GALEX–SDSS–WISE LEGACY CATALOG (GSWLC): STAR FORMATION RATES, STELLAR MASSES, AND DUST ATTENUATIONS OF 700,000 LOW-REDSHIFT GALAXIES

GSWLC is built around the SDSS Main Galaxy Sample (MGS; Strauss et al. 2002), the most extensive spectroscopic survey of the low-redshift ($z\lt 0.3$) universe. More specifically, GSWLC includes all MGS-like SDSS galaxies that fall within the GALEX footprint, covering $\sim 90 \%$ of the SDSS area, or $\sim 8000$ deg². Galaxies are kept in the sample regardless of the detection in the UV, thus retaining the optical selection. SDSS and GALEX data were obtained through the SDSS CasJobs SQL server.

The majority of low-redshift galaxies in SDSS were targeted spectroscopically as part of the magnitude-limited MGS, one of the three original ("legacy") spectroscopic surveys (the others being the luminous red galaxy [LRG] and quasar surveys). Legacy surveys were completed in 2008 with the release of DR7 (Abazajian et al. 2009) and cover a large contiguous area in the northern Galactic cap and three separate stripes in the southern Galactic cap (Figure 1). These areas lie almost entirely in the northern sky ($\delta \gt -10^\circ$) and mostly at high Galactic latitude ($| b| \gt 30^\circ$).

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The MGS selection algorithm targets nonstellar objects with well-measured photometry brighter than ${r}_{\mathrm{petro}}=17.77$, with some additional cuts based on surface brightness (Strauss et al. 2002). The magnitude limit of MGS yields a sample of galaxies peaking at $z\sim 0.1$, with very few galaxies above z = 0.3.

Selection of SDSS targets is performed on DR10 (Ahn et al. 2014), based on the SpecPhoto table, which combines primary (nonduplicate) photometric objects with primary spectroscopic observations. Nevertheless, in 25 cases more than one primary spectrum was found for the same photometric object, in which case we selected the spectrum that was closest to the photometric position, leaving 730,288 unique objects (objects with a unique ObjID). These SDSS targets constitute shaded areas in Figure 1.

Our selection for inclusion in GSWLC consists of only two criteria:

$$\begin{eqnarray}&&{r}_{\mathrm{petro}}\lt 18.0\\ &&0.01\lt z\lt 0.30.\end{eqnarray} \tag{ 1 }$$

The first criterion replicates the MGS brightness cut, with some rounding to allow for targeting photometry fluctuations. The second cut removes stars and very nearby galaxies whose photometry is likely to be less accurate because of their large angular size (West et al. 2010), and whose redshifts are poorer indications of the distance (Tully et al. 2016). GSWLC therefore includes the entire MGS, complemented by MGS-like galaxies from other programs that fall within the brightness (and, effectively, the redshift) cut of MGS: 5.2% from BOSS (typically ellipticals), and the remaining 2.1% from other surveys (QSO, SEGUE). For studies that focus on the general population of galaxies, it is strongly recommended to use only the MGS galaxies (flag_mgs = 1 in GSWLC).

GSWLC includes all SDSS targets within areas covered by GALEX, regardless of a UV detection. GALEX has observed the sky in 12. wide circular fields ("tiles"), with a wide range of exposure times (Morrissey et al. 2007). The greatest UV sky coverage is provided by shallow ($\sim 100$ s) observations, most of which were taken as part of the All-sky Imaging Survey (AIS). GALEX could not safely point in the direction of bright stars, so even the AIS's coverage contains holes. Observations of medium depth, corresponding to one GALEX orbit ($\sim 1500$ s), are the basis for the Medium Imaging Survey (MIS), which specifically targeted areas within the SDSS footprint. For select fields, deeper observations were obtained by co-adding the observations from multiple orbits, to produce the Deep Imaging Survey (DIS), with nominal exposure time of 30,000 s.

Since the accuracy of UV photometry, and consequently of the derived physical properties, will depend on the depth of the observations, we produce three separate catalogs, each approximately corresponding to shallow (all-sky; A), medium (M), and deep (D) UV imaging surveys. The catalogs are designated as GSWLC-A, GSWLC-M, and GSWLC-D. Each catalog is based only on GALEX imaging of a certain depth, even if deeper exposures of an object exist:

$$\begin{eqnarray}&&\mathrm{GSWLC} \mbox{-} {\rm{A}}:\ {t}_{\mathrm{NUV}}\leqslant 650\\ &&\mathrm{GSWLC} \mbox{-} {\rm{M}}:\ 650\lt {t}_{\mathrm{NUV}}\lt 4000\\ &&\mathrm{GSWLC} \mbox{-} {\rm{D}}:\ {t}_{\mathrm{NUV}}\geqslant 4000,\end{eqnarray} \tag{ 2 }$$

where the exposure times in near-UV (NUV) band are given in seconds. Far-UV (FUV) exposure times are typically identical to NUV times (the two bands were observed simultaneously), except in cases when the FUV image was missing due to camera malfunction. Note that in GSWLC-M we also include individual visits used for DIS co-adds, since the exposure times of individual visits fall in the range for GSWLC-M.

To define the final samples for inclusion in the catalogs, we take all SDSS targets from Section 2.1 that fall within 06 of the GALEX tile centers of the specific UV survey (A, M, or D). This gives the following final sample sizes:

$$\begin{eqnarray}&&\mathrm{GSWLC} \mbox{-} {\rm{A}}:\ 640,659\ (88 \% )\\ &&\mathrm{GSWLC} \mbox{-} {\rm{M}}:\ 361,328\ (49 \% )\\ &&\mathrm{GSWLC} \mbox{-} {\rm{D}}:\ 48,401\ (7 \% )\end{eqnarray} \tag{ 3 }$$

where the percentage indicates the fraction of all SDSS DR10 targets. GSWLC-M contains 7× as many galaxies as the MIS sample used in S07. Since GALEX surveys are nested, objects in the deeper catalogs are mostly included in the shallower ones. The number of unique galaxies encompassed by the three catalogs, 658,911, is therefore only slightly larger than the number of objects in GSWLC-A and corresponds to 90% of the SDSS target sample.

GALEX data are taken from the final data release (GR6/7).¹¹ Matching of SDSS to GALEX is in general a nontrivial task (Budavári et al. 2009) because of the changes in galaxy morphology with wavelength and different resolutions ($5^{\prime\prime}$ for GALEX versus $1\buildrel{\prime\prime}\over{.} 3$ for SDSS). Furthermore, the GALEX data release contains detections of the same objects from multiple tiles. Thus, one needs to address the cases when multiple UV candidates exist for an optical source, and when the UV source may be a blend of two or more optical sources.

In our case, the problem of SDSS–GALEX matching is significantly alleviated by the fact that it involves relatively bright objects, having low sky density. In particular, we find that there are essentially no cases of genuine multiple UV candidates within the $5^{\prime\prime}$ search radius. The choice of search radius is based on GALEX positions of isolated SDSS targets, for which we find negligible bulk offset with respect to SDSS ($0\buildrel{\prime\prime}\over{.} 2$ in either R.A. or decl.) and $1\sigma$ 1D positional uncertainty of $1\buildrel{\prime\prime}\over{.} 3$. When multiple UV candidates are nominally present, they are either due to multiple observations (overlapping tiles) or from NUV and FUV detections of the same object that were erroneously left as separate sources in the GALEX merged-band catalog. When there are multiple observations of the same object, we take the one from the tile with the longest FUV exposure (if no candidate has an available FUV image, the tile with the longest NUV exposure is selected).

While each SDSS object has an unambiguous GALEX match, the UV measurement may still be affected by blending of several objects independently detected in SDSS. We will address this issue and describe the implemented solution in Section 3.

