HERSCHEL FAR-INFRARED AND SUBMILLIMETER PHOTOMETRY FOR THE KINGFISH SAMPLE OF NEARBY GALAXIES

PACS imaging was obtained in scan mode, along two perpendicular axes for improved image reconstruction, at the medium scan speed of 20'' s⁻¹. The 45° orientation of the array with respect to the scan direction contributes to a more uniform spatial coverage. Two Astronomical Observation Requests (AORs) were carried out for joint 70 and 160 μm imaging, and an additional two AORs were utilized for joint 100 and 160 μm observations, resulting in a total of four AORs for 160 μm imaging. Three or six repetitions were carried out for each AOR, depending on an individual galaxy's far-infrared surface brightness as gauged from Spitzer/MIPS data. The integrations achieved per pixel lead to approximate 1σ surface brightness sensitivities of σ_sky ∼ 5, 5, and 2 MJy sr⁻¹ at 70, 100, and 160 μm, respectively, for the fainter subset of galaxies and approximately $\sqrt{2}$ times larger for the brighter subset. The PACS calibration uncertainties are _{cal, ν}/f_ν ∼ 5%, according to Version 2.3 (2011 June 8) of the PACS Observer's Manual.

The raw ("Level 0") data were processed using Version 5.0 of HIPE (Ott 2010). Besides the standard pipeline procedures, the conversion from Level 0 to Level 1 data included second-level deglitching and corrections for any offsets in the detector sub-matrices. Scanamorphos²² (Roussel 2011) Version 12.5 was used to process the Level 1 PACS scan map data. Its main task is to subtract the brightness drifts caused by the low-frequency noise (comprising both the thermal drifts of the telescope and detectors and the flicker noise of the individual bolometers), before projecting the data onto a changeable spatial grid. The algorithm employs minimal assumptions about the noise and the signal, and extracts the drifts from the data themselves, taking advantage of the redundancy built in to the scan observations. With the nominal settings used by the KINGFISH survey, the drifts can be determined on timescales greater than or equal to 0.7 s at 70 and 100 μm, and 0.9 s at 160 μm (for a sampling interval of 0.1 s). These timescales correspond to lengths between 1.5 and 2.5 times the beam FWHM, from 160 μm to 70 μm. Second-level deglitching was performed, and the option to detect and mask brightness discontinuities was also used. The data are weighted by the inverse square high-frequency noise of each bolometer in each scan.

The ("Level 2") output of Scanamorphos is in the form of a FITS cube for each filter. The four planes are the signal map, the error map, the map of the drifts that have been subtracted, and the weight map. There is currently no propagation of the errors associated with the successive processing steps in the pipeline. In each pixel the error is defined as the unbiased statistical estimate of the error on the mean. The brightness unit is Jy pixel⁻¹, and the pixel size is ∼1/4 of the beam FWHM, i.e., 14 at 70 μm, 17 at 100 μm, and 285 at 160 μm.

SPIRE imaging data were taken in Large-Map mode to an extent tailored to each galaxy's size (out to at least ∼1.5 times the optical size). Either two or four scans were obtained for each galaxy based on its Spitzer/MIPS far-infrared surface brightness. The resulting 1σ limiting surface brightnesses are approximately σ_sky ∼ 0.7, 0.4, and 0.2 MJy sr⁻¹ at 250, 350, and 500 μm, respectively, for the fainter subset and $\sqrt{2}$ larger values for the brighter galaxies. Calibration uncertainties for SPIRE data are estimated at _cal/f_ν ≈ 7%, following Version 2.4 (2011 June 7) of the SPIRE Observer's Manual. However, the uncertainties are strongly correlated between the three bands and thus the uncertainty on some SPIRE quantities such as the f_ν(250 μm)/f_ν(500 μm) flux density ratio, for example, are less than the simplistic $\sqrt{2} \times 7$% expectation.

SPIRE observations for six of our galaxies were obtained in the Herschel Reference Survey (Boselli et al. 2010): NGC 4254, NGC 4321, NGC 4536, NGC 4569, NGC 4579, and NGC 4725; those observations were not duplicated for KINGFISH. The only notable difference between the SPIRE observations for the Herschel Reference Survey and those for KINGFISH is that three scans were employed (versus either two or four for KINGFISH observations, as described above).

