K (e.g., Leipski et al. 2014; Xu et al. 2015b), at least twice the CMB temperature for the relevant redshift range (T_CMB ∼ 18 K at z ∼ 5.5), a correction is not significant compared with the other uncertainties in our derivations.

For quasars at z ∼ 1−6, emission-line ratios are found to trace (super)solar gas metallicities (up to ∼10 Z_⊙) in broad-line regions (BLRs) without any strong indication of redshift evolution (Nagao et al. 2006, 2012; Jiang et al. 2007; Juarez et al. 2009). However, the mass of the BLRs is small (${10}^{2}\mbox{--}{10}^{4}\;{M}_{\odot }$) and might not be representative of the overall formation history of the galaxy. Wang et al. (2010a, 2011a) showed that the star formation can be enhanced in the accretion flow of the AGN, possibly resulting in locally increased metallicity. The narrow-line regions (NLRs) of quasars at z ∼ 1−4 are also found to be around solar metallicity without strong evolution (Matsuoka et al. 2009). In contrast with the BLRs, the typical size of the NLRs (∼10¹–10⁴ pc; Bennert et al. 2006a, 2006b) is comparable to the size of the host galaxies. The only quasar beyond z ≳ 5 with an NLR metallicity constraint is TN J0924−2201, a Type 2 radio galaxy at z = 5.19 (Matsuoka et al. 2011). Considering the small sample size and uncertainty of the metallicity calibration, the result for TN J0924−2201 does not provide much knowledge of the metallicity in the z ≳ 5 quasars. We do not have observational constraints on the metallicity of these quasar hosts from emission-line analysis.

Another possible approach to get metallicity constraints on (or near) distant quasar hosts is from analyzing the absorbers with high H i content (${N}_{\text{H I}}\gtrsim {10}^{20}\;{{\rm{cm}}}^{-2}$), or so-called damped Lyα (DLA) systems, at the redshift of the quasar (Hennawi et al. 2009; Zafar et al. 2011). Hennawi et al. (2009) reported the discovery of a bright Lyα blob associated with the z = 3 quasar SDSS J124020.91+145535.6 and gave a lower limit to the gas metallicity $Z\gtrsim 1/10\;{Z}_{\odot }.\;$Zafar et al. (2011) studied a physical quasar pair Q0151+048 (z ∼ 1.9) and suggested an overall metallicity of 0.01 Z_⊙ for a DLA associated with one member. The redshifts of these two quasars are relatively low. It is also not clear whether they are representative of the general population. As argued by Finley et al. (2013), statistical study shows that the absorption of the associated DLAs is more likely to happen in the galaxies neighboring the quasar, rather than in the AGN host galaxy. Further detailed studies on larger samples are needed to make any conclusive argument.

Several works argued that some massive galaxies at high z have solar metallicity (e.g., Maiolino et al. 2008; Mannucci et al. 2009; Rawle et al. 2014). It is possible that these objects are mature and highly evolved. However, we should be cautious about the derived metallicity with very limited data points for individual sources. Convincing measurements of metallicity at high z require more understanding of the ISM in these systems. For 2.0 < z < 2.5 galaxies, statistical studies based on multiple metallicity tracers show that their metallicities drop at large masses (Cullen et al. 2014; Maier et al. 2014). For the very early universe, simulations suggest that Population III stars contribute little to the chemical enrichment of the ISM (Valiante et al. 2009). The existence of a huge population of low-metallicity systems between the cosmic reionization and z > 2.5 should be expected. Since high-z quasars are originally identified by their AGN features, the properties of their host galaxies should not be much biased by the selection. It is therefore plausible that the high-z quasar host galaxies have metallicities moderately, if not substantially, below solar.

In this work, hints for the low metallicity of the AGN host galaxies at z ≳ 5 are from the successful reproduction of the observed SEDs based on two-component fits, as shown in Section 3.3. The high dust temperature and boosted MIR emission are two major features of the IR SED of Haro 11, a dwarf galaxy with metallicity Z ∼ 1/3 Z_⊙. For the IR SED of these quasars, the low-metallicity Haro 11 template works significantly better than the normal SF templates.

