THE SPECTRAL ENERGY DISTRIBUTIONS AND INFRARED LUMINOSITIES OF z ≈ 2 DUST-OBSCURED GALAXIES FROM Herschel^* AND Spitzer

As was described in the introduction, DOGs show two types of rest-frame near-IR SEDs, "power-law" sources with a rising SED across the Spitzer IRAC bands, and "bump" sources with a peak or break in their SED across the IRAC bands. This bump has been associated with the photospheres of late-type stars, and appears at rest-frame 1.6 μm. Distinguishing between bump versus power-law samples is complicated by the bump shifting in the observed Spitzer bands for objects at different redshift.

The SEDs were visually classified into bump versus power-law, based on the rest-frame 1–8 μm SED. Sources with a clear 1.6 μm peak in their SED were selected as bump sources. The two samples are well segregated, in IRAC color-color space as shown in Figure 2. The power-law sources are red in both [3.6]–[4.5] color and [4.5]–[8.0] color. In contrast, the bump sources tend to be fairly blue in [4.5]–[8.0] color. The near-IR SED classifications are given in Table 3. 58% of the spectroscopic sample are power-law sources and 42% are bump sources. Again these fractions are only representative of this sample and not the larger DOG population which appear to favor bump sources especially at the lower 24 μm flux density levels (e.g., Figure 1).

Bussmann et al. (2012) also provide a rest-frame near-IR classification based on the IRAC photometry. These previous efforts used linear fits to the IRAC data to classify the DOGs and were designed to statistically separate out the two classes. Even though these previous classifications did not consider the redshift dependence of the position of the stellar bump they still agree with the new visual classifications for 89% of the sample. For the 11% where the two classifications disagree, we have chosen to use the visual classification, because it accounts for differences in redshift.

As part of the Herschel GTO time, the Boötes field was observed with the SPIRE far-IR imager by the HerMES team (P.I. Oliver). The central 2 deg² were observed to a depth of ∼80 s in all three SPIRE filters (250, 350, and 500 μm). An additional annulus, with an outer diameter of ∼3 deg surrounding this central field, was imaged to a shallower depth of ∼30 s, again in all three SPIRE filters. These images were processed through the Herschel Level 1 data reduction pipeline and made publicly available. The pipeline reduced images were used here to measure the far-IR flux densities of the DOGs in Boötes.

We combined the SPIRE observations into 250, 350, and 500 μm mosaiced images using the SWarp package (Bertin et al. 2002). Image alignment was set by the header world coordinate system assigned to the images from the data reduction pipeline. These were adequate to align the images to sub-pixel precision, without significant loss of resolution. The same SWarp parameters were used to mosaic the instrument noise images. The noise image mosaics were used to determine the formal photometric uncertainty of each measured galaxy as described below.

While this paper is only concerned with the SPIRE photometry for the 113 DOGs in this sample, we chose to generate a complete catalog of point-sources in the SPIRE mosaics. This approach allowed for better characterization of the photometric uncertainties and detection limits, as well as the alignment between the Herschel and Spitzer images.

Photometry of the Herschel mosaic images was carried out with a two step process. First, the DAOphot (Stetson 1987) FIND routine was used to identify sources in each mosaic image. FIND selects point-like sources in the signal maps. The detection threshold was set low (e.g., 2σ above the noise level) to allow for the largest possible number of matches between the far-IR Herschel data and the mid-IR Spitzer data. Second, the IDL two-dimensional Gaussian fitting routine, MPFit2DPeak (written by Craig Markwardt), was used to determine the flux density of each source. Throughout the mosaic process, the images retained the original flux density units of Jy beam⁻¹. Thus the flux density of a point source in Jy is given by the peak value of a Gaussian fit to the source. MPFit2DPeak returns the peak pixel value and the formal uncertainty for each measurement based on the instrument noise image and flux density level of the peak.

