EARLY SCIENCE WITH THE LARGE MILLIMETER TELESCOPE: EXPLORING THE EFFECT OF AGN ACTIVITY ON THE RELATIONSHIPS BETWEEN MOLECULAR GAS, DUST, AND STAR FORMATION

5MUSES is a Spitzer IRS mid-IR spectroscopic survey of 330 galaxies selected from the SWIRE and Spitzer Extragalactic First Look Survey fields (details in Wu et al. 2010). It is a flux-limited sample selected at 24 μm using MIPS observations from the Spitzer Space Telescope, with S₂₄ > 5 mJy. Crucially, 5MUSES is a representative sample at intermediate redshift (the median redshift of the sample is 0.14, 1.8 Gyr ago) of galaxies with L_IR ∼ 10¹⁰–10¹² L_☉, bridging the gap between large samples of local SFGs, LIRGs, and ULIRGs and high-redshift observations of LIRGs and ULIRGs. Complete details of the Spitzer data reduction are found in Wu et al. (2010). For the present study, we make use of the Spitzer IRS short-low (SL) spectroscopy, spanning the range 5.5–14.5 μm.

A 24 μm selection criteria could potentially bias the sample toward warmer sources. Magdis et al. (2013) reports the FIR observations of the 5MUSES sources with the Herschel Space Observatory. Of 188 5MUSES sources covered by the observations, 154 (82%) are detected at 250 μm. The authors also determine that the 250 μm flux densities of the whole population of galaxies in the observed field with S₂₄ > 5 mJy (the 5MUSES detection limit) and that of the 5MUSES sample is drawn from the same distribution, indicating that the dust temperatures of 5MUSES are not significantly warmer than other IR luminous galaxies. In Section 3.2, we compare the 5MUSES sources to high-redshift ULIRGs, also selected at 24 μm, from the GOODS-Herschel survey. For the high-redshift ULIRGs, Pope et al. (2013) find no difference between 70 μm selected sources (∼24 μm rest frame) and submillimeter selected sources in terms of PAH and CO luminosities. The high-redshift ULIRGs in this work are drawn from a larger parent population of Spitzer IRS sources (Kirkpatrick et al. 2012). Kirkpatrick et al. (2012) find that 97% of GOODS-Herschel sources with a 100 μm detection also have a 24 μm detection, ensuring that for high-redshift LIRGs and ULIRGs, a 24 μm selection criteria does not bias the selection toward warmer sources.

From the 5MUSES sample, we selected 24 sources that span a range of PAH equivalent widths (EW; calculated for the full sample in Wu et al. 2010), as PAH EW is correlated with the mid-IR strength of an AGN (Armus et al. 2007). All 24 μm sources have spectroscopic redshifts determined from fitting the mid-IR spectral features. These sources were chosen for a pilot CO(1–0) study specifically because they exhibit a range of PAH strengths and because the spectroscopic redshifts are such that we can observe the CO(1–0) transition with the Large Millimeter Telescope (LMT). These sources were also selected according to L_IR, such that every source is observable in a reasonable (≲ 90 minutes) amount of time during the LMT Early Science phase. Our sample spans a redshift range of z = 0.04–0.36 and L_IR = 1.8 × 10¹⁰–1.3 × 10¹² L_☉. Details are listed in Table 1.