The raw SPIRE data are processed through the early stages of HIPE (Version 5.0) to fit slopes to the data ramps and to calibrate the data in physical units. A line is fit to the data for each scan leg after masking out the galaxy, and this fit is subtracted from the data. Discrepant data (usually due to a rogue bolometer, of which there are <1 per map) are also masked, and the data are mosaicked using the mapper in HIPE. The map coordinates are then adjusted so that the position of the point sources (measured using StarFinder; Diolaiti et al. 2000) matches those in the MIPS 24 μm images. Finally, the images are converted to surface brightness units by dividing by the beam areas published in the SPIRE Observer's Manual: 423, 751, and 1587 $\mbox{\rlap{$\sqcap $}$\sqcup $}$'' at 250, 350, and 500 μm, respectively. Pixel sizes are 6'', 10'', and 14'' at 250, 350, and 500 μm, respectively.

At far-infrared/submillimeter wavelengths the emission from the sky (above the atmosphere) largely comes from Milky Way cirrus and background galaxies. However, the bolometer arrays of Herschel are not absolute photometers, and thus any map produced by any software is the superposition of an estimate of the true sky emission and an unknown (large) offset. Hereafter this superposition is referred to as simply the "sky." While the post-pipeline-processed KINGFISH SPIRE and PACS images have their overall sky levels removed to zeroth order, a procedure has been adopted to remove a more refined local sky value for each galaxy. To accomplish this local sky subtraction, for each PACS and SPIRE image a set of sky apertures has been defined that collectively circumscribes the galaxy, projected on the sky close enough to the galaxy to measure the "local" sky but far enough away to avoid containing any galaxy emission (Figure 1). The emission from any prominent neighboring and/or background galaxies that are projected to lie within the sky apertures is removed before the sky is estimated. The total sky area, derived from the sum of the areas from all sky apertures, is typically significantly greater than that covered by the galaxy aperture itself, thereby limiting the contribution of uncertainty in the sky level to the overall error budget. The mean sky level per pixel is computed from the collection of these sky apertures, the value is scaled to the number of pixels in the galaxy aperture, and the result is subtracted off from the overall galaxy aperture counts (all done within IRAF/IMCNTS).

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G. Aniano et al. (2012, in preparation) follow a different procedure for subtracting the sky emission from KINGFISH imaging, including fitting a tilted plane to the sky for each galaxy instead of a single value approach adopted here. G. Aniano et al. (2012, in preparation) study the spatial variations in the far-infrared/submillimeter spectral energy distributions and thus a more detailed characterization of the local sky is necessary. The effects of most sky gradients cancel out in extracting spatially integrated fluxes; the two approaches yield generally consistent global fluxes.

The elliptical apertures used for global photometry are listed in Table 1. The apertures are chosen by eye to encompass essentially all of the emission at every wavelength; aperture corrections described below are incorporated to recover the amount of any light that lies beyond these apertures. The average ratio of aperture major axis length 2a to the de Vaucouleurs D₂₅ optical major axis is 1.45 (with a 1σ dispersion in this ratio of 0.45). The same aperture is used to extract the flux at each wavelength studied here, and they are very similar, if not identical, to those used for SINGS photometry (Dale et al. 2007), for the 57 galaxies that overlap the two samples. As a test of the robustness of the aperture choices, the global flux densities using these apertures are compared to the values obtained using apertures with 5% larger and 5% smaller semiminor and semimajor axes. The impact of using ∼10% larger or ∼10% smaller aperture areas is a median difference of less than 1% on the flux densities for all wavelengths.

Prior to extracting fluxes from aperture photometry, any emission from neighboring or background galaxies is identified and removed from the area covered by each aperture. The identification is assisted by ancillary data at shorter wavelengths and higher spatial resolution (e.g., Spitzer/IRAC 3.6 and 8.0 μm, HST optical, and ground-based Hα imaging). The removal is accomplished via IRAF/IMEDIT by replacing the values of contaminated pixels with the values from a random selection of nearby sky pixels, thereby incorporating the same noise statistics as the sky. Usually the removal of such emission affects the global flux at less than the 1% level, but in a few cases the impact is quite important, e.g., NGC 1317 lies within the aperture of NGC 1316, and background galaxies in the fields of the fainter dwarfs like Ho II and DDO 053 would contribute significantly to the integrated flux (by up to ∼30%–50%) if not removed (see also Walter et al. 2007).