UV detection rates of SDSS objects ($3\sigma$ threshold, either UV band) are 54% for GSWLC-A, 74% for GSWLC-M, and 84% for GSWLC-D. Besides the UV survey depth, the detection rates depend strongly on the galaxy's sSFR or color, as can be seen from Figure 2, where we plot the detection rates as a function of r-band magnitude, separately for blue ($g-r\lt 0.7$) and red galaxies.

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GSWLC utilizes WISE observations at 22 $\mu {\rm{m}}$ (WISE channel W4) to determine SFRs independently from the UV/optical SED fitting. The depth of WISE observations over the sky is not uniform (6 ± 1 mag Vega), but it is still much more uniform than the GALEX depth and essentially covers the entire sky without gaps. The FWHM of the W4 PSF is $12^{\prime\prime}$. We use 22 $\mu {\rm{m}}$ photometry from two independent reductions of WISE data. The first is the official AllWISE Source Catalog,¹² hosted at the IPAC Infrared Science Archive (IRSA) at the Caltech/JPL, and the second is the "unWISE" reduction (Lang et al. 2016),¹³ where SDSS detections served as forced photometry priors.

To match SDSS to AllWISE, we take the closest candidate in a $5^{\prime\prime}$ search radius. Note that AllWISE detections and astrometry are based on simultaneous PSF-matched fits to all channels. Thus, the shorter-wavelength channels (3.4 (W1) and 4.6 $\mu {\rm{m}}$ (W2)), which have smaller PSF widths ($6^{\prime\prime}$) and higher signal-to-noise ratio (S/N), will dominate the astrometric accuracy ($\lt 0\buildrel{\prime\prime}\over{.} 5$). This makes the adopted search radius sufficient to capture genuine matches and justifies taking the closer candidate in the case of multiple matches (3.2% of cases). The detection rate of SDSS targets at 22 $\mu {\rm{m}}$ (based on the $2\sigma$ threshold of profile magnitudes) is 32%, which is lower than the detection rate of GALEX.

Since the unWISE catalog is derived based on SDSS DR10 detections, no matching is required (sources already carry SDSS ObjID). Forced photometry increases the S/N of measured fluxes, so the $2\sigma$ detection rate is 41%, one-third higher than that of the official catalog.

Near-IR photometry (JHK_s) is taken from the Two Micron All Sky Survey (2MASS) Extended Source Catalog (XSC), also hosted at IRSA. We match SDSS to 2MASS XSC by selecting the closest candidate within the $5^{\prime\prime}$ search radius. The detection rate of SDSS targets is 48%.

SDSS offers several choices for galaxy photometry: modelMag (magnitude extracted assuming either a de Vaucouleurs or an exponential profile), cmodelMag (weighted average of de Vaucouleurs and exponential magnitudes), and petroMag (surface-brightness-dependent aperture magnitude). The usual practice in SED fitting is to use fluxes that yield the most accurate colors. Of SDSS magnitudes, ModelMag best fulfills that role. We confirm that this is the optimal choice by finding that the best-fitting models (based on optical fitting alone) have three times lower median ${\chi }^{2}$ when modelMag is used as opposed to cmodelMag or petroMag. Also, sSFRs obtained from UV/optical SED fitting that uses modelMag magnitudes have a smaller scatter with respect to sSFRs from WISE and from ${\rm{H}}\alpha$. While ModelMag produces stable colors, the degree to which it will estimate the total light will depend on galaxy size, morphology (Bernardi et al. 2010; Taylor et al. 2011), and color gradient. Simard et al. (2011) and Meert et al. (2016) have derived magnitudes that were designed to better capture the total light in each band. Readers can use those catalogs to scale our estimates of the stellar mass and SFR, if that is required for their goals. Based on the comparison of ModelMag and Meert et al. (2016) r-band magnitudes, the typical correction should nevertheless be relatively modest (+0.03 ± 0.08 dex).

The GALEX source catalog offers only one measure of flux that is recommended for galaxies: MAG_AUTO, a Kron elliptical aperture magnitude derived by SExtractor (Bertin & Arnouts 1996). We investigate the differences in the methodology of this measurement compared to the one used for SDSS photometry, as well as the effects of lower GALEX resolution, by deriving MAG_AUTO magnitudes of 1000 randomly selected SDSS targets whose g-band images were degraded to match GALEX resolution. By comparison with isolated sources, we find that the differences between GALEX-resolution MAG_AUTO and SDSS-resolution modelMag are dominated by systematic offsets (up to 0.4 mag) arising from close companions (especially at $d\lt 10^{\prime\prime}$) that become blended in lower resolution, rather than the differences in the methodology of magnitude measurement ($\lt 0.1$ mag difference).

To account for the systematics that arise from both the difference in GALEX and SDSS resolutions and the methods of flux measurement, we derive and implement several corrections to UV fluxes. Corrections are derived by comparing the UV magnitudes predicted from optical-only SED fitting of star-forming galaxies ($g-r\lt 0.7$) with the actual UV magnitudes. While any individual predicted UV magnitude is crude ($\sigma \approx 0.4$ mag in NUV), the corrections are accurate owing to a very large number of galaxies that define them.

First, we confirm that there are no zero-point offsets between the predicted and the actual UV magnitudes. Next, we find that a small edge-of-detector correction is required for NUV, but not FUV, photometry. NUV magnitudes of sources that appear in the outermost $8^{\prime}$ annulus of the field of view, which accounts for 40% of the detector area, are up to 0.1 mag too bright, possibly because of an inaccurate flat fielding. The amount of correction depends linearly on the radial position within the annulus:

$$\begin{eqnarray}&&{\mathrm{NUV}}_{\mathrm{corr}}=\mathrm{NUV}+0.78\ \mathrm{FOV}-0.37,\quad \mathrm{FOV}\gt 0.47\end{eqnarray} \tag{ 4 }$$

where FOV is the distance from the center of the tile in degrees.

Next, we derive the centroid shift correction. The shift between optical and UV positions arises due to random errors, mostly from the lower accuracy of the GALEX astrometry, but also from the differences in UV versus optical morphology, which have a slight effect on the measured magnitudes. Again, using the difference between predicted and observed NUV magnitudes, we find the following correction:

$$\begin{eqnarray}&&{\mathrm{UV}}_{\mathrm{corr}}=\mathrm{UV}+0.054\ {\rm{\Delta }}x-0.049,\qquad {\rm{\Delta }}x\gt 0\buildrel{\prime\prime}\over{.} 7\end{eqnarray} \tag{ 5 }$$

where ${\rm{\Delta }}x$ is the shift between GALEX and SDSS positions in arcseconds. A correction is not applied when ${\rm{\Delta }}x\leqslant 0\buildrel{\prime\prime}\over{.} 7$, where random errors dominate. We apply the same correction to NUV and FUV magnitudes.