These methods were used to measure 15748, 9118, and 5281 sources with flux densities greater than 20 mJy in the 250, 350, and 500 μm mosaics, respectively. Figure 3 (upper panel) shows the flux density distribution of these detections.

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The photometric accuracy (limited by flux boosting from source confusion) and precision (i.e., photometric noise) were determined by populating the images with artificial sources and recovering their fluxes. These tests accounted for the effects of source confusion and background variations from unresolved cirrus. Artificial sources were created by scaling a very luminous source of known flux from each input image. Artificial sources were placed randomly across each image and their fluxes were measured at the input locations. This approach was analogous to determining the photometry of the DOGs, because the location of each DOG is also known ahead of time from the Spitzer data. This test was not designed to recover the completeness limit of the Herschel images.

Each mosaic was populated with 100,000 artificial sources, placed randomly, one at a time, so as to not increase the crowding. Input flux densities ranged from 400 mJy to 5 mJy. The flux density of each artificial source was measured with the same method as the real sources, including the same five arcsec positional threshold for matching the peak location. Figure 3 (middle panel) shows (measured flux - input flux)/(input flux) as a function of input flux. The photometric precision is given by the standard deviation of the flux differences (solid lines in Figure 3, middle and bottom panels), whereas the photometric accuracy is given by the median of the flux differences (dot-dashed lines in Figure 3, middle and bottom panels).

The bottom panel of Figure 3 summarizes the results for the artificial source tests. The photometric precision is better than ∼20% at 25 mJy for the 250 and 350 μm images. The 500 μm images show a 20% uncertainty at 30 mJy. In addition to the photometric noise, there is an increasing photometric bias (flux boosting) at fainter flux density levels, with the returned flux higher than the input flux. This can be understood in the context of background confusion boosting the measured flux of the artificial source. The photometric bias is smaller than 10% at 20 mJy for the 250 and 350 μm images, and smaller than 10% at 25 mJy for the 500 μm image. No correction for this bias was applied to the final photometry.

These results summarize the typical uncertainties across the SPIRE images. However, the true uncertainty of a given source will depend on the local confusion which might be better or worse than average. The precision and accuracy of the DOG photometry could well be better than the numbers quoted above. Not only are the DOG locations known, but the locations of other far-IR sources are known as well. If we run our artificial source tests in locations that exclude the locations of existing 24 μm sources (excluding locations within 2 pixels of known sources) then the photometry achieves a 20% precision at roughly 20, 20, and 25 mJy (for the 250, 350, and 500 μm images, respectively). These levels represent a best case scenario, and we will take these as the canonical photometric upper-limits for DOGs that are undetected in the SPIRE images.

We match the full 250 μm catalog to the full 24 μm catalog (E. Le Floc'h et al., in preparation) of the Boötes field. For each 24 μm source, the nearest 250 μm source was determined. A plot of the difference in R.A. and Decl. between the two catalogs (Figure 4) reveals a linear spatial shift of 125 and 20 in R.A. and Decl., respectively. After applying these positional offsets to the Herschel positions, matches were selected for objects with a separation of <5'', roughly 1/3 of the 250 μm point-spread function (PSF) size. Of the 28391 24 μm sources (brighter than 0.3 mJy) in the Boötes survey field, we find good SPIRE 250 μm matches (brighter than 20 mJy) for 6327 or 22%.

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After matching the 24 μm sources to 250 μm counterparts, matches were made to sources in the longer wavelength data, based on the 250 μm positions. Approximately ∼12% of the 24 μm sources have a counterpart at 350 μm, while ∼6% have a 500 μm counterpart.