Xu et al. (2015b) discovered a warm MIR component of some Type 1 quasars at $z\sim 0.7\mbox{--}2.5,$ which cannot be reproduced by the combination of the AGN template and normal SF template. This warm excess is found to be more prominent at higher redshifts in their sample. As shown in Section 3.3, a strong MIR SED excess also does exist when fitting the host galaxy with normal SF templates for the z ≳ 5 quasars. In contrast, by introducing the Haro 11 template, the MIR part of the SED of the z ≳ 5.0 quasars is reproduced better: there is no strong hint of the warm excess for the majority of the quasars. The low metallicity of the host galaxy is a possible explanation for many such warm excesses at high z: the dust population in the low-metallicity environment tends to be dominated by small-size grains, which would result in substantial emission in the MIR. Owing to the increase of the MIR emission, the effective dust temperature fit from the whole IR SED is also boosted. Nonetheless, a small number of z ≳ 5 quasars still show an MIR warm excess, such as J0338+0021 and J1602+4228, even with the Haro 11 template fitting. We suggest that such additional warm excess not reproduced by the "Haro 11 + AGN" SED model could be due to an extreme circumnuclear starburst, or that the host galaxy has a much lower metallicity.

In estimating an SFR, the largest uncertainty comes from the assumed star formation calibration. In Appendix B, the star formation determination for the low-metallicity dwarf galaxies is discussed. We show that the Kennicutt (1998) IR star formation law is still valid to roughly estimate the obscured SFRs for the low-metallicity dwarf galaxies, including Haro 11. Besides the obscured star formation, we also consider the unobscured star formation as revealed by the UV emission. As shown in Appendix B.2, Haro 11 has a low UV SFR estimate, which is only ∼10% of that deduced from the FIR. For a 2000 M_⊙ yr⁻¹ IR SFR, the corresponding UV SFR would be 200 M_⊙ yr⁻¹, consistent with the upper limit given for the archetypal z ∼ 6 quasar J1148+5251 (Mechtley et al. 2012). The UV star formation of high-luminosity quasar host galaxies at z ∼ 2.6 is also found to be quite weak (Cai et al. 2014). These examples indicate that a low contribution to the estimated SFR from the UV is appropriate for quasar host galaxies identical to those for J1148+5251 and the Cai et al. (2014) quasar sample. However, we cannot rule out the possibility that some of the host galaxies at the epoch of reionization have larger escape fractions than Haro 11 and hence a large fraction of UV emission, causing us to underestimate their total SFRs.

Many censored data points also make the SFR estimation difficult. For the quasars with at least two detections in the FIR, the host galaxies are reasonably well fit. The derived SFRs are on the order of 10³ M_⊙ yr⁻¹, a typical value also found by other authors (e.g., Wang et al. 2008a; Leipski et al. 2014). For quasars without any FIR detections, we could only determine the upper limits of their SFRs. As described in Section 2.3, we consider all the censored data points during the fitting process. For sources without FIR detections, the fitted upper limits on the SFRs are based on templates constrained by multiple 3σ nondetections and result in overestimated SFR constraints. To solve this problem, we scale the host template to each nondetected 3σ-limit observation, derive the respective SFR, and pick the lowest one as the final constraint on the quasar host SFR. The value c_SFR in Table 3 is the factor by which the fit through the upper limits was reduced. During this process, the contribution of the fitted AGN component is fixed and subtracted when deriving the SFR.

For the HDD quasars, the AGN template fails at λ ≳ 1.0 μm. In addition, none of them are detected in the FIR. To derive conservative upper limits for their SFRs, we assume that all their FIR emission comes from the host galaxy. Consequently, we ignore the fitted AGN component when we scale the host template to the observations.