By far the most significant correction for UV magnitudes is due to blending. The degree to which a GALEX magnitude will be affected by blending will depend on both the relative brightness of the nearest companion (any SDSS photometric object) and its separation (d) from the target. We construct corrections (same for NUV and FUV) as a function of the difference in g magnitude (${\rm{\Delta }}g={g}_{\mathrm{comp}}-{g}_{\mathrm{target}}$) for four ranges of separation:

$$\begin{eqnarray}&&{\mathrm{UV}}_{\mathrm{corr}}=\mathrm{UV}-0.036\ {\rm{\Delta }}g+0.37,\qquad d\lt 4^{\prime\prime} \\ &&{\mathrm{UV}}_{\mathrm{corr}}=\mathrm{UV}-0.046\ {\rm{\Delta }}g+0.35,\qquad 4^{\prime\prime} \leqslant d\lt 10^{\prime\prime} \\ &&{\mathrm{UV}}_{\mathrm{corr}}=\mathrm{UV}-0.019\ {\rm{\Delta }}g+0.15,\qquad 10^{\prime\prime} \leqslant d\lt 15^{\prime\prime} \\ &&{\mathrm{UV}}_{\mathrm{corr}}=\mathrm{UV}-0.006\ {\rm{\Delta }}g+0.04,\qquad 15^{\prime\prime} \leqslant d\lt 20^{\prime\prime} .\end{eqnarray} \tag{ 6 }$$

We note that even though the corrections to UV magnitudes may be significant for individual objects (in particular those with a close blended companion), the SFRs for the majority of star-forming galaxies are not significantly affected by their application.

We use FUV fluxes measured at NUV positions (FUV_NCAT) rather than from independent FUV detections, as they provide more robust UV color. Both NUV and FUV measurements require a $3\sigma$ threshold in FLUX_AUTO.

SDSS and GALEX photometry must be corrected for galactic reddening. We find that the combination of extinction coefficients from Peek & Schiminovich (2013) for UV bands and Yuan et al. (2013) for optical bands produces somewhat better fits ($\sim 10 \%$ smaller ${\chi }^{2}$) than the corrections based on Schlegel et al. (1998) or on Yuan et al. (2013) alone. We reproduce the adopted corrections here:

$$\begin{eqnarray}{A}_{\mathrm{FUV}} & = & 10.47\,E(B-V)+8.59\,E{(B-V)}^{2}\\ & & -82.8\,E{(B-V)}^{3}\\ {A}_{\mathrm{NUV}} & = & 8.36\,E(B-V)+14.3\,E{(B-V)}^{2}\\ & & -82.8\,E{(B-V)}^{3}\\ {A}_{u} & = & 4.39\,E(B-V)\\ {A}_{g} & = & 3.30\,E(B-V)\\ {A}_{r} & = & 2.31\,E(B-V)\\ {A}_{i} & = & 1.71\,E(B-V)\\ {A}_{z} & = & 1.29\,E(B-V).\end{eqnarray} \tag{ 7 }$$

Photometry catalogs usually list only random flux errors, without systematic or calibration errors. We find that the default CIGALE padding of formal photometry errors by the addition (in quadrature) of 0.1 mag to catalog magnitude errors to account for systematic errors in models and photometry leads to a significant loss of derived physical parameter accuracy, as evidenced by 50% larger scatter when derived SFRs are compared with independent SFR estimates. Instead, following S07, we add more modest calibration errors (determined from repeat observations) of (0.052, 0.026, 0.02, 0.01, 0.01, 0.01, 0.01) mag in (FUV, NUV, u, g, r, i, z), plus the u-band red leak error of ${\sigma }_{u,\mathrm{RL}}=0.0865{(r-i)}^{2}+0.0679(r-i)$, derived in S07 based on the description of the red leak in Abazajian et al. (2004). The validity of the adopted calibration errors is verified by constructing the distribution of magnitude residuals (fitted minus real magnitude divided by the total error), which follow unit Gaussians.

We derive what we refer to as "mid-IR SFRs" using two types of 22 $\mu {\rm{m}}$ magnitude (flux) measurements. The first is what the AllWISE Source Catalog calls a profile-fitting magnitude (w4mpro). The profile is simply the PSF, so these magnitudes are essentially PSF magnitudes and are thus most appropriate for unresolved sources. Since the PSF FWHM at 22 $\mu {\rm{m}}$ is $12^{\prime\prime}$, which is larger than 91% of galaxies (r₉₀ size), these magnitudes are reasonably appropriate for SDSS galaxies. Yet, PSF magnitudes will systematically underestimate the flux in larger galaxies. This is largely remedied in forced photometry from the unWISE catalog, which applies SDSS-measured galaxy profiles (convoluted with W4 PSF) as photometry priors.

To derive emission-line SFRs (which we call "${\rm{H}}\alpha$ SFRs"), we use ${\rm{H}}\alpha$ and ${\rm{H}}\beta$ fluxes from the MPA/JHU catalog, based on DR7.¹⁴ Measurement of emission-line fluxes is described in Tremonti et al. (2004). We also use the emission-line (BPT diagram; Baldwin et al. 1981) classification of galaxies from the MPA/JHU catalog, derived as described in Brinchmann et al. (2004, hereafter B04).

Physical parameters from UV/optical SEDs are derived using CIGALE (Noll et al. 2009; M. Boquien et al. 2016, in preparation), a powerful code that produces libraries (grids) of model SEDs and performs the SED fitting. The code was originally written in Fortran and recently rewritten in Python. It is continually being improved and expanded in capabilities. We use the most recent Python version 0.9, which offers full control over parameters that specify SF history, dust attenuation, and emission-line fluxes. This flexibility has proved essential in order to derive robust results.

Model SEDs produced by CIGALE, and from which model photometry is extracted, consist of UV/optical/near-IR stellar emission ($\lambda \lesssim 5\,\mu {\rm{m}}$) and, optionally, the IR dust emission ($\lambda \gtrsim 5\,\mu {\rm{m}}$). A third, also optional component is the nebular emission (lines and continuum). For reasons discussed in Section 4, we will restrict the SED fitting to stellar emission, with the contribution of emission lines included.

CIGALE synthesizes stellar emission based on either Bruzual & Charlot (2003, BC03) or Maraston (2005, M05) SPS. The most important difference between them is in the treatment of the TP-AGB phase of stellar evolution (Maraston 2011; Marigo 2015). CIGALE cannot currently include the contribution of emission lines in conjunction with M05 models, which, as we will demonstrate, are important for obtaining robust measurements. Therefore, we opt to use BC03 models. The use of BC03 models may anyhow be a more appropriate choice, given some evidence that BC03 models better reproduce optical and near-IR colors than M05 models (Conroy & Gunn 2010a; Kriek et al. 2010; Zibetti et al. 2013).

CIGALE can also perform Bayesian SED fitting and report the physical parameters and their errors. Bayesian SED fitting consists of building PDFs of physical parameters by assigning probabilities to each model spectrum (at a matching redshift) based on the goodness of fit between the model and observed broadband SEDs. The methodology has been described in detail in S07, da Cunha et al. (2008), and other papers. Walcher et al. (2011) and Conroy (2013) provide comprehensive reviews of various aspects of SED fitting. While SED fitting represents an optimal way to extract information from photometry (and/or spectra), it will be limited by the uncertainties in stellar and dust attenuation models (Conroy et al. 2009, 2010b; Conroy & Gunn 2010a; Mitchell et al. 2013) and the choice of priors (e.g., appropriate SF histories and dust attenuation laws).

In order to specify the modeling assumptions (e.g., which dust model or parameterization of SF history to use), the usual practice is to select the parameters that yield the smallest relative differences between the observed and the best-fitting model photometry, i.e., that minimize some average ${\chi }^{2}$ of the sample. However, in some cases different modeling assumptions may lead to marginal changes in ${\chi }^{2}$ (suggesting that UV/optical SED is degenerate with respect to them). We will therefore require both the internal consistency (small ${\chi }^{2}$) and the external one: maximum correlation of the SED fitting SFR with respect to two entirely independently derived SFR tracers (mid-IR and ${\rm{H}}\alpha$).

In our analysis we assume a Chabrier IMF (Chabrier 2003). CIGALE assumes a flat WMAP7 cosmology (${H}_{0}=70$ km s⁻¹ Mpc⁻¹, ${{\rm{\Omega }}}_{m}=0.27$).

