A TWO-PARAMETER MODEL FOR THE INFRARED/SUBMILLIMETER/RADIO SPECTRAL ENERGY DISTRIBUTIONS OF GALAXIES AND ACTIVE GALACTIC NUCLEI

For the updated mid-infrared spectrum we adopt the 5–34 μm "pure" star-forming curve from (Spoon et al. 2007, their spectrum "1C"), who utilized the Spitzer archives to analyze a sequence of mid-infrared spectral shapes among AGNs, ULIRGs, and star-forming galaxies. Important benefits to updating the mid-infrared with Spitzer data are the inclusion of prominent fine-structure lines (e.g., [Ne iii] 15.6 μm, [S iii] 18.7 μm, and [S iii] 33.5 μm) and the 17 μm PAH complex, the latter of which accounts for up to 10% of the total PAH emission in normal star-forming galaxies (see Figure 2 of this work and Table 7 of Smith et al. 2007). As was done in Dale et al. (2001), we scale the empirical mid-infrared spectrum to the amplitude of the Désert et al. (1990) PAH templates via integrating over the 12 μm IRAS filter. The shape of the mid-infrared continuum beyond 15 μm was also fixed to that of the Désert et al. (1990) PAH templates. Besides these modifications to the mid-infrared spectrum, the star-forming templates are otherwise unchanged. We continue to utilize a single-parameter family (i.e., α_SF) to describe the full range of PAH/very small grain/large grain and overall spectral shapes for normal star-forming galaxies. Moreover, it should be noted that we continue to assume optically thin infrared emission, and thus do not include in our model any absorption features such as the 9.7 μm silicate trough found in many ULIRGs (e.g., Armus et al. 2007). While this simplification will fail to appropriately characterize all the nuances in mid-infrared spectra for samples specifically selected to be infrared-luminous (e.g., GOALS; Stierwalt et al. 2013), there are very few deeply obscured systems in infrared flux-limited surveys like 5MUSES (Wu et al. 2010).

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While the star-forming templates themselves from Dale & Helou (2002) are only slightly modified, we introduce here a fundamental addition to the templates by incorporating a second parameter, one that accounts for accretion disk-powered infrared luminosity.

Until recently, the state-of-the-art in panchromatic AGN SEDs was still the pioneering work of Elvis et al. (1994), who studied 47 non-blazar quasars from the radio through 10 keV X-rays. However, the recent influx of large multi-wavelength databases has allowed for more complete reconstructions of AGN SEDs. For example, in 2011 Shang and collaborators updated the Elvis et al. (1994) work using data from 85 non-blazar quasars. The data involved in their analysis include X-ray, far- and near-ultraviolet, optical, near-, mid-, and far-infrared, and radio spectroscopy and/or photometry. Shi et al. (2013) utilize Spitzer infrared spectral (5–30 μm) and imaging (24, 70, and 160 μm) data from all Palomar–Green quasars to generate a median mid-infrared spectrum similar to that of Shang et al. (2011). These quasars are UV selected and thus are minimally obscured Type 1 AGNs. Figure 3 provides a comparison of several AGN/quasar infrared templates available from the literature as well as the maximum and minimum curves based on the clumpy torus models of Schartmann et al. (2008). We adopt here the median spectrum of Shi et al. (2013) since they have carefully attempted to remove any star formation-related contributions from the host galaxies, including forcing the template beyond 70 μm to drop like a blackbody (νf_ν∝λ⁻⁴; see their Figure 3). Several features are evident in this median quasar spectrum of Shi et al. (2013), including the broad silicate emission features near 10 and 18 μm and the [O iv] 25.9 μm fine-structure lines that are seen in many AGNs (Hao et al. 2005; Armus et al. 2007).

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Figure 2 displays this median quasar SED of Shi et al. (2013) in addition to a suite of normal star-forming galaxy curves spanning a range in α_SF. To simulate the spectral appearance of a source for which the emission has contributions from both an AGN and normal star formation, we employ linear mixing over the 5–20 μm wavelength range. For this work we have developed mixed combinations for 5–20 μm AGN fractions running from 0% to 100%, spaced at 5% intervals.⁶ Figure 4 shows how the resulting infrared–radio SEDs appear for a variety of combinations of AGN and star-forming emission.