Diffraction inevitably results in a small portion of the galaxy emission appearing beyond the chosen apertures, however, and thus aperture corrections are formulated to mitigate this effect. Aperture corrections are empirically determined from a comparison of fluxes from smoothed and unsmoothed Spitzer/IRAC 8.0 μm imaging, which has a native resolution of ∼18. The aperture correction for a given PACS or SPIRE flux is the ratio of the flux from the unsmoothed 8.0 μm image to the flux from the 8.0 μm image smoothed to the same point-spread function (PSF) as the Herschel image in question. Due to the typically generous aperture size and sharp Herschel PACS and SPIRE PSFs, the amplitudes of the KINGFISH global photometry aperture corrections are typically quite small, with median values of 1.0 at all wavelengths and maximum values of 1.03 for PACS and between 1.07 and 1.13 for SPIRE. This technique assumes that a galaxy's profile in the far-infrared matches that of its (mostly) PAH profile in the mid-infrared, and there may in fact be appreciable differences in the two emission profiles.

The uncertainties in the integrated photometry _total are computed as a combination in quadrature of the calibration uncertainty _cal and the measurement uncertainty _sky based on the measured sky fluctuations and the areas covered by the galaxy and the sum of the sky apertures, i.e.,

$$\begin{equation} \epsilon _{\rm total} = \sqrt{\epsilon _{\rm cal}^2 + \epsilon _{\rm sky}^2} \end{equation} \tag{ 1 }$$

with

$$\begin{equation} \epsilon _{\rm sky} = \sigma _{\rm sky} \Omega _{\rm pix}\, \sqrt{N_{\rm pix}+{N_{\rm pix}}^2/N_{\rm sky}}, \end{equation} \tag{ 2 }$$

where σ_sky is the standard deviation of the sky surface brightness fluctuations, Ω_pix is the solid angle subtended per pixel, and N_pix and N_sky are the number of pixels in the galaxy and (the sum of) the sky apertures, respectively. For the few sources undetected by Herschel imaging, 5σ upper limits are derived assuming that a galaxy spans all N_pix pixels in the aperture,

$$\begin{equation} f_\nu (5\sigma \,{\rm upper\ limit}) = 5\, \epsilon _{\rm sky}. \end{equation} \tag{ 3 }$$

Table 2 presents the spatially integrated flux densities for all 61 KINGFISH galaxies for all six Herschel photometric bands. The tabulated flux densities include aperture corrections (Section 3.4) and have Galactic extinction (Schlegel et al. 1998) removed assuming A_V/E(B − V) ≈ 3.1 and the reddening curve of Li & Draine (2001).²³ No color corrections have been applied to the data in Table 2. The most recent calibrations are used for both SPIRE and PACS photometry, including the "FM, 6" PACS calibration which lowers the fluxes for extended sources by 10%–20% compared to the previous calibration, as described in the HIPE 7.0.0 documentation.

The superior sensitivity and angular resolution of Herschel enables a more detailed investigation of the faintest galaxies in our sample. For example, Dale et al. (2007) provide marginally significant MIPS flux densities at 70 and 160 μm for NGC 1404 and DDO 165, but they caution that the emission appearing within the apertures for these galaxies potentially derives from background galaxies. It is now clear based on the Herschel maps that these targets were indeed not detected by Spitzer (nor Herschel) at λ ⩾ 70 μm.

The suite of far-infrared filter bandpasses available for Herschel and archival Spitzer data allows a direct comparison of the global flux densities measured for the SINGS and KINGFISH galaxy samples. The Spitzer and Herschel fluxes at 70 and 160 μm are on average consistent; Figure 2 shows that the (error-weighted) ratios of Spitzer/Herschel flux densities agree fairly well, after accounting for differences in the Spitzer and Herschel spectral responses and calibration schemes. The agreement at 70 μm is within 3% (with a 12% dispersion in the ratio), while at 160 μm the MIPS flux densities are typically 6% larger (with a 16% dispersion). Galaxies fainter than ∼1 Jy show a much larger dispersion in these ratios, but the flux densities for these targets are more susceptible to errors in sky estimation (Section 3.3).