We perform SED fitting on UV and optical photometry (0.15–0.9 $\mu {\rm{m}}$), omitting the longer-wavelength stellar emission (1.1–5.4 $\mu {\rm{m}}$). The near-IR photometry is excluded because it increases the reduced ${\chi }^{2}$ values and worsens (albeit slightly) the correlations with mid-IR and ${\rm{H}}\alpha$-derived SFRs. Parameters from the SED fitting are reliable to the extent that the models are able to reproduce the observed colors. We find that the model photometry, based on either BC03 or M05, does not accurately reproduce the near-IR colors from 2MASS photometry. In particular, both models imply a strong correlation between J − K and i − J, which is not seen in the data (S. Salim 2016, in preparation).

Stellar mass estimates based on near-IR photometry are often perceived as more accurate and/or more precise than those based on optical bands, or that, at the minimum, the near-IR photometry improves the precision of stellar mass estimates. The reasoning underlying this claim is that stellar emission peaks in the near-IR and that near-IR mass-to-light ratio is less sensitive to the stellar population age and the effects of dust. While these arguments are correct, they do not take into account large modeling discrepancies in the near-IR mass-to-light ratios (McGaugh & Schombert 2014), arising due to the uncertainties in our understanding of the post-main-sequence phases of stellar evolution, the phases that dominate the energy output in the near-IR (Conroy 2013). For example, van der Wel et al. (2006) find that the inclusion of near-IR photometry in SED fits leads to discrepancies with respect to dynamical masses, and that these discrepancies depend on the SPS model used.

Even if there existed no major uncertainties in the models and no discrepancies between the models and the data (thus, no concerns that the near-IR will affect the accuracy of mass estimates), the improvement in the precision of stellar masses achieved by adding the near-IR photometry to the optical photometry is much more modest than usually assumed. Taylor et al. (2011) have studied physical parameters derived from mock observations of GAMA galaxies when just the optical photometry, or optical plus UKIDSS-depth near-IR photometry, was used to perform the SED fitting. They show that the improvement in the precision of stellar masses when the near-IR photometry is added to SED fitting is small (0.05 versus 0.06 dex; their Figure A2). The parameter whose precision improves the most is the stellar metallicity. Indeed, the sensitivity of near-IR luminosities, and even red optical bands (i or z), to metallicity (e.g., Figure 9 of Courteau et al. 2014; Figure 10 of Taylor et al. 2011) is another reason why near-IR alone is a more problematic tracer of stellar mass than the multiband optical light.

In the following three sections we discuss the choice of modeling parameters, starting with SF histories and metallicities.

BC03 models are available for six stellar metallicities, of which we use the higher four, from 0.2 to 2.5 Z_⊙, which is an adequate range for most galaxies in SDSS (Gallazzi et al. 2005).

We have considered two different parameterizations of SF history offered by CIGALE: two-component exponential and delayed exponential. In the two-component exponential model, the SF history is a composite of two exponentially declining functions (τ models), each with its own starting epoch (age) and e-folding time. The normalization of the younger population is specified by the mass fraction f, which can also be set to zero, resulting in a single exponential model. Each component starts at maximum value and then decreases monotonically. In contrast, the delayed exponential SF history is smooth (e.g., Gavazzi et al. 2002): it starts from zero SFR, reaches a peak at some time, and then declines. It is given by

$$\begin{eqnarray}&&\mathrm{SFR}\propto \displaystyle \frac{t}{{\tau }^{2}}{e}^{-t/\tau }.\end{eqnarray} \tag{ 9 }$$

We find that as long as the parameters are chosen so that the model colors (and more specifically, model sSFRs) cover the range of colors or sSFRs present in observations (for delayed SFHs this requires allowing $\tau \lt 0$ in Equation (9)), either SF history will produce similar stellar masses and SFRs. Specifically, there is no systematic difference for masses of non-main-sequence, low-sSFR galaxies (log sSFR $\lt -11$), while the difference in masses for actively star-forming galaxies is typically 0.1 dex. The difference in SFRs is similar in degree (see also Boquien et al. 2014) and of the same sign, which means that the difference in sSFRs is less than the difference in either mass or SFR. While both parameterizations perform reasonably well, the two-component exponential SF histories yield better fits (geometric mean of reduced ${\chi }^{2}$ of 0.7 versus 1.0), presumably because, by not being smooth, they are able to better match the bursty SF history of low-mass galaxies (Weisz et al. 2011). We thus adopt the two-component exponential parameterization.

Delayed exponential models have been preferred over exponential models in some recent studies (e.g., Simha et al. 2014). However, there are important differences among the exponential models. If a single-exponential model is assumed to have started in the early universe (e.g., ${t}_{0}\sim {10}^{10}$ yr), in order to acknowledge the fact that galaxies contain ancient stellar populations no matter how dominant the current episode of SF may be (Aloisi et al. 2007), then such a model will fail to reproduce the sSFRs of many star-forming galaxies today, simply because log sSFR${}_{\max }=\mathrm{log}\,{t}_{0}^{-1}=-10$. It is this naive implementation of the exponential model (e.g., Simha et al. 2014) that results in inferior performance. The problem of the single-exponential model not producing high sSFRs can be alleviated by allowing the starting epoch of the model to be more recent than the big bang. Though later-epoch galaxy formation is obviously not realistic, it can instead be interpreted as the epoch of peak of SF activity. Variable starting time was assumed in essentially all work that based their SF histories on a single exponential, including S07, which in addition had stochastic bursts superimposed on exponential models.

Allowing recent starting times for the exponential model results in SFRs that are comparable to more sophisticated models.¹⁶ However, this approach will neglect ("outshine") any old population, resulting in somewhat underestimated masses (Papovich et al. 2001; Michałowski et al. 2014). This problem is resolved with a two-component exponential model used here, where one component corresponds to high-redshift SF. While more realistic SF histories may have multiple bursts, or are in general quite variable (Weisz et al. 2011), modeling these features with high temporal precision is unimportant from the standpoint of broadband SED fitting, where even the characteristics of the most recent burst cannot be constrained with any precision because of the burst age versus burst amplitude degeneracy (e.g., Smith & Hayward 2015).

The parameters of the adopted two-component exponential model are as follows. The formation time of the old population is 10 Gyr before the observation epoch, with e-folding times that span a range from 850 Myr (fast decline that defines the lower sSFR limit of log sSFR = −13.8) to a nearly constant 20 Gyr (which has declined only 0.2 dex since formation). Formation times for the younger component span from 100 Myr (the shortest timescale to which UV observations are sensitive) to 5 Gyr. Their e-folding time is 20 Gyr, i.e., nearly constant. In order to produce the highest sSFRs observed today (log sSFR $\sim -8$), the mass fraction of the younger component must span up to f = 0.5. Thus, our library of SF histories looks like old exponentials with various decay times, with a relatively flat burst superimposed.

CIGALE allows the dust attenuation law to be specified as a simple power law ($k{(\lambda )}_{\mathrm{PL}}\propto {\lambda }^{\alpha }$, following Charlot & Fall 2000), or according to the Calzetti et al. (2000) recipe ($k{(\lambda )}_{\mathrm{Cal}}$). The Calzetti curve can be modified so that the overall slope becomes more or less steep, by multiplying it by the power law of slope δ (Noll et al. 2009):

$$\begin{eqnarray*}&&k{(\lambda )}_{\mathrm{mod}}=k{(\lambda )}_{\mathrm{Cal}}{(\lambda /5500\mathring{\rm A} )}^{\delta }.\end{eqnarray*}$$

Note that slope modification changes R_V from 4.05, the value it has for the Calzetti curve. The attenuation law can be further modified to include a UV bump of varying strength (Stecher 1965; Fitzpatrick & Massa 1986; Conroy et al. 2010a).