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To date most efforts to disentangle infrared emission from AGNs and star formation have focused on utilizing mid-infrared continuum data sets (e.g., Laurent et al. 2000; Murphy et al. 2009; Mullaney et al. 2011; Wu et al. 2011) or a combination of the mid-infrared continuum plus mid-infrared fine-structure lines (e.g., Genzel et al. 1998; Peeters et al. 2004; Armus et al. 2007; Dale et al. 2009). A common complementary technique for identifying AGN contributions, especially useful when mid-infrared spectral data are unavailable, involves combinations of flux ratios that utilize data from three or four broadband filters (e.g., Lacy et al. 2004; Stern et al. 2005; Yan et al. 2013; Kirkpatrick et al. 2013; Mendez et al. 2013). Figure 5 shows how the various combinations of the star-forming and AGN templates appear in two different infrared color–color diagrams (assuming rest wavelengths). Using such continuum diagnostics, one can estimate both the AGN fractional contribution as well as the characteristics of the star-forming portion of the galaxy, e.g., dust temperature. The colors for local actively star-forming galaxies (filled squares) shown in Figure 5 come from Siebenmorgen & Krügel (2007), the colors for normal star-forming galaxies (open circles) are from Dale et al. (2012), and the colors for the local AGN M87 (filled triangle) are from NED; the f_ν(70 μm)/f_ν(500 μm) color for M87 falls below the displayed range since the 500 μm flux is overwhelmed by synchrotron radiation (Baes et al. 2010). While some (SINGS/KINGFISH) galaxies from Dale et al. (2012) have nuclei that are distinguished by Seyfert or LINER characteristics, very few have their global luminosity dominated by an active nucleus (Moustakas et al. 2010). Note that our color–color analysis does not to extend to wavelengths shorter than 8 μm and thus cannot be directly compared to Spitzer IRAC color–color analyses (e.g., Lacy et al. 2004; Stern et al. 2005). This restriction is by design: the Spoon et al. (2007) star-forming template begins at 5 μm, a feature which conveniently minimizes complications arising from stellar emission.

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The strengths of various PAH features have been widely used to diagnose the main power source of a galaxy (e.g., Genzel et al. 1998; Laurent et al. 2000; Armus et al. 2007; Smith et al. 2007; Spoon et al. 2007; Dale et al. 2009; Hernán-Caballero et al. 2009; Diamond-Stanic & Rieke 2010; Wu et al. 2010; Shang et al. 2011). These studies suggest that EW (PAH 6.2 μm) ≈ 0.2 μm is an approximate delineation between sources predominantly powered by AGNs and those mostly powered by star formation. Figure 6 shows how the PAH (6.2 μm) equivalent widths for our models depend on far-infrared color. The different curves show the trends for a variety of AGN fractions; the 6.2 μm equivalent width for the Spoon et al. (2007) pure star-forming curve used here is ∼0.5 μm. As can be seen from the figure, larger AGN fractions correspond to lower equivalent width, attributable to the fact that the adopted AGN template is essentially devoid of PAH emission features. Moreover, each trend of connected points in Figure 6 dips to lower equivalent widths at warmer far-infrared colors, a feature that complicates using the 6.2 μm equivalent width as a pure AGN/star-forming diagnostic. This effect of diminished PAH strength (equivalent width) as a function of star formation activity level is weakly built in to the star-forming models (see Figure 6 of Dale et al. 2001), echoing the results of diminished PAH emission for regions permeated by hard radiation fields (Madden et al. 2006). The effect is accentuated when an AGN continuum is added to the mid-infrared. In addition, even "pure" star-forming galaxies exhibit a significant dispersion in the equivalent width of PAH features (e.g., 0.2 dex at 6.2 μm; Wu et al. 2010), a dispersion that these simple models do not incorporate. However, in agreement with the references listed above, this plot shows that EW (PAH 6.2 μm) ≈ 0.2–0.3 μm could roughly be used as a demarcation between sources powered by star formation and AGN activity.

