BALANCING THE ENERGY BUDGET BETWEEN STAR FORMATION AND ACTIVE GALACTIC NUCLEI IN HIGH-REDSHIFT INFRARED LUMINOUS GALAXIES

Spitzer IRS observations were taken as part of Spitzer program GO-20456 (P.I.: R.-R. Chary) in 2006 April/May. These low-resolution (R = λ/Δλ ∼ 100) spectroscopic observations were made using the spectral staring mode, which observed each target at two nod positions (per cycle) within the slit. In Table 2, we provide the ramp times and the total number of cycles used per low-resolution module. We note that a study focusing on the SMGs included in this sample can be found in Pope et al. (2008a) where complete details on the observation strategy and data reduction steps are also presented. The actual spectra, shifted into the rest frame, are shown in Figure 1 along with associated errors. The expected positions of the 3.3, 6.2, 7.7, 8.6 and 11.3 μm PAH features, along with the 9.7 μm silicate absorption feature, are indicated with vertical lines.

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For cases where PAH features in the IRS spectra are clearly identified, redshifts were measured directly as described in Pope et al. (2008a). The redshifts for the remaining galaxies were taken from existing optical spectroscopy (Table 1). We note that there were some discrepancies in the IRS and optical spectroscopic redshifts (i.e., GN-IRS 5,9,15, and 16) in which case the IRS-derived redshifts were used. GN-IRS 5 and 9 are both SMGs for which the discrepancies between their IRS and optical redshifts are discussed in Appendix B of Pope et al. (2008a). Pope et al. (2006) report that the optical (z = 0.884) redshift associated with GN-IRS 16, also an SMG, is not the true counterpart. The discrepancy for GN-IRS 15 is thought to arise from a superposition of sources. The optical morphology of this source is quite complex, having several components and a range of colors. Thus, we strongly suspect that we are seeing a superposition of a mid-infrared bright galaxy located at z = 2.20 and a foreground galaxy at z = 1.362.

The final redshift range among the sample spans 0.6 ≲ z ≲ 2.6 with a median of 1.88. A total of 15 galaxies have a redshift between 1.4 ≲ z ≲ 2.6, which is almost exactly the nominal redshift range for the BzK color selection where a comparison with the Daddi et al. (2007b) results are appropriate. In addition, seven of the galaxies have redshifts between 0.6 ≲ z ≲ 1.2 and are intended to be representative of the LIRG population.

Infrared imaging of the GOODS-N field was obtained at 16, 24, and 70 μm using the Spitzer Space Telescope. The 24 μm observations of GOODS-N were taken as part of the GOODS legacy program (P.I.: Dickinson) and reach an rms of ∼5 μJy (see Chary 2007). The spectroscopic sample presented here spans the range 220–1220 μJy.

IRS peak-up observations at 16 μm (Teplitz et al. 2005) were made covering an area slightly less extended than the GOODS-N 24 μm map. Only one of the sample galaxies, GN-IRS 1, lies outside the areal coverage of the 16 μm map. These 16 μm data have an rms of ∼6 μJy and only sources with a S/N greater than 5 were considered as a detection. Of the 21 sources in the 16 μm image field of view, two were not detected and their flux densities were set to the upper limit value of 30 μJy. The 16 μm flux densities among the detected sources span a factor of ∼25, ranging from ∼40 to 1050 μJy with a median value of ∼280 μJy.

MIPS 70 μm observations were carried out as part of program GO-3325 (P.I.: Frayer) and the FIDEL project (P.I.: Dickinson). The full field extends beyond the 24 μm coverage and data processing details can be found in Frayer et al. (2006). The typical point-source noise of the 70 μm data is ∼0.55 mJy (Frayer et al. 2006), ∼1.6 times larger than the confusion noise level of σ_c = 0.35 ± 0.15 mJy estimated by Frayer et al. (2009). Sources having a flux density >2 mJy and a S/N >6 were considered detections, leading to a total of nine sources; all other sources were assigned an upper limit of 3 mJy since this value corresponds to a differential completeness of ∼80% (Magnelli et al. 2009). The median 70 μm flux density among the detected sources is ∼5.5 mJy and ranges between ∼2.2 and 14.2 mJy, spanning a factor of roughly 6. The photometric uncertainty including calibration uncertainties and confusion is ∼10% at 16 and 24 μm and ∼20% at 70 μm.

X-ray imaging of GOODS-N was obtained with the Chandra X-ray Observatory for a 2 Ms exposure (Alexander et al. 2003). The full band (0.5–8.0 keV) and hard band (2.0–8.0 keV) on-axis sensitivities are ∼7.1 × 10⁻¹⁷ and 1.4 × 10⁻¹⁶ erg cm^-2 s⁻¹, respectively. Of the 22 sample galaxies, 12 were matched with an X-ray counterpart reported by Alexander et al. (2003). For the remaining 10 sources, upper limits were measured assuming Γ = 1.4.

Among the 12 X-ray detected sources we find that the 0.5–8.0 keV flux spans more than 2 orders of magnitude, ranging from 9 to 1120×10⁻¹⁷ erg cm^-2 s⁻¹, with a median flux of 56 × 10⁻¹⁷ erg cm^-2 s⁻¹ (Table 3). Eight sources have secure detections in the hard band (2.0–8.0 keV) while only upper limits could be measured for the remaining 14 sources. Of those sources detected, the range in the 2.0–8.0 keV flux spans between 25 and 1050×10⁻¹⁷ erg cm^-2 s⁻¹ (i.e., a factor of ∼40) with a median flux of ∼100 × 10⁻¹⁷ erg cm^-2 s⁻¹.

The GOODS-N field has been imaged extensively in four bands, B₄₃₅, V₆₀₆, i₇₇₅, and z₈₅₀ using the Advanced Camera for Surveys (ACS) on the Hubble Space Telescope (Giavalisco et al. 2004). Additional ground-based imaging of GOODS-N in the U band was obtained using the prime-focus MOSAIC camera on the KPNO Mayall 4 m telescope (Giavalisco et al. 2004; Capak et al. 2004). The 3σ upper limits of the UBViz photometry are 0.027, 0.048, 0.048, 0.091, and 0.131 μJy, respectively.

The GOODS-N field was observed with the Very Large Array (VLA) for a total of 165 hr using all four configurations (G. Morrison et al. 2009, in preparation). Given that the VLA is a centrally condensed array, the observing time per configuration was scaled as follows, A-array (1), B-array (1/4), C-array (1/16), and D-array (1/64) (Owen & Morrison 2008). This integration time scaling provides the best sensitivity for larger sources. The final radio map has a local rms at the phase center of ∼4 μJy. All sources in the IRS spectroscopic sample were matched with a S/N >4 radio source to a radius of 1'' except for GN-IRS 13, which had a S/N ∼ 3.3. The 20 cm flux densities span a factor of ∼9 (i.e., ∼21–202 μJy) with a median value of ∼98 μJy.