We systematically tested various modifications of the Calzetti attenuation law. We produce model grids where the range of color indices lies between $E(B-V)=0.1$ and 0.6 mag for the young ($\lt 10$ Myr) population (i.e., the dust affecting the nebular lines; equivalent to ${A}_{{\rm{H}}\alpha }=0.25$–1.5 mag). Attenuation that affects older stars, and therefore most of the stellar continuum, is taken to be smaller by a factor of 0.44, following Calzetti et al. (2000). The tests were carried out with galaxies classified in the BPT diagram as star-forming, for which mid-IR luminosity and dust-corrected ${\rm{H}}\alpha$ luminosity provide reliable estimates of SFR. The results are illustrated in Figure 4. The upper panels show the comparison between sSFR obtained from the SED fitting, assuming the standard Calzetti curve, which has no UV bump, and independently derived mid-IR and ${\rm{H}}\alpha$ sSFRs. Note that the comparison is carried out in terms of sSFR, which better reveals systematic trends than the usual SFR comparison (Section 7). Similar trends are seen versus mid-IR and ${\rm{H}}\alpha$. The differences increase with the increasing sSFR until log sSFR${}_{\mathrm{SED}}=-9$, in the sense that the values derived from SED fitting assuming the Calzetti curve tend to be up to 0.4 dex higher. At still higher sSFRs, however, there is reasonable agreement between the sSFRs, as expected, since the Calzetti curve was derived from starburst galaxies with high sSFRs.

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The middle row shows the comparisons when the Calzetti law is modified to include a UV bump of varying intensity (from no bump to 4× the Milky Way [MW] value). The UV/optical SED fits become formally better (geometric mean of reduced ${\chi }^{2}{\rm{s}}$ goes from 1.3 to 0.8), and the correlation with mid-IR and ${\rm{H}}\alpha$ sSFRs improves (from $\sigma =0.40$ to 0.32 dex, for mid-IR comparison). However, the nonlinearity (the slope of the correlation featuring logarithms of sSFRs not being unity) persists, as well as a tail of galaxies with unusually low sSFRs.

The bottom row shows the comparisons when the Calzetti attenuation law is further modified to make it steeper (with $\delta =-0.5$ and −1.0), in addition to allowing the UV bump. There is now a significant reduction in scatter with respect to mid-IR and ${\rm{H}}\alpha$ sSFRs ($\sigma =0.23$), and the relation is fairly linear. This is our adopted dust attenuation model. We note that achieving this level of agreement between SED-fitting sSFRs and mid-IR sSFRs requires both the steepening of the attenuation curve and the addition of the UV bump. Just steepening the slope of the attenuation curve does remove most of the nonlinearity with respect to mid-IR sSFR (plot not shown), but still yields relatively high reduced ${\chi }^{2}$ of 1.0, regardless of the amount of steepening. In other words, the combination of the two modifications is necessary to achieve both the small ${\chi }^{2}$ values and good agreement with other indicators.

The agreement between SED and mid-IR SFRs demonstrates that the energy balance is fulfilled when this modified attenuation law is used: the energy absorbed by the dust in the stellar SED matches the energy emitted in the IR.

We note that assuming an attenuation curve in a power-law form, having slopes $\alpha =-1.0$ (preferred by the majority of galaxies) and $\alpha =-1.5$, and adding the UV bump to them has a similar effect to modifying the standard Calzetti curve as described in the preceding paragraph. For comparison, the standard Calzetti curve can be approximated in the UV range by a power law of slope $\alpha =-0.5$.

It must be stressed that the differences in sSFR obtained with various attenuation laws are largely driven by the changes in SFR, rather than M_*. The stellar masses of star-forming galaxies obtained with the Calzetti dust attenuation law are on average only 0.06 dex lower than the stellar masses obtained with the modified law. However, the masses of a small number of individual galaxies, especially those with very high sSFR, can differ up to 0.4 dex in either direction, i.e., the dispersion of the two mass estimates increases with sSFR. For completeness, we report that for passive galaxies the use of the Calzetti dust law yields stellar masses that are 0.06 dex higher than the ones obtained with our modified attenuation law, and this difference is rather constant from one passive galaxy to another, i.e., it has a small dispersion of only 0.02 dex.

We conclude that while star-forming galaxies may be governed by a range of attenuation laws, they generally exhibit a steeper law than the standard Calzetti curve ($\delta =-0.6$, on average) and include a UV bump (1.1 times the MW value, on average). This average curve has ${R}_{V}\approx 2.5$, compared with R_V = 4.05 for the Calzetti curve, and agrees well with the curve derived empirically by Conroy et al. (2010a): an MW-like curve with R_V = 2.0 instead of R_V = 3.1 (reducing R_V makes the curve steeper). Evidence for a steeper-than-Calzetti curve has been found in other studies as well (Charlot & Fall 2000; Buat et al. 2011; Hao et al. 2011; Wild et al. 2011; Salmon et al. 2015), though not as steep as the one found here and in Conroy et al. More detailed investigation of these results and their implications will be presented in a separate paper.

Finally, we describe how we account for the flux from emission lines, which can have a significant effect on broadband fluxes and colors of galaxies with high equivalent widths (Papovich et al. 2001; Kauffmann et al. 2003b; Pacifici et al. 2015). CIGALE calculates the contribution of 124 lines, specified by metallicity (taken to equal the stellar metallicity of SPS models) and ionization parameter. We select the lowest ionization parameter available, $\mathrm{log}U=-3$, as it produces the biggest improvements and is closest to direct measurements (Dopita et al. 2000; Liang et al. 2006).

The formal quality of UV/optical fits is significantly improved by correcting for emission-line flux (geometric mean of ${\chi }_{\mathrm{red}}^{2}$ drops from 1.2 to 0.7). More importantly, accounting for emission lines significantly improves the correlation of SED sSFRs with other indicators. For galaxies with high sSFRs, not correcting for emission lines produces offsets of up to 0.5 dex, as can be seen by comparing Figure 5, which does not correct for emission lines, with the lower row of Figure 4. Emission-line correction makes very little difference for stellar masses, which change by $\lt 0.01$ dex on average.

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While the addition of emission lines to model fluxes results in overall improvement, the correction is not perfect. Nebular metallicity is fixed to stellar metallicity, which is not realistic. Also, the ionization parameter of many galaxies is lower than the minimum ionization parameter available in CIGALE. We see some redshift-dependent trends in SFR, as lines straddle across the bandpasses. We account for this systematic offset (∼0.1 dex on average) by deriving an average correction, in 0.01-wide bins of redshift, with respect to SFRs from B04 (using galaxies classified as star-forming; Section 8.2), and applying it to all SFRs from the SED fitting. We use B04 SFRs for this correction instead of mid-IR SFRs, because the latter are available for only 63% of star-forming galaxies. Nevertheless, the correction would have been essentially identical if mid-IR SFRs were used.

In summary, for each 0.01-wide redshift bin, from 0.01 to 0.30, we calculate a grid of 342,720 models, a factor-of-3 increase in the number of models and a factor-of-5 increase in redshift resolution with respect to what was used in S07.