Finally, a visual check of the SPIRE images was made at the location of each of the 113 DOGs with redshifts to determine if those with measured far-IR flux densities show an actual source in the image, and that DOGs without a far-IR match do not show a significant source. In all cases, a DAOphot detection resulted in a visually confirmed source (see Figure 5). However, several DOGs that were undetected in the DAOphot catalogs did appear to contain a source at 250 μm. Usually these were sources that were somewhat blended with a nearby neighbor causing the centroid of the final object to be offset from the 24 μm source at a larger separation than our match criteria of 5''. For these cases, we fit the source by hand, forcing the centroid of the Gaussian to the position of the 24 μm detected DOG, and setting a background level to account for blended neighbor. This "by hand" photometry was performed for 17 of the 113 DOGs in our sample.

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Of the 113 DOGs in the sample, 68 (60%) are detected at 250 μm, 56 (50%) are detected at 350 μm, and 35 (31%) are detected at 500 μm. All of those DOGs detected at 350 and 500 μm are also detected at 250 μm. The detection rate at 250 μm for 24 μm selected DOGs is significantly higher than for the 24 μm catalog of Boötes sources as a whole.

The mid-to-far-IR SEDs of the DOGs were classified by comparing them to scaled up versions of local ULIRGs (see Figure 5). Mrk 231 is a Type-1 AGN-dominated ULIRG (Sanders et al. 1988), although it also likely hosts some star formation (Downes & Solomon 1998; Davies et al. 2004) which contributes to its far-IR flux at the 10%–30% level (Armus et al. 2007). NGC 6240 is a starburst-dominated ULIRG (Lutz et al. 2003; Armus et al. 2006). It also hosts an AGN; however, the AGN contributes <10% of the IR flux (Max et al. 2005; Armus et al. 2006). Arp 220 is the nearest ULIRG and is also a starburst. It possesses an extreme far-IR/mid-IR ratio, much larger than other local ULIRGs (Armus et al. 2007). Figure 5 shows that the mid-to-far-IR SEDs of the DOGs span a range of shapes with some more like Mrk 231, and others resembling NGC 6240.

As with the near-IR classifications, we first visually classify the mid-to-far-IR SEDs of the sample, based primarily on the observed 250/24 μm luminosity ratio. Figure 6 shows the classification statistics for both bump and power-law DOGs. Three results are immediately obvious from this figure: (1) the power-law DOGs are less likely to be detected in the SPIRE bands than the bump DOGs, only 49% of the power-law DOGs are detected, while 76% of the bump DOGs are detected; (2) of the power-law DOGs that are detected, 84% have AGN-like (Mrk 231) mid-to-far-IR SEDs; and (3) of the bump DOGs that are detected, 80% have starburst-like (NGC 6240 or Arp 220) mid-to-far-IR SEDs. The mid-IR-to-far-IR SED classifications for the full sample of SPIRE detected sources are given in Table 3.

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The mid-to-far-IR SED classifications are being driven by the 250/24 μm flux density ratio. To see this more easily, Figure 7 plots the 250/24 μm ratio for the DOGs as a function of redshift. Overplotted is this same ratio for the local templates redshifted to match the DOGs. The power-law DOGs tend to have smaller 250/24 μm ratios than the bump sources, matching the redshifted 250/24 μm ratios of Mrk 231 (with significant scatter). Similarly the bump DOGs match the redshifted 250/24 μm ratios of NGC 6240 (again with significant scatter), even across the z = 2 redshift, where the 8 μm PAH features enter the 24 μm passband.

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With the SPIRE far-IR observations we can, for the first time, observationally constrain the total infrared luminosities, L_IR (8–1000 μm), of a large sample of DOGs. However, even with the far-IR SPIRE observations, the SED is still only sampled at a few additional, though key, wavelengths. Thus a measure of the total IR luminosity still requires some assumptions.

We choose a simple approach for estimating IR luminosity. First we interpolate between the mid-IR and far-IR flux densities. Then, for the long wavelength tail, we apply a blackbody curve, multiplied by ν^1.5 to account for the dust emissivity (see for instance Draine 2003). We select a characteristic temperature for the far-IR tail of 40 K, although because the bulk of the luminosity is coming out at shorter wavelengths the total IR luminosity is relatively insensitive to the temperature used. A 25% change in the far-IR temperature typically results in less than a 5% change in the estimated luminosity. We interpolate the flux points in F_λ versus λ space, which, as can be seen in Figure 5 reproduces the shapes of the far-IR dust humps reasonably well. The resulting L_IR measurements are tabulated in Table 3.