The GOODS-N field was imaged at 850 μm by a number of programs using the Submillimeter Common-User Bolometer Array (SCUBA) and the data were combined into the SCUBA "supermap" (Borys et al. 2003; Pope et al. 2005). The eight SMGs targeted for IRS spectroscopy were selected from the "supermap" sources with robust identifications (Pope et al. 2006) in addition to three SCUBA photometry sources from Chapman et al. (2005). Only two of the 11 SMGs are detected at 70 μm (Huynh et al. 2007). The 850 μm flux densities span a range between 2 and 9 mJy with a median flux density 5.2 mJy. For the remaining nondetected IRS targets, 3σ upper limits were calculated from the 850 μm SCUBA supermap. The only exception is GN-IRS 20 which lies outside the areal coverage of the SCUBA maps.

Infrared luminosities are extrapolated by fitting the mid-infrared spectra and photometric data to the SED templates of Chary & Elbaz (2001), and then integrating between 8 and 1000 μm. We choose to fit to the templates of Chary & Elbaz (2001) since they have been found to exhibit 24/70 μm flux density ratios which are more representative of the average actually measured for galaxies at z ∼ 1 than either the Dale & Helou (2002) or Lagache et al. (2003) templates (Magnelli et al. 2009). The best-fit SEDs are determined by a χ² minimization procedure in which the SED templates are allowed to scale such that they are being fitted for luminosity and temperature separately. Consequently, the amplitude and shape of the SEDs scale independently to best match the observations. Weights are derived using the uncertainties of the input photometry (i.e., the S/N of each input photometric band). When fitting the mid-infrared spectra, having N individual measurements for each wavelength in the spectra, the individual flux density is weighted by its S/N and an additional factor of 1/N so as to not give too much weight to the mid-infrared portion of the spectrum in the fitting. The normalization constant is then determined by a weighted sum of observed-to-template flux density ratios for all input data used in the fitting. Errors in the fits are determined by a standard Monte Carlo approach using the photometric uncertainties of the input flux densities.

Since we are interested to see to what extent the mid-infrared excesses reported by Daddi et al. (2007a, 2007b) can be solely attributed to improper SED fitting rather than the presence of an embedded AGN, we compute IR luminosities in a number of ways. First, like Daddi et al. (2007a), we perform the SED fitting using the 24 μm flux density alone; Chary & Elbaz (2001) and Dale et al. (2001) SED templates are fit independently, and their integrated 8–1000 μm luminosities are then averaged. The associated IR luminosity is designated as L²⁴_IR. The difference between the resultant L²⁴_IR from the two sets of SED templates is characterized as a systematic error. We emphasize here that IR luminosities derived in this manner assume that the mid-infrared to total-infrared correlations imprinted in local SED templates are valid at all redshifts.

Next, we use all available spectroscopic and photometric data in the SED fitting: IRS spectra, 16, 24, 70, and 850 μm flux densities where possible. IR luminosities for four out of the 22 sources that are neither detected at 70 or 850 μm (i.e., GN-IRS 12, 17, 19, and 20) are estimated by averaging the IR luminosities from the best-fit Chary & Elbaz (2001) and Dale et al. (2001) SEDs. Due to the nondetection of the four sources at wavelengths close to the peak of the FIR emission, these IR luminosities are considered to be upper limits. In the cases where only upper limit values are available for the photometric data, they are not incorporated into the χ² minimization but are used to reject fits which have flux densities above the associated upper limit. The IR luminosities derived from these fits are labeled as L^all_IR and are assumed to be the best-fit estimate of the true IR luminosity for each source. In addition, we also calculate IR luminosities by fitting the SED templates to all available photometry (i.e., including the 850 μm data where possible) to assess how well the PAH features can be characterized by fitting photometric data alone. These values are labeled as L^phot_IR. We give L²⁴_IR, L^all_IR, and L^phot_IR values for each galaxy in Table 4.

Since it is more likely that mid-infrared spectroscopy and submillimeter imaging will not be available for a large number of sources in many deep fields, we also calculate IR luminosities as above excluding these data. A comparison of these IR luminosities, identified as L^16,24,70_IR, to those calculated using all available photometry will help quantify the reliability of SED fitting using 16–70 μm photometry alone. The IR luminosities derived by this fitting method are also given in Table 4 and are considered to be upper limits for sources not detected at 70 μm.

To illustrate the differences in the best-fitting SEDs using these four methods, we plot the best-fitting Chary & Elbaz (2001) templates along with the spectroscopic and photometric data, for three different sources (GN-IRS 2, 4, and 15) in Figure 2. A comparison of each fitting method zoomed in on the mid-infrared range of 5–15 μm, where PAH emission may be present, is also shown for each galaxy in Figure 3 along with the actual spectra. While the SMGs in our sample have been presented in Pope et al. (2008a), we note that our SED fitting method differs from theirs. We do not include an extinction term and exclude the radio photometry which allows us to assess the FIR–radio correlation among the galaxies. Consequently, for the SMGs in our sample we find that the Pope et al. (2008a) luminosities range from being a factor of ∼0.8 to ∼4.6 times that of our derived IR luminosities, and are a factor of ∼1.2 times larger, on average.

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In the local universe, there exists a remarkably tight correlation between the FIR (42.5–122.5 μm) and predominantly nonthermal radio continuum emission from star-forming galaxies (de Jong et al. 1985; Helou et al. 1985; Condon et al. 1991; Yun et al. 2001). Following a similar quantitative treatment of the FIR–radio correlation (i.e., Helou et al. 1985), we use the total IR (8–1000 μm) luminosity, rather than the FIR fraction, to parameterize the IR–radio correlation such that,

$$\begin{equation} q_{\rm IR} \equiv \log \left(\frac{L_{\rm IR}}{3.75\times 10^{12}L_{\nu }(20\; {\rm cm})}\right). \end{equation} \tag{ 1 }$$

For a sample of 164 galaxies without signs of AGN activity, Bell (2003) reports a median q_IR value of 2.64 and a scatter of 0.26 dex.

We can estimate the rest-frame 1.4 GHz radio luminosities of our spectroscopic sample using

$$\begin{equation} L_{\nu }{(20\; {\rm cm})} = 4\pi D_{\rm L}^{2} S_{\nu }(20\; {\rm cm})(1+z)^{\alpha -1}, \end{equation} \tag{ 2 }$$

where D_L is the luminosity distance. This calculation includes a bandwidth compression term of (1 + z)⁻¹ and a K-correction of (1 + z)^α to rest frame 1.4 GHz. This assumes a synchrotron power law of the form S_ν ∝ ν^−α where the spectral index α∼0.8 (Condon 1992).

Thus, by setting 〈q_IR〉 ≈ 2.64, we can derive the infrared luminosities from the radio-specific luminosities with

$$\begin{equation} L_{\rm IR}^{\rm RC} = 1.64\times 10^{15}L_{\nu }(20\; {\rm cm}). \end{equation} \tag{ 3 }$$

We assign a factor of ∼2 uncertainty to these luminosities since this is the intrinsic scatter among and within (e.g., Murphy et al. 2006, 2008) star-forming systems in the local universe. The radio-based IR luminosities and q_IR ratios are given in Table 4 for each galaxy.