Table 1. CO(1–0) Measurements of the 5MUSES Sample

ID	R.A.	Decl.	za	rmsb	FWHM	SCOΔvc	$L_{\rm CO}^\prime$c
	(J2000)	(J2000)	(CO)	(mK)	(km s−1)	(Jy km s−1)	(109 K km s−1 pc2)
5MUSES-200	16:12:50.9	+53:23:05.0	0.043	0.70	⋅⋅⋅	<2.53	<0.21
5MUSES-179	16:08:03.7	+54:53:02.0	0.053	0.32	348 ± 20	11.3 ± 0.93	1.46 ± 0.12
5MUSES-169	16:04:08.3	+54:58:13.1	0.064	0.72	306 ± 67	4.47 ± 1.08	0.84 ± 0.20
5MUSES-105	10:44:32.9	+56:40:41.6	0.068	0.84	251 ± 20	7.19 ± 1.27	1.54 ± 0.27
5MUSES-171	16:04:40.6	+55:34:09.3	0.078	0.87	345 ± 48	7.60 ± 1.45	2.14 ± 0.41
5MUSES-229	16:18:19.3	+54:18:59.1	0.082	0.72	386 ± 33	11.3 ± 1.48	3.53 ± 0.46
5MUSES-230	16:18:23.1	+55:27:21.4	0.084	0.87	305 ± 50	6.38 ± 1.25	2.09 ± 0.41
5MUSES-234	16:19:29.6	+54:18:41.9	0.100	0.70	217 ± 25	6.24 ± 0.69	2.93 ± 0.33
5MUSES-132	10:52:06.6	+58:09:47.1	0.117	1.30	181 ± 44	4.28 ± 0.92	2.77 ± 0.60
5MUSES-227	16:17:59.2	+54:15:01.3	0.134	0.24	247 ± 26	1.17 ± 0.34	1.00 ± 0.29
5MUSES-141	10:57:05.4	+58:04:37.4	0.140	0.48	203 ± 29	3.06 ± 0.62	2.86 ± 0.58
5MUSES-158	16:00:38.8	+55:10:18.7	0.145	0.73	458 ± 78	5.17 ± 1.23	5.21 ± 1.24
5MUSES-225	16:17:48.1	+55:18:31.1	0.145	0.46	400 ± 146	4.52 ± 0.57	4.55 ± 0.57
5MUSES-273	16:37:31.4	+40:51:55.6	0.189	0.34	241 ± 69	1.81 ± 0.40	3.16 ± 0.69
5MUSES-136	10:54:21.7	+58:23:44.7	0.204	0.36	477 ± 78	2.30 ± 0.55	4.69 ± 1.11
5MUSES-294	17:12:32.4	+59:21:26.2	0.210	0.38	⋅⋅⋅	<1.60	<3.47
5MUSES-216	16:15:51.5	+54:15:36.0	0.215	0.27	331 ± 60	1.82 ± 0.36	4.14 ± 0.83
5MUSES-194	16:11:19.4	+55:33:55.4	0.224	0.54	⋅⋅⋅	<2.62	<6.49
5MUSES-249	16:22:14.8	+55:06:14.2	0.237	0.41	⋅⋅⋅	<1.72	<4.80
5MUSES-250	16:23:13.1	+55:11:11.6	0.237	0.48	599 ± 40	5.56 ± 0.68	15.5 ± 1.89
5MUSES-275	16:37:51.4	+41:30:27.3	0.286	0.61	950 ± 163	7.77 ± 1.38	32.0 ± 5.68
5MUSES-313	17:18:52.7	+59:14:32.1	0.322	0.47	⋅⋅⋅	<2.09	<10.1
5MUSES-156	15:58:33.3	+54:59:37.2	0.340	0.47	⋅⋅⋅	<2.17	<12.8
5MUSES-101	10:41:59.8	+58:58:56.4	0.360	0.32	⋅⋅⋅	<1.34	<8.91

Notes. Sources are ordered by increasing redshift. ^aRedshift determined by fitting center of CO(1–0) line. Redshift errors scale with S/N, with the typical error of 0.0003 corresponding to S/N ∼ 5. For the sources with 3σ upper limits, we list z_IR. ^bThe rms is determined over the entire 38 GHz spectrum. ^c3σ upper limits are listed for six sources where we were not able to detect a line.