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Figures 3 and 4 provide a color–color snapshot of the Herschel global photometry. As expected, a clear correlation is seen in Figure 3 when the flux density ratios on both axes involve wavelengths that straddle the broad infrared peak of emission for most galaxies. Figure 4, on the other hand, demonstrates that the galaxy spectral energy distributions in general do not form a simple one-parameter sequence. Galaxies are more complicated, with mixtures of dust temperatures and distributions of grain properties that vary from one galaxy to another. The galaxy types are fairly well distributed in terms of their infrared/submillimeter colors, though the Sc and Sd spirals tend to cluster toward cooler infrared colors (i.e., smaller values of f_ν(70 μm)/f_ν(160 μm), f_ν(70 μm)/f_ν(250 μm), and f_ν(100 μm)/f_ν(500 μm)) and the magellanic irregulars (Type Im) have relatively large 500 μm flux densities. This latter issue will be revisited in Section 4.6.

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Figure 5 shows the observed infrared/submillimeter spectral energy distributions for the KINGFISH sample. Included in each panel, when available, are the Two Micron All Sky Survey (2MASS) K_s, ISO 6.75 and 15 μm, Spitzer 3.6, 4.5, 5.8, 8.0, 24, 70, and 160 μm, IRAS 12, 25, 60, and 100 μm, Herschel 70, 100, 160, 250, 350, and 500 μm, and SCUBA 450 and 850 μm band fluxes derived from this work and Dale et al. (2007, 2009). These data nominally reflect the global emission at each wavelength, but as pointed out in Draine et al. (2007), a subset of the SCUBA images suffers from various technical and observational issues. The data processing for scan-mapped SCUBA observations (NGC 4254, NGC 4579, and NGC 6946) removes an unknown contribution from extended emission; the areas mapped by SCUBA for NGC 1097, NGC 4321, and NGC 4736 were small and thus any errors in the large aperture corrections determined by Dale et al. (2007) for these three systems would have a significant impact on their inferred global fluxes; and the extra-nuclear submillimeter emission at 850 μm is unreliably mapped in NGC 4594 due to contamination by an active galactic nucleus. Indeed, for all these special cases except NGC 4736, the SCUBA data appear to fall appreciably below expectations based on extrapolations from the superior Herschel data.

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To extract physical parameters from the broadband spectral data, the spectral energy distributions were fitted with the models of Draine & Li (2007), models based on mixtures of amorphous silicate and graphitic dust grains that effectively reproduce the average Milky Way extinction curve and are consistent with observations of polycyclic aromatic hydrocarbon (PAH) features and the variety of infrared continua in local galaxies. Draine & Li (2007) use the size distributions of Weingartner & Draine (2001) for dust in the diffuse Milky Way, except for adjustment of the parameters that characterize the PAH size distribution. The Draine & Li (2007) dust models use the far-infrared and submillimeter opacities for graphite and amorphous silicate from Li & Draine (2001). Li & Draine (2001) used the graphite opacity from Draine & Lee (1984), but made small modifications to the amorphous silicate opacity. The imaginary part of the amorphous silicate dielectric function ₂(λ) was adjusted in order for the model to better match the average high Galactic latitude dust emission spectrum measured by COBE/Far-InfraRed Absolute Spectrophotometer (FIRAS) (Wright et al. 1991; Reach et al. 1995; Finkbeiner et al. 1999). The adjustments were modest: ₂(λ) was unchanged for λ < 250 μm, and modified by less than 12% for 250 μm < λ < 1100 μm. With this dielectric function for the amorphous silicate component, the Draine & Li (2007) model gives generally good agreement with the observed submillimeter emission from the Milky Way diffuse ISM. Thus the Draine & Li (2007) model has in effect been "tuned" to reproduce the diffuse emission from the local Milky Way. While the dust model used here is referenced as coming from Draine & Li (2007), in fact two small changes have been incorporated since that publication: (1) there have been some small changes in some of the PAH band parameters, and (2) the graphite dielectric function has been modified to broaden out an opacity peak near 30 μm. These changes are described in G. Aniano et al. (2012, in preparation).

Building upon an idea put forth by Dale et al. (2001), Draine & Li (2007) model interstellar dust heating within a galaxy with a δ-function in interstellar radiation field intensity U coupled with a power-law distribution over U_min < U < U_max,

$$\begin{eqnarray} dM_{\rm dust}/dU &=& M_{\rm dust} \Bigg[ (1-\gamma) \delta (U-U_{\rm min})\nonumber\\ && + \gamma {\alpha -1 \over U_{\rm min}^{1-\alpha } - U_{\rm max}^{1-\alpha }} U^{-\alpha } \Bigg], \end{eqnarray} \tag{ 4 }$$

where U is normalized to the local Galactic interstellar radiation field, dM_dust is the differential dust mass heated by a range of starlight intensities [U, U + dU], M_dust is the total dust mass, and (1 − γ) is the portion of the dust heated by the diffuse interstellar radiation field defined by U = U_min. The minimum and maximum interstellar radiation field intensities span 0.01 < U_min < 30 and 3 < log U_max < 8. See Section 5.5 of Dale et al. (2001) for a physical motivation of the power-law distribution in U, and Figure 4 of Draine & Li (2007) for examples of translating U to dust temperature for different grain sizes.