3.3.1. IR-based SFRs

Using the conversion given in Kennicutt (1998), calibrated for a Salpeter (1955) initial mass function (IMF) with mass limits between 0.1 and 100 M_☉, we can express our IR luminosities as SFRs such that

$$\begin{equation} \left(\frac{{\rm SFR_{IR}}}{M_{\odot }\; {\rm yr}^{-1}}\right) = 1.73 \times 10^{-10} \left(\frac{L_{\rm IR}}{L_{\odot }}\right). \end{equation} \tag{ 4 }$$

Since we have estimated IR luminosities in different manners, we identify each corresponding SFR accordingly; SFR²⁴_IR: SEDs fit by 24 μm flux densities alone; SFR^all_IR: SEDs fit using all available data (i.e., our best-fit estimates); SFR^RC_IR: using the IR–radio correlation to derive corresponding IR luminosities for which to estimate a SFR.

3.3.2. UV-Based SFRs

We also estimate SFRs using rest-frame UV-specific luminosities of each galaxy where possible. After putting the observed UBViz data into the rest-frame, 1500 Å flux densities were computed by linearly interpolating along the power-law fits between photometric data points landing in the wavelength range between 1250–2600 Å. Again taking the Kennicutt (1998) conversion, assuming the same Salpeter (1955) IMF (0.1 − 100M_☉), we can express the resultant UV-specific luminosities in terms of a SFR such that,

$$\begin{equation} \left(\frac{{\rm SFR_{UV}}}{M_{\odot } {\rm yr}^{-1}}\right) = 5.36\times 10^{5} \left(\frac{L_{\rm UV}}{L_{\odot } {\rm Hz^{-1}}}\right). \end{equation} \tag{ 5 }$$

For a total of 11 galaxies (i.e., half of the sample) there are less than two photometric points in the rest-frame wavelength range of 1250–2600 Å. In these cases the flux upper limits were used to set a corresponding upper limit on each source's rest-frame UV luminosity.

To estimate the amount of extinction at 1500 Å we use the method described by Meurer et al. (1999) which relates the amount of extinction to the slope of the UV continuum between 1250 and 2600 Å, defined as β. Since the redshifts of the sample galaxies are all less than z ∼ 2.6, any correction to the UV slope due to absorption by the intergalactic medium is negligible.

While the relation of Meurer et al. (1999) is calibrated for A₁₆₀₀, we use modeled extinction curves (i.e., Weingartner & Draine 2001; Draine 2003), to translate this into an extinction at 1500 Å such that A₁₅₀₀ = 1.05A₁₆₀₀ leading to a final relation of

$$\begin{equation} A_{1500} = 4.65 + 2.09 \beta. \end{equation} \tag{ 6 }$$

We designate SFRs estimated using the extinction-corrected UV luminosities as SFR^corr_UV. Of the 11 sources having less than two photometric detections in the rest-frame wavelength range of 1250–2600 Å, two (GN IRS 16 and 20) have at least one detection and one reliable upper limit in this wavelength range allowing us to estimate a reasonable lower limit for β. For the remaining nine galaxies, a UV extinction correction was not applied (i.e., β ≈ −2.2). The observed and extinction-corrected UV-specific luminosities are given, along with the values of β, in Table 5.

Table 5. X-ray and UV Luminosities

ID (1)	log L0.5-8.0 keV (L☉) (2)	log L2.0-8.0 keV (L☉) (3)	log LUV (L☉ Hz−1) (4)	log LcorrUV (L☉ Hz−1) (5)	β
1	10.16	10.13	<−5.50	<−5.50	⋅⋅⋅
2	<8.91	<9.14	−4.74	−3.23	−0.47
3	8.14	<8.03	<−4.94	<−4.94	⋅⋅⋅
4	9.59	9.49	−5.11	−3.09	0.14
5	<8.75	<8.94	<−5.43	<−5.43	⋅⋅⋅
6	<8.85	<9.07	<−5.32	<−5.32	⋅⋅⋅
7	<8.64	<8.84	<−5.44	<−5.44	⋅⋅⋅
8	7.96	7.86	<−4.78	<−4.78	⋅⋅⋅
9	8.67	8.72	−4.85	−3.46	−0.61
10	9.79	9.48	<−4.41	<−4.41	⋅⋅⋅
11	8.69	<8.47	−4.83	−2.96	−0.03
12	<8.81	<9.04	−4.98	−3.76	−0.82
13	<7.85	<8.05	−5.20	−3.18	0.14
14	8.12	<8.16	−6.18	−3.69	0.71
15	<8.98	<9.24	−5.18	−4.04	−0.91
16	8.43	<8.56	<−5.59	<−4.04	<−0.42
17	<8.80	<9.05	−4.23	−3.96	−1.95
18	8.97	8.94	−4.57	−2.53	0.18
19	8.75	8.73	<−5.53	<−5.53	⋅⋅⋅
20	<9.24	<9.49	<−5.50	<−2.69	<1.09
21	9.23	9.20	−5.55	−2.48	1.40
22	<7.87	<8.07	<−5.60	<−5.60	⋅⋅⋅

Notes. Column (1): source ID. Column (2): K-corrected full band (0.5–8.0 keV) luminosities. Column (3): K-corrected hard band (2.0–8.0 keV) luminosities. Column (4): linearly interpolated 1500 Å specific luminosities. Column(5): extinction-corrected 1500 Å specific luminosities. Column(6): slope of the UV continuum between 1250 and 2600 Å which is used to estimate extinction following Meurer et al. (1999).

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For the 11 sources which do not have a sufficient number of photometric points in the 1250–2600 Å range to properly measure β, the SFR is considered to be a lower limit given that the extinction correction could not be measured and is likely significant for these sources; i.e., due to the fact that the sample is 24 μm selected, the optical nondetections are probably not from the source being intrinsically dim, but rather from the extinction factor being extremely large.

To compare IR and X-ray energetics of these systems, the rest-frame 0.5–8.0 keV and 2.0–8.0 X-ray luminosities are calculated as

$$\begin{equation} L_{\rm X} = 4\pi D_{\rm L}^{2} f_{\rm X}(1+z)^{\Gamma -2}, \end{equation} \tag{ 7 }$$

where D_L is the luminosity distance, f_X is the X-ray flux in a particular band, and Γ is the observed or assumed photon index (Table 3). The 0.5–8.0 and 2.0–8.0 keV luminosities are given in Table 5. We also note here that three of the 12 X-ray sources (i.e., 25%) are optically faint, having only IRS-derived redshifts between 1.7 ≲ z ≲ 1.9. This is precisely the redshift range where optically faint X-ray sources are predicted to lie (Alexander et al. 2001; Mainieri et al. 2005).

Using the IRS data, we follow the procedure described in detail by Pope et al. (2008a) to quantify the AGN contribution to the total IR energy budget. This is done by first decomposing the IRS spectra into two components; one associated with star formation (PAH template) and the other associated with the hot dust continuum emission arising from an embedded AGN. The star-forming component is fit using the starburst composite template of Brandl et al. (2006) while the AGN component is characterized by a power law with both normalization and slope as free parameters. The effect of extinction is considered independently for the PAH and continuum components using a modeled extinction curve (i.e., Weingartner & Draine 2001; Draine 2003). Upon finding the best fit between the spectra and combination of PAH template plus continuum component, the fraction of mid-infrared emission arising from the continuum component is taken to be the AGN contribution. For those galaxies whose spectra did not have high enough S/N or lacked PAH features to allow for a proper decomposition, an upper limit to the AGN strength was obtained by fitting a power law to the continuum of the spectra and integrating below it. The mid-infrared AGN fractions are given for each galaxy in Table 4.