We ignore the results for J0017−1000 and J1443+3623 of sample-A, whose host contribution is too minimal to be evaluated. From the Kaplan–Meier analysis,³  the mean IR host galaxy luminosity of sample-A is

$$\begin{eqnarray*}&&\langle \mathrm{log}({L}_{{\rm{SF,IR}}}/{L}_{\odot })\rangle =12.51\pm 0.10,\qquad \quad {\rm{(sample}}\;{\rm{A)}}\end{eqnarray*}$$

which corresponds to an average SFR

$$\begin{eqnarray*}&&\langle {\rm{SFR}}\rangle ={621}_{-128}^{+161}\;{M}_{\odot }\;{{\rm{yr}}}^{-1}.\quad \quad (\mathrm{sample}\;{\rm{A}})\end{eqnarray*}$$

Another approach to compute the average SFR is to analyze the stacked SEDs. As shown in Figure 4 and Table 5, the fraction of the host contribution is too small to give any physical constraints on the SFR of the stacked SEDs of Herschel partly detected and nondetected quasars. We simply conclude that substantial star formation only happens in the Herschel FIR-detected stacked SED, whereas the star formation in other stacked SEDs is minimal and set to be zero. Then an arithmetic mean of sample-A is

$$\begin{eqnarray*}&&\langle {\rm{SFR}}\rangle =643\;{M}_{\odot }\;{{\rm{yr}}}^{-1}.{\rm{(A-stacked)}}\end{eqnarray*}$$

This result is almost the same as that from the Kaplan–Meier analysis for individual sources, confirming the validity of the result from the Kaplan–Meier estimator.

Table 5.  SED Decomposition Results for the Stacked Quasar SEDs

Source	N	Redshift	LIR/1013L⊙	fhost, IR	${\chi }_{\nu }^{2}$	SFR(M⊙ yr−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)
FIR-detected	10	5.34	4.08	0.47	0.63	3666
Partly detected	14	5.31	2.04	0.00	0.20	≲1.5 (?)
Nondetected	33	5.20	0.87	0.00	0.61	∼0 (?)

Note. Results of full IR fits. Upper-limit data points are included in the evaluation process. Column (1): type of stacked SED. Column (2): the number of stacked quasars. Column (3): average redshift. Column (4): the total IR luminosity (8–1000 μm) estimated from the "Haro 11 + AGN" two-component SED fit. Column (5): the fraction of luminosity of the host template contribution to the whole fit SED, based on results from the "Haro 11 + AGN" decomposition. Column (6): reduced chi-square from the "Haro 11 + AGN" decomposition. Column (7): estimation of the star formation rate.

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For sample-B, after rejecting SDSS J2329–0301 owing to its minimal host contribution, we use the Kaplan–Meier approach to derive a mean IR luminosity for 32 quasars:

$$\begin{eqnarray*}&&\langle \mathrm{log}({L}_{{\rm{SF,IR}}}/{L}_{\odot })\rangle =12.27\pm 0.22,\quad {\rm{(sample}}\;{\rm{B)}}\end{eqnarray*}$$

which corresponds to an average SFR

$$\begin{eqnarray*}&&\langle {\rm{SFR}}\rangle ={357}_{-142}^{+236}\;{M}_{\odot }\;{{\rm{yr}}}^{-1}.{\rm{(sample}}\;{\rm{B)}}\end{eqnarray*}$$

This estimate is subject to systematic errors because the majority of the sample-B members only have submillimeter measurements at 1.2 mm, and these fall well beyond the peaks of their FIR SEDs. Therefore, any deviation of the SED from the template will result in significant errors in the estimate of IR luminosity. Nonetheless, within the errors, this $\langle \text{SFR}\rangle$ is similar to that from sample-A. In fact, we will show in Section 5.5 that the indicated slightly lower SFRs for sample-B are as might be expected from the generally lower luminosities of their AGNs.

We believe that the average SFR estimated above is robust even if Haro 11 is not representative for some quasar host galaxies. As shown in Section 3.1, the results from the Haro 11 template are not substantially different from the normal SF templates in Rieke et al. (2009). In fact, the AGN template is principally fixed by data points at ∼1–5 μm, leaving the SF template to be matched to the MIR to FIR SED. The large range between the maximum SFRs and the averages suggests that star formation is very "bursty" in the host galaxies, and that the averages can be considered to represent the rates integrated over time. These issues are discussed in Section 5.5.