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The LMT is a 50 m millimeter-wave radio telescope on Volcán Sierra Negra, Mexico, at an altitude of 4600 m (Hughes et al. 2010). The high elevation allows for a median opacity of τ = 0.1 at 225 GHz in the winter months. For the Early Science phase, the inner 32.5 m of the primary reflector is fully operational. The primary reflector has an active surface and a sensitivity of 7.0 Jy K⁻¹ at 3 mm. The pointing accuracy (rms) is 3'' over the whole sky and 1–2'' for small offsets (<10°) from known sources.

During 2014 March and April, we observed our 24 sources with the Redshift Search Receiver (RSR; Erickson et al. 2007; Chung et al. 2009). The RSR is comprised of a dual beam, dual polarization system that simultaneously covers a wide frequency range of 73–111 GHz in a single tuning with a spectral resolution of 100 km s⁻¹. This large bandwidth combined with a high spectral resolution is ideal for measuring the CO integrated line luminosities in high-redshift sources. In our intermediate redshift sample, the large bandwidth allows us to observe the CO(1–0) transition for sources spanning a wide range of redshifts. The beam size of the RSR is frequency dependent, such that θ_b = 1.155λ/32.5 m. The beam size depends on the frequency of the observed CO(1–0) line, and at the median redshift, z = 0.145, the RSR has a beam size of 22''.

Typical system temperatures ranged from 87–106 K during our observations. Weather conditions varied over the eight nights of observations, with τ = 0.07–0.28. All observations were taken at elevations between 40°–70° where the gain curve is relatively flat. On source integration times ranged from 5–100 minutes and were determined by estimating $L_{\rm CO}^\prime$ from L_IR using the average ratio from Carilli & Walter (2013). The integration times were estimated to obtain a >3σ detection of the expected integrated line luminosity in each source according to the LMT integration time calculator. We obtained >3σ detections of 17 out of 24 targets. With the sole exception of 5MUSES-313, where the requested on source integration time was not completed, the desired rms was reached for all sources. The rms has been calculated using the full spectrum from 73–111 GHz. We list the rms in Table 1 for each source. There is no correlation between rms and S/N, so low CO(1–0) emission appears to be an intrinsic property of our undetected sources.

Data were reduced and calibrated using DREAMPY (Data REduction and Analysis Methods in PYthon). DREAMPY is written by G. Narayanan and is used specifically to reduce and analyze LMT/RSR data. It is a complete data reduction package with interactive graphics. For each observation scan, four distinct spectra are produced from the RSR. After applying appropriate instrumental calibrations from the DREAMPY pipeline, certain frequencies where known instrument artifacts are sometimes present were removed. There are no known bandpass features in the spectral regions where the CO(1–0) lines are expected. For each observation, linear baselines were calculated outside the region of the CO(1–0) line, and the rms estimated from the baseline of the full spectrum is used when all data for a given source are averaged together to produce the final spectrum. The averaging is a weighted average where the weights are set to 1/rms².

We checked whether aperture corrections were necessary using the empirical relation derived in Saintonge et al. (2011a) and the optical radii from NASA/IPAC Extragalactic Database. We calculated at most a 10% aperture correction for our lowest redshift galaxies which have the largest angular extent. Given the uncertainty inherent in applying a correction formula, we have opted not to apply any aperture corrections.

From the final spectrum for each source, in units of antenna temperature, we determined the locations of the CO(1–0) peak by fitting a simple Gaussian to the spectrum close to the frequency 115.271/(1 + z_IR), allowing for a generous 10% uncertainty in z_IR, where z_IR was derived by fitting the mid-IR spectral features (described in Section 2.3). In Table 1, we list z_CO, the redshift determined from the peak of the CO(1–0) emission. In all cases, the redshifts derived from fitting the CO(1–0) line agree with the mid-IR redshifts within (Δz/(1 + z_IR)) < 0.1%. The RSR is designed for blind redshift searches, and we test the reliability of our CO(1–0) detections by performing blind line searches over the full 38 GHz spectra. For 94% (16/17) of the objects that we claim detections for, a blind line search identifies the correct redshift. For 5MUSES-225, known noise artifacts elsewhere in the spectrum confuse the redshift solution. However, since redshifts are known for our targets, we can nevertheless reliably measure the CO(1–0) emission at the correct redshift.