Next, to characterize the fraction of the IR luminosity arising from an AGN, we scale the SED template of Mrk 231 (a nearby ULIRG whose IR luminosity is known to be dominated by an AGN; Armus et al. 2007) to the AGN fraction of the rest-frame ∼5–12 μm luminosity (i.e., the luminosity in the rest-frame wavelength range having IRS coverage per source) and integrate the SED from 8 to 1000 μm. This is illustrated in Figure 4 where we show the best-fit Chary & Elbaz (2001) SED for GN-IRS 7 along with the observed IRS spectra, the scaled SED of Mrk 231 (i.e., the AGN contribution), and the difference between the best-fit SED and the scaled SED of Mrk 231 (i.e., the contribution by star formation alone). The observed mid-infrared spectra clearly match the shape of the best-fit SED.

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The values of L^AGN_IR are given for each galaxy in Table 4. By subtracting these values from the IR luminosities obtained through our SED fitting, we can estimate the amount of IR luminosity arising from star formation alone such that

$$\begin{equation} \left(\frac{\rm SFR_{\rm IR}^{\rm noAGN}}{M_{\odot } {\rm yr}^{-1}}\right) = 1.73\times 10^{-10}\left(\frac{L_{\rm IR}^{\rm all,noAGN}}{L_{\odot }}\right), \end{equation} \tag{ 8 }$$

where L^noAGN_IR = L^all_IR − L^AGN_IR. Similarly, we can also calculate an AGN-subtracted SFR from the 24 μm data by SED fitting the 24 μm photometry after first subtracting off AGN fractions extrapolated from those given in Table 4; the corresponding IR luminosities and SFRs are denoted as L^24,noAGN_IR and SFR^24,noAGN_IR, respectively. We have assumed that the underlying mid-infrared continuum arises purely from an AGN, however, hot dust associated with vigorous star formation may also contribute to the mid-infrared continuum emission as well. Therefore, the mid-infrared AGN fractions, and associated estimates for the IR luminosities of the AGN, should all be considered conservative upper limits.

In Figure 2, we plot the best-fitting Chary & Elbaz (2001) SEDs for three sources (GN-IRS 2, 4, and 15) to illustrate the three fitting methods. While the addition of the IRS spectra and submillimeter data to the available Spitzer 16, 24, and 70 μm photometry does not seem to significantly alter the choice of the fit, the fits using 24 μm flux densities alone are highly discrepant. Zooming in on the 5–15 μm mid-infrared regions of the four different Chary & Elbaz (2001) fits for each galaxy in Figure 3, one easily sees that by using 24 μm flux densities alone the equivalent widths of the aromatic features observed in the IRS spectra are underestimated by the Chary & Elbaz (2001) templates, resulting in highly discrepant estimates of IR luminosity.

The range of IR luminosities derived by fitting the 24 μm photometry alone span a range between 4.3 × 10¹¹ and 4.2 × 10¹³L_☉ (i.e., nearly 2 orders of magnitude) with a median of 7.5 × 10¹²L_☉. Looking at the best-fit estimates for the IR luminosities among the entire sample, we find that they range between 3.2 × 10¹¹ and 1.1 × 10¹³L_☉ (i.e., a factor of ∼35) having a median of 2.2 × 10¹²L_☉. The 24-μm-derived IR luminosity is a factor of ∼4 larger than that for the best-fit estimates, on average.

Using our best-fit IR luminosities, we also note that 16 out of the 22 sample galaxies are classified as ULIRGs while the remaining six are LIRGs. Looking at the differences between the 24 μm to our best-fit IR luminosities, the discrepancy is found to be much larger among the ULIRGs than for the LIRGs. The 24-μm-derived IR luminosities are larger than the best-fit IR luminosities by a factor of ∼5, on average, for the ULIRGs while being only ∼1.2 times larger, on average, for the LIRGs.

To quantify how well the mid-infrared spectral features are matched by the various SED fitting methods, we compare the ratio from the peak of the 7.7 μm PAH feature to the median flux density in the 9–11 μm trough region (i.e., 9.7 μm silicate absorption feature). Given that the wavelength coverage varies for each object, making it difficult to properly estimate the true continuum levels (e.g., Pope et al. 2008a), we choose to compare this ratio rather than actual PAH equivalent widths. Furthermore, choosing these features enables us to calculate this ratio for nearly the entire sample; we do not have spectroscopic coverage over the rest-frame 9–11 μm region for GN-IRS 16.

When fitting the SEDs using the 24 μm photometry alone the peak-to-trough ratios are ∼0.24 ± 0.15 times the peak-to-trough ratios measured for the observed spectra (i.e., a factor of ∼4 times smaller), on average. By instead fitting the SEDs using all of the photometric data, the peak-to-trough ratios are now ∼0.75 ± 0.84 times the ratios of the actual data (i.e., ∼35% smaller), on average. Similarly, when the mid-infrared spectra are included in the fitting with all of the photometric data, the peak-to-trough ratios are found to be ∼0.75 ± 0.58 times the ratios for the observed spectra, on average, suggesting that fitting with mid-infrared and FIR photometry alone does a reasonable job choosing templates with the correct mid-infrared spectral features. Consequently, it appears that the improper estimates of IR luminosities from fitting with 24 μm photometry alone are most likely due to the fact that local high-luminosity galaxies do not exhibit large PAH equivalent widths relative to galaxies of similar luminosity at higher redshifts. This result is consistent with that of Desai et al. (2007) who showed that local ULIRGs typically have PAH equivalent widths that are significantly smaller than those measured for ULIRGs at high redshift. Since the strongest PAH features, lying in between 6 and 12 μm, begin to redshift into the observed 24 μm band at z ≳ 1.4, we expect the discrepancies between the fitting methods and estimates for the IR luminosity of galaxies, to increase with increasing redshift. For the sample galaxies in the redshift range between 1.4 ≲ z ≲ 2.6, we find that the peak-to-trough ratios of the SEDs chosen by fitting the 24 μm data alone and using all of the available photometric data are an average factor of ∼0.19 ± 0.11 (i.e., ∼5 times smaller) and ∼0.88 ± 0.94 (i.e., ∼14% smaller) times those measured for the data, respectively.

We also note that by remeasuring the peak-to-trough ratios of the best-fit SEDs after subtracting the fitted AGN component, the median ratios are ∼1.11 ± 0.30 and ∼1.49 ± 0.42 for the entire sample and galaxies at z ≳ 1.4, respectively. This result demonstrates that the AGN/star-formation decomposition is fairly reliable and that, as previously stated, we likely overestimate the true AGN contribution by assuming that all of the mid-infrared continuum emission arises from hot dust associated with the AGN. These statistics exclude three galaxies (GN-IRS 1, 13, 17) for which the AGN component oversubtracts the continuum of the best-fit SEDs resulting in a negative peak-to-trough ratio. Including them in the above calculations does not affect the median values, but increases the dispersion significantly.