From the SED fitting we report the logarithm of the current stellar mass (M_*), the logarithm of the SFR averaged over the past 100 Myr (the timescale for UV emission), and dust attenuations in FUV, B, and V rest-frame bands. For each of these parameters CIGALE builds a PDF. The nominal value of the reported parameter is the average of the PDF. We have performed mock fitting, in which true parameters are known, and find that the average of the PDF better retrieves the parameters than the median, and much better than the parameter corresponding to the best-fitting model. The best-fitting parameters are volatile and suffer from grid discreteness (e.g., Taylor et al. 2011). The formal error of the parameter is taken as the second moment (standard deviation) of the PDF. By default CIGALE applies a minimum error in the case in which the error from the PDF is lower than it, but we have disabled this adjustment. Instead, we caution the reader that the robustness of the error estimated from the PDF will depend on the goodness of the fit, i.e., it will be most accurate when ${\chi }_{r}^{2}\sim 1$.

The MPA/JHU catalog is the most widely used source of stellar masses for SDSS galaxies. Prior to DR7, the most recent version of this catalog, the MPA/JHU catalog listed stellar masses derived in Kauffmann et al. (2003b), using a method that combines photometric information to assess dust attenuation and spectroscopic indices to constrain the SF history and mass-to-light ratio. Spectroscopic indices were measured within the fiber, so the method assumed no M/L gradients. In the DR7 version of the MPA/JHU catalog, the method from Kauffmann et al. was replaced with the Bayesian SED-fitting method, using only the optical broadband photometry from SDSS (modelMag) and models described in S07. Here we will only present comparisons with respect to the DR7 version of the MPA/JHU catalog.

As described in Section 5, GSWLC uses different specifications of SF histories and dust extinction from those used in S07 and the MPA/JHU catalog. Furthermore, unlike the MPA/JHU catalog (but like S07), GSWLC uses the constraints offered by UV photometry. Figure 9 shows the difference between GSWLC and MPA/JHU stellar masses as a function of sSFR. Again, we prefer the presentation of the results in this relative, distance-independent way over the usual mass versus mass comparison. On average, GSWLC stellar masses are somewhat higher than the MPA/JHU ones, with typical differences being 0.03 dex for passive galaxies and ∼0.13 dex for the active ones. The scatter of the difference in mass, 0.07 dex, is consistent with the formal estimates of the mass error (Figure 6). The inclusion of the UV photometry is responsible for a 0.04 dex increase for active galaxies. The remaining 0.09 dex increase for active galaxies (and 0.03 dex increase for passive ones) is mostly due to our use of two-component exponential SF histories. We confirm that the difference would not have been present if we had used the delayed exponential histories instead (Equation (9)). The critical difference between the delayed exponential and our implementation of the two-component exponential SF history is that in the latter the old component starts in the early universe, whereas the delayed exponential, having a single peak, will be shifted toward later epochs. Recently, Sorba & Sawicki (2015) have reported that the masses of nearby high-sSFR galaxies obtained by summing up the masses in individual "pixels" are up to 0.1 dex higher than the masses from integrated light. They proposed that the difference arose from "outshining" of the old, fainter populations in galaxies with younger populations (high sSFR). It appears that our use of the two-component exponential SF history, in which the old component is set to have started in the early universe, may have recovered this deficit.

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More recently, stellar masses for SDSS galaxies were published by Mendel et al. (2014) and Chang et al. (2015). The differences of GSWLC masses with respect to these masses follow the trends we have shown with respect to masses from the MPA/JHU catalog: little difference for passive galaxies, and up to 0.2 dex difference for galaxies with high sSFR.

Comparison of our masses obtained with and without the UV photometry reveals that in the case when there is another photometric source within 2''–3'', the masses obtained from joint UV and optical photometry will be biased upward by 0.05 dex, presumably because of the unaccounted blending in the UV. This affects only a few percent of all sources.

The MPA/JHU catalog also provides SFRs, and until recently it was the only publicly available source of SFRs for SDSS galaxies. SFRs derived in the MPA/JHU catalog follow the method of B04, with modifications introduced in the most recent (DR7) version of the catalog. We first describe both the original method and its modifications, but the comparison will be presented only for the DR7 version of the MPA/JHU catalog.

MPA/JHU catalog (and the original B04) SFRs are often described as ${\rm{H}}\alpha$ or emission-line SFRs. This is accurate only for the portion of a galaxy contained within the fiber, and only for galaxies classified as star-forming using the BPT diagram, for which the AGN contribution to emission lines should be negligible. For galaxies with an AGN contribution or having weak lines (altogether 78% of SDSS galaxies), B04 derive SFR in the fiber based on a relation between the emission-line sSFR and D4000 index, constructed from star-forming galaxies. Next, the SFR estimate within the fiber is aperture-corrected to produce the total (integrated) SFR. B04 performs this correction by first establishing the relationship between fiber sSFR and the fiber broadband colors of star-forming galaxies and then applying these relations in a Bayesian fashion to the light outside of the fibers to arrive at the out-of-fiber SFR. The total SFR is then obtained as the sum of fiber and out-of-fiber SFRs. The DR7 MPA/JHU catalog modifies the procedure for deriving out-of-fiber SFRs, by instead performing the SED fitting to ugriz photometry, using the models and methods described in S07. Altogether, the SFR method of the MPA/JHU catalog (and original B04) is an emisison-line/D4000/SED-fitting hybrid. The temporal sensitivity of such SFRs will be between the $\sim 10\,\mathrm{Myr}$ timescales traced by the emission lines and the ∼1 Gyr timescale for u-band light.

S07 presented detailed comparison of their SED SFRs and the original SFRs from B04. GSWLC contains many improvements over the S07 methodology, as does the MPA/JHU catalog with respect to B04. The comparison of GSWLC-M and DR7 MPA/JHU total sSFRs is given in Figure 10. It uses the same division of galaxies into SF, AGN, and "no ${\rm{H}}\alpha$" categories as employed earlier. In order to decouple SFR and mass systematics, both sSFRs are obtained by normalizing by the same mass (from GSWLC). Note that for 3% of galaxies in the MPA/JHU catalog the total SFRs are present even when masses are not. We find that in those cases the reported total SFR is incorrect and assumes the value of fiber SFR. We exclude those values from the comparison.

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sSFRs for star-forming galaxies (left panel) agree very well, with a scatter of $\sigma =0.18$, which is smaller than the scatter of SED sSFRs with respect to mid-IR or ${\rm{H}}\alpha$ sSFRs (Figures 7 and 8). The comparison for AGN hosts reveals some systematic discrepancies, especially for intermediate sSFRs, which can in some cases reach ∼1 dex. We have already seen similar, but smaller, offsets in comparison with ${\rm{H}}\alpha$ fiber sSFRs, which we attributed to optically (spectroscopically and photometrically) inconspicuous SF. If we intentionally leave out the UV bands from our SED fitting, the resulting (ill-constrained) sSFRs are drawn to lower values (because the majority of models with red optical colors have low sSFRs), in better agreement with B04 values, which derive the greater part of their SFR (the out-of-fiber portion) from similar optical-only SED fitting.

Similar trends are present in galaxies with little or no ${\rm{H}}\alpha$ emission in the fiber (right panel), except that the majority of galaxies have low sSFRs (log sSFR${}_{\mathrm{SED}}\lt -11$). In this class of galaxies there exists a peculiar feature: a cloud of galaxies lying ∼1 dex above the 1:1 line, having high SED sSFRs (log sSFR${}_{\mathrm{SED}}\gt -10$), but much lower MPA/JHU sSFRs. We confirm that these galaxies have robust SED fits and are UV detected. In Section 7 we mentioned that "no ${\rm{H}}\alpha$" galaxies with high sSFRs are probably post-starburst galaxies. Such galaxies are traditionally identified as E+A galaxies, based on their Balmer absorption features (Dressler & Gunn 1983). Now we inspect the spectra of ∼200 of these outliers and confirm the presence of Balmer absorption lines. Visually (gri composites), these galaxies appear like red early-type galaxies, often with white centers, suggesting a central (post-)starburst. We match our sample to the Goto (2007) catalog of E+A galaxies (online version updated with SDSS DR7 data) and confirm that the majority of their E+As are found in this region of the plot. Why do the two methods yield discrepant SFRs for these galaxies? We find that the SED-fitting (s)SFRs of E+A galaxies are very sensitive to the assumed dust attenuation law, more so than the normal star-forming galaxies. The (s)SFRs that we obtain for E+As assuming the modified attenuation law are an order of magnitude higher than what would be derived using the nominal Calzetti law. The reduced ${\chi }^{2}{\rm{s}}$ are 5 times lower when the modified attenuation law is used. From this we conclude that the high recent (s)SFRs of E+As that we derive in GSWLC are more likely to represent true levels of SF averaged over the past 100 Myr.