As can be seen in Figure 5, when a DOG SED is well matched to a local template the L_IR inferred for the DOG from the local template matches the L_IR from this simple interpolation, to within better than 20%. Thus, while we could perform multi-component fits to our 2–4 IR data points, the L_IR measurements are unlikely to change significantly from this simple approach.

Figure 8 plots a histogram of the L_IR measurements for both the power-law and bump DOGs detected in the SPIRE images. Even though the power-law DOGs are less likely to be detected at 250 μm and have smaller 250/24 μm ratios, they tend to have higher luminosities than the bump sources. While the bump sources typically have ULIRG luminosities of L_IR = 10¹²–10¹³ L_☉, the power-law DOGs show a large fraction with L_IR >10¹³ L_☉. A K-S test reveals that the two distributions are extremely unlikely (<1%) to be drawn from the same parent distribution. However, this is driven almost exclusively by the lack of lower luminosity power-law DOGs, which is most likely a selection bias. Explanations for these results will be discussed in Section 4.

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Most local ULIRGs cannot be fit by a single dust temperature (Marshall et al. 2007), but rather contain both warm and cold components. Because the DOGs are selected to be luminous at 24 μm (e.g., rest-frame 8 μm at z = 2), they likely host significant amounts of warm and hot dust that will not be probed by the SPIRE observations. However, the SPIRE measurements provide a characteristic temperature for the far-IR emission in the DOGs, which can be compared to the temperatures of other samples measured in the same way.

The Herschel SPIRE observations sample the far-IR SEDs of the DOGs near to the dust emission peak at rest wavelengths of 80–100 μm. Assuming the dust emission follows a simple blackbody, the 250/350 μm flux density ratio yields a characteristic temperature for the far-IR emitting dust peak (e.g., Dunne et al. 2000; Draine 2003; Bussmann et al. 2009a). To determine the far-IR dust temperature we construct synthetic dust models given by

$$\begin{equation} S_\nu = B_\nu (T) *\nu ^\beta, \end{equation} \tag{ 1 }$$

where B_ν (T) is the blackbody Planck curve and β is the dust emissivity. For this study, we assume a typical emissivity value of β = 1.5 (e.g., Draine 2003), and create 90 template spectra each with a different temperature ranging from 10 to 100 K. These synthetic spectra are then sampled at the SPIRE wavelengths, shifted to account for the redshifts of each DOG. A fit between the model 250/350 μm flux density ratios with the actual data (Figure 9), reveals a characteristic far-IR temperature for each DOG. Uncertainties on the temperatures, are estimated by altering the 250/350 μm ratios by their photometric uncertainties and recalculating the temperature. The measured 250/350 μm ratios as a function of redshift and dust temperature are shown in Figure 9, for the 56 DOGs that were detected in both bands.

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Figure 10 shows histograms of the measured far-IR dust temperatures for the power-law and bump DOGs. The temperatures range from 19 K to 58 K. However, the bulk of the temperatures are between 20 and 40 K. In fact, the four DOGs with far-IR dust temperatures measured to be above 50 K all have large temperature uncertainties, meaning that their temperatures are not significantly different from the larger sample. Overall, there appears to be a trend of increasing dust temperature with increasing IR luminosity. A similar trend is seen in local ULIRGs (e.g., Armus et al. 2007). However, as will be discussed in the following section, this trend may be partially the result of the Herschel detection limits which vary with dust temperature.

