A MULTIWAVELENGTH STUDY OF A SAMPLE OF 70 μm SELECTED GALAXIES IN THE COSMOS FIELD. I. SPECTRAL ENERGY DISTRIBUTIONS AND LUMINOSITIES^*

Spitzer-COSMOS (S-COSMOS; Sanders et al. 2007) is a Spitzer legacy survey designed to cover the entire 2 deg² COSMOS field with both the MIPS and IRAC instruments. The deep IRAC data for the full COSMOS field was taken during cycle 2 (2006 Jan) with a total of 166 hr to cover the field in all four bands (3.6, 4.5, 5.6, and 8 μm) down to a total depth of 1200 s. The 5 σ sensitivity at 3.6 μm is 0.9 μJy. For a detailed description of the data reduction of all S-COSMOS data, see Sanders et al. (2007).

The MIPS coverage of the COSMOS field was taken during cycles 2 and 3. The aim of the cycle 2 observations was to obtain shallow (80, 40, and 8 s per pixel at 24, 70, and 160 μm, respectively) imaging over a large ∼4 deg² area centered on the COSMOS field. In addition to the shallow imaging, deeper imaging was obtained for a small test region covering ∼8% of the field. The total depths obtained over this test region were 3200, 1560, and 320 s at 24, 70, and 160 μm, respectively, with a 5σ sensitivity of 0.071, 7.5, and 70 mJy. Deep MIPS imaging was obtained for the entire field during cycle 3 (2007 Jan–May and 2008 Jan) with a depth of 3400, 1350, and 273 s at 24, 70, and 160 μm with a 5 σ sensitivity of 0.08, 8.5, and 65 mJy, respectively.

The cycles 2 and 3 MIPS 24 μm data were combined and reduced using the MOPEX package (Makovoz & Khan 2005) to produce a final mosaic. The source catalog was produced using SExtractor (Bertin & Arnouts 1996) for source detection and the DAOPHOT package (Stetson 1987) for measuring flux densities using the point-spread function (PSF) fitting technique. This final catalog is >90% complete above 80 μJy and ∼80% complete above 60 μJy. Details on the 24 μm observations, data reduction, and source properties are presented in Le Floc'h et al. (2009).

The raw 70 and 160 μm data were reduced using the Germanium Reprocessing Tools (GeRT) and then combined using the MOPEX package. The source detection was done using the Astronomical Point-Source Extraction (APEX) tools within MOPEX. The systematic photometric errors are 5% and 12% at 70 and 160 μm, respectively. Details on the 70 and 160 μm observations, data reduction, catalogs, and source counts are presented in Frayer et al. (2009).

The HST/ACS images were taken during HST cycles 12 and 13 as part of the COSMOS treasury survey. A total of 583 orbits were used to obtain a coverage of 1.64 deg² in the F814W filter. The ACS images were taken between 2003 October and 2005 June and reach a depth of 27.2 mag (5σ). Details of the ACS images, including their calibration and reduction, are given in Koekemoer et al. (2007). In addition to the ACS images, NICMOS parallel images were taken over ∼6% of the ACS area in the F160W (H band) filter down to a depth of 25.9 mag (5σ). The high resolution of the ACS images (FWHM = 009) is necessary for the detailed morphological analysis presented in Paper II. The NICMOS parallel images (FWHM = 016) are particularly useful for studying the effects of morphological k-corrections. Due to the requirement of morphological information for this study, we limited our sample to sources within the ACS area.

The ground-based UV, optical, and near-infrared (NIR) coverage consists of data taken with Subaru–SuprimeCam (B_J, V_J, g⁺, r⁺, i⁺, z⁺), CFHT–Megacam (u*, i*), UKIRT–WFCAM (J), and CFHT–WIRCAM (K_S). The complete description of the data reduction of the optical and NIR ground-based data can be found in P. Capak et al. (2010, in preparation).

The broadband optical data (B_J, V_J, g⁺, r⁺, i⁺, z⁺) were taken in 2004–2005 using SuprimeCam on the 8 m Subaru Telescope on Mauna Kea in Hawaii. The seeing ranged from 04 to 20 and the depth at i⁺ is 26.2 mag. Deep u* and i* images were obtained using the Megacam camera at the 3.6 m Canada–France–Hawaii Telescope (CFHT) with a depth of 26.5 mag at u*.

The J band images were taken in several observing runs between 2004 and 2007 with the Wide-field Camera on the 3.8 m United Kingdom Infrared Telescope (UKIRT) and the K_S band images were taken in queue mode between 2005 and 2007 with the Wide-field Infrared Camera (WIRCAM) at CFHT. The data were reduced using custom scripts in IRAF.²⁰ The TERAPIX software Scamp (Bertin 2006) was used to calculate the astrometric solution and the final images were combined using Swarp (Bertin et al. 2002). The final catalogs are complete to J = 23.7 and K_S = 23.5 mag. For details on the reduction of the K_S images, see McCracken et al. (2009).

Photometry for all of these data sets was produced using SExtractor in dual mode (Bertin & Arnouts 1996) using the I-band image as the detection image and have been combined into a master catalog.

UV data were taken using the Galaxy Evolution Explorer (GALEX) in 2004. Four pointings of 50 ks each were used to observe the entire COSMOS field (Zamojski et al. 2007) in the near- and far-ultraviolet bands (NUV and FUV). The u* images from CFHT were used as a prior for the flux measurements of the GALEX images. These data reach a limiting magnitude of 25.7 and 26.0 in the FUV and NUV, respectively.

The COSMOS field was observed with the XMM-Newton satellite in 2004–2005 for a total of ∼1.5 Ms (Hasinger et al. 2007). A total of 1887 point sources were detected in at least one of the bands (soft: 0.5–2 keV, hard: 2–10 keV, and ultrahard: 5–10 keV). The limiting fluxes in each of these bands are 5 × 10⁻¹⁶, 2 × 10⁻¹⁵, and 5 × 10⁻¹⁵ erg cm⁻² s⁻¹ for the soft, hard, and ultrahard bands, respectively (Cappelluti et al. 2009). The Chandra-COSMOS survey (C-COSMOS) observed the central 0.5 deg² of the COSMOS field to a depth of 160 ks and an outer 0.4 deg² to a depth of 80 ks with the Chandra X-ray Observatory (Elvis et al. 2009). The flux limits obtained are 1.9 × 10⁻¹⁶ and 7.3 × 10⁻¹⁶ erg cm⁻² s⁻¹ for the soft (0.5–2 keV) and hard (2–10 keV) bands, respectively. A total of 1761 point sources have been detected and are presented in the catalog of Elvis et al. (2009). In this paper, we use the optical identification catalogs (Brusa et al. 2009; F. Civano et al. 2010, in preparation) from both of these data sets to identify AGNs among our 70 μm selected sample of galaxies.

