SPECTRAL ENERGY DISTRIBUTIONS OF LOCAL LUMINOUS AND ULTRALUMINOUS INFRARED GALAXIES

The infrared luminosity, L_IR, that is discussed throughout this paper refers to the luminosity emitted in the wavelength range 8–1000 μm. The values of L_IR given in Table 1 have been adopted from the RBGS using the following prescription reproduced from Perault (1987) and Sanders & Mirabel (1996):

$$\begin{eqnarray} F_{\rm IR} &=& 1.8 \times 10^{-14} (13.45 f_{12} + 5.16 f_{25}\nonumber \\ && + 2.58 f_{60} + f_{100})\; \rm {[W m^{-2}]}, \end{eqnarray} \tag{ 2 }$$

$$\begin{equation} L[8\hbox{--}1000 \,\mu {\rm m}] = 4 \pi D^2_L F_{\rm IR} \; [L_\odot ], \end{equation} \tag{ 3 }$$

where f₁₂, f₂₅, f₆₀, and f₁₀₀ are the flux densities in Jy at 12, 25, 60, and 100 μm, respectively, and D_L is the luminosity distance.

Given the availability of our new IRAC, MIPS, and SCUBA data points, we can now test the above IRAS approximation and the validity of the assumed SED, in particular longward of 100 μm, for the local (U)LIRG population. We compute a new total infrared luminosity, L_IR = 8–1000 μm, by using χ² minimization to fit the MIR–FIR–submillimeter portion (14 data points) of the SEDs with different dust models and a modified blackbody fit (CE, DH, SK, mBB; Chary & Elbaz 2001; Dale & Helou 2002; Siebenmorgen & Krügel 2007; Casey 2012; Table 9). For the CE models, 105 templates with infrared luminosity ranging from L_IR = 10^8.44 to L_IR = 10^13.55 have been used. For the DH models, the 64 templates employed exhibit infrared luminosity within the range of 10^8.32–10^14.34. The SK template library in LEPHARE consists of spatially integrated SEDs computed for starbursts of different radii, total luminosity, visual extinction, dust density within hot spots, and the luminosity ratio of hot spots to total as a secondary parameter based on Siebenmorgen & Krügel (2007). We utilized the models with radii = 1 kpc, L_IR = 10^10.1–10^14.7, A_V = 2.2–119 mag, n_hs = 10²–10⁴ cm⁻³, and OB luminosity to total luminosity of 40%–90%. Lastly, the model-independent mBB fit is essentially the sum of a mid-infrared power law at λ < 50 μm and a single-temperature graybody at λ > 50 μm (Casey 2012):

$$\begin{equation} S(\lambda) = N_{bb}\frac{\left(1-e^{- \left(\frac{\lambda _0}{\lambda }\right)^\beta }\right)\dsty \left(\frac{c}{\lambda }\right)^3}{e^{hc/\lambda kT}-1} + N_{pl}\lambda ^\alpha e^{- \left(\frac{\lambda }{\lambda _c}\right)^2}, \end{equation} \tag{ 4 }$$

where T is the far infrared dust temperature, λ₀ is the wavelength corresponding to an optical depth of unity, λ_c is the wavelength, where the mid-infrared power law turns over, β is the emissivity, and α is the spectral index of the power-law component. We let β and α vary to fit the SED where adequate data exist (see more details in Casey 2012).

The comparison of L_IR values is shown in Figure 8. The CE and DH model fits have large scatters (0.07 dex and 0.08 dex) around the IRAS values. The SK model fits exhibit a large scatter (0.05 dex) around the systematic offset of −0.03 dex from the IRAS luminosities. The mBB fit values are ∼0.02 dex systematically lower than the IRAS values, which translates to ∼5% of the infrared luminosity at L_IR = 10¹² L_☉ level. The disagreement with the IRAS values is primarily due to the inadequate color assumptions implied in the coefficients of Equation (2). The scatter and discrepancy exhibited by the luminosities derived from the model-dependent templates are due to limitations in the step size within the model grids.