In Figure 5, we plot L²⁴_IR, L^all_IR, and L^RC_IR versus redshift for the 70 μm detected galaxies. Although the different IR luminosity estimates largely agree for the z < 1.4 sources, the three sources at z > 1.4 have IR luminosities derived from fitting the 24 μm flux densities alone that are larger by an average factor of ∼4 than what is found when fitting the SEDs with all available data.

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Since the 70 μm detections could potentially be sampling objects with the warmest FIR dust color temperatures, we also compare the different IR luminosity estimates of all sources in our sample in Figure 6. We find a significant change in this ratio with redshift. While the objects near z ∼ 1 all have ratios around unity, galaxies in a redshift range between 1.4 ≲ z ≲ 2.6 exhibit ratios of ∼4.6 ± 1.4, on average. We also note that galaxies lying at redshifts below and above z ∼ 1.4 typically have L²⁴_IR values below and above ∼3 × 10¹²L_☉, respectively. This result is consistent with that of Papovich et al. (2007) whom report that IR luminosities derived from stacking 70 and 160 μm data for a sample of 24 μm bright (i.e., f_ν(24 μm)>250 μJy) galaxies lying in a redshift range between 1.5 ≲ z ≲ 2.5, are a factor of 2–10 lower than those inferred from using only 24 μm flux densities. A similar comparison with the radio continuum based luminosities over the same redshift range shows that the 24 μm based IR luminosities are higher by a factor of ∼1.5 ± 1.9, on average.

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It is unclear if this discrepancy is due to the flux limit of our sample which implies that we are sampling sources with high luminosities at z ∼ 2 for which no local analogs exist. This would suggest that the extrapolation of the local SEDs to these high-redshift sources is invalid. A second possibility is that z ∼ 2 sources have sufficiently low metallicities that the infrared SEDs deviate from those of z ∼ 1 or local galaxies. A third possibility that has been suggested is that warm dust continuum emission from an obscured AGN in these sources is biasing the 24 μm flux upward and resulting in overestimates of the SFR (Daddi et al. 2007a).

The SFRs inferred from the 24-μm-derived IR luminosities overestimate those inferred from our best-fit IR luminosities, corrected for any contributions from AGN (SFR^noAGN_IR; see Section 3.5) by a factor of ∼6, on average, among the entire sample. To see whether this overestimation by fitting the 24 μm photometry is the result of excess mid-infrared emission arising from hot-dust emission associated with the presence of an AGN, we refit the 24 μm flux densities to the SED templates after correcting them by the corresponding mid-infrared AGN fraction. We find that SFRs calculated using IR luminosities derived by SED fitting 24 μm flux densities after subtracting the mid-infrared AGN contributions are ∼2.5 ± 2.3 times larger, on average, than the values of SFR^noAGN_IR among the entire sample. There also appears to be a redshift dependence such that the SFRs calculated using IR luminosities derived by SED fitting 24 μm flux densities after subtracting the mid-infrared AGN contributions are ∼1.0 ± 0.4 and ∼3.3 ± 2.2 times larger, on average, than the values of SFR^noAGN_IR for galaxies at redshifts below and above z ∼ 1.4, respectively.

We believe that IR luminosities are overestimated by fitting local SEDs to 24 μm photometry alone because of differences in PAH equivalent widths among galaxies of similar luminosity at different redshifts. This conclusion is supported by our findings in Section 4.2 where we compared the observed PAH strengths to those from the different SED fits. Alternatively, this result could also imply that using Mrk 231 to approximate the AGN component is inappropriate. However, given that we believe our mid-infrared AGN fractions and IR luminosity estimates for the AGN to be conservative upper limits, this is unlikely to be a dominant effect.

In order to assess the reliability of the different SFR indicators, we make a cross comparison between the UV, radio, and IR SFR estimates. We examine how these estimates compare for galaxies located at redshifts below and above z ∼ 1.4.

4.5.1. z < 1.4 Galaxies

4.5.2. z > 1.4 Galaxies

Daddi et al. (2007a) have identified discrepancies between the UV, radio, and IR-derived SFR estimates in z ∼ 2 galaxies selected using the BzK selection technique. We select the 15 galaxies in our sample with 1.4 ≲ z ≲ 2.6 which matches the redshift range spanned by the BzK selection. Figure 7 shows the ratio of SFRs inferred from the 24 μm data (plus the uncorrected UV-based SFR) to those estimated from extinction-corrected UV measurements for these 15 galaxies. Galaxies which are not detected in the optical, such that their UV slopes could not be estimated, are plotted as upper limits although they are difficult to interpret. Their best-fit IR-derived SFRs are nearly 2 orders of magnitude larger than the uncorrected UV-based SFRs, on average. However, their extinction-corrected UV SFRs could potentially be very large, reducing the plotted ratio.

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Daddi et al. (2007a) defined sources for which

$$\begin{equation} \log \left({\rm \frac{SFR_{IR} + SFR_{UV}}{SFR_{UV}^{corr}}}\right) > 0.5 \end{equation} \tag{ 9 }$$

to be "mid-infrared excess" sources. While the numerator adds the contribution of energetic emission from young massive stars that is not absorbed and reemitted by dust grains to obtain a total SFR, the extincted UV SFR is often negligible compared to the IR-based SFR term.

Not surprisingly, we find that all seven galaxies for which we do not have UV slope measurements, and thus cannot make UV extinction corrections, all meet the mid-infrared excess criterion. For these sources to fall below the mid-infrared excess criterion would require an average extinction of A_V ≳ 1.7 mag; and to fall to a ratio near unity requires an average extinction of A_V ≳ 2.2 mag. As for the remaining eight sources, we find that six are identified as having mid-infrared excesses: GN-IRS 2, 4, 9, 12, 15, and 17.

The two sources for which we do not find any mid-infrared excess, due to their steep UV corrections, are GN-IRS 18 and 21. Both GN-IRS 18 and 21 are X-ray detected, however, GN-IRS 18 is also an SMG. Morphologically, GN-IRS 18 appears extended possibly due to a major merger event. The extinction estimated for GN-IRS 18 is A_V ≈ 1.92 mag, only 0.16 mag larger than the median extinction found for all sample galaxies for which the rest-frame UV slope could be measured. The extinction estimated for GN 21, however, is the largest among the entire sample at A_V ≈ 2.89 mag. While their optical extinctions differ significantly, these are the only two sources having extinction-corrected UV SFRs in excess of 1000 M_☉ yr⁻¹.

By plotting again the ratio of IR + UV to UV-corrected SFRs, this time instead using our best-fit IR luminosities, versus redshift in the middle panel of Figure 7, we find that two of the six previously identified mid-infrared excess galaxies (GN-IRS 4 and 9) are no longer mid-infrared excess sources. These two galaxies are also the only ones among the six to have hard X-ray detections. In fact, only two sources, GN-IRS 2 and 15, seem to remain definitive "mid-infrared excess" galaxies given that GN-IRS 12, which barely lies above the mid-infrared excess threshold, and GN-IRS 17 are not detected at either 70 or 850 μm implying that their associated best-fit IR luminosities are technically upper limits. If, on the other hand, we use the radio continuum based SFRs to construct the same plot, as shown in the bottom panel of Figure 7, we find that while points have shifted downward, only GN-IRS 4 is no longer considered a mid-infrared excess source leaving five of the original six mid-infrared excess galaxies above the threshold.