A sum of three different spectral energy distributions is fit to each galaxy: a blackbody of temperature T_* = 5000 K, which Smith et al. (2007) find to be a good approximation to the stellar profile beyond 5 μm, along with two dust components. Following Draine et al. (2007), the sum can be expressed as

$$\begin{eqnarray} f_{\nu }^{\rm model} &=& \Omega _* B_\nu (T_*) + {M_{\rm dust} \over 4 \pi D^2} \big[ (1-\gamma) p_\nu ^{(0)}(q_{\rm PAH},U_{\rm min})\nonumber\\ &&+ \gamma p_\nu (q_{\rm PAH},U_{\rm min},U_{\rm max},\alpha) \big], \end{eqnarray} \tag{ 5 }$$

where Ω_* is the solid angle subtended by stellar photospheres, D is the distance to the galaxy, and γ and (1 − γ) are the fractions of the dust mass heated by the "power-law" and "delta-function" starlight distributions, respectively. p⁽⁰⁾_ν(q_PAH, U_min) and p_ν(q_PAH, U_min, U_max, α) are, respectively, the emitted power per unit frequency per unit dust mass for dust heated by a single starlight intensity U_min and dust heated by a power-law distribution of starlight intensities dM/dU∝U^−α extending from U_min to U_max. The U = U_min component may be interpreted as the dust in the general diffuse ISM. The power-law starlight distribution allows for dust heated by more intense starlight, such as in the intense photodissociation regions (PDRs) in star-forming regions. For simplicity, emission from dust heated by U > U_min will be referred to as the "PDR" component, and the emission from dust heated by U = U_min will be referred to as the "diffuse ISM" component. Finally, the fractional contribution by total dust mass from PAHs, denoted q_PAH, varies between 0% and 12% with a model grid spacing of 0.1% in q_PAH.

Draine et al. (2007) find that fits to the (SINGS) global spectral energy distributions of nearby galaxies are insensitive to the minimum radiation field intensity, the maximum radiation field intensity, and the power-law parameter α. We adopt their choice to fix U_max = 10⁶ and α = 2 to minimize the number of free parameters. Draine et al. (2007) use a minimum value of 0.7 for U_min, but we choose to extend this range down to 0.01 due to the availability of SPIRE data longward of 160 μm and the resulting potential for having detected very cold dust emission. The free parameters Ω_*, M_dust, q_PAH, U_min, and γ are found via χ² minimization:

$$\begin{equation} \chi ^2 = \sum _b {\big(f_{\nu,b}^{\rm obs} - f_{\nu,b}^{\rm model}\big)^2 \over \big(\sigma _{b}^{\rm obs}\big)^2 + \big(\sigma _{b}^{\rm model}\big)^2}, \end{equation} \tag{ 6 }$$

where f^model_{ν, b} is the model flux density obtained after convolving the model with the b filter bandpass, σ^obs_b is the uncertainty in the observed flux density, and σ^model_b is set to 0.1f^model_{ν, b} to allow for the uncertainty intrinsic to the model.

Figure 5 displays the fits of the Draine & Li (2007) models to the combined broadband observations from the Spitzer and Herschel observatories. The median reduced chi-squared value is near unity (∼0.7), and with just a few exceptions the fits are quite reasonable. The most challenging spectral energy distributions to fit involve spatially variable Milky Way cirrus coupled with a faint target, and thus any errors in determining the value of the local sky has a relatively large impact on the inferred fluxes (i.e., dwarf galaxies such as DDO 053, M81 dwarf B, and the faint elliptical NGC 0584).

A wealth of information can be extracted from such fits. Figure 6, for example, uses these fits to provide a glimpse into how the global spectral energy distributions depend on the star formation rate and total infrared luminosity. The infrared spectral energy distributions typically peak at shorter wavelengths for KINGFISH galaxies with higher star formation rates and infrared luminosities. There are exceptions to these generalizations, however, especially for lower luminosity systems. A full tabulation of the output parameters for the KINGFISH sample will be presented in G. Aniano et al. (2012, in preparation). Here we restrict our analysis of the output parameters to (1) evaluating the impact of including the Herschel data in these fits, and (2) comparing the dust masses found through Draine & Li (2007) fits with those from single-temperature modified blackbody fits.