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Figure 7 shows the best fits of the AGN/star-forming curves to the subset of 5MUSES sources that have Herschel SPIRE data available; Figure 8 provides similar displays for fits to GOALS sources. The fits are carried out via a χ² minimization using infrared colors:

$$\begin{equation} \chi ^2 = \sum _{i,j<i} {\left(\log {f_{\nu,i}^{\rm obs} \over f_{\nu,j}^{\rm obs}} - \log {f_{\nu,i}^{\rm model} \over f_{\nu,j}^{\rm model}} \right)^2 \over \left(\sigma _{i,j}^{\rm obs}\right)^2}, \end{equation} \tag{ 2 }$$

where $\log {f_{\nu,i}^{\rm obs}/ f_{\nu,j}^{\rm obs}}$ and $\log {f_{\nu,i}^{\rm model} / f_{\nu,j}^{\rm model}}$ are respectively the observed and model colors involving bandpasses i and j, and $\sigma ^{\rm obs}_{b}$ is the uncertainty in the observed color. The model colors are obtained after convolving the model with the appropriate filter bandpasses. The colors used in the 5MUSES fits involve all possible combinations of the Spitzer IRAC 5.8/8.0 μm, Spitzer MIPS 24/70/160 μm, and Herschel SPIRE 250/350/500 μm flux densities, except for the minority of higher redshift targets for which the central wavelengths of certain shorter-wavelength filter bandpasses correspond to rest wavelengths shorter than 5 μm. For example, the 5.8 and 8.0 μm data are not used in the fit for 5MUSES-130 at z = 1.814 and the 5.8, 8.0, and 24 μm data are not used in the fit for 5MUSES-312 at z = 4.270. The colors used in the GOALS fits involve Spitzer IRAC 5.8/8.0 μm, Spitzer MIPS 24/70/160 μm, and IRAS 12/25/60/100 μm data, where available.

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View extended figure (9 panels)

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View extended figure (8 panels)

The values of α_SF and the mid-infrared AGN percentage found in each subpanel of Figures 7 and 8 correspond to the median value obtained after carrying out 1000 Monte Carlo simulations of each fit. For each Monte Carlo simulation, a random (Gaussian deviate) flux offset, scaled according to the measured uncertainty, was added to each flux. Typical uncertainties are a few to several percent, with a slight increase as the number of available fluxes decreases. The use of a different AGN template such as the one from Kirkpatrick et al. (2012) displayed in Figure 3, where the spectrum rises more steeply in the mid-infrared, results in mid-infrared fractions that differ by 2%–3% (with a scatter of a few to several percent) compared to those resulting from the use of the Shi et al. (2013) quasar template (see the bottom row of Figure 9).

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The mid-infrared AGN fractions for galaxies from the 5MUSES and GOALS surveys are provided within the subpanels of Figures 7 and 8. Sixty-eight (eighty-nine) percent of the 5MUSES (GOALS) subsample studied here have mid-infrared AGN fractions less than 50%, and the mid-infrared AGN fraction unsurprisingly scales strongly with luminosity (see Section 4.5). These 5.8–500 μm SED-fitting-based mid-infrared AGN fractional estimates for both the 5MUSES survey and the GOALS survey can be compared to estimates found in the literature (see the top row of Figure 9). The 5MUSES mid-infrared AGN fractions are compared to those from Wu et al. (2011), who utilize the 5–35 μm continuum data and various templates of AGN and star-forming systems. The GOALS mid-infrared AGN fractions are compared to those from Petric et al. (2011), who employ the mid-infrared spectroscopic diagnostic of Laurent et al. (2000) which compares the slope of the 5–15 μm continuum and the equivalent width of the 6.2 μm PAH feature to templates of pure AGN, star formation, and photo-dissociation regions. The mean differences between our mid-infrared AGN percentages and those from the literature are relatively close to zero—13% for 5MUSES and 2% for GOALS—and the standard deviations in the differences are 18% (5MUSES) and 15% (GOALS). In an attempt to understand the systematic 13% difference for the 5MUSES sample, we tried various combinations of including/excluding photometry from certain filters in the fits, but every combination tested yielded similar results. Thus, the difference is more fundamental than merely the difference in wavelength ranges utilized in our fits and those of Wu et al. (2011).