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Comparing the fits of the different templates and the mBB at 12, 25, 60, 100, and 850 μm, the residuals between the data and the different fits are the smallest for mBB. The SK fits result in similarly minimal residuals except at the short wavelengths, whereas the CE and DH fit residuals exhibit the largest scatters. The main reason for the mismatch to the data is that the detailed infrared SED models have many degrees of freedom and very large template libraries at discrete temperatures and other grid parameters. In contrast, the analytical mBB fit provides more fitting flexibility and is designed to represent the data as accurately as possible, despite having only three free parameters and not accounting for the mid-infrared polycyclic aromatic hydrocarbon features. Since for this paper we only measure L_IR, T_dust, and M_dust, we choose to adopt the mBB fit results for the rest of the analyses.

Fitting graybody of a single dust temperature to the FIR SED from the blackbody peak (∼100 μm) to 1000 μm, we determine and present the temperature of the dust in Table 9: mean T_dust = 33.2  ±  6.2 K. This temperature is ∼10 K cooler than that determined from the Perault (1987) prescription (see discussion in Casey 2012). With the lack of long-wavelength data points, the latter assumes a single-temperature dust emissivity model ∝ν⁻¹ fit to the fluxes in the four IRAS bands (as described in Sanders & Mirabel 1996), often adopting a peak shortward of the true peak now revealed when data points longward of 100 μm are present. The MIPS 160 μm and the SCUBA 850 μm points are invaluable for constraining the real peak, and this will be nailed when the Herschel far-infrared imaging observations are completed for the entire GOALS sample. Dust masses were calculated using the 850 μm flux from the SED and Equation (8) in Casey et al. (2011):

$$\begin{equation} M_{\rm dust} = \frac{S_\nu D^2_{\rm L}}{\kappa _\nu B_\nu (T)} \propto \frac{D^2_{\rm L}}{\kappa _\nu \nu ^2}\quad , \end{equation} \tag{ 5 }$$

where S_ν is the flux density at frequency ν, κ_ν is the dust mass absorption coefficient at ν, B_ν(T) is the Planck function at temperature T, and D_L is the luminosity distance. We adopted a dust absorption coefficient of κ₈₅₀ = 0.15 m² kg⁻¹ (Weingartner & Draine 2001; Dunne et al. 2003). We derived a mean dust temperature M_dust = 10^7.3 M_☉ for the sample.

We note that dust temperatures and masses depend critically on a thorough understanding of the radiative transfer involved as well as the underlying geometry of the dust cloud. This dust temperature can be taken as a characteristic T_dust for the system (measured from the peak of the SED). Clearly the physics of these galaxies is more complex, comprised of many dust reservoirs of different temperatures. Unfortunately, investigating this is beyond the current scope of observations and this work. We included our derivation of the dust temperature primarily as a baseline for comparison to the high-z universe, though we caution that the physical interpretation of that quantity remains uncertain.

Stellar masses for the (U)LIRGs in our sample have been computed via two methods using two different IMFs, and the resulting masses are given in Table 10. Here, we discuss the differences among these measurements.

The two methods adopted for mass determination were to fit the UV–NIR part of the SEDs and to scale from the H-band luminosity. The H band is usually selected for stellar mass conversion because it is at or near the photospheric peak of the stellar SED, and is thought not to be contaminated by hot dust emission from AGNs (Hainline et al. 2011). However, problems with H-band scaling may also arise due to thermally pulsing asymptotic giant branch stars for SEDs with a significant contribution from young stellar populations (Walcher et al. 2011). On the other hand, the SED-fitted masses encompass the stellar component contributing to the optical peak, taking into account the treatment of dust with the designated dust extinction law. For the ensuing discussion, we focus on comparing the SED-fitted masses derived from using two different IMFs.

Our optical–NIR SED fitting procedure is based on stellar population synthesis models from Bruzual & Charlot (2003) using 10 different broadband UV, optical, and infrared bands. Two different IMFs were used: a Chabrier IMF (Chabrier 2003) and a Salpeter IMF (Salpeter 1955). Since the IMF dictates the scaling of the mass-to-light (M/L) ratio in converting luminosity to mass via its slope and mass cutoffs, we compare the masses derived from these two IMFs and assess their differences (Figure 9). The lower and upper mass cutoffs employed were 0.1 M_☉ and 100 M_☉, respectively (Bruzual & Charlot 2003); no additional adjustments to the parameters of the IMFs have been made. The models assumed a star formation history with SFH = e^−t/τ, where τ, varying from 1–30, is the e-folding parameter in years. The metallicity (Z = 0.004, 0.008, and0.02) has been treated as a free parameter as well.