Spectra (with T_A in mK) and the best-fit Gaussians are shown in Figure 1. We integrate under the Gaussian to determine the line intensities, I_CO, in K km s⁻¹. We convert the line intensity to S_CO Δv using a conversion factor of 7 Jy K⁻¹, calibrated specifically for the LMT Early Science results, and we convert to $L^\prime _{\rm CO}$ following the equation in Solomon & Vanden Bout (2005) after correcting for cosmology differences. The CO(1–0) luminosities are listed in Table 1.

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Our analysis centers around comparing the molecular gas emission, traced by $L_{\rm CO}^\prime$, with the dust emission, traced primarily through L_IR. L_IR(5–1000 μm) values are calculated in Wu et al. (2010). The authors create synthetic IRAC photometry using the Spitzer IRS spectra and then fit a library of templates to the synthetic IRAC photometry and MIPS 24, 70, and 160 μm photometry. The final spectral energy distribution (SED) for each galaxy is created by combining the mid-IR spectroscopy with the best-fit template. Finally, the authors calculate L_IR by integrating under the SED from 5–1000 μm. Twelve of the sources in our study also have photometry from SPIRE on the Herschel Space Observatory (Magdis et al. 2013). We test whether including this longer wavelength data changes L_IR for these 12 sources, and find excellent agreement, such that there is less than a 3% difference between L_IR calculated with and without SPIRE data. For the purposes of this study, we wish to use the standard definition: L_IR(8–1000 μm). We correct the L_IR(5–1000 μm) values from Wu et al. (2010) to L_IR(8–1000 μm) by scaling by 0.948, a conversion factor which was determined using composite LIRG and ULIRG SEDs from Kirkpatrick et al. (2012). In addition, Wu et al. (2010) uses a slightly different cosmology with H₀ = 70 km s⁻¹ Mpc⁻¹. Over our range of redshifts, this requires an average conversion factor of 0.970 to account for the difference in cosmologies. To summarize, we calculate

$$\begin{equation} L_{\rm IR}^{\rm tot}(8\hbox{--}1000\,\mu {\rm m})=L_{\rm IR}^{\rm Wu} \times 0.948 \times 0.970. \end{equation} \tag{ 1 }$$

These values are listed in Table 2.