The total AGN luminosity can be estimated from integrating the Elvis template (e.g., Hao et al. 2014; Xu et al. 2015b. Since our fits are limited to the IR (1–1000 μm), the total AGN luminosity can be derived by scaling an IR-to-bolometric correction of 5.28 (Xu et al. 2015b) to the AGN total IR luminosity L_IR,AGN.⁴ Before that, we check the validity of the Elvis template in the UV/optical bands. As shown in Figure 4, the Elvis et al. (1994) template reproduces the UV to MIR stacked SED of these quasars well. For individual sources, although there are some detailed offsets, the Elvis template generally matches the observations. The monochromatic flux at rest frame 1450 Å is a frequently used indicator of AGN UV continuum brightness in the literature. By applying a scaling factor of 4.65⁵ on the νL_ν(1450 Å), the AGN bolometric luminosity can be estimated. Taking mag(1450 Å) in the literature as a crude but independent tracer of AGN bolometric luminosity, in Figure 7 we plot the mag(1450 Å)-based AGN bolometric luminosities against the L_FIR-based ones. There is a small offset from 1:1 on the correlation between the AGN luminosities from mag(1450 Å) and from the IR bolometric correction, which can be explained by possible UV extinction. In summary, though the normalization of the AGN template is constrained by the rest-frame NIR to MIR data points, the residuals of observed UV/optical SEDs from the IR fit to the Elvis template are generally small.

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Leipski et al. (2014) pointed out 11 quasars with a dearth of very hot dust. We confirm their peculiarity by comparing their observed SEDs with the Elvis template. If normalized at UV/optical wavelengths, the Elvis template clearly overestimates the observed SED beyond rest frame 1 μm. Since we do not have a clear picture of the full wavelength SED of these HDD objects, their luminosities are hard to derive. We still rely on the L_FIR-based luminosity, rather than UV-based luminosity, for two reasons: (1) the UV–optical SED could suffer extinction, thus underestimating the total bolometric luminosity; (2) the UV emission is not isotropic while the sources are optically thin in the NIR and MIR (Marconi et al. 2004). Judging by the UV/optical observation, we do not expect the template-derived luminosity to have more than one order-of-magnitude deviation from the observed one. In Figure 7, it is interesting to note that the HDD quasars in this work generally follow the same trend as normal quasars.

Finally, we can derive the average AGN bolometric luminosity of sample-A with standard error to be

$$\begin{eqnarray*}&&\langle {L}_{{\rm{AGN}}}\rangle =5.287\times \langle {L}_{{\rm{AGN,IR}}}\rangle \\ &&\approx (7.48\pm 0.62)\times {10}^{13}\;{L}_{\odot }.\quad \quad {\rm{(sample}}\;{\rm{A)}}\end{eqnarray*}$$

Similarly, sample-B has

$$\begin{eqnarray*}&&\langle {L}_{{\rm{AGN}}}\rangle \approx (2.63\pm 0.14)\times {10}^{13}\;{L}_{\odot }.{\rm{(sample}}\;{\rm{B)}}\end{eqnarray*}$$

This value is ∼36% of sample-A.

We now compare the relative strength between SF activities and AGN luminosities of z ≳ 5 quasars with that of relatively low-z and intermediate-z quasars. In Figure 8, we put the average values for z ≳ 5 quasars on the relation between SF IR luminosity, ${L}_{{\rm{SF,IR}}},$ and AGN luminosity, L_AGN, for the Xu et al. (2015b) Type 1 quasar sample. The average properties of the z ≳ 5 quasars fall along the fit relation. This is unexpected, however, since quasars at z ≳ 5 and those at z < 3 should be in different star formation phases. From a theoretical perspective, there should be no star formation main sequence as is the case in the z < 3 universe, but bursts of star formation and periods of near-zero SFRs, likely due to the dynamically disturbed gas within the galaxy halo (e.g., Muratov et al. 2015). Current observations suggest that the star formation in some z > 5 quasars is extremely vigorous with SFRs at levels of $\gtrsim {10}^{3}\;{M}_{\odot }\;{{\rm{yr}}}^{-1}$ (e.g., Wang et al. 2008a) or relatively mild with SFRs ≲ 50 M_⊙ yr⁻¹ (e.g., Willott et al. 2013). Despite this large dispersion, an underlying relation between the average host star formation and AGN luminosity, which has been suggested for very luminous AGNs at z ≲ 2.5 (e.g., Netzer 2009; Rosario et al. 2012), seems to already exist at z ∼ 5−6.