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In general, the mean difference between the masses derived from both methods is at the level of 0.26 ± 0.41 dex, with the masses generally being underestimated from the Salpeter IMF. This was unexpected given that Salpeter IMF tends to result in higher stellar masses due to the difference in treatment of the low-mass end—the Chabrier IMF tends to be flatter and therefore more physical. Under the same input parameters the stellar models with Chabrier IMF fitted the UV light in our SEDs better than their Salpeter counterparts. We also note that the Chabrier IMF incorporates a more up-to-date treatment of UV radiation from young stars in starburst populations, and thus the Chabrier masses have been adopted as the stellar masses for the local (U)LIRGs.

Figure 10 shows the (U)LIRGs as a distribution of SED-fitted mass in logarithmic scale. All but 3 of the 64 objects fall within 2σ of the mean mass, log (M_⋆/M_☉) = 10.79 ± 0.40.

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For the individual subsamples of 53 LIRGs and 11 ULIRGs, we find the mean stellar masses to be log (M_⋆/M_☉) = 10.75 ± 0.39 for the LIRGs, and log (M_⋆/M_☉) = 11.00 ± 0.40 for the ULIRGs. The factor of ∼2 lower mean stellar mass for LIRGs is primarily due to a decreasing "low-mass tail" of objects with masses in the range log (M_⋆/M_☉) = 9.3–10.3. On the other extreme, the most massive object (UGC 08058 = Mrk 231) appears to show hot dust emission from the central AGN, which contributes about 20% of the H-band flux (Surace & Sanders 1999, 2000). Thus for this one object, we have corrected the fitted stellar mass accordingly.

Our results are consistent with estimates of the mass of objects of similar luminosity at higher redshift: log (M_ULIRG/M_☉) ∼ 10.51 ± 0.45 (from Takagi et al. 2003, where the two-tailed unpaired p-value for the differences between our ULIRG masses gives 0.052, which is not statistically significant); and log (M_LIRG/M_☉) ∼ 10.5 (from Melbourne et al. 2008, who found that (U)LIRGs are more massive than "normal," non-LIRG galaxies that are morphologically irregular and spiral galaxies from the GOODS-S field, where log (M_normal/M_☉) ∼ 9.5).

Using the light contribution from the UV and IR, we determine the SFR for the unobscured and obscured stellar populations, respectively. The recipe from Wuyts et al. (2011) gives the following calibration for converting from infrared and monochromatic UV luminosity at 2800 Å to SFR:

$$\begin{equation} {\rm SFR_{UV+IR}} [M_\odot \,{\rm yr}^{-1}] = 1.09 \times 10^{-10} (L_{\rm IR} + 3.3 L_{2800})/L_\odot \quad. \end{equation} \tag{ 6 }$$

Decomposing this quantity into separate UV and IR components, we consider the contribution to the total SFR from the UV and IR luminosities individually (Table 11). SFR_UV ranges from <1 to ∼10 M_☉ yr⁻¹, while SFR_IR is up to ∼50 times larger. We show the fold enrichment of SFR_IR to SFR_UV as a function of infrared luminosity in Figure 11. The logarithmic difference for the LIRGs centered at 1.49 ± 0.66 dex, while that for the ULIRGs is more clustered at 1.90 ± 0.24 dex. This figure highlights that while the infrared SFR in ULIRGs is ∼100 times that determined from the UV, the fold enrichment in the LIRGs is only ∼30 times with a large scatter potentially due to the large variations in dust geometry (i.e., single spirals undergoing minor merger events as opposed to major-merging pairs).