To summarize, we find that by using the best-fit IR luminosities we can definitively account for 2/6 mid-infrared excess sources (i.e., 1/3 of those found using 24 μm derived IR luminosities). This fraction is increased to 2/3 by assuming that we are still overestimating the IR luminosities of the two galaxies for which we only have upper limits at FIR wavelengths. The median ratio of best-fit IR to extinction-corrected UV SFRs for sources in the redshift range between 1.4 ≲ z ≲ 2.6 is ∼4. By instead using the radio continuum and FIR–radio correlation to derive IR luminosities, the median ratio between the radio derived-to-extinction-corrected UV SFRs is even larger at ∼7. We investigate in the discussion below whether the contribution from an obscured AGN is large enough to account for the discrepancy between the IR and UV SFR estimates among these sources.

As discussed in Section 4.5.2, we find that even after using the best-fit IR luminosities, L^all_IR, to derive SFRs, we still find 4/8 sources in the redshift range between 1.4 ≲ z ≲ 2.6 with measurable UV slopes to exhibit excesses in the infrared relative to what is measured by extinction-corrected UV data (middle panel of Figure 7). To see if the observed excess is in fact due to the presence of an obscured AGN, we estimate the fraction of AGN power contributing to the total IR luminosity using our mid-infrared spectroscopy as described in Section 3.5.

In the left panel of Figure 8 we plot the ratio of our best-fit IR derived SFRs, plus an unobscured UV component, to the extinction-corrected UV SFRs against the mid-infrared AGN fractions before and after subtracting the AGN contribution to the total IR luminosity. We find that 3/8 galaxies having redshifts between 1.4 ≲ z ≲ 2.6 and which continue to exhibit an excess of IR emission have mid-infrared AGN fractions that are larger than 60%. Using the Mrk 231 SED as outlined in Section 3.5, we can estimate the contribution of AGNs to the total IR luminosity.

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Looking at the entire sample (i.e., all 22 galaxies), we find that AGNs account for ∼30% of the total IR luminosity, on average, with a range of ∼10%–70% (Table 4). This is similar to the average AGN contribution of ∼30% we find among the hard band X-ray detected sources. Interestingly, we also find that the average contribution to the total IR luminosity by AGN is also ∼30% for both subsamples of SMGs and non-SMGs. This contribution by the AGN to the IR luminosity of SMGs is a factor of ∼2 times larger than that reported by Pope et al. (2008a) which we attribute to the differences in the IR luminosities arising from differences in the SED fitting methods; as previously stated, Pope et al. (2008a) included the radio photometry in their SED fitting leading to IR luminosities typically larger than those presented here.

In the right panel of Figure 8, we plot AGN luminosity versus the difference between the 24 μm and best-fit estimate IR luminosities. A clear trend of increasing AGN luminosity with increasing overestimation of the IR luminosity using 24 μm photometry alone is observed; or, in other words, AGN luminosity appears to scale with increasing mid-infrared luminosity. Performing an ordinary least-squares fit to the data, we find that

$$\begin{equation} \log \left(\frac{L_{\rm IR}^{\rm AGN}}{L_{\odot }}\right) = (0.50 \pm 0.04) \log \left(\frac{L_{\rm IR}^{24} - L_{\rm IR}^{\rm all}}{L_{\odot }}\right) + (5.61 \pm 0.52). \end{equation} \tag{ 10 }$$

While the differences between the 24 μm and best-fit IR luminosities are large for galaxies having large (i.e., ≳60%) mid-infrared AGN fractions, we find these quantities to be unrelated for galaxies having smaller mid-infrared AGN fractions. We also find that the AGN luminosity accounts for only 16% of the difference between the 24 μm derived and best-fit IR luminosities, on average. This indicates that the AGN contribution to the mid-infrared excesses, which would result in overestimates of IR-based SFRs, is close to negligible when compared to the improper bolometric correction applied when estimating total IR luminosities by fitting local SED templates with 24 μm data alone. As shown in Section 4.4, SFRs derived by subtracting the AGN fraction from the 24 μm photometry are larger than the AGN-corrected best-fit IR SFRs by a factor of ∼1 to ∼3.3, on average for redshifts below and above z ∼ 1.4, respectively. Furthermore, the AGN-corrected 24 μm SFRs are factors of ∼1 to ∼68 times larger than the corresponding UV-corrected SFRs for sample galaxies at redshifts above z ∼ 1.4. Therefore, the AGN is not the dominant source of the inferred "mid-infrared excesses" among these systems.

Since the FIR–radio correlation is thought to solely arise from the processes associated with massive star formation, we looked to see if the IR/radio ratios themselves are sensitive to the fractional AGN power by comparing the ratio of L^AGN_IR/L^all_IR with q_IR values. A trend was not found suggesting that q_IR is insensitive to the fractional IR output by the AGN. This result likely arises because the AGN contributes to the radio and infrared emission by different amounts.

5.1.1. The Persistence of "Mid-Infrared Excess" Sources

By subtracting off our estimate of the AGN contribution to the total IR luminosity, we determine whether this is enough to account for the remaining IR excesses for galaxies in Figure 7. We recreate the top and middle panels of Figure 7 in the top and bottom panels of Figure 9, respectively, by computing the 24-μm-derived and best-fit IR-based SFRs after subtracting off the estimated AGN contribution for the eight galaxies having optical detections which allowed for proper estimates of extinction-corrected UV SFRs; the decrease in IR SFRs is indicated by vertical lines.

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Among these sources we find that (L²⁴_IR − L^24,noAGN_IR)/L²⁴_IR and (L^all_IR − L^all,noAGN_IR)/L^all_IR are both ∼45%, on average. However, even by using the AGN-corrected 24 μm SFRs, none of the previously identified mid-infrared excess sources are removed. While the AGN fractions are similar in both cases, the AGN-subtracted 24 μm SFRs are still ∼6 times larger, on average, than the AGN-corrected SFRs using the best-fit IR luminosities. In the bottom panel of Figure 9 we find that by subtracting the AGN luminosities we are able to account for the observed IR excesses in only one more source; GN-IRS 12, which is plotted as an upper limit, is now no longer considered to have excess IR emission. Therefore, of the eight sources with optical detections such that we can estimate a UV extinction correction in the redshift range between 1.4 ≲ z ≲ 2.6, 6 of which would be classified as "mid-infrared excesses" using 24 μm-based IR SFRs, three (GN-IRS 2, 15, and 17) remain mid-infrared excess sources even after the subtraction of the AGN component.