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By taking an average of the SFRs of quasar host galaxies in the largest sample at z ∼ 5−7, we can retrieve a rough time-averaged SFR during the lifetime of these quasar host galaxies. In other words, we assume that the relative number of host galaxies with very active star formation (SFR $\sim {10}^{3}\;{M}_{\odot }\;{{\rm{yr}}}^{-1}$) to those without significant star formation (SFR $\lesssim 10\;{M}_{\odot }\;{{\rm{yr}}}^{-1}$) reflects the relative time duration of the starbursting phase to the quiescent phase of the galaxies. Since stars lose mass quickly after leaving the main sequence, we can ignore their contribution to the stellar mass of the galaxy. The main-sequence lifetime of a star with mass M is

$$\begin{eqnarray}&&{\tau }_{{\rm{MS}}}=10\times {(M/{M}_{\odot })}^{-2.5}\;{\rm{Gyr}}\;.\end{eqnarray} \tag{ 7 }$$

Then we have a simple model relating the stellar mass M_* to the galaxy growth time Δt and the initial mass function (IMF) $\xi (m)$ as

$$\begin{eqnarray}&&\langle {M}_{*}\rangle \sim {\displaystyle \int }_{0}^{{\rm{\Delta }}t}{\displaystyle \int }_{{M}_{{\rm{low}}}}^{{M}_{\odot }{(t/10)}^{-0.4}}\xi (m)\langle {\rm{SFR}}\rangle {dmdt},\end{eqnarray} \tag{ 8 }$$

where M_low is the minimum stellar mass, which is assumed to be 0.1 M_⊙; ${M}_{\odot }{(t/10)}^{-0.4}$ is the maximum stellar mass of stars that are still on the main sequence at time t (unit: Gyr); and Δt is the epoch of galaxy mass assembly.

To start, we simply assume a standard Salpeter IMF (Salpeter 1955) and estimate the increase in host galaxy stellar mass since the start of the cosmic reionization, i.e., $z={8.8}_{-1.4}^{+1.7}$ (Planck Collaboration et al. 2015), corresponding to a universe age of ${0.573}_{+0.150}^{-0.122}$ Gyr. Then the time duration Δt from reionization to the average age of the quasars in our sample ($\langle z\rangle$ = 5.5) is ${\rm{\Delta }}t={0.489}_{-0.150}^{+0.122}$ Gyr. Taking the average SFR for sample-A and solving the integration in Equation (8), we derive the stellar mass that could form in a z ∼ 5.5 quasar to be

$$\begin{eqnarray}&&\langle {M}_{*}\rangle \approx {3.0}_{-0.9}^{+0.7}\times {10}^{11}\;{M}_{\odot }.\end{eqnarray} \tag{ 9 }$$

This rough estimate is not highly sensitive to the starting redshift, nor to the form of the standard IMF (see Table 6). For example, if we assume a start at z = 20, the total stellar mass increases by less than a factor of two. We can also change the power-law Salpeter IMF to a more realistic Kroupa & Weidner (2003) IMF with a turnover below ∼1 M_⊙ and use the updated IR star formation calibration in Kennicutt & Evans (2012). The derived M_* is lower by up to 10%. As a result, we estimate that the SFRs we deduce for the host galaxies are likely to result in formation of a net mass $\;(3\mbox{--}5)\times {10}^{11}{M}_{\odot }$ during the major assembly phases for these quasar host galaxies. Although this result was derived for sample-A, the high average SFR also exhibited for sample-B indicates that it is generally true for high-redshift quasars.

Table 6.  Estimation of a Typical Host Galaxy Mass

IMF	SFR (M⊙ yr−1)a	M* (${M}_{\odot }$)b	M* (M⊙)b
		z0 = 8.8	z0 = 20
Salpeter	621	3.02 × 1011	5.42 × 1011
Kroupa	534c	3.00 × 1011	4.80 × 1011

Notes.

^aValues derived from sample-A. ^bStellar masses derived based on Equation (8); z₀ is the redshift when the first galaxies begin to assemble their masses. ^cKennicutt & Evans (2012) updated their original IR star formation calibration (Kennicutt 1998) with the Kroupa & Weidner (2003) IMF. The SFR should be reduced to ∼86%.