The power-law and bump DOGs span a similar range of dust temperatures but the median dust temperature of the bump DOGs is lower than the median temperature of the power-law DOGs. Both samples appear to be significantly cooler than a complete sample of local ULIRGs (from the IRAS Bright Galaxy Sample; see Soifer et al. 1987; Armus et al. 2007) measured in the same way at the same rest-frame wavelengths. To estimate temperatures of the local ULIRGs, we redshift their SEDs to z = 2, then observe them in the Herschel SPIRE bands, determining their 250/350 μm flux density ratio in the same way as the high-z galaxies.

The temperature measurements are given in Table 3 and will be discussed further in the following section.

Previously, 12 of the DOGs in the sample were observed at the Caltech Sub-mm Observatory with SHARC-II at 350 μm (Bussmann et al. 2009a). Only 4 were detected, while upper limits were derived for the remainder of the sample. The Herschel photometry are in good agreement with the previous results, returning fluxes below the SHARC-II detection limits, and roughly matching (within 1σ–2σ) the fluxes of the DOGs that SHARC-II did detect. The SHARC-II sample targeted several of the brightest 24 μm sources, which are predominantly power-law DOGs. As we have shown, these sources generally have low 350/24 μm flux density ratios, and therefore are difficult to detect at 350 μm. Sub-mm programs targeting 24 μm bright bump sources have generally shown a higher detection rate (e.g., Lonsdale et al. 2009; Kovács et al. 2010; Chapman et al. 2010), as expected, given their propensity for higher 350/24 μm flux density ratios.

Several of the DOGs in our sample were also previously detected at 70 and 160 μm with deep Spitzer MIPS images (Tyler et al. 2009). These observations constrain the blue side of the far-IR dust peak. Seven DOGs were detected in 70 μm band while 10 were detected in the 160 μm band. From these observations Tyler et al. (2009) calculated L_IR for 11 sources. The new SPIRE derived estimates of L_IR agree with the Taylor estimates to within 20%, which is quite good considering the potentially large systematic uncertainties.

One of the surprising results from our study is that while the bump DOGs are more likely to have detections at SPIRE wavelengths (see Figure 6), the power-law DOGs that are detected are likely to have higher L_IR's (see Figure 8). Selection biases summarized in Figure 11 may be playing a role in these results. This figure compares the 24 μm flux densities of those DOGs that are detected at 250 μm with those that are undetected. While the bulk of the bump DOGs with F_ν (24) <1 (mJy) are detected at 250 μm, less than 50% of the power-law DOGs are detected. This is not surprising as the 250/24 μm ratio is small for the power-law DOGs and typically much larger for the bump DOGs.

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When a power-law DOG is detected at 250 μm it tends to have a larger 24 μm flux density for a given 250 μm flux density compared with the bump DOGs. Therefore SPIRE-detected power-law DOGs will be more IR luminous (on average) than the bump sources.

However, luminosity may not be the only selection bias in the Herschel data. Another bias to consider is the temperature of the far-IR emitting dust (e.g., Chapman et al. 2004, 2005; Pope et al. 2006; Casey et al. 2009; Symeonidis et al. 2011). Figure 10 plots the IR luminosity of the DOGs as a function of the far-IR dust temperature. For Herschel-detected DOGs, galaxies with higher IR luminosities tend to have warmer dust temperatures. This result can be explained at least in part by the SPIRE detection limits for galaxies of a given temperature and IR luminosity (colored lines). The warm-side limits were generated by scaling the SEDs of a complete set of 12 local ULIRG (which span a range of temperatures from 35 to 60 K) to different IR luminosities, and "observing" them at high-z in the Herschel bands. We then determined the luminosity at which they would be detected in the SPIRE 250 μm band (to a 20 mJy limit), at the same rest wavelength as the DOGs as a function of redshift. For instance, at z = 1 any 20 K ULIRGs will be detected in SPIRE observations of Boötes, but only the most IR luminous (e.g., L_IR >10^12.6 L_☉) 50 K ULIRGs will be detected. None of the local ULIRGs would actually be detected in SPIRE if they were above z = 1.4. The cold temperature detection limits (T < 30 K) were generated in a similar way with modified blackbody spectra. As can be seen in Figure 10, there are also strong selection biases against detecting very cold sources with SPIRE.