Table 2. Infrared and Star Formation Properties

ID	$\log L_{\rm IR}^{\rm tot}$a	fAGN, midIR	fAGN, IRb	Typec	$\log L_{\rm IR}^{\rm SF}$	log L6.2	log M*	sSFRd	Desig.e
	(L☉)				(L☉)	(L☉)	(M☉)	(Gyr−1)
5MUSES-200	10.36	0.23	0.12	Comp	10.31	8.04	10.48	0.09	MS
5MUSES-179	10.22	0.24	0.13	Comp	10.17	7.95	11.08	0.01	MS
5MUSES-169	10.79	0.06	0.03	SFG	10.79	8.45	10.82	0.11	MS
5MUSES-105	10.88	0.16	0.08	SFG	10.85	8.38	10.79	0.13	MS
5MUSES-171	11.06	0.08	0.04	SFG	11.05	8.54	10.93	0.16	MS
5MUSES-229	11.10	0.12	0.06	SFG	11.08	8.62	11.36	0.06	MS
5MUSES-230	11.09	0.00	0.00	SFG	11.09	8.98	10.46	0.50	SB
5MUSES-234	11.03	0.15	0.08	SFG	11.00	8.52	10.47	0.40	SB
5MUSES-132	11.30	0.00	0.00	SFG	11.30	9.16	10.67	0.51	SB
5MUSES-227	11.08	0.57	0.30	Comp	10.91	8.63	10.73	0.18	MS
5MUSES-141	11.14	0.67	0.36	Comp	10.93	8.71	11.15	0.07	MS
5MUSES-158	11.41	0.23	0.12	Comp	11.36	8.87	10.99	0.28	SB
5MUSES-225	11.09	0.29	0.15	Comp	11.02	8.61	10.99	0.13	MS
5MUSES-273	11.40	0.45	0.24	Comp	11.28	8.78	10.97	0.23	MS
5MUSES-136	11.39	0.77	0.41	AGN	11.13	9.03	11.41	0.06	MS
5MUSES-294	11.55	0.16	0.08	SFG	11.52	8.97	11.49	0.12	MS
5MUSES-216	11.39	0.14	0.07	SFG	11.37	9.06	10.71	0.53	SB
5MUSES-194	11.72	0.81	0.43	AGN	11.44	8.34	11.19	0.21	MS
5MUSES-249	11.63	0.12	0.06	SFG	11.61	9.26	10.96	0.52	SB
5MUSES-250	11.63	0.05	0.03	SFG	11.63	9.44	11.29	0.26	MS
5MUSES-275	12.00	0.79	0.42	AGN	11.73	9.46	11.13	0.47	SB
5MUSES-313	11.81	0.41	0.22	Comp	11.70	9.12	10.64	1.36	SB
5MUSES-156	12.06	0.31	0.16	Comp	11.99	9.24	10.17	7.70	SB
5MUSES-101	11.91	0.82	0.43	AGN	11.63	9.03	10.86	0.68	SB

Notes. ^aThe $L_{\rm IR}^{\rm tot}$ values are scaled from Wu et al. (2010); see Section 2.3 for details. ^bThe fraction of L_IR(8–1000 μm) due to heating by an AGN. ^cStar forming galaxies (SFG) have f_{AGN, midIR} < 0.2 (f_{AGN, IR} < 0.1); AGNs have f_{AGN, midIR > 0.7} (f_{AGN, IR} > 0.4); composites (Comp) have f_{AGN, midIR} = 0.2–0.7 (f_{AGN, IR} = 0.1–0.4) ^dCalculated using $L_{\rm IR}^{\rm SF}$. ^eMain sequence (MS) or starburst (SB) according to Equation (3), where sSFR is calculated using $L_{\rm IR}^{\rm SF}$.

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When an AGN is present, $L_{\rm IR}^{\rm tot}$ can have a non-neglible contribution from dust heated by an AGN, and hence L_IR does not directly translate to an SFR. We diagnose the presence and strength of an AGN through mid-IR (5–15 μm rest frame) spectral decomposition. We follow the technique outlined in detail in Pope et al. (2008) which we summarize here. We fit the individual spectra with a model comprised of three components: (1) the star formation component is represented by the mid-IR spectrum of the prototypical starburst M 82 (Förster Schreiber et al. 2003). We have verified our choice of starburst template by comparing with the starburst composite SED from Brandl et al. (2006) and find no difference in the decomposition results; (2) the AGN component is determined by fitting a pure power-law with the slope and normalization as free parameters; (3) an extinction curve from the Draine et al. (2003) dust models is applied to the AGN component. The extinction curve is not monotonic in wavelength and contains silicate absorption features, the most notable for our wavelength range being at 9.7 μm. We tested applying additional extinction to the star formation component beyond that inherent in the M 82 template and found this to be negligible for all sources. We fit all three components simultaneously. For each source, we quantify the strength of the mid-IR AGN, f_{AGN, midIR}, as the fraction of the total mid-IR luminosity coming from the power-law continuum component. The PAH EW from Wu et al. (2010), initially used to select our sample, directly relates to the mid-IR AGN fraction, supporting the reliability of our diagnostic. Our decomposition technique is illustrated in Figure 2.