Ultimately, we find that even after correcting for the presence of an AGN, the IR-based SFRs are a factor of ∼2.8 times larger, on average, than those derived from extinction-corrected UV measurements for 1.4 ≲ z ≲ 2.6 galaxies with secure estimates of their rest-frame UV slopes. Or, in other words, AGNs are only able to account for ∼35% of the excess IR emission measured, on average. Since we do not believe our IR luminosities are overestimated by such a large amount, given the small uncertainties associated with our SED fitting, we interpret this result to suggest that using the UV slope to derive an extinction correction is not appropriate for the entire sample; extinctions are underestimated thereby yielding underestimates for the UV-derived SFRs. This may not be too surprising given that there are catastrophic failures using the rest-frame UV slope to derive the extinction for galaxies having both low and high extinctions. If extinction within a galaxy is too high, this method will fail simply because the galaxy's ISM will become optically thick. In the case of low extinction the UV slope will no longer be as sensitive to the amount of extinction since variations arising from contributions by a galaxy's old stellar population will become important (Reddy et al. 2006).

5.1.2. AGN-Dominated Sources

5.1.3. Are "Mid-Infrared Excess" Sources DOGs?

We compare the results of our SED fitting to situations when only mid-infrared photometry (e.g., at 16 and/or 24 μm) along with additional measurements at 70 μm are available. Such a comparison is especially important for the FIDEL fields, because of their deep 70 μm imaging, as well as for upcoming dedicated Herschel programs such as GOODS-Herschel (GOODS-H; P.I.: D. Elbaz).

In the third panel of Figure 10 we plot the ratio of IR luminosities derived by fitting the 16, 24, and 70 μm photometry to L^all_IR as a function of redshift. The median ratio has a value of ∼1.02 ± 0.51. We find the ratio to be approximately constant with increasing redshift, with average values of ∼1.01 ± 0.06 and ∼1.20 ± 0.61 for redshifts below and above z ∼ 1.4, respectively, suggesting that the systematic variations introduced by the presence of strong PAH emission redshifting into the 24 μm band at z ≳ 1.4 is largely taken into account by having the additional 70 μm data point. We also see that the dispersion significantly increases with redshift. We therefore believe that using mid-infrared photometry with the addition of a 70 μm measurement provides fairly reliable estimates for the true IR luminosity compared to when fitting with the 24 μm data alone. We also note that it is the addition of the 70 μm data, and not the additional 16 μm photometry, which is responsible for the improved determination of IR luminosities.

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In the first (top) panel of Figure 10 we plot the ratio of IR luminosities derived by fitting the 16 and 24 μm photometry to those using all of the available data versus redshift. The median ratio of 16+24 μm derived to our best-fit IR luminosities is ∼1.17±1.65. As with the comparison made above, the median and dispersion in the ratio of IR luminosity estimates increases with redshift, going from ∼0.99 ± 0.19 to ∼1.29 ± 1.82 at redshifts below and larger than z ∼ 1.4. This is of course not surprising since fitting the 16 and 24 μm photometry for redshifts beyond z ∼ 1 is complicated by the presence of PAH and silicate absorption features being redshifted into both bands. Instead, taking the ratio of 24 + 70 μm derived to our best-fit IR luminosities, we find a median ratio of ∼1.07±0.45 which is illustrated in the second panel of Figure 10. Similarly, we find the median ratio to remain near unity for galaxies below and above z ∼ 1.4, however, the increase in the dispersion between these subsets is less significant being ∼1.04 ± 0.13 and ∼1.29 ± 0.53, respectively. Furthermore, we find that the addition of the 16 μm photometry to SED fitting the 24 and 70 μm data does not result in largely different IR luminosity estimates; the median ratio of IR luminosities from fitting the 16–70 μm data to those from fitting only the 24 and 70 μm data is ∼1.03 ± 0.29 and ranges from ∼1.03 ± 0.12 to ∼1.03 ± 0.34 for galaxies below and above z ∼ 1.4, respectively. Such a comparison is useful since most deep fields only have coverage at 24 and 70 μm. Consequently, the addition of the 16 μm photometry does not appear to improve the fitting significantly compared with the addition of the 70 μm data.

It is interesting to see how including the mid-infrared spectra affects the SED template fitting compared to when using only the available photometry. We plot the ratio of L^phot_IR/L^all_IR as a function of redshift in the bottom panel of Figure 10. We find that the ratio has a median that is approximately unity and a dispersion of ±0.22. While the median of the ratio remains near unity for redshifts below and above z ∼ 1.4, we again find that the dispersion increases with redshift, taking values of ∼0.06 and ∼0.26 in these redshift bins, respectively.

Furthermore, we find that using the 70 μm data alone to derive IR luminosities does not appear to be reliable as this method significantly underestimate the true IR luminosity. Among the 70 μm detected sources (only 2/9 which are SMGs), the best-fit IR luminosities are larger by an average factor of ∼1.9 ± 0.22 than the IR luminosities derived from the 70 μm data alone. Such a result is expected if the average galaxy at high redshift has an SED which is cooler than that of a local galaxy at the same luminosity (e.g., Pope et al. 2006; Kovács et al. 2006; Huynh et al. 2007). However, to make a conclusive statement about such an effect requires a precise sampling of the full IR SED, including the peak, which we do not have.

Seeing that the addition of 70 μm data, alone, to mid-infrared photometry yields relatively reliable estimates of IR luminosity among these galaxies, FIDEL observations (i.e., deep 70 μm imaging) of the entire GOODS-N field are used to better constrain estimates of the IR luminosity for all 24 μm detected sources having spectroscopic redshifts in E. J. Murphy et al. (2009, in preparation). By doing so, we are able to improve estimates for how the IR luminosity density evolves with redshift and characterize better the number density of mid-infrared excess sources.

Using these data also enables us to look at the behavior of the FIR–radio correlation among a diverse group of galaxies spanning a redshift range between 0.6 ≲ z ≲ 2.6. In calculating the radio-based IR luminosities and associated SFRs we have assumed that the FIR–radio correlation remains constant with redshift. We will now try to verify if such an assumption was appropriate.

5.3.1. Lack of Evolution with Redshift

In Figure 11, we plot q_IR, defined in Equation (1), as a function of redshift. Infrared luminosities are estimated from SED fitting using all available photometry and the IRS spectroscopy. The median q_IR value, plotted as dot-dashed line in Figure 11, is 2.41 ± 0.39 dex, below, but consistent with, the local value of 2.64 ± 0.26 (Bell 2003). Interestingly, we note that the four galaxies having the largest mid-infrared AGN fractions (GN-IRS 2, 15, 17, and 21) have q_IR values very near the canonical ratio, being within 0.18 dex, on average. This indicates that the FIR–radio correlation is a poor discriminant of obscured AGN activity.

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While the correlation appears to remain linear with redshift for the few objects being studied here, more than 50% of the SMGs in this sample (i.e., 7/11) have IR/radio ratios <2.24. This is a factor of ≳2.5 below the average value measured in the local Universe for both normal star-forming galaxies and ULIRGs. These galaxies drive the large dispersion found among the entire sample relative to what is found in the local Universe. The SMGs show a scatter in q_IR of 0.44 dex compared to 0.27 dex for the non-SMGs suggesting a more heterogeneous population. In contrast, 12/13 ULIRGs in the Yun et al. (2001) sample, (i.e., excluding a single, radio-loud AGN), have a median IR/radio ratio which is 33% larger than the canonical value and a dispersion of only 0.28 dex. While the average q_IR value for the non-SMGs is 2.43 dex, nearer to the local value of 2.64 dex, the median q_IR value among all SMGs in the sample is 2.14 dex, a factor of ∼3.2 times lower than the canonical value.