The temperature bias requires that objects with warmer dust must have higher IR luminosities to be detected in SPIRE. Thus, the Herschel non-detected sources could be missed because they are lower luminosity, have a warmer temperature, or both. However, above L_IR = 10¹³ L_☉, even the warm objects (40–60 K) should be detected regardless of redshift (Figure 10). Therefore, the undetected DOGs, including the 51% of the power-law sources that are not detected, must have L_IR <10¹³ L_☉.

Figure 12(a) shows the L_IR/νL_ν(24 μm observed-frame) ratio as a function of redshift. For the power-law DOGs, the L_IR/νL_ν(24) values lie in a fairly tight range of 6.5 ± 1.4. This suggests that the 24 μm luminosity can be used to predict the IR luminosities of the power-law DOGs to within roughly 20%.

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The scatter in Figure 12(a) is significantly larger for the bump DOGs so a similarly simple prediction is not possible for their L_IR's. However, the flux-dependent relation predicted by Chary & Elbaz (2001) appears to predict L_IR for the bump DOGs with reasonable accuracy. Figure 12(b) compares the Herschel-derived L_IR's of the DOGs to the predicted values from the templates of Chary & Elbaz (2001). For the bump DOGs, these relations work across the full range of L_IR's. Not surprisingly, these relations tend to overpredict the L_IR's of the power-law DOGs, as they were designed for star-forming galaxies, not obscured AGN, which have larger 24 μm contributions from warm dust. However, even for the power-law DOGs the Chary & Elbaz (2001) relations are good to within 50%.

The fact that the Chary & Elbaz (2001) templates work so well for the bump DOGs is somewhat surprising because these relations have been shown to fail for other samples of optically-bright high-z ULIRGs (e.g., Pope et al. 2006; Muzzin et al. 2010; Elbaz et al. 2011; Rujopakarn et al. 2011). These other studies find that most high-z ULIRGs are just scaled up versions of local star-forming galaxies rather than having far-IR SEDs similar to local ULIRGs. The situation is reversed for the bump DOGs, local ULIRG templates are a good match to the 250/24 μm flux density ratios and hence IR luminosities of the bump DOGs.

While these relations work for the sources that are detected in the SPIRE data, they may not work for the DOGs that are not detected in SPIRE, especially the large numbers of undetected power-law DOGs. In order for these relations to work more generally, the undetected DOGs must have similar 250/24 μm ratios as the detected DOGs. The upper limits on the 250/24 μm flux density ratios of SPIRE-undetected DOGs (shown in Figure 7) tend to be at or below the flux ratios for the detected DOGs at a given redshift. However, the limits are not dramatically lower than the flux densities for the detected sources.

A simple stacking analysis on the Herschel images of the undetected DOGs gives a mean 250/24 μm flux density ratio of 7.8 ± 1.3 for the power-law DOGs, and 21.3 ± 4.6 for the bump DOGs. (To get sufficient statistics we needed to bin across the full redshift range for the two sample types.) As with the limits, these values are at the low end of the distributions of 250/24 μm flux density ratios of the SPIRE detected DOGs. Thus we may be seeing evidence for a modest change in the mid-to-FIR SED shape for some DOGs. It is not clear if this change is purely a luminosity effect, with the undetected sample having lower total L_IR for a given 24 μm flux density, or if this change is a far-IR temperature effect, with the undetected DOGs possibly lacking a large reservoir of the coldest dust. That being said, the simple relations for estimating L_IR given above are likely to be off by only modest amounts, as the detected sources with low 250/24 μm flux density ratio have measured L_IR's to within 50% of their Chary & Elbaz (2001) predicted values. This agreement is far superior to the previous uncertainties on L_IR for the DOGs which exceeded factors of two (Dey et al. 2008).