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Figure 7 compares (ratios of) the output parameters γ, q_PAH, U_min, and M_dust when the fits are executed with and without the inclusion of Herschel photometry. All four parameters are relatively unchanged, on average, when Herschel broadband data are added to those from Spitzer. The largest average deviation in the ratio from unity is seen in the top panel, where the fraction of dust heated by PDRs found by using both Spitzer and Herschel data is on average (21 ± 4)% larger than that using just Spitzer data. Interestingly, the largest dispersions in the distributions in Figure 7 are for U_min and M_dust, indicating the importance of Herschel data in assessing these parameters. In addition, all four parameters show ratio distributions that are fairly evenly distributed about their means, though the scatter shrinks for cooler galaxies. At first blush it may be surprising that the inclusion of Herschel far-infrared/submillimeter has any impact on a parameter such as q_PAH that is sensitive to mid-infrared PAH features, but recall that q_PAH is the PAH mass abundance with respect to the total dust mass, and clearly Herschel photometry has an important role in determining the latter. Finally, even though U_min was allowed to go as low as 0.01, the smallest fitted value using the combined Spitzer and Herschel data sets is 0.6, similar to the U_min floor advocated by Draine et al. (2007).

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Figure 8 shows the same ratios plotted as a function of oxygen abundance (Moustakas et al. 2010). The dependence of KINGFISH dust masses on metallicity are consistent with those found by Galametz et al. (2011) in a study of 52 galaxies with submillimeter data: dust masses computed for metal-rich (metal-poor) galaxies are smaller (larger) when submillimeter data are included in the fit. Galametz et al. (2011) argue that most metal-rich galaxies have their dust emission peak in the far-infrared beyond 160 μm, and that submillimeter data are required to fine-tune dust measures for such systems. KINGFISH galaxies with oxygen abundances 12 + log (O/H) greater (less) than 8.1 on the empirical Pilyugin & Thuan (2005) metallicity scale are computed to have an average of 0.06 ± 0.03 dex less (0.28 ± 0.09 dex more) dust mass when submillimeter data are used. This demarcation in metal abundance is similar to that studied by others in quantifying, for example, the relative importance of PAH emission in galaxies (e.g., Hunt et al. 2005; Draine et al. 2007; Smith et al. 2007; Engelbracht et al. 2008). In short, perhaps KINGFISH data show metallicity-dependent dust mass trends similar to those found by Galametz et al. (2011), but it would be useful to have more data to confirm any such trend.

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Galaxy dust masses are typically estimated by fitting a single modified blackbody to a selection of infrared/submillimeter continuum fluxes,

$$\begin{equation} M_{\rm dust} = {f_\nu D^2 \over \kappa (\nu _0) B_\nu (T_1)} \left({\nu _0 \over \nu }\right)^{\beta _1}, \end{equation} \tag{ 7 }$$

or in some cases a superposition of two modified blackbodies of two different dust temperatures,

$$\begin{equation} M_{\rm dust} = \frac{f_\nu D^2}{\kappa (\nu _0)} \left[x B_\nu (T_1) \left(\!{\nu \over \nu _0}\!\right)^{\beta _1} + (1-x)B_\nu (T_2) \left(\!{\nu \over \nu _0}\!\right)^{\beta _2} \right]^{-1}, \end{equation} \tag{ 8 }$$

where κ(ν₀) is the dust mass absorption coefficient at the reference frequency ν₀, T₁ and T₂ are the modeled dust temperatures, β₁ and β₂ are the dust emissivity indices, and 0 < x < 1; some authors choose to fix the dust emissivity index(indices) (e.g., Dunne & Eales 2001; Kovács 2006; Pascale et al. 2009). While such approaches provide quick and simple routes to gauging the dust mass, they do not capture the full range of dust temperatures inherent to any galaxy. However, due to their popularity it is instructive to compare blackbody-based dust masses to those determined from more nuanced models.