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We compare this mass with typical masses for the central BHs in these galaxies, $\sim {10}^{8}\mbox{--}{10}^{9}\;{M}_{\odot }$ (e.g., Jiang et al. 2007; Kurk et al. 2007, 2009; Willott et al. 2010a; De Rosa et al. 2011; Jun et al. 2015). It appears that the formation of stellar mass is adequate to establish ${M}_{{\rm{BH}}}/{M}_{*,\mathrm{total}}$ at 0.1%–1%, which is in good agreement with estimates of this parameter locally (e.g., Kormendy & Ho 2013 and references therein), and with the evidence at $z\lesssim 2$ that the ratio does not evolve substantially with redshift (Kormendy & Ho 2013). If some of the $z\gtrsim 5$ host galaxies have a larger escape fraction than Haro 11 and hence their SFRs are underrepresented by our approach, this conclusion is strengthened. Our conclusion agrees with the measurement of the dynamical masses of these systems (Willott et al. 2015), which also indicates very little evolution of this ratio with redshift up to z ∼ 6.

The sample used to compute the SEDs of low-metallicity galaxies is from the DGS (Madden et al. 2013). This sample covers the full metallicity range observable in the local universe, with 12 + log(O/H) ranging from 7.14 to 8.43, and spans four orders of magnitude in SFRs.

The FIR data adopted here are mainly from Rémy-Ruyer et al. (2013).⁶ A total of 48 dwarf galaxies were observed with PACS and SPIRE on board the Herschel Space Observatory at 70, 100, 160, 250, 350, and 500 μm. For I Zw 18, we update with the Herschel data from Fisher et al. (2014). We also collect the NIR to MIR photometry data for the whole sample from WISE (Wright et al. 2010) at 3.4, 4.6, 12, and 22 μm. A total of 47 of these galaxies were found to have low-resolution MIR spectroscopic observations from the Spitzer archive. We collect the staring-mode Spitzer/IRS spectra from the Cornell Atlas of Spitzer/IRS Sources (CASSIS; Lebouteiller et al. 2011)⁷ and adopt the post-BCD products from the Spitzer Heritage Archive (SHA) for mapping-mode observations, which were reduced in the SSC pipeline version S18.18. The latter spectral maps are combined into a single spectrum to represent the MIR emission continuum of the galaxy. However, since the surface brightnesses of dwarf galaxies are typically low, only a few Spitzer spectra have high enough signal-to-noise ratio (S/N) continuum to be useful for our derivation of the full IR SEDs. Finally, we focus on 19 DGS galaxies to study their IR SEDs.

In Rémy-Ruyer et al. (2013), a simple modified blackbody is fit to the FIR photometry of the DGS sample to derive dust properties like temperature, mass, and emissivity index. After introducing the WISE MIR data at 12 and 22 μm, the FIR SED peak shifts toward a shorter wavelength for the majority of sources, leading to a higher dust temperature. A single (modified) blackbody is not enough to represent the full IR SED, since galaxies always have a range of dust temperatures (e.g., Dunne & Eales 2001; Willmer et al. 2009; Galametz et al. 2012; Kirkpatrick et al. 2012).⁸

Here we utilize the Casey (2012) procedure (hereafter CMC fits) to address the MIR excess. Casey (2012) developed a fitting routine to fit the IR data points with a modified blackbody plus a power-law component. The MIR component is described as an analytical function

$$\begin{eqnarray}&&S{(\lambda )}_{{\rm{MIR}}}={N}_{{\rm{MIR}}}{\lambda }^{\alpha }{e}^{-{(\lambda /{\lambda }_{c})}^{2}}\;,\end{eqnarray} \tag{ 10 }$$

where α is the MIR power-law slope and λ_c the power-law turnover wavelength. The normalizing factor ${N}_{\mathrm{mid}-\mathrm{IR}}$ and turnover wavelength λ_c are bounded with other parameters. We relax the bounding condition of λ_c to fit the diverse SEDs of the DGS sample, leaving other configurations unchanged (see Casey 2012). Since the light from old stellar populations may contribute to the SED (mainly at short wavelengths), we assume that the emission in the WISE W1 band is completely stellar and scale a Rayleigh–Jeans tail to estimate the stellar contribution to other bands. The final SED fit is done for λ > 8 μm data points after subtracting the possible old population stellar contribution from the observed fluxes.