The errors in L^all_IR appear too small to explain this systematic departure from the canonical IR/radio ratio among the SMGs; by increasing L^all_IR values by the 3σ errors and recomputing q_IR, the median value among the SMGs is 2.16 dex, still a factor for ∼3 times lower than the canonical ratio. This result is consistent with the findings of Kovács et al. (2006) who reported similarly low IR/radio ratios for a sample of ≈15 SMGs out to z ∼ 3.5 detected at 350 and 850 μm. The possible reasons for the observed systematic departure off the FIR–radio correlation for this galaxy population are discussed below.

Assuming that the uncertainty in our estimates of IR luminosity are not responsible for the low IR/radio ratios among the SMGs, there are a number of physical explanations for why galaxies may have IR/radio ratios that are significantly lower than the local correlation value. First we note that a single spectral index was used to K-correct all of the observed radio flux densities. While we have assumed a radio spectral index of α ≈ 0.8, it would take a negative slope (i.e., α ≈ −0.4) to return the average IR/radio ratio back to the canonical value for the SMGs. Flat or inverted spectra associated with such indices are indicative of AGN (e.g., gigahertz peaked sources arising from synchrotron self-absorption). The radio spectral slopes for z ∼ 2 ULIRGs are typically not found to exhibit such indices; Sajina et al. (2008) report that only 3/48 Spitzer-selected ULIRGs have radio spectral indices between 610 MHz and 1.4 GHz (i.e., α^610MHz_1.4GHz) < 0.4. Each of these sources also shows very weak PAH emission which is unlike the SMGs presented here.

Kovács et al. (2006) attributed the low IR/radio ratios to a possible decrease in the effective dust emissivity index for SMGs compared to local star-forming galaxies. However, this is hard to prove without a fine sampling of the full IR SED. The simplest explanation is extra radio emission due to the presence of an AGN. Optical spectroscopy of the SMGs indicates the presence of AGN activity (e.g., Swinbank et al. 2004; Chapman et al. 2005). Analysis of the X-ray data on SMGs also indicates the presence of an AGN in most SMGs (Alexander et al. 2005). Thus, it is very likely that some of the radio emission arises from the nuclear black hole as can be seen by the fact that a number of the most deviant q_IR values are in fact detected in the hard band (2.0–8.0 keV) X-rays.

In order to assess if the departure from the canonical q_IR value for the SMGs is due to radio emission from an AGN, we recompute q_IR ratios by first subtracting the AGN component of the IR luminosity and attempting to make a similar correction to the radio. This is done by assuming that, like the IR emission, the radio emission of Mrk 231 is dominated by its AGN. This is reasonable since Mrk 231 has a q_IR = 2.39, nearly a factor of ∼2 below the nominal value for star-forming galaxies. Taking the 20 cm flux density of Mrk 231 of 0.309 Jy (Condon et al. 2002a) along with its redshift (z = 0.042), the corresponding 20 cm specific luminosity is 3.36 × 10⁻³L_☉Hz⁻¹. The fraction of radio power associated with the AGN for each galaxy was then estimated by scaling the radio luminosity of Mrk 231 by the mid-infrared AGN fractions of the mid-infrared luminosity obtained in Section 3.5. This contribution is then subtracted from the measured 20 cm specific luminosities for each galaxy before computing the new IR/radio ratios.

Rather than decreasing the dispersion among the sample galaxies, this attempt to remove emission arising from the AGN has actually increased the dispersion from 0.49 to 0.54 dex. This result suggests that the fractional infrared output of the AGN does not scale with the fractional output in the radio, consistent with what was found in Section 5.1 by comparing the fractional AGN power with q_IR.

Another explanation for the low IR/radio ratios may be related to galaxy–galaxy interactions. The morphology of SMGs seems to suggest major mergers which are driving intense bursts of star formation (e.g., Chapman et al. 2003). In the local universe, a number of interacting galaxy pairs (i.e., so called "Taffy" galaxies) exhibit IR/radio ratios which are a factor of ∼2 lower than the canonical value (Condon et al 1993; Condon et al. 2002b). These systems are characterized by a synchrotron "bridge," a region of bright radio continuum connecting the galaxy pairs which is thought to arise from a recent interaction and likely contain both cosmic rays and magnetic fields. The excess radio emission arising from the gaps between these galaxy pairs typically accounts for half of the total radio emission from the entire system. If SMGs have indeed undergone a similar major-merger event, leading to molecular gas and synchrotron bridges between galaxy pairs which do not yet facilitate a significant amount of ongoing star formation, this scenario may explain the lower IR/radio ratios.

On the other hand, perhaps the extreme starbursts occurring within SMGs lead to physical conditions which affect the acceleration and cooling processes of cosmic-ray electrons which boost the synchrotron emissivity. The sample of SMGs presented here is far too small to properly address this question, which will be discussed in a future paper.

A comparison of the AGN and 0.5–8.0 keV luminosities are shown in Figure 12 for the entire sample. There exists a loose relationship between the IR and full band X-ray luminosities of AGN dominated sources (i.e., quasars) such that L_0.5-8.0keV/L_IR ∼ 0.025 (e.g., Elvis et al. 1994) as indicated by the solid line in Figure 12. We also include the fit to AGN-classified SMGs presented in Alexander et al. (2005) having an average L_0.5-8.0keV/L_IR ratio of ∼0.002.

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When the AGN luminosities are plotted against the full band X-ray luminosities we find that nearly every galaxy, save GN-IRS 1 and GN-IRS 10, remains either near or above the AGN-classified SMG relation and well away from the canonical AGN relation line for quasars. Despite the fact that GN-IRS 1 and GN-IRS 10 are hard band X-ray detected, they have mid-infrared AGN fractions which are ≲50%. In fact, the median mid-infrared AGN fraction among all hard band X-ray detected sources is ∼44% with a range of ∼23%–62%. This indicates that a hard band X-ray detection does not necessarily imply a galaxy is AGN dominated.

We believe that the reason most sources lie generally above the AGN-classified SMG relation is primarily from the overestimation of AGN luminosities; as previously stated, the mid-infrared AGN fractions and associated AGN luminosities should be thought of as upper limits since hot dust contributing to the mid-infrared continuum emission may be powered by star formation. Alternatively, there is some uncertainty on the absorption corrections to the X-ray flux, and it is possible that they could be a factor of ∼2 higher (Alexander et al. 2008b). It is also possible that the AGN in these sources contribute significantly more to the total IR output than the few percent suggested for SMGs by Alexander et al. (2005) arising from a large AGN dust covering factor. The four galaxies having the largest mid-infrared AGN fractions (GN-IRS 2, 15, 17, and 21), three of which are thought to be Compton-thick AGNs (GN-IRS 2, 15, and 17), all lie well away from the typical quasar relation suggesting that they have significantly larger dust covering fractions than quasars.