Elbaz et al. (2011) present the Herschel-derived far-IR SEDs of star-forming galaxies in the GOODS fields. They find that the bulk of them, including the z = 1–2 LIRGs and ULIRGs, follow an infrared main sequence which they define based on the "IR8" parameter, where IR8 = L_IR/L₈ and L₈ = νL_ν(8 μm) is the luminosity at rest-frame 8 μm. L₈, is a good proxy for the PAH emission strength from star formation. For most star-forming galaxies in the local universe, PAH strength tracks L_IR in a predictable fashion, e.g., IR8 = L_IR/L₈ ∼ 4 (Elbaz et al. 2011). These normal star-forming galaxies define the infrared main sequence and also show a tight range of specific star formation rates (see for instance, Noeske et al. 2007; Elbaz et al. 2007; Daddi et al. 2007, 2009; Pannella et al. 2009; Magdis et al. 2010). However, for galaxies undergoing a rapid starburst, PAH strength no longer tracks L_IR, and IR8 increases. In the local universe, ULIRGs typically lie off of the IR main sequence. They have IR8 ≫ 4 (Figure 13 shows the local sample assembled in Elbaz et al. 2011, drawn from AKARI, ISO, and Spitzer missions). At z = 1–2, however, Elbaz et al. (2011) find that most LIRGs and ULIRGs not only have scaled up L_IR values but also scaled up PAH strength. This suggests that the mode of star formation in the typical z = 1–2 LIRGs and ULIRGs is more similar to local star-forming galaxies than it is to local ULIRGs, and that selecting on L_IR alone is not a good way to isolate extreme star-bursting galaxies.

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To compare the DOGs with these other samples, we calculate IR8 values for all of our sample galaxies detected in Herschel. For the bump DOGs we use a scaled version of the NGC 6240 template to estimate L₈, and for the power-law DOGs we use a scaled up Mrk 231 template. We scale the template to match the observed 24 μm flux of the DOG. Then, as was done by Elbaz et al., we measure the mean flux density at rest-frame 8 μm within a "filter" that matches the Spitzer IRAC 8 μm filter (i.e., channel 4). We then convert to L₈ using the luminosity distance.

Figure 13 compares the IR8 values from Elbaz et al. (2011) with those of the DOGs. As described above, the bulk of the GOODS galaxies lie in a tight range of 1 < IR8 < 8, with a peak at IR8 = 4. The GOODS-sample does contain a tail of galaxies with IR8 > 8 which are classified as burst mode galaxies. In contrast with the typical GOODS galaxies, the median IR8 values of the DOGs are significantly higher. The power-law DOGs show a tight distribution centered on IR8 ∼ 6. We saw this same result in the previous section where we found L_IR/νL_ν(24 μm observed frame) = 6.5 ± 1.4. In contrast, the bump DOGs show an wide range in IR8, but prefer high values. Only a handful are near the peak of the normal GOODS galaxies of IR8 = 4. The IR8 values of the bump DOGs are closer to those of the local ULIRGs (which also have high IR8 values) and the star-bursting samples in GOODS, rather than the main-sequence z = 2 ULIRGs. They also overlap with sub-mm galaxies which typically have even higher IR8 ∼ 20 (Pope et al. 2008b).

For those 11 bump DOGs observed with Spitzer IRS (Desai et al. 2009) we directly measured L₈ from the spectrum. All of the IRS derived IR8 values match those derived from NGC 6240 to within better than 50%, and in no cases do the IRS derived values change whether a DOG would be in the starburst versus main-sequence region of the IR8 plot. For 7 of the 11 bump DOGs observed with IRS, the IRS derived IR8 values are higher than those derived from NGC 6240.