The COSMOS field was observed with the Very Large Array (VLA) at 1.4 GHz as part of a VLA Large Project in 2004–2005 for a total of 280 hr in A and C configurations to cover the entire 2 deg² (Schinnerer et al. 2007). The data have a mean rms noise of 10.5 μJy beam⁻¹ and a 5 σ sensitivity of 55 μJy. The catalog used here consists of ∼2417 sources with signal-to-noise ratio (S/N) >5 (Bondi et al. 2008).

Spectra of the 70 μm sources were obtained from several different sources. The first is a follow-up survey of 24 μm sources in the deep MIPS test region of the field using DEIMOS on Keck II. The complete survey details will be described in J. S. Kartaltepe et al. (2010, in preparation). The observations were taken on five nights between 2007 and 2009 using the 600 l mm⁻¹ grating with a 1'' wide slit and typical slit lengths of ∼6''. The typical wavelength coverage with these settings is 4000–10,000 Å with a dispersion of 0.65 Å per pixel and a spectral resolution of 4.6 Å. The total integration times were between 1 and 3 hr, depending on the magnitudes of the sources. The data were reduced using the DEEP2 pipeline²¹ and redshifts were measured individually for each source and a quality flag 1–4 was assigned, with 4 being a very secure redshift based on multiple lines, 3 being a likely redshift based on multiple lines, 2 being a less reliable redshift often based on only one line and a noisy spectrum, and 1 being a best-guess redshift based on a noisy spectrum. A total of 62 70 μm detected sources have DEIMOS spectroscopy.

Spectra were also drawn from the zCOSMOS-bright 10k sample (Lilly et al. 2007) observed with the Visible Multi-Object Spectrograph (VIMOS; Le Fèvre et al. 2003) on the 8 m Very Large Telescope (VLT) in Paranal, Chile. This sample consists of the first 10,000 galaxies from a large flux-limited (I < 22.5) survey of galaxies over the entire COSMOS field. The zCOSMOS-bright survey used the R ∼ 600 MR grism with a velocity resolution of <100 km s⁻¹ and a wavelength range of 5550–9650 Å.

Additional spectra have been obtained from a survey of 677 XMM-Newton selected AGN candidates with the Inamori Magellan Areal Camera and Spectrograph (IMACS) on the 6.5 m Magellan (Baade) Telescope from 2005 to 2008 on a total of 18 clear nights (Trump et al. 2007, 2009). The 200 and 150 l mm⁻¹ gratings were used. The wavelength range of these spectra is 5600–9200 Å with a resolution of 10 Å for the lower resolution 150 l mm⁻¹ grating. While AGNs were the main targets of this survey, additional sources were observed when possible. Similarly, Prescott et al. (2006) conducted a spectroscopic survey of quasar candidates using the Hectospec multiobject spectrograph on the 6.5 m MMT on Mount Hopkins using the 270 l mm⁻¹ grating and covering a wavelength range of 3100–9000 Å. Four sources were also observed using the Focal Reducer and low dispersion Spectrograph (FORS1) on the VLT (PI: C. Faure) covering a wavelength range of 3300–11,000 Å (Anguita et al. 2009).

In addition to the surveys described above, spectra of the 70 μm sources were found on the NASA Extragalactic Database (NED) public archive from the Sloan Digital Sky Survey (SDSS; Abazajian et al. 2009) and the Two-degree Field Galaxy Redshift Survey (2dFGRS; Colless et al. 2001). See Table 2 for a summary of the spectroscopic surveys and a breakdown of the number of sources that were observed by each.

In order to ensure the most reliable identification of the optical counterpart for each source in our sample, we first matched the cleaned 70 μm catalog to the 24 μm catalog. Figure 2 shows the separation between the 70 μm source positions and the nearest (as well as the second and third nearest) 24 μm source. Seventy nine of the 70 μm sources (4.5%) do not have a 24 μm counterpart within the 18'' 70 μm beam or there is one on the very edge that does not appear to be a likely counterpart. The vast majority of these sources (92%) are at the low S/N end (3 < S/N < 4). In order to be not detected at 24 μm, these sources would have to have a 70 to 24 μm flux ratio of > 100. Sources with this extreme flux ratio are very rare in the rest of the sample with 24 μm counterparts (at the 1% level). Physically, such a large flux ratio is possible at z>2 where 24 μm could potentially pass through a silicate absorption feature at rest-frame 8 μm; however, given the large number of sources not detected it is unlikely that all of them are such extreme high-redshift sources. Furthermore, there are no sources in the local universe with such extreme ratios between rest-frame 8 and 24 μm. This, combined with their low S/N, indicates that they are most likely spurious detections and we therefore remove them from further analysis.

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Of the remaining 1664, 1528 sources were successfully matched to a 24 μm counterpart. Of the 1528 successfully matched sources, 759 (∼50%) have a single isolated 24 μm source within the 70 μm beam making the identification of the correct counterpart straightforward. For 513 sources (∼34%) there is more than one 24 μm source in the beam but the most likely counterpart is clear (i.e., the source closest to the center of the beam is also the brightest at 24 μm). Two hundred and fifty six sources (∼17%) have more than one 24 μm source in the beam but the likely counterpart is not as clear as in the previous case. For these sources we chose the source with the highest 24 μm flux as the best-guess match to the counterpart. Although it is possible that some fraction of these "best-guess" matches are the wrong counterpart, we find that the results of our analysis do not change if they are left out. We estimate that our false match rate is on the order of 2.5%. For the 136 sources that cannot be matched, there either appears to be more than one equally likely counterpart or the 70 μm source appears to be a blend of multiple 24 μm sources. It is highly probable that the multiple 24 μm sources within the beam each contribute to the 70 μm flux, and therefore it is not possible to determine an accurate 70 μm flux for each source. Leaving these sources in our sample will only add an additional uncertainty, therefore we omit these ambiguous sources from further discussion.

We then matched the remaining 1528 sources with believable 24 μm counterparts to the IRAC source positions. All but nine of them have a clear match within 2'' of the 24 μm source position. For these nine, the 24 μm source appears to be a blend of two IRAC sources so we remove them from the sample for the same reasons described above. For the remaining 1520 sources, we then matched the IRAC counterparts to the optical I-band positions and found clear counterparts for all but 11. Five of these appear to be two optical sources with blended IRAC photometry, so we also exclude these five sources from our sample. The remaining six sources (0.3%) do not have an optical counterpart above the flux limit of the catalog. Without an optical counterpart we have no redshift measurement for these six sources and thus cannot obtain an estimate of the total infrared luminosity, so we exclude them from our final sample but note that their IRAC/MIPS properties do not appear to differ from the rest of the sample. Of the remaining 1508 sources, five are stars and so we remove them from the final sample as well. This results in a final sample size of 1503 70 μm selected sources with reliable counterparts at 24 μm, the IRAC bands, and the optical. We believe that the 9% of the sources removed from our sample (136 + 9 + 11) due to their inability to be matched will not affect our final result and removing them leaves us with a robust sample.