8.2.1. On the Systematics of MPA/JHU SFRs Reported by SAMI Galaxy Survey

Recent campaigns to obtain resolved spectra with integral field spectroscopy have reported systematic differences with respect to SFRs from the MPA/JHU catalog. In particular, Richards et al. (2016), using preliminary data from the SAMI Galaxy Survey (Allen et al. 2015), find a nonlinear, i.e., SFR-dependent, relation between their and MPA/JHU SFRs (which they refer to as B04 SFRs), in the sense that galaxies with high SAMI SFRs have underestimated MPA/JHU SFRs. The discrepancy is already $\sim 0.3$ dex at log ${\mathrm{SFR}}_{\mathrm{SAMI}}\approx 0.6$, the highest SFRs in their sample (we convert all SFRs from Richards et al. to Chabrier IMF). Richards et al. attribute the discrepancy to possible biases in B04 methodology for deriving aperture corrections.

In our analysis so far we have shown that GSWLC specific SFRs of star-forming galaxies have no significant systematics with respect to either mid-IR sSFRs or sSFRs from the MPA/JHU catalog. This implies, and we confirm it to be true, that MPA/JHU and mid-IR sSFRs agree between themselves as well. While this seems to imply that MPA/JHU measurements are not biased, it is necessary to verify if such results hold for SFRs, and not just the sSFRs.

Figure 11 shows SED-fitting SFRs against MPA/JHU SFRs in the upper panel and mid-IR SFRs against MPA/JHU SFRs in the lower panel. In both comparisons, the linear fits (blue dashed lines) follow closely the 1:1 relation. White solid lines show the relation between SAMI and B04 SFRs (adjusted to Chabrier IMF), over the range of SFRs covered in Richards et al. (2016).¹⁷ The discrepancies suggested by the Richards et al. relation are clearly excluded with either the SED-fitting or the mid-IR SFR. Results are unchanged when the redshift range of galaxies is restricted to match the redshift range of the SAMI Galaxy Survey. Apparently, more work is needed to understand the source of differences. For now, we conclude that the total MPA/JHU SFRs of actively star-forming galaxies do not appear to be biased when compared with two independent measures of integrated SFR.

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All-sky far-IR observations that would enable direct measurement of the total IR luminosity across SDSS are only available from relatively shallow IRAS and AKARI surveys, with preferentially more luminous galaxies (Ellison et al. 2016). In order to produce IR luminosity estimates for a significant portion of the SDSS spectroscopic sample, Ellison et al. (2016) apply an artificial neural network (ANN) technique, using IR luminosities from Rosario et al. (2016) as the training set (these IR luminosities were discussed in Section 4). The idea behind the ANN is to establish intrinsic correlations between observable quantities of the training set and the target quantity (in this case the IR luminosity) and then apply these correlations to estimate ("predict") the target quantity in the full data set. The robustness of ANN estimates should be tested by comparing them with the independent measurements of the target quantity for an unbiased subsample drawn from the full data set. In the case of Ellison et al. (2016), the parameters employed to estimate the IR luminosities using ANN include, in addition to the redshift, the photometric (magnitudes, colors) and spectroscopic measurements (emission-lines strengths and D4000 break), as well as the stellar mass. The connection between the fiber and total quantities is established by also including the mass in the fiber and the r-band fiber covering fraction. The input parameters come from the MPA/JHU DR7 catalog. The requirement to have available all of the parameters in the target data set limits the application to 45% of SDSS galaxies, typically the ones with stronger emission lines. IR luminosities of the training set are recovered with the typical accuracy of $\sigma \sim 0.1$ dex, with no major systematics (Ellison et al. 2016).

In Figure 12 we show the comparison of GSWLC sSFRs from the SED fitting against sSFRs converted from Ellison et al. (2016) IR luminosities using Equation (8). The comparison is limited to galaxies with ${\sigma }_{\mathrm{ANN}}\lt 0.1$, a cut recommended in Ellison et al. (2016) to remove the galaxies whose estimated IR luminosities may be uncertain. ${\sigma }_{\mathrm{ANN}}$ essentially measures the degree to which a target galaxy is represented in the training set. The larger the value, the less likely the target galaxy is represented in the training set, and its IR luminosity may therefore be uncertain. The application of the cut on ${\sigma }_{\mathrm{ANN}}$ decreases the number of galaxies with ANN IR luminosities from 330,000 to 250,000, or one-third of SDSS. The comparison of sSFRs of star-forming galaxies (left panel) shows good general agreement, with mild nonlinearity (slope of 1.23), which can be traced to the differences between WISE and Herschel-WISE specific IR luminosities (Section 4). If the galaxies with ${\sigma }_{\mathrm{ANN}}\gt 0.1$ were included in the comparison, the scatter at high sSFRs would increase, presumably because such galaxies are rare in the training set. ANN IR luminosities are available for 77% of galaxies in this class (after the application of the ${\sigma }_{\mathrm{ANN}}$ cut), which is higher than the WISE detection rate of 63%.

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For galaxies classified as AGNs (the middle panel), the correlation is present when log sSFR${}_{\mathrm{SED}}\gt -11$, but with ANN sSFRs tending to be higher, especially for galaxies with high sSFR. Below log sSFR${}_{\mathrm{SED}}=-11$ there is no correlation. Both of these behaviors mimic the comparison of SED-fitting sSFRs with mid-IR sSFRs (Section 7 and Figure 7, middle panel). Excess sSFR for AGNs with higher sSFRs, which in the case of mid-IR sSFRs we attributed to AGN dust heating, is somewhat surprising, because it would be expected that the AGN contribution, which drops above 40 $\mu {\rm{m}}$ (Mullaney et al. 2011), will be significantly diminished in the total IR luminosity. However, we remind the reader that ANN luminosities are trained on IR luminosities derived from a combination of 22 $\mu {\rm{m}}$ flux (which is subject to AGN contamination) and three submillimeter flux points that lie well beyond the IR SED peak (and are therefore not as sensitive to the current SF, and more to the cold dust mass). More detailed analysis on the contribution of type 2 AGNs to IR SEDs lies outside of the scope of this paper.

After the application of the ${\sigma }_{\mathrm{ANN}}$ cut, the IR luminosities from Ellison et al. (2016) are available for only 1% of galaxies having weak or no ${\rm{H}}\alpha$ (right panel). For a handful of such objects with high sSFRs (including confirmed E+As) the match between the SED-fitting and ANN sSFRs is good, but for the great majority, the ANN IR luminosities, when interpreted as SFRs, tend to be too high because of the dust heating from older stars, as already discussed in Section 7.