For the comparison involving GOALS, a (nonparametric) Spearman rank correlation test yields a correlation coefficient of 0.43 for the 58 targets for which reliable mid-infrared AGN fractions are available from both Petric et al. (2011) and this work. For the 5MUSES subsample of 74 targets studied here, the correlation coefficient is 0.68. Thus, for both samples there is less than a 1% probability that the correlation occurred purely through chance.

Simple prescriptions for estimating the total luminosity over 5–1100 μm ⁷ can be obtained from linear combinations of different broadband fluxes, e.g.,

$$\begin{eqnarray} L_{\rm TIR}&=&\eta _1\nu L_\nu (25\,\mu {\rm m}) + \eta _2\nu L_\nu (60\,\mu {\rm m}) + \eta _3\nu L_\nu (100\,\mu {\rm m}) \nonumber \\ &&({IRAS}\hbox{-}{\rm based}), \end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray} L_{\rm TIR}&=&\zeta _1 \nu L_\nu (24\,\mu {\rm m}) + \zeta _2 \nu L_\nu (70\,\mu {\rm m}) + \zeta _3 \nu L_\nu (160\,\mu {\rm m}) \nonumber \\ && ({Spitzer}\hbox{-}{\rm based}), \end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray} L_{\rm TIR}&=&\xi _0 \nu L_\nu (8\,\mu {\rm m}) + \xi _1 \nu L_\nu (24\,\mu {\rm m}) + \xi _2 \nu L_\nu (70\,\mu {\rm m})\nonumber \\ && + \xi _3 \nu L_\nu (160\,\mu {\rm m}) \hspace{5.69046pt} ({Spitzer}\hbox{-}{\rm based}), \end{eqnarray} \tag{ 5 }$$

where the coefficients are functions of the AGN fractional contribution to the 5–20 μm mid-infrared luminosity (for other recent formulations see also Boquien et al. 2010; Elbaz et al. 2011; Galametz et al. 2013). The coefficients are derived from a singular value decomposition solution to an overdetermined set of linear equations involving the individual broadband luminosities as well as the total infrared luminosity (TIR). Table 1 gives the various coefficients for a range of mid-infrared AGN fractions and assuming rest-frame quantities. For the pure star-forming sequence (i.e., the top row of 0% AGN), the coefficients are similar to those already published in Dale & Helou (2002).

The maximum error listed in Table 1 indicates the largest deviation of the TIR approximation, with the respect to the actual TIR, observed for the sequence of star-forming models parameterized by α_SF. The noticeably smaller maximum errors of the 24/70/160 μm combination implies that this filter triplet does a better job of sampling the full infrared profile than the more wavelength-limited IRAS 25/60/100 μm combination; likewise, using the four 8/24/70/160 μm Spitzer fluxes better captures the full range of model variations than using just the three Spitzer/MIPS fluxes. The 70 and 160 μm coefficients in Equations (4) and (5) have formally been derived assuming Spitzer/MIPS bandpasses, but similar values are obtained for Herschel/PACS 70 and 160 μm bandpasses.

Figure 10 shows how the 5MUSES sample is biased toward AGNs at higher infrared luminosities. Above a luminosity of L(TIR) ∼ 5 × 10¹¹ L_☉, nearly all 5MUSES sources with Spitzer and Herschel photometry are estimated to be dominated by AGNs. For reference, a similar evolution in AGN fraction with luminosity is seen for infrared-selected AKARI sources (see Figure 5 in Goto et al. 2011). The U et al. (2012) subset of the GOALS sample covers a much more limited range in luminosity and hence any trend is difficult to ascertain.

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