We plot the differential source counts (dN/dS × S^2.5) for the final sample of 1503 sources in Figure 3 along with the published source counts from S-COSMOS (Frayer et al. 2009) and GOODS-N (Frayer et al. 2006). The source counts for our sample match the published source counts very well except at the lowest flux bin (S70< 6.5 μJy). This indicates that spurious sources at low S/N do not have a significant contribution and that the sample is therefore reliable though incomplete at these low flux levels.

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The cross matching at 160 μm was done by looking for 160 μm sources near each of the 70 μm sources. For the vast majority of the cases (89%), only one 70 μm source was identified as a possible match to a 160 μm source. For most of the cases where more than one 70 μm source could have been identified as a possible match, one was much closer to the center of the beam and the other was far enough away that the choice was unambiguous (9%). For the handful of ambiguous cases (remaining 2%), we chose the brighter 70 μm source as the match. In total, we find that 463 of the 1503 70 μm selected sources (∼31%) are detected at 160 μm.

All of the UV–NIR (including GALEX, IRAC, and all of the ground-based optical and NIR) multiwavelength photometry was used to produce a photometric redshift catalog for all galaxies (Ilbert et al. 2009) and X-ray detected AGNs (Salvato et al. 2009) in the COSMOS field. Thanks to the depth and broad range of this multiwavelength coverage, the COSMOS photometric redshifts have an unprecedented accuracy of dz/(1 + z) = 0.007 at i⁺ < 22.5 and 0.012 at i⁺ < 24 out to z < 1.25. The AGN photometric redshifts have an accuracy of dz/(1 + z) = 0.02 and 0.03 for i⁺ < 22.5 and 22.5 < i⁺ < 25, respectively. The number of outliers for both galaxies and AGNs are negligible. The accuracy and high precision of these photometric redshifts allows us to use our entire sample for the analysis of the properties of 70 μm sources instead of limiting our sample to those with spectroscopy as has generally been done in the past.

The redshift distribution of the entire 70 μm sample is shown in Figure 4. Photometric redshifts are available for all of the 1503 galaxies in the sample. One hundred and fifty four of these sources are detected in the X-ray by XMM-Newton and Chandra, and so we use the photometric redshifts determined by Salvato et al. (2009). Our 70 μm selected sample peaks at z ∼ 0.35 and the number of sources drops beyond (z ∼ 1). However, given our large sample size, a significant number (273: 18%) are detected at 1 < z < 3.

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Reliable spectroscopic redshifts are available for 602 sources in the sample (∼40%) and are represented by the filled histogram in Figure 4. Column 5 in Table 2 lists the number of sources in our sample that have spectra from each of the different redshift surveys. Several sources have redshifts available from more than one source. For these objects, we compared each available redshift to check their reliability and chose the best one. A comparison between the photometric and spectroscopic redshifts for those sources with very secure redshifts (quality flags 3 and 4) is shown in Figure 5. The XMM-Newton sources are shown as the red points and use the photometric redshifts of Salvato et al. (2009). The overall dispersion in this infrared selected sample is 0.02 × (1 +  z). There are only nine catastrophic failures (|z_p − z_s|/(1 + z_s)>0.15) in the sample (1.7%). For the rest of the paper, we adopt the spectroscopic redshift for those sources with reliable spectroscopy and the photometric redshift for the rest of the sample.

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Figure 6 shows a compilation of all 1503 SEDs ranging from the UV through the FIR binned by redshift and normalized at 1 μm. Overplotted in blue is the median SED for each redshift bin. All of the photometry used to construct these SEDs, the redshifts, and the quantities derived in this paper (such as L_IR) are listed in Table 3.

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Using the XMM-Newton and Chandra X-ray catalogs (Brusa et al. 2009; F. Civano et al. 2010, in preparation) of the COSMOS field, we identified which of the 70 μm selected sources are detected at X-ray energies. One hundred and nineteen of the sources were detected by XMM-Newton and 103 by Chandra with 68 detected by both, for a total of 154 X-ray detected sources. The spatial distribution of the sources detected by both XMM-Newton and Chandra is shown in Figure 7. This plot illustrates the relative areas observed with both telescopes within the ACS coverage area. The rest-frame X-ray luminosities for each of these sources was calculated from the hard band (0.5–10 keV) fluxes with an assumed power-law photon index of Γ = 1.7 and is shown in the top panel of Figure 8 as a function of redshift. One hundred and thirty two (85%) of these sources have L_X>10⁴² erg s⁻¹ (dashed line in Figure 8) and so are likely to be AGNs.

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Figure 9 shows the distribution of hardness ratios ((H − S)/(H + S), where H = 2–10 keV and S = 0.5–2 keV) for the 102 X-ray sources in the sample that are detected in both the soft and hard X-ray bands. For the remaining objects, 24 are completely hard (i.e., no detection in the soft band), 29 are completely soft (no hard band detection), and only upper limits are available for three. Overplotted on this histogram (dotted line) is the normalized distribution for the entire X-ray selected population that is detected in both bands. These two populations show striking differences. Whereas the full X-ray population has a hardness ratio that peaks around −0.5, the 70 μm selected population appears bimodal, with peaks at ∼−0.5 and 0.35. The 70 μm selected population of X-ray detected AGNs is on average harder than the general X-ray selected population. The large hardness ratios of some of the 70 μm sources indicate that there is significant obscuration present in these galaxies absorbing UV and soft X-ray emission.

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Five hundred and sixty two of the 70 μm sources were matched to a radio source within 1 arcsec. For each of these sources, we estimated the rest-frame 1.4 GHz luminosity (L_1.4 GHz) using Equation (5) of Yang et al. (2007) and applying a k-correction assuming a power law of the form F_ν ∝ ν^−α where α, the radio spectral index, is assumed to be ∼0.7 (Condon 1992). The radio luminosity is presented in the bottom panel of Figure 8 as a function of redshift for all 562 radio detected sources in our sample.

Using this subsample of objects detected in both the radio and infrared, we investigated the infrared–radio correlation. Even though this correlation has been shown to hold over a wide range in redshift and luminosity (e.g., Helou et al. 1985; Condon et al. 1991a; Yun et al. 2001; Appleton et al. 2004; Ibar et al. 2008), there is some evidence that it might break down at extreme infrared luminosities or at high redshift (e.g., Kovács et al. 2006; Sajina et al. 2008; Younger et al. 2009). A complete analysis of the evolution of the infrared–radio correlation with redshift is beyond the scope of this paper; however, a full treatment of this issue will be discussed in Sargent et al. (2009). Condon et al. (1991b) found the mean value of q for BGS starbursts to be 〈q〉 = 2.34 with a very small dispersion (σ ∼ 0.19). This is in excellent agreement with the results from Yun et al. (2001) who found 〈q〉 = 2.34 for a sample of 1809 galaxies from the IRAS 2 Jy sample. The Yun et al. (2001) study also found that there were slight variations in q with IR luminosity. For faint IR sources, they found values of q that were slightly higher than the mean and for bright IR sources they found a higher overall dispersion (σ ∼ 0.33).