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The mean log SFR_{UV + IR} for the GOALS ULIRGs is 2.25 ± 0.16 and that for the LIRGs is 1.57 ± 0.19. Corresponding specific SFRs (sSFR = SFR_{UV + IR}/M_⋆) have been computed and are also listed in Table 11. The effect on SFR from UV emission and trends with infrared luminosity as seen in the GOALS (U)LIRGs as well as the comparison to a nearby lower-luminosity sample (SINGS; Kennicutt et al. 2003) have been discussed extensively in Howell et al. (2010). Compared with the Howell et al. (2010) sample (with median sSFR = 3.9 × 10⁻¹⁰ yr⁻¹), the median sSFR of our sample is 6.8 × 10⁻¹⁰ yr⁻¹, or equivalent to a mass-doubling timescale of 1.5 Gyr. Our median sSFR value is higher because the GALEX sample is more complete at the lower-luminosity end (with less extinction by dust). The slope of the $\log {\rm {\rm sSFR}}\hbox{--}{\rm log} M_\star$ relation is −0.78 (or 0.22 in log SFR–logM_⋆ space) for the (U)LIRGs, which is shallower than that reported for the high-z infrared main-sequence galaxies (Rodighiero et al. 2011; Daddi et al. 2007).

Different wavelengths offer different methods for diagnosing AGN candidates; a multi-wavelength SED study allows simultaneous access to these various indicators and may be used to evaluate their effectiveness. We employ the radio–infrared flux ratio (q) as defined by Condon et al. (1991) and the criteria specified by Yun et al. (2001; radio-excess: q < 1.64; infrared-excess: q > 3.0) as the basis of our comparison. Figure 12 shows q plotted as a function of L_IR along with its distribution in the right panels. The mean 〈q〉 = 2.41 ± 0.29 for the sample. With these limits, there are two LIRGs (with L_IR < 11.6) identified as radio-excess sources. These objects may be potential AGN hosts with a compact radio core or radio jets and lobes (Kartaltepe et al. 2010; Sanders & Mirabel 1996). On the other end, both of the infrared-excess sources are ULIRGs, which may be hosting dense and compact starbursts, or a dust-enshrouded AGN.

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For objects with X-ray detection, we define two different criteria for identifying X-ray AGNs: (1) L_HX > 10⁴² erg s⁻¹ (Kartaltepe et al. 2010) and (2) hardness ratio, HR >−0.3 (Iwasawa et al. 2011). Seven systems qualified as an X-ray AGN by the first criterion, six by the second, and three of these objects were identified by both. Both radio-excess sources are very luminous in the HX band. All the HR >−0.3 AGN candidates are ULIRGs, though there may be a selection bias since all 11 of 11 ULIRGs in the GOALS sample have been observed and detected in the X-ray, but only 16 of 53 LIRGs have been observed thus far. Chandra observations of the lower-luminosity LIRGs have been proposed and awarded in Cycle 14 (PI: Sanders) to complete the sample.

Power-law SED provides a complementary way to select AGNs that might be heavily obscured and opaque to HX emission. We apply a criterion based on log (νL_4.5) − log (νL_2.2) > 0 to select galaxies with power-law SED shape in the near-IR, corresponding to F_ν spectral slope of 0.4 (Kartaltepe et al. 2010; Alonso-Herrero et al. 2006; Donley et al. 2007). Only three power-law AGN candidates are identified in the sample, and the two ULIRGs among these are both X-ray AGN candidates.

Additional MIR-based selection criteria have been devised to identify heavily obscured AGNs missed in deep X-ray surveys. In particular, selection based on IRAC color cuts (Lacy et al. 2004; Stern et al. 2005) is insensitive to obscuration but can trace AGN-heated dust, providing a powerful technique for discerning luminous obscured and unobscured AGNs. The revised IRAC color selection by Donley et al. (2012) is designed to incorporate the best aspects of the current IRAC wedges but to minimize star-forming contaminants and has been adopted here for selecting IRAC AGN candidates (see Equations (1) and (2) in Donley et al. 2012). This set of criteria results in seven IRAC AGN candidates in our sample, two of them being ULIRGs. Interestingly, most of the IRAC AGNs are below the median q of the sample (q_med = 2.41), with two of them being radio-excess sources.

Our last AGN indicator comparison involves selection based on optical emission line diagnostics. Yuan et al. (2010) applied a Sloan Digital Sky Survey based semiempirical optical spectral classification scheme to a large sample of local infrared galaxies, 57 of which are in our current sample. Among these, two are Seyfert 1 galaxies and 14 are Seyfert 2 systems. These Seyferts bear a distribution in q similar to that of the entire sample.