Considering the very different methods of estimating the IR luminosities, it is interesting to see how the ANN IR luminosities from Ellison et al. (2016) compare to the ones we obtain from WISE. This is shown in Figure 13, for all galaxies for which the two measurements are available (and with the ${\sigma }_{\mathrm{ANN}}\lt 0.1$ cut applied). The comparison, extending over three orders of magnitude, is fairly good, in terms of both offset and the scatter ($\sigma =0.17$). Some systematic differences are present, especially at $\mathrm{log}{L}_{\mathrm{IR}}\gt 11$, which is not surprising considering that the training set peters out at those luminosities. Overall, the IR luminosities from Ellison et al. (2016) represent remarkably good estimates considering that they were determined from optical properties alone, but their use as SFRs is subject to the same caveats (AGN dust heating and breakdown for passive galaxies) as the SFR obtained from WISE mid-IR data.

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In Section 4 we mention that new SED-fitting codes allow the modeling of the SED to extend into the IR, by including the dust emission. This approach is used in MAGPHYS (da Cunha et al. 2008), which models the IR SED as a sum of various SED components, the relative contribution of which is mildly related to the galaxy's sSFR. CIGALE allows the IR SED to be modeled according to one of the four published template sets, without constraints on the shape. In both cases the dust luminosity (i.e., the total IR luminosity) is normalized to match the stellar emission absorbed in the UV/optical/near-IR. Such IR luminosity will therefore include dust heating from stars of all ages.

Stellar plus dust emission modeling is applied in Chang et al. (2015), who use MAGPHYS to perform the SED fitting simultaneously on optical (ugriz) photometry from SDSS and mid-IR photometry from WISE (3.4, 4.6, 12, and 22 $\mu {\rm{m}}$). Of these nine bands, all but the longest two WISE bands will be dominated by the stellar emission. Emission at 12 and 22 $\mu {\rm{m}}$, if detected, will help constrain the dust luminosity and therefore the SFR (if the dust is primarily heated by young stars).

We follow the analysis established in previous sections, and in Figure 14 we present comparisons between our SED-fitting sSFRs and sSFRs from Chang et al. (2015), again split by galaxy type.¹⁸ Note that we normalize both sSFRs using our stellar mass. Galaxies classified as star-forming on the BPT diagram (left panel) compare well, but show a tail of anomalously low values of Chang et al. sSFRs, which causes the best-fit line to deviate from unity. However, if the tail is excluded, the nonlinearity disappears, and a small bulk offset of 0.09 dex remains. We find that the offset is entirely due to the $\sim 1/3$ of galaxies that are not detected at 22 $\mu {\rm{m}}$ but only at 12 $\mu {\rm{m}}$, for which Chang et al. (s)SFRs are on average 0.17 dex lower than our SED-fitting (s)SFRs. For galaxies with 22 $\mu {\rm{m}}$ detection, the scatter with respect to SED sSFRs is 0.17 dex, compared to 0.23 dex between SED sSFRs and sSFRs from WISE 22 $\mu {\rm{m}}$ alone (Figure 7, left panel). This reduction of scatter demonstrates that the 12 $\mu {\rm{m}}$ photometry (a wavelength at which WISE is significantly more sensitive than to 22 $\mu {\rm{m}}$) helps constrain the SFRs compared to when 22 $\mu {\rm{m}}$ is used alone. However, when 12 $\mu {\rm{m}}$ is used to obtain the IR luminosity (or SFR) without the 22 $\mu {\rm{m}}$ measurements, it leads to a systematic underestimate.

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For AGN hosts (the middle panel), the tail of anomalously low sSFR values is more extensive than for the star-forming galaxies. We confirm that these galaxies have UV detections and that the UV emission drives the sSFR estimate in our SED fitting to higher values than when the UV is omitted from the SED fitting, as in the case of the Chang et al. (2015) SED fitting. UV is not expected to be contaminated by nonstellar emission in these (type 2) AGNs. Furthermore, the UV emission is extended, suggestive of SF. Optical colors alone are not sensitive to such low levels of SF (Kauffmann et al. 2007) and are equally red for truly quiescent galaxies and those with intermediate sSFRs (Fang et al. 2012). When the SED fitting is performed without UV constraints, the sSFR defaults to very low values of the majority of optically red models.

For AGN hosts with high sSFRs, the excess seen in other IR-based sSFRs is now smaller. This is true whether the galaxy was detected at both 12 and 22 $\mu {\rm{m}}$ or just at 12 $\mu {\rm{m}}$, suggesting that 12 $\mu {\rm{m}}$ flux is much less affected by AGN-heated hot dust than the 22 $\mu {\rm{m}}$, so that when included in the SFR estimate it mitigates the excess. That 22 $\mu {\rm{m}}$ suffers more AGN contamination is corroborated by the fact that out of 12 $\mu {\rm{m}}$-detected AGNs, 80% are also detected at 22 $\mu {\rm{m}}$, whereas this fraction was 60% for star-forming galaxies. Previously, Donoso et al. (2012) have found that the 12 $\mu {\rm{m}}$ luminosity is not affected by an AGN contribution in all but a handful of the most luminous sources (but they did not perform analogous assessment of 22 $\mu {\rm{m}}$ emission).

For galaxies with weak or no ${\rm{H}}\alpha$ (right panel), the Chang et al. (2015) values agree well for some of the galaxies with high sSFRs, with a small offset that we attribute to the preponderance (90%) of 12 $\mu {\rm{m}}$-only detections in this category, which we have shown to have somewhat underestimated SFRs in Chang et al. As in the case of comparison with MPA/JHU catalog SFRs, the E+As, or more generally, the post-starburst galaxies, again form a cloud of points offset from the 1:1 relation. As discussed in Section 8.2, the offset in (s)SFRs is attributable to the differences in the assumed dust attenuation laws, to which the E+As appear to be particularly sensitive. Comparison with entirely independent IR SFRs, as well as better quality of SED fits, suggests that the high (s)SFRs obtained with the modified attenuation law in GSWLC are more realistic. Finally, for galaxies in the "no ${\rm{H}}\alpha$" class with log sSFR $\lt -11$ the estimates largely agree, but are quite uncertain.

The general conclusion is that the Chang et al. (2015) SFRs are reliable for galaxies with log sSFR${}_{{\rm{C}}15}\gt -10.7$, regardless of the galaxy type, and especially when a galaxy is detected at 22 $\mu {\rm{m}}$. When sSFRs are low, Chang et al. (2015) correctly attribute the mid-IR emission to old populations and not the ongoing SF. However, in doing so, the weak signal from the actual SF, detectable in the UV, is in some cases lost, leading to anomalously low values of sSFR.

Chang et al. (2015) provide an estimate of the dust luminosity, i.e., the total IR luminosity. In Figure 15, we compare it to the IR luminosity that we derive from WISE 22 $\mu {\rm{m}}$. There is a good overall agreement, and the scatter is smaller than in the comparison involving Ellison et al. (2016) ${L}_{\mathrm{IR}}$, no doubt because WISE and Chang et al. IR luminosities are somewhat correlated through the use of the same 22 $\mu {\rm{m}}$ photometry. There is, however, a small fraction (1.8%) of galaxies for which there is a $\sim 1$ dex discrepancy in ${L}_{\mathrm{IR}}$. These galaxies produce a bump in the distribution of specific luminosities (log $({L}_{\mathrm{IR}}/{M}_{* }$)) when using Chang et al. (2015) IR luminosities, but not with WISE values. Most of these galaxies do not have ${L}_{\mathrm{IR}}$ from the Ellison et al. (2016) catalog, but when they do, they agree with our IR luminosity from WISE. Finally, the direct comparison of Chang et al. IR luminosities with IR luminosities from Herschel (plot not shown) confirms that Chang et al. IR luminosities are underestimated when they are based on 12 $\mu {\rm{m}}$ detection without the 22 $\mu {\rm{m}}$ detection.

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