We computed the value of q as defined originally by Helou et al. (1985) as the ratio between the FIR (a combination of infrared flux measurements from 60 and 100 μm) and the flux at 1.4 GHz. We adopted this definition to allow for a direct comparison with previous work. For our sample of 562 radio detected 70 μm selected sources, we compute q using the rest-frame 60 and 100 μm flux densities obtained from the best-fit SED template and the k-corrected 1.4 GHz flux density. The resulting q distribution for our sample is shown in Figure 10 as a function of L_IR (top) and redshift (bottom). We find a wide range in q (0.65–3.7) with an average q of 2.36 and a dispersion of 0.39 overall, in agreement with previous studies. However, we find that this dispersion increases dramatically with L_IR with an increase in both radio-excess (small values of q) and infrared-excess (large values of q) galaxies. For the LIRGs and ULIRGs in the sample, we find 〈q〉 = 2.34 ±  0.31 and 〈q〉 = 2.42 ±  0.50, respectively. It is thought that the slightly higher mean q at high luminosities is the result of incredibly high radio free–free opacity (Condon et al. 1991b). However, we note that this effect should decrease with L_IR in our sample as the rest-frame radio frequency probed increases, and therefore, the infrared excess observed in these sources is not likely to be caused by this opacity effect.

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We obtained the total infrared luminosity, L_IR (8–1000 μm), for each source in our sample by fitting the 8, 24, 70, and 160 μm data points to various SED templates using the SED fitting code Le Phare²² written by S. Arnouts and O. Ilbert. We weighted each of the four points equally to avoid overweighting the points with the smallest error bars, which are typically those at shorter wavelengths (i.e., 8 and 24 μm). The 8 μm data point was only used at low redshifts. Once it shifted below 7 μm, it was no longer used due to confusion with PAH features and since the 24, 70, and 160 μm data points well represent the portion of the SED that contributes the bulk of the infrared luminosity. Beyond z ∼ 2.4, the 24 μm point is no longer used for the same reason.

We used four different template libraries for the SED fitting—Chary & Elbaz (2001), Dale & Helou (2002), Lagache et al. (2003), and Siebenmorgen & Krügel (2007). We chose to use these template libraries since they represent a wide range of SED shapes and luminosities and they are widely used in the literature. Here, we briefly describe how each of these libraries was derived and discuss the differences between them. For more information on these template libraries, see the original papers and the detailed description in Symeonidis et al. (2008).

Chary & Elbaz (2001): this template library consists of 105 templates based on the SEDs of four "prototypical" galaxies (Arp220: ULIRG; NGC 6090: LIRG; M82: starburst; and M51: normal star-forming galaxy). They were derived using the Silva et al. (1998) models with the MIR region replaced with ISOCAM observations. These templates were then divided into two portions (4–20 μm and 20–1000 μm) and interpolated between to arrive at a set of libraries of varying shapes and luminosities. The Dale et al. (2001) templates are also included in this set to extend the range of shapes.

Dale & Helou (2002): these templates are updated versions of the Dale et al. (2001) templates which used the model of Desert et al. (1990). This model involves three components, large dust grains in thermal equilibrium, small grains semistochastically heated, and stochastically heated PAHs. They are based on IRAS/ISO observations of 69 normal star-forming galaxies in the wavelength range 3–100 μm. Dale & Helou (2002) improved upon these models at longer wavelengths using SCUBA observations of 114 BGS (Soifer et al. 1989) galaxies, 228 galaxies with ISOLWS (52–170 μm; Brauher 2002), and 170 μm observations for 115 galaxies from the ISOPHOT Serendipity Survey (Stickel et al. 2000). All together, these 64 templates span the IR luminosity range 10⁸–10¹²L_☉.

Lagache et al. (2003): this library of starburst templates was built on the model of Maffei (1994), which uses the dust emission model of Desert et al. (1990), with a few modifications applied. First they replace the PAH portion of the templates with the one from Dale et al. (2001), then they increase the proportions of PAHs and very small grains while adding in extinction, and finally, they broaden the FIR peak and flatten the SED at long wavelengths. This library also includes templates of normal star-forming galaxies derived from the ISOPHOT serendipity survey (Stickel et al. 2000), the FIRBACK galaxy SEDs, and long-wavelength data taken from Dunne et al. (2000) and Dunne & Eales (2001).

Siebenmorgen & Krügel (2007): This template library consists of over 7000 model SEDs derived using a radiative transfer and dust model described in Kruegel (2003). This model uses the assumption of spherical symmetry and divides the starburst luminosity into two classes, that from OB stars in dense clouds (L_OB) and the total from all other stars (L_tot–L_OB). Five parameters are varied in the calculations to create the grid of template SEDs: (1) the total IR luminosity ranges from 10¹⁰to10¹⁴ L_☉, (2) the radius of the starburst nucleus: 0.35, 1, 3, 9, and 15 kpc, (3) the visual extinction of the nucleus: A_V = 2.2, 4.5, 7, 9, 18, 35, 70, and 120 mag, (4) the ratio of the luminosity contributed by the OB stars to the total luminosity: L_OB/L_tot= 0.4, 0.6, and 0.9, and (5) the dust density in the hot spots: n^hs = 10², 10³, and 10⁴ cm⁻³. Combinations of parameters that are considered to be physically unlikely are left out of the final grid.

For each of the above template libraries, the best-fit model was chosen by finding the one with the lowest χ² value and allowing for rescaling of the templates. The total infrared luminosity was then calculated from the best-fit template by integrating from 8 to 1000 μm. A sample of SEDs and the best fit from each template library is shown in Figure 11 for a range of luminosities. We visually inspected the fits and found that they typically work just as well for AGNs as for non-AGNs (in the 8–1000 μm range) since our fit does not include all of the IRAC data points which would be the most affected by an AGN. For the final L_IR, we adopt the value of the best fit of all the template libraries. This final value is shown in Figure 12 as a function of redshift and is presented in Table 3. Since the template library is so large, a range of templates can be used to adequately fit the data points. We use this range, along with the 1σ uncertainties in the redshift measurement, to calculate the uncertainty on the final derived L_IR given in Table 3. In total, we identify 687 LIRGs, 303 ULIRGs, and 31 HyLIRGs.