In Table 7, we list the basic information and fit parameter values. In Figure 9, we show the SED continuum fits for the 19 DGS galaxies. We also present the results of single modified blackbody fits (only on Herschel data) for comparison.

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Figure 10 shows the full IR SEDs (after adding the Spitzer spectra) for the 19 DGS galaxies. The MIR continua derived from the photometry fitting and those directly obtained from the MIR spectra are consistent. The MIR regions of these low-metallicity objects present substantial forbidden-line emissions and weak or no polycyclic aromatic hydrocarbon emission (e.g., Wu et al. 2006, 2007), which contribute little to the continuum. For the final model SEDs of the 19 DGS galaxies, we discard the MIR portion of the fit SED continua based on WISE and Herschel photometry and replace it with scaled Spitzer spectra.

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Figure 11 compares the 19 low-metallicity templates with the normal SF galaxy templates in Rieke et al. (2009). The SEDs of these dwarf galaxies show a lot of variation. Compared with the solar-metallicity galaxies, the low-metallicity IR SEDs derived in this work tend to have the following features:

• 1.  
  Higher FIR dust temperature. For the low-metallicity galaxies, the typical dust temperature is T_dust = 34 ± 7.7. Our value is similar to the result by Rémy-Ruyer et al. (2013) (T_dust ∼ 32 K). Compared with the Herschel KINGFISH sample (T_dust ∼ 23 K; Rémy-Ruyer et al. 2013), which contains more metal-rich environments, the dust in these low-metallicity systems is generally warmer.
• 2.  
  Steeply rising MIR continua. For low-metallicity galaxies in this work, the MIR continua slope α = 3.8 ± 0.8, which is much larger than typical values in normal galaxies (α = 2.0 ± 0.5 in Casey 2012; 1.7–2.2 in Blain et al. 2003).
• 3.  
  Weaker aromatic features. The contribution of aromatic features to the IR SED of low-metallicity galaxies is substantially lower than normal galaxies. The weaker aromatic features with decreasing metallicity have been reported by many authors (e.g., Engelbracht et al. 2005, 2008; Madden et al. 2006).

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All of these features can be explained by a rich population of small (and/or hot) grains in the low-metallicity environments (e.g., Madden et al. 2006). In addition, some authors also report millimeter excess emission in these dwarf systems (e.g., Galliano et al. 2003, 2005; Galametz et al. 2009). Since the origin of this excess is not clear and its contribution to the IR luminosity is tiny, we do not consider it in this work.

The SFR can be estimated by the 8–1000 μm IR emission, following the Kennicutt (1998) star formation law,

$$\begin{eqnarray}&&{\rm{SFR}}({\rm{IR}},{M}_{\odot }\;{{\rm{yr}}}^{-1})=4.5\times {10}^{-44}L(\mathrm{IR},\mathrm{erg}\;{{\rm{s}}}^{-1})\;.\end{eqnarray} \tag{ 11 }$$

This relation is widely used for high-z galaxies, though it was originally established for local starbursting galaxies. However, it is not clear whether and how it is valid for low-metallicity dwarf galaxies.

In general, the star formation in a galaxy can be both dust obscured and dust unobscured. For unobscured star formation, tracers that probe direct stellar light (e.g., the GALEX FUV at 0.153 μm) or ionized gas tracers (e.g., Hα, Paα) are used. For dwarf galaxies, Lee et al. (2009) find that FUV has a better performance than Hα in tracing the star formation, since the latter tends to underpredict the total SFR relative to the FUV for low-luminosity systems. Therefore, we use the FUV star formation law derived in Salim et al. (2007), a study that includes dwarf galaxies, to calculate the dust-unobscured SFR:

$$\begin{eqnarray}&&{\rm{SFR}}({\rm{FUV}},{M}_{\odot }\;{{\rm{yr}}}^{-1})\\ &&=1.08\times {10}^{-28}{L}_{\nu }(\mathrm{FUV},\mathrm{erg}\;{{\rm{s}}}^{-1}\;{\mathrm{hz}}^{-1})\;.\end{eqnarray} \tag{ 12 }$$