Figure 9 compares the dust masses obtained by using a single-temperature modified blackbody (Equation (7)) to those obtained in Section 4.4. Both approaches utilize the results of Li & Draine (2001) for dust absorption cross sections, and in particular ν₀ = c/250 μm = 1.20 THz and κ(ν₀) ≈ 0.48 m² kg⁻¹ are used for the SPIRE 250 μm band in determining the (modified) blackbody dust mass. In addition, both the dust temperature T_d and the dust opacity coefficient β are allowed to freely vary in the fit for each galaxy; the ranges for the fitted values are quite reasonable given that KINGFISH does not contain any extreme objects: 18 ≲ T_d ≲ 40 K and 1.2 ≲ β ≲ 1.9 (Figure 10; see Skibba et al. 2011 for similar results based on modified blackbody fits to KINGFISH targets). In order to avoid contributions from stochastically heated dust grains in the computation of the blackbody-based dust masses, the top panel of Figure 9 shows results when only Herschel photometric bands from 100 μm through 500 μm are included in the fits. Results are not significantly different when 70 μm data are included (bottom panel); the median ratio in the top (bottom) panel is 0.53 (0.46). Figure 9 indicates that single-temperature (modified) blackbody dust masses typically underestimate the values obtained through a Draine & Li (2007) formalism by nearly a factor of two (∼1.9), and there is a trend toward larger underestimates for galaxies exhibiting cooler far-infrared colors.

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Similar results are obtained after fixing β to either 1.5 or 2.0, except for the situation where the blackbody fits are carried out over the wider 70–500 μm wavelength baseline for β = 2.0. In that case the fitted dust temperatures are lower in order to compensate for an overly steep emissivity dependence on wavelength, resulting in larger quantities of dust and only a 25% underestimate in the dust mass compared to those obtained from Draine & Li (2007), echoing the findings in Magrini et al. (2011). Dunne & Eales (2001) likewise find a factor of two deficiency for single blackbody-based dust masses, in their case compared to the dust mass derived from two (modified) blackbodies (see also Skibba et al. 2011). Figure 11 shows a primary reason for the discrepancy: even when limited to λ ⩾ 100 μm photometry, single-temperature blackbody fits overestimate the dust temperature, thus underestimating the dust mass. The single-temperature model does not account for the contribution of warm dust emitting at shorter wavelengths and the temperatures are driven toward higher values in the attempt to fit both the short- and long-wavelength far-infrared emission. This effect is accentuated for galaxies with cooler large dust grains whose emission peaks at longer infrared wavelengths. A more comprehensive and detailed comparison of various dust mass indicators is studied in K. D. Gordon et al. (2012b, in preparation).

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As described in Section 1, several studies of dwarf galaxies show significant excess emission at submillimeter wavelengths. Inspection of Figure 5 shows that only a few spiral and elliptical KINGFISH galaxies have 500 μm fluxes that are noticeably above the fitted model curves (e.g., NGC 3049 and NGC 5474). However, it is interesting that dwarf/irregular/Magellanic galaxies preferentially show this excess. There are a total of 12 KINGFISH galaxies of Type Im (Magellanic irregular), Type I0 (non-Magellanic irregular), or Type Sm (Magellanic spiral), and of the nine with detections at 500 μm, eight show hints of 500 μm emission above the Draine & Li (2007) model fit (IC 2574, Holmberg I, Holmberg II, M81 dwarf B, NGC 2915, NGC 4236, NGC 5398, and NGC 5408; see also Figure 3). Quantitatively, the observed 500 μm excess can be defined with respect to the model prediction at 500 μm, namely,

$$\begin{equation} \xi (500\,\mu {\rm m}) = { \nu f_\nu (500\,\mu {\rm m})_{\rm observed} - \nu f_\nu (500\,\mu {\rm m})_{\rm model} \over \nu f_\nu (500\,\mu {\rm m})_{\rm model} }. \end{equation} \tag{ 9 }$$

A dozen KINGFISH galaxies show ξ(500 μm) > 0.6, including all eight of the dwarf/irregular/Magellanic galaxies listed above. However, it should be noted that interpreting ξ(500 μm) for these systems is complicated by the fact that they are typically faint in the far-infrared/submillimeter (e.g., Walter et al. 2007) and thus their measured flux values are the least reliable. Nonetheless, it is interesting that the lowest metallicity objects in the KINGFISH sample are the sources most likely to show a submillimeter excess and thus potentially harbor the coldest dust or have peculiar dust grain characteristics. A detailed analysis of the submillimeter excess in KINGFISH galaxies is being carried out by Galametz et al. (2011), K. D. Gordon et al. (2012a, in preparation), and L. Hunt et al. (2012, in preparation).