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The depth and breadth of the 70 μm imaging in the COSMOS field allow us to obtain a more accurate measurement of the total infrared luminosity than has previously been possible for samples selected at 24 μm. The long wavelength selection means we can be confident in our estimate even at high redshifts since we are still probing the infrared slope of the SED (35 μm at z = 1 and 23 μm at z = 2). In addition, this large sample size of sources, including many that are also detected at 160 μm, enables us to statistically quantify how well we could have measured the luminosity if we only had detections in a subset of the infrared bands. This information is particularly useful for comparing our results to other studies of sources selected at 24 μm.

Figure 13 shows a comparison of our estimate of L_IR for the subsample of sources detected at 160 μm (463 sources in total) with the estimate excluding the 160 μm data point (based only on 8, 24, and 70 μm). The solid line represents a one-to-one relationship and the lower panel shows the difference between these two measurements. Since the majority of 70 μm selected sources are not detected at 160 μm, it is important to understand and quantify this relationship. While the internal scatter of the points is quite small (σ = 0.20 dex), there appears to be a significant offset (of 0.20 dex on average) between the estimates with and without the 160 μm data point, which increases with L_IR. This offset indicates that the L_IR determined without the 160 μm data point is underestimated by 0.20 dex on average.

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In an attempt to isolate the possible cause of this offset, Figures 14 and 15 contain the same plot divided into several flux and redshift bins, respectively. The offset is largest for the sources at the faintest flux levels (0.36 dex at 4 mJy < F(70) < 8 mJy) and is negligible at the brightest fluxes (0.11 dex at F(70)>20 mJy). When divided into redshift bins, the largest offsets are seen at the high-redshift end. The mean offset and internal dispersion for each redshift and flux bin are summarized in Table 4. There are a few possible explanations for the observed offset. One is that the intrinsic noise in the 160 μm measurement at these low flux levels biases the fit toward higher estimates than if the source was not detected at 160 μm at all. However, this explanation seems unlikely since the offset remains even when using higher S/N cuts at both 70 and 160 μm. Another possibility is that at higher redshifts the 70 μm detection samples too short a wavelength to put much of a constraint on the best-fit template. This would result in an overall larger scatter but not an offset. And finally, it is possible that the detection at 160 μm preferentially picks out sources with a colder dust component than the rest of the 70 μm population.

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To test our fitting routine, we fit the same data points (8–160 μm from IRAC and MIPS) for a set of 67 local LIRGs and ULIRGs from the Great Observatory All-Sky LIRG Survey (GOALS; Armus et al. 2009). As for the COSMOS sources, we obtained the best-fit L_IR with and without the 160 μm point and plot the comparison in Figure 16. For these local sources, we do not see the same offset that we see in the COSMOS sources and the intrinsic scatter is much smaller (σ = 0.08 dex). In addition, the L_IR obtained from this fit agrees very well with L_IR in the literature from the IRAS data points. This test gives us confidence that the offset we observe is not due to a problem with the fitting routine and also indicates that the rest-frame 70 μm data point is at a long enough wavelength to obtain an accurate measurement of L_IR at low redshift. We also find that the template libraries based empirically on local sources tend to fit the data points better, as is expected. As an additional test, we fit only the 8 and 24 μm data points for the local sources (roughly corresponding to observed 24 and 70 at z ∼ 2) and find an overall scatter of ∼ 0.17 dex. This result is consistent with the typical uncertainty we obtain for the COSMOS sources.

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Symeonidis et al. (2008) performed a similar comparison with 43 sources from the Extended Groth Strip. They derived an empirical relation (Equation (1) in Symeonidis et al. 2008) to obtain L_IR directly from the 24, 70, and 160 μm flux measurements without the need to fit templates or apply k-corrections. This relation was found by summing the approximate contributions to the total infrared luminosity obtained using triangles and polygons of heights determined by the fluxes at the three MIPS wavelengths. They then add in a correction for the systematic offset found between this approximation and their total L_IR found through template fitting to arrive at the final equation. They found that this equation agrees well with their 43 EGS sources at all L_IR with a very small scatter (0.06 dex). Figure 17 shows a comparison of the L_IR derived here for the COSMOS sources and that using the Symeonidis et al. (2008) equation. We also find excellent agreement and a small scatter (0.06 dex overall), however, we find that the scatter increases beyond 10¹² L_☉ (∼ 0.1 dex). A closer inspection of the sources with the largest deviation from the equation indicates that at these redshifts, the 160 μm point is not long enough to constrain the peak of the emission and therefore, a wider range of templates fit the points than at lower redshifts.

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For the remaining 1042 sources without a detection at 160 μm, the relationship shown in Figures 13–15 indicates that an empirical correction may be needed. However, such a correction factor may not be warranted if those sources detected at 160 μm are intrinsically different from those not detected. Figure 18 shows the distribution of 70 μm fluxes for these two subsamples. The sources detected at 160 μm are clearly weighted toward the bright end of the flux distribution.

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To further examine the properties of the sources not detected at 160 μm, we fit templates to their mean SED using a stacked 160 μm data point in several redshift and flux bins in the same manner as the detected sources. The resulting comparison is shown as the colored points in Figure 19. While these stacked points show a similar amount of scatter as the 160 μm detected sources, they do not show the same systematic offset. For the stacked sources, the luminosity obtained with the 160 μm point is in agreement with the luminosity obtained without it. This suggests that the sources detected at 160 μm are indeed biased toward colder sources. Therefore, a correction to the L_IR for the rest of the 70 μm sample is not necessary. Instead, we include the scatter in the relationship as an additional source of uncertainty and include this in our error bars in Figure 12. Thus, the typical uncertainty for sources detected at 160 μm is 0.05 dex, while for those not detected it is ∼ 0.2 dex.

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Since MIPS is the most sensitive at 24 μm, samples selected at this wavelength are very useful and will continue to be used in the future. Therefore, it is essential to understand how well their total infrared luminosities can be determined with just this data point. To test this, we obtained the best-fit template using just the 24 μm data point. Since there is only one point, the templates are not really fit but instead the best match to the 24 μm flux at the source redshift is obtained from each of the template libraries without allowing for rescaling. For the final luminosity estimate, we chose to use the Siebenmorgen & Krügel library since it was the best match for the vast majority of sources using 70 and 160 μm and has the largest variety of SED shapes. Figure 20 shows the comparison between luminosity estimates using all available bands and using only the 24 μm point for both 160 μm detected and non-detected sources. The scatter in this relationship is much larger (σ ∼ 0.4 dex) and the difference can be up to 1 dex for some sources. A larger offset is also seen for the sources detected at 160 μm than those not, consistent with the results discussed in the previous section. The large scatter indicates that luminosity estimates for samples based solely on 24 μm detection alone can be off by a significant amount and many LIRG and ULIRG samples in the literature based on 24 μm may actually be contaminated by lower luminosity sources since their number densities are higher though it is possible that this effect is mitigated by the slight offset (∼ 0.1 dex on average) obtained without the 70 μm data point.