The dust-obscured star formation can be determined from the dust-processed light at wavelengths where dust emission dominates (e.g., the 24 μm emission, the total IR emission). We use the MIPS 24 μm star formation law in Rieke et al. (2009):

$$\begin{eqnarray}&&{\rm{SFR}}(24\;\mu {\rm{m}},{M}_{\odot }\;{{\rm{yr}}}^{-1})=2.02\times {10}^{-43}L(24\;\mu {\rm{m}},\mathrm{erg}\;{{\rm{s}}}^{-1})\;.\end{eqnarray} \tag{ 13 }$$

The final SFRs of these dwarf galaxies are assumed to be a sum of these two components, which will be compared with that derived from the total IR luminosity (Equation (11)).

We collect GALEX FUV and MIPS 24 μm data to derive the star formation. All of the 19 dwarf galaxies above have MIPS 24 μm observations, and 14/19 have GALEX FUV observations. We retrieve their photometry from the catalog of Spitzer Enhanced Imaging Products⁹ and the GALEX offical online catalog.¹⁰ IC 10, NGC 4214, UM 311, and VII Zw 403 either are too extended or have a close companion in their MIPS 24 μm images; thus, they were removed from the comparison. Additionally, He 2-10, HS 0017+1055, and Mrk 1450 are dropped from the comparison due to the lack of GALEX observations. In Table 8, we listed the derived SFRs for all the dwarf galaxies studied in this work.

In Figure 12, we compare the SFRs derived from the 8–1000 μm IR emission and those derived from the combined GALEX FUV and MIPS 24 μm emission. Within a three-order-of-magnitude dynamical range, the SFRs from these two approaches are generally consistent, without any obvious offset due to metallicity effects. Thus, we conclude that the behavior of the Kennicutt (1998) L_TIR star formation law is similar to other star formation indicators for the population of dwarf galaxies, at least for those studied in this work, and not very sensitive to metallicity.

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As discussed in Section 2, Haro 11 was selected as the candidate galaxy template for high-z galaxies. With ample observations presented in the literature, its SFR can be estimated using various star formation indicators, including the 8–1000 μm IR luminosity, MIPS 24 μm emission, Hα emission line luminosity, and FUSE/GALEX FUV luminosity. Following the calibrations listed above, we estimate its SFRs and summarize these results in Table 9.

The SFR determined from the 24 μm emission is ∼1.8 times higher than that from either L_IR or L(Hα). This discrepancy is a direct consequence of its hot SED (Engelbracht et al. 2008) and the resulting large fraction of its L_IR emitted at 24 μm (see Figure 13).¹¹ Given the close agreement in the SFRs from Hα and L_IR, we conclude that Haro 11 falls above the trend line in Figure 12 because FUV+24 μm overestimates the SFR and L_IR gives a valid estimate. Moreover, since Haro 11 presents very young stellar populations (Adamo et al. 2010), the contamination of emission from old stars to the FIR emission is negligible, which makes the L_IR, following the Kennicutt (1998) SF law, a robust tracer of the obscured star formation.

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We use the FUV luminosity based on GALEX observation and assume the star formation law in Salim et al. (2007) to estimate the unobscured star formation. The final adopted SFR of Haro 11, which is 34.0 M_⊙ yr⁻¹, is based on a combination of GALEX FUV emission and the 8–1000 μm IR emission. We can finally relate the IR luminosity and FUV luminosity of Haro 11 to its total SFR, which includes both the obscured and the unobscured, as

$$\begin{eqnarray}&&{{\rm{SFR}}}_{\text{Haro 11}}({M}_{\odot }\;{{\rm{yr}}}^{-1})=5.00\times {10}^{-44}L(\mathrm{IR},\mathrm{erg}\;{{\rm{s}}}^{-1})\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&\quad =\;1.92\times {10}^{-10}L(\mathrm{IR},{L}_{\odot }).\end{eqnarray} \tag{ 15 }$$

This is the star formation law used for the Haro 11 template in the main part of this paper.