Elbaz et al. (2011) point out that IR8 values tend to increase when the star formation is occurring in morphologically compact regions. In the local ULIRGs, these highly compact star-forming regions are typically the result of major mergers funneling gas to the centers of these systems. It is not clear if the same merger related processes are leading to the high IR8 values of the DOGs. While there is certainly evidence for some merging in the DOG samples (Melbourne et al. 2009; Bussmann et al. 2009b; Donley et al. 2010), the fractions with obvious major merger signatures remain small, less than 30%.

For the bump DOGs there does appear to be a trend of decreasing effective radius with increasing IR8 value, as shown in Figure 14. This result may be indicating that the high IR8 values of the DOGs are also associated with more compact geometry. We caution, however, the sample with radius measurements is small. In addition, these sizes are measured from near-IR HST (Bussmann et al. 2009b, 2011) and Keck AO (Melbourne et al. 2008, 2009) images of the DOGs, and therefore trace the stellar light rather than the star-forming gas. A better comparison would be to determine the characteristic sizes of the star-forming gas itself, for instance with the Atacama Large Millimeter Array (ALMA).

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The moderately high IR8 values of the power-law DOGs also differentiate them from the lower luminosity AGN in GOODS. Elbaz et al. (2011) shows that both the X-ray selected and IR selected AGN in GOODS tend to follow the same IR8 trend lines (i.e., IR8 ∼ 4) as the non-AGN systems. In contrast the power-law DOGs prefer somewhat higher IR8 values (IR8 ∼ 6). This basically means that for a given amount of rest-frame 8 μm flux the power-law DOGs have higher IR luminosities than the typical GOODS AGN. The power-law DOGs could have higher fractions of cold dust than the GOODS AGN, which would tend to increase L_IR without increasing L₈, or they could just be producing more IR luminosity for a given amount of PAH emission.

Some star formation, even in the power-law DOGs, would not be a major surprise. For instance, Mullaney et al. (2011) found that the X-ray selected AGN in GOODS have far-IR SEDs very similar to normal star-forming galaxies and are likely to have ongoing star formation. Likewise, while the IR luminosity of Mrk 231 is dominated by hot dust from an AGN, there is strong evidence for significant circum-nuclear star formation of as much as 100 M_☉ yr⁻¹ (Davies et al. 2004). Thus the power-law DOGs, which have SEDs similar to Mrk 231, may also host some star formation. This additional star formation could increase IR8 if it is also in a low PAH mode.

Again, the DOGs that are not detected in Herschel may behave differently in the IR8 plots from the detected ones. However, their IR8 limits do not suggest significantly lower IR8 values (see Figures 13 and 14), except for a handful of sources. Pope et al. (2008a) showed that for 12 lower luminosity (L_IR  ∼  1 × 10¹²) DOGs in the GOODS field that IR8 ≃ 7, so there may be some luminosity dependence on these results.

While the IR8 values and the observed-frame 250/24 μm ratios of the DOGs are similar to the local ULIRGs, their far-IR dust temperatures (as measured by the observed-frame 250/350 μm ratio) tend to be cooler. The median temperature of the Herschel-detected bump DOGs is 30 K, which is 10–20 K deg cooler than the local ULIRGs measured in the same way (see Section 3.3). The dust temperatures of the Herschel-detected power-law sources are only slightly higher (median T = 35 K). In fact, the median far-IR temperature of the bump DOGs is also about 10 deg cooler than the median temperature of the GOODS star-burst samples.

Sub-mm galaxies also exhibit extreme star formation rates and cold dust temps (e.g., Chapman et al. 2005; Kovács et al. 2006; Chapman et al. 2010). The bump DOGs show very similar far-IR temperatures to the sub-mm galaxies. Thus, while the Herschel-detected DOGs appear to primarily be scaled up versions of local ULIRGs, they also likely host additional cold dust not seen in local ULIRGs or the other high-z starbursts, except for sub-mm galaxies. These results may suggest a deeper connection between bump DOGs and sub-mm galaxies, than was possible to make based on shorter wavelength data alone.