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Figures 6 and 21 show the full range of SEDs that we observe for the 70 μm selected sample of galaxies binned by redshift and L_IR with the median SED in each bin overplotted as a blue line. The median SEDs are similar to sources observed locally for sources at low luminosity (e.g., Dale et al. 2007; SINGS, L_IR < 10¹¹ L_☉) and at high luminosity (e.g., V. U et al. 2010, in preparation; RBGS, L_IR>10¹¹ L_☉). All of these studies have shown that the median UV-to-FIR SEDs have two prominent thermal peaks (the optical stellar peak and the FIR dust peak) and, in addition, a range of spectral shapes, particularly in the UV (0.2–0.5 μm), NIR (2–5 μm), and MIR (10–30 μm). With the large number of sources in our 70 μm sample, we can finally begin to quantify the full extent of these variations and explore how different parts of the SED correlate with each other and with L_IR. As should already be known from studies of smaller samples of local objects (e.g., RBGS: Sanders et al. 2003; 1 Jy ULIRG Survey: Kim & Sanders 1998), it is clear that a single archetypical template for a given infrared luminosity (e.g., Arp 220 or Mrk 231 for ULIRGs) would not be applicable for all objects with that luminosity.

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The median SEDs clearly show several general features. First, most of them show the 1.6 μm peak of the stellar bump. This feature becomes less pronounced at higher luminosities. The SEDs also display a prominent 5 μm dip at low luminosities which becomes less clear at high luminosities. The 7.7 μm PAH emission feature is also evident at L_IR < 10¹¹ L_☉ near 8 μm but becomes less evident in the higher luminosity bins as rest frame 7.7 μm is no longer probed. However, in the highest luminosity bins, 24 μm approaches rest-frame 7.7 μm and this enhancement is still not observed, possibly due to the median SED being dominated by AGNs at those luminosities. Many of the SEDs show an increase in emission toward the UV, indicative of the big blue bump (Malkan & Sargent 1982; Sanders et al. 1989; Elvis et al. 1994) seen in many AGNs. The GALEX data points, particularly at high redshift where they probe further into the FUV, point to a broad maximum for many of these sources.

To provide a more quantitative measure of the spread in SED shapes, we compute three spectral indices (logarithmic rest-frame νL_ν ratios) probing three different wavelength regimes: UV/optical from 0.2 to 0.5 μm (α^0.5_0.2), NIR from 2 to 5 μm (α⁵₂), and MIR from 10 to 30 μm (α³⁰₁₀). These spectral indices are plotted against each other in Figures 22–24 binned by L_IR. All three of these plots show strong trends with L_IR. α⁵₂ increasing with L_IR as sources become dominated by power-law SEDs (see Section 5.2). This is also evident in Figure 24 where the sources with high α⁵₂ form a separate distinct branch at intermediate values of α³⁰₁₀. For galaxies with low values of α⁵₂, α³⁰₁₀ is low at low luminosities and steadily increases with L_IR. α^0.5_0.2 spans a wide range at all L_IR (a range of nearly 3 orders of magnitude) and has lower values on average at the most extreme luminosities.

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5.1.1. 160/70 μm Flux Ratios

In addition to the SED shapes described above, our large 70 μm sample and the substantial number of detections at 160 μm makes it particularly useful to investigate the 160/70 μm flux ratios as a crude measure of the characteristic dust temperature for the FIR peak emission. Figure 25 shows the observed FIR colors (νF_ν(160)/νF_ν(70)) as a function of redshift and L_IR for all 70 μm sources detected at 160 μm. For those not detected at 160 μm, the colored points on the plot represent the colors obtained from their stacked 160 μm fluxes. To put these values in context we also overplot the flux ratios for local IRAS 60 μm selected sources from the RBGS over a wide range of L_IR (10⁸–10^12.5 L_☉) with MIPS observations obtained as a part of GOALS or the Spitzer Infrared Nearby Galaxies Survey (SINGS; Kennicutt et al. 2003; Dale et al. 2007). A typical error bar for the sources detected at 160 μm is shown in the corner. The overall scatter of the data points remains the same even with a cut at larger S/N, indicating that the observed trends are likely real. The local sources span a large range in νF_ν(160)/νF_ν(70) from 0.2 to 5 and show a strong trend with L_IR. Also overplotted in gray are a set of values obtained from the Dale & Helou (2002) templates spanning an L_IR range of 10^8.3–10^13.5 from top to bottom as a function of redshift. These templates span most of the range occupied by the COSMOS 70 μm selected sources (the full set of libraries covers the entire range of colors observed at each redshift but we show just this one library for illustration). The sources not detected at 160 μm span the lower portion of the range occupied by the sources detected at 160 μm. This result is expected if the 160 μm detection preferentially selects colder sources than the rest of the sample.

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We obtained rest-frame νF_ν(160)/νF_ν(70) values by using the 70 and 160 μm fluxes determined from the best-fit IR template used to estimate L_IR. These values are plotted in Figure 26 as a function of redshift and luminosity. As a note of caution, since these values are dependent on the best-fit SED template this adds an extra source of uncertainty, particularly at the high-redshift end (where shorter rest-frame wavelengths are observed). We find that the COSMOS sources span the same range of colors (and thus dust temperatures) as the local sources but that there is an apparent excess of colder sources at higher luminosities, similar to the result of Symeonidis et al. (2009). However, our interpretation is that this excess is likely a result of the longer wavelength selection (rest-frame 80 μm at z ∼ 1 versus 60 μm locally) and the fact that the peak of emission is not well constrained at these redshifts and thus a wide range of templates can fit the data points. Future surveys at FIR and submillimeter wavelengths with Herschel and SCUBA2 will be able to disentangle the temperature-dependent selection effects and investigate the dust temperature distributions of high-redshift galaxies.

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Both X-ray and radio detections are traditional methods used to identify potential AGNs in high-redshift galaxies. The vast majority of the 70 μm selected galaxies that are detected in the X-ray (86%) have an X-ray luminosity greater than 10⁴² erg s⁻¹ and are therefore bona fide AGNs. The 22 lower luminosity sources are all at low redshifts (z < 0.35). Most of the X-ray detected AGNs have power-law SEDs (though not all), particularly at high L_IR. Many sources that are not detected as AGNs in the X-ray also have a power-law SED. These are possibly heavily obscured (Compton thick) AGNs that are opaque even to hard X-ray emission (Polletta et al. 2006).

Since α⁵₂ is a measure of the νF_ν slope between 2 and 5 μm, it is therefore a good way to select power-law galaxies. Anything above zero on the y-axis of Figure 22 or the x-axis of Figure 24 has the shape of a power law in the NIR, i.e., these objects neither have a strong 1.6 μm bump nor a dip at 5 μm. The α⁵₂>0 cutoff here corresponds to a F_ν spectral slope of 0.4 (similar to what is used as a power-law slope cutoff in the literature, e.g., Alonso-Herrero et al. 2006 and Donley et al. 2007). X-ray detected AGNs span almost the entire area of the spectral index plots rather than being clearly separated the way the power-law galaxies are. However, they do on average have lower α³⁰₁₀ as AGNs in the local universe do.

We select all sources with α⁵₂>0 to be power-law AGN candidates. A total of 166 (11.2%) objects satisfy this criterion. Forty five of these are detected in the X-ray (∼ 27%; a slightly lower fraction than found by Alonso-Herrero et al. 2006 and Donley et al. 2007 but consistent with the shallower COSMOS X-ray depths). A few differences between power-law galaxies detected in the X-ray and those not detected in the X-ray can be seen in their SEDs. Those sources detected in the X-ray tend to display the full range of properties in the UV where only one or two sources that are not X-ray detected appear bright in the UV. The prominence of the UV emission in the X-ray detected power-law galaxies could be evidence that these sources tend to be less obscured than the non-X-ray-detected sources and hence are transparent to UV (and X-ray) emission. The SEDs of the non-X-ray detected power-law galaxies also tend to have a steeper slope.

We use the infrared–radio correlation as another way to investigate the energy source. Using the limits defined in Yun et al. 2001; five times larger radio or IR flux than expected from the infrared–radio correlation) for radio-excess (q < 1.64) and infrared-excess (q>3.0) objects we find many objects that fall into these two categories. In total there are 27 radio-excess sources, six of which (22%) are also detected as X-ray AGNs (as shown in Figure 27). The fraction of objects that this population represents increases with L_IR from 4 (2%) at <10¹¹ L_☉, to 5 (2%) LIRGs and 16 (14%) ULIRGs. Radio-excess sources are believed to be potential AGN hosts where the extra radio emission seen comes from either a compact radio core or from associated radio jets or lobes (Sanders & Mirabel 1996).

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All 14 of the infrared-excess objects are ULIRGs or HyLIRGs and represent 11% of the sample at these luminosities. Six (43%) of them are X-ray detected AGNs. A total of 25 of the obscured AGN candidates (64%) described in Section 5.2.2 are detected in the radio and have 〈q〉 = 2.54 ± 0.63. Five of these (two X-ray AGNs) are infrared-excess objects. It is interesting to note that the IR excess objects contain a higher fraction of X-ray detected AGNs than the radio-excess objects. It is also interesting to note that many of the radio- and infrared-excess sources also have a power-law SED (see Figure 27).

5.2.1. IRAC Color Selected AGNs

Color selection in the MIR has also been shown to be an effective way to select potential AGNs (Stern et al. 2005; Lacy et al. 2004) as these colors can separate star-forming galaxies with a stellar bump at 1.6 μm from those with a power-law-like SED. Also, this method can potentially find dust-obscured AGNs since the MIR wavelengths are not as affected by extinction as the UV and optical. Following the criteria of Stern et al. (2005), we used the color–color IRAC plot (see Figure 28) to select potential AGNs and compare these sources with those found using four other methods. A total of 232 sources meet the Stern et al. criteria, representing ∼ 15% of the entire 70 μm sample. Of these 232, 82 (35%) are detected as AGNs in the X-ray. This is 62% of the total X-ray AGN population, which means the other 50 X-ray AGNs are not selected by this method. According to Stern et al., this method is good at selecting broad-line AGNs (selects ∼ 91%) and not as good at selecting narrow-line AGNs (∼ 40%) with an overall contamination rate of ∼ 20%. Donley et al. (2007) show that this region of the plot can be contaminated by starburst-dominated ULIRGs (like Arp 220) and normal star-forming galaxies. If we assume that 20% of the 232 objects are potentially contaminants, this leaves us with 186 actual AGNs, or about 1.5 times the number detected in the X-ray. Of the potentially obscured objects described in the following section (F(24 μm)/F(R)>10³), 36 out of the 60 match these color criteria as do 33 out of the 56 that also have R − K>4.5. Most of the power-law galaxies (62%) fall in a narrow region in the Stern et al. (2005) selection box but many (∼ 35%) fall outside this region. Very few of these objects fall in the lower left corner of the selection region, indicating that this is possibly the region that contributes most of the contamination in the selection (consistent with the results of Donley et al. 2008). Thirteen of the radio-excess sources are also selected by the Stern et al. criteria.

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5.2.2. Obscured AGN Candidates

Fiore et al. (2008, 2009) have shown that obscured AGNs tend to have high MIR-to-optical flux ratios and red R − K colors. The 24 μm to R-band flux ratio for each of the 70 μm sources in the sample is shown in Figure 29 as a function of R − K color with AGNs selected through four other methods overplotted. The dotted lines show the cuts of (R − K)_Vega>4.5 and F(24 μm)/F(R)>10³ defined in Fiore et al. (2008) for selecting candidate-obscured AGNs at high redshift. Fifty six of the galaxies in our sample make both of these cuts and 14 of them are detected in the X-rays. Three are detected only in the hard band and one only in the soft band. The remaining sources have a median hardness ratio of 0.2. The redshifts of these galaxies range from 0.7 to 2.5 with the median being z = 1.5, confirming the results of Fiore et al. (2008). Additionally, four galaxies match the MIR-to-optical flux ratio criteria but are bluer than the (R − K)_Vega>4.5 magnitude cutoff. Of these, one is detected as an AGN in the X-ray with a detection only in the hard band. These four sources have redshifts that range from z = 1.2 to 2.4 with a median redshift of 2.1—a similar distribution to the sources with red R − K colors. The 24 μm to R-band flux ratio correlates with the total infrared luminosity (as expected for obscured AGNs where the luminosity from the nuclear regions is greatly reduced by the obscuring material) and those above the cutoff of 10³ are predominantly ULIRGs and HyLIRGs. We consider all 61 of these galaxies to be obscured AGN candidates.

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It is also worth noting that this selection is similar to other IR/optical color selections in the literature, such as dust-obscured galaxies (Dey et al. 2008) and infrared bright, optically faint galaxies (Yan et al. 2004; Houck et al. 2005; Weedman et al. 2006). The dust-obscured galaxy color cut (R − [24]>14) is actually the same as the one used here and is expected to select high-redshift (z ∼ 2) extremely luminous galaxies with large column densities of dust.

5.2.3. AGN Fraction Among Luminous and Ultraluminous Infrared Galaxies

In the local universe, the AGN fraction of galaxies is known to increase very strongly with L_IR. Using spectroscopic diagnostics of a sample of 200 luminous infrared galaxies from IRAS, Veilleux et al. (1995) found that 62% of objects at the highest luminosities were AGNs. A similar study of the 1 Jy sample of ULIRGs (Veilleux et al. 1999) found that above L_IR>10^12.3, ∼ 50% of objects are AGNs. Tran et al. (2001) found a similar transition luminosity of L_IR>10^12.4 L_☉ between objects whose luminosities are dominated by starburst emission and those dominated by AGNs. Above this transition they found that "most ULIRGs appear AGN-like." With the large sample of objects over the wide range of luminosities probed by our 70 μm selected sample, we can address the question of whether this trend holds out to higher redshifts.

Table 5 shows the total number of galaxies in each L_IR bin along with the number of X-ray detected sources over the full area, in the area covered by Chandra, and in the area with the deepest Chandra coverage. The total fraction of X-ray detected AGNs increases with increasing L_IR, from 5% at L_IR < 10¹⁰ L_☉ to ∼ 15% for ULIRGs and ∼ 42% for HyLIRGs, however, these numbers are lower limits due to the uneven X-ray coverage across the field. The fraction increases when limited to the smaller areas with deeper X-ray coverage, though the small numbers make a statistical analysis difficult. This indicates that as many as 12% of LIRGs, 30% of ULIRGs, and 43% of HyLIRGs are AGNs with detectable X-ray emission. For the rest of the discussion here, we use the fractions obtained over the entire area.

Table 5. Fraction of 70 μm Sources Detected in the X-ray

log(LIR/L☉)	Median	Number	X-ray: Full Areaa	X-ray: Chandra Areab	X-ray: Chandra Deep Areac
	Redshift		No. (%)	No. (%)	No. (%)
< 9.0	0.02	3	0	0	0
9.0–10.0	0.10	58	3 (5.2)	1 (3.6)	0
10.0–10.5	0.17	140	8 (5.7)	4 (5.2)	2 (4.9)
10.5–11.0	0.27	281	18 (6.4)	14 (8.0)	9 (9.6)
11.0–11.5	0.47	376	35 (9.3)	27 (12.0)	15 (13.6)
11.5–12.0	0.77	311	28 (9.0)	27 (14.1)	14 (14.7)
12.0–12.5	1.05	219	29 (13.2)	19 (13.0)	14 (16.3)
12.5–13.0	1.47	84	20 (23.8)	13 (29.5)	9 (34.6)
>13.0	2.00	31	13 (41.9)	6 (46.2)	3 (42.9)
All LIR	0.50	1503	154 (10.2)	111 (12.3)	66 (14.0)

Notes. ^aPercentage of 70 μm sources detected in the X-ray by XMM-Newton and Chandra over the full ACS area of the COSMOS field. The XMM-Newton observations cover 100% of this area. ^bPercentage of 70 μm sources detected in the X-ray by XMM-Newton and Chandra in the area of the field observed by Chandra (55% of the ACS area) as illustrated in Figure 7. ^cPercentage of 70 μm sources detected in the X-ray by XMM-Newton and Chandra in the area of the field with deep Chandra coverage (30% of the ACS area).

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Table 6 shows the fraction of candidate AGNs found by each method (including X-ray detected, radio selected, IRAC color selected, power-law galaxies, and potentially obscured objects). If we add up all of the galaxies that fall into any of the possible AGN candidate categories (total column in Table 6), then we find that the AGN fraction ranges from 3% at L_IR < 10¹⁰ L_☉ to ∼ 70%–100% for ULIRGs and HyLIRGs (illustrated in Figure 30). There is likely to be some contamination in this estimate, particularly from the IRAC color selection method. If we leave out the IRAC selected objects, the AGN fraction goes from 2% for objects with L_IR < 10¹⁰ L_☉ to 10% for LIRGs, 51% for ULIRGs, and 97% for HyLIRGs. This result is in excellent agreement with the AGN fraction in the local universe, indicating that high-redshift ULIRGs are indeed similar to local sources in this respect.

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Table 6. AGN Fraction by Luminosity Bin

log$(\rm L_{\rm IR}/L_{\odot })$	Median	Number	X-ray AGNa	PLb	IRACc	Obscuredd	Radio Excesse	Totalf
	Redshift		No. (%)	No. (%)	No. (%)	Candidates	No. (%)	No. (%)
< 9	0.02	3	0	0	1 (33)	0	0	1 (33)
9.0–10.0	0.10	58	0	0	1 (1.7)	0	2 (3.4)	2 (3.4)
10.0–10.5	0.17	140	2 (1.4)	0	2 (1.4)	0	1 (0.7)	5 (3.6)
10.5–11.0	0.27	281	12 (4.3)	0	10 (3.6)	0	1 (0.4)	18 (6.4)
11.0–11.5	0.47	376	28 (7.4)	3 (0.8)	19 (5.1)	1 (0.3)	3 (0.8)	40 (10.6)
11.5–12.0	0.77	311	28 (9.0)	8 (2.6)	40 (12.9)	9 (2.9)	2 (0.6)	61 (19.6)
12.0–12.5	1.05	219	29 (13.2)	73 (33.3)	82 (37.4)	22 (10.0)	11 (5.0)	123 (56.2)
12.5–13.0	1.47	84	20 (23.8)	52 (61.9)	56 (66.7)	18 (21.4)	5 (6.0)	73 (86.9)
>13.0	2.00	31	13 (41.9)	30 (96.8)	21 (67.7)	11 (35.5)	2 (6.5)	31 (100.0)
All LIR	0.50	1503	132 (8.8)	166 (11.0)	232 (15.4)	61 (4.1))	27 (1.8)	354 (23.6)

Notes. ^aNumber and percentage of objects that are detected as AGN in the X-ray (see Section 5.2 for details). ^bNumber and percentage of objects that have power-law SEDs as defined in Section 5.2. ^cNumber and percentage of objects whose colors match the AGN candidate criteria of Stern et al. (2005). ^dNumber and percentage of objects whose infrared-to-optical flux ratios (F(24 μm)/F(R)>10³) match the Fiore et al. (2008) criteria of potentially obscured AGN. ^eNumber and percentage of objects with a radio excess (five times more radio flux than expected from the radio–IR correlation). ^fTotal number and percentage of objects that fall into any of the AGN candidate categories.

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The redshift and L_IR distribution for the AGN candidates found using each method is shown in Figure 31. Those objects that are also selected in the X-ray are shown by the filled histogram. It is interesting to note that while the X-ray selection finds objects at a wide range in redshifts and L_IR, each of the other methods has a narrower range and typically identifies objects at higher luminosities. The IRAC color selection finds two peaks in the redshift distribution, one at z ∼ 0.35 and the other at z ∼ 1.15. For the radio, IRAC, and power-law selections the X-ray seems to detect objects over the full range of redshifts and L_IR. The majority of the power-law objects are ULIRGs or HyLIRGs with only a few (∼10) with LIRG luminosities.

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