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We use the mid-IR AGN strength, f_{AGN, midIR}, to determine the total contribution of the AGN to $L_{\rm IR}^{\rm tot}$. To estimate the conversion between f_{AGN, midIR} and f_{AGN, IR}, we use 22 composite SEDs created from >300 LIRGs and ULIRGs spanning a redshift range of z = 0.5–3 (A. Kirkpatrick et al. 2015, in preparation). We decompose the mid-IR portion of the composite SEDs following the technique outlined above. We then decompose the full SED, from 0.5–1000 μm, by fitting a pure AGN template and a star formation template. We find that the total IR AGN contribution is 53% ± 12% of the mid-IR AGN strength (f_{AGN, IR} = 0.53 × f_{AGN, midIR}). For the 5MUSES sample, where we lack enough data points to accurately decompose the full-IR SED, we scale the mid-IR AGN strength by 0.53 to estimate the total AGN contribution, f_{AGN, IR}, to $L_{\rm IR}^{\rm tot}$, and we use this value to calculate $L_{\rm IR}^{\rm SF}$, the IR luminosity attributed to star formation. In the analysis that follows, we separate our sources according to f_{AGN, midIR}, resulting in three categories: (1) purely SFGs have f_{AGN, midIR} < 0.2 (f_{AGN, IR} < 0.1); (2) AGNs have f_{AGN, midIR} > 0.7 (f_{AGN, IR} > 0.4); and (3) composites have f_{AGN, midIR} = 0.2–0.7 (f_{AGN, IR} = 0.1–0.4).

We are also interested in the strength of the PAH emission, since this is expected to trace star formation and photodissociation regions within molecular clouds. By comparing the PAH emission with L_IR and CO(1–0) emission, we have three separate tracers of the dust and gas in the ISM which are expected to correlate with star formation. We quantify the PAH emission as L_6.2, the luminosity of the isolated 6.2 μm line. We fit a continuum on either side of this feature at 5.9 μm and 6.5 μm and remove the continuum component. We then integrate under the continuum subtracted emission feature to obtain L_6.2. None of our sources are extended at 8.0 μm using the Spitzer IRAC images, so aperture corrections are not necessary when comparing the Spitzer and LMT luminosities. We list L_6.2, $L_{\rm IR}^{\rm SF}$, f_{AGN, midIR}, and f_{AGN, IR} in Table 2.

The specific star formation rate (sSFR) is the ratio of SFR to stellar mass. Shi et al. (2011) determined stellar masses for the 5MUSES sample by fitting Bruzual & Charlot (2003) population synthesis models to optical and near-IR broadband photometry assuming a Chabrier initial mass function (IMF). We adopt these stellar masses, and we calculate the SFR from $L_{\rm IR}^{\rm SF}$ according to

$$\begin{equation} \left(\frac{\rm SFR}{M_\odot \, {\rm yr}^{-1}}\right) = 1.509\times 10^{-10} \left(\frac{L_{\rm IR}^{\rm SF}}{L_\odot }\right), \end{equation} \tag{ 2 }$$

assuming a Kroupa IMF and a constant star formation rate over the past 100 Myr (Murphy et al. 2011b). We do not convert between a Chabrier IMF and a Kroupa IMF for this formula, since the conversion is very small (Zahid et al. 2012).

The galaxy main sequence can be used to classify galaxies as either normal SFGs or starbursts based on whether they have an enhanced SFR for a given M_*. This relationship is a slowly varying function of redshift. Elbaz et al. (2011) present a relationship between sSFR and the time since the Big Bang in Gyr, t_cosmic, for the galaxy main sequence (see Equation (13) in Elbaz et al. 2011). The relation in Elbaz et al. (2011) is derived assuming a Salpeter IMF, an L_IR–SFR conversion from Kennicutt (1998), and a cosmology with H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_m = 0.3, and $\Omega _\Lambda =0.7$. We convert the relation from a Salpeter IMF to a Kroupa IMF using $M_\ast ^{\rm Kroupa}=0.62\,M_\ast ^{\rm Salpeter}$ (Zahid et al. 2012). We convert t_cosmic to the cosmology used in this paper by multiplying by 1.02, appropriate for our redshift range. Finally, the SFRs are related by SFR_Murphy11 = 0.86 SFR_Kennicutt98 (Kennicutt & Evans 2012). Applying all of these conversions gives the MS relation appropriate for the present work:

$$\begin{equation} {\rm sSFR}_{\rm MS}\, ({\rm Gyr^{-1}}) = 38\times t_{\rm cosmic}^{-2.2}. \end{equation} \tag{ 3 }$$

If a galaxy has a sSFR a factor of two greater than sSFR_MS, it is classified as a starburst. We use z_CO and $L_{\rm IR}^{\rm SF}$ to calculate sSFR_MS and list the stellar masses along with the main sequence/starburst designations in Table 2. We plot sSFR versus z for our sample in Figure 3. We show the sSFR calculated using $L_{\rm IR}^{\rm tot}$ (gray open symbols) and the sSFR calculated using $L_{\rm IR}^{\rm SF}$ (filled symbols). We color the sources according to whether they are SFGs (blue), composites (green), or AGNs (red), according to f_{AGN, IR} (see Section 2.3). Removing the AGN contribution to $L_{\rm IR}^{\rm tot}$, which we have done for all sources, has the effect of moving two of our sources from the starburst region onto the main sequence. Two sources, 5MUSES-136 and 5MUSES-179, lie below the main sequence, possibly indicating that they are transitioning to a more quiescent evolutionary stage. In this small sample, we observe no obvious association of AGN strength with distance from the main sequence, similar to what is seen in Elbaz et al. (2011).

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In the local universe, the SK law is traditionally expressed in terms of surface densities, which necessarily require resolved measurements of star formation and molecular gas (Schmidt 1959; Kennicutt 1998; Shi et al. 2011; Kennicutt & Evans 2012). At higher redshifts, resolved measurements are often not feasible, and global measurements of the SFR and molecular gas are used instead. The ratio of L_IR, directly related to a global SFR, and $L^\prime _{\rm CO}$ is commonly referred to as the star formation efficiency (Young & Scoville 1991; Solomon & Vanden Bout 2005). It is essentially the integrated version of the SK law without the uncertain conversion from CO to H₂ mass. This quantity is also related to the inverse of the gas depletion timescale which describes how long a galaxy could continue to form stars at the current rate if the gas reservoir is not replenished (e.g., Saintonge et al. 2011b).

In general, L_IR correlates with $L^\prime _{\rm CO}$, although there is significant scatter. L_IR is primarily measuring the reradiated light from newly formed stars (with some contribution from an older stellar population), while $L^\prime _{\rm CO}$ is measuring the reservoir of molecular gas available to form stars in the future; hence the dust and gas do not necessarily trace star formation on the same timescales. CO emission can also be present between molecular clouds, introducing more scatter in the relationship between L_IR and $L_{\rm CO}^\prime$. To account for this scatter, many authors propose two relationships, one for starbursts, undergoing an enhanced $L_{\rm IR}/L_{\rm CO}^\prime$, and one for normal SFGs (e.g., Daddi et al. 2010b; Genzel et al. 2010; Carilli & Walter 2013; Tacconi et al. 2013). If a galaxy undergoes a burst of star formation that also triggers AGN growth, this could account for some of the scatter in $L_{\rm IR}/L_{\rm CO}^\prime$. Initially, as an embedded AGN grows more luminous, it heats some of the surrounding dust, but is enshrouded enough that the host galaxy is still visible (e.g., Sanders et al. 1988; Hopkins et al. 2006; Kirkpatrick et al. 2012). The increase in the amount of warm dust heated by the AGN will enhance L_IR but may not yet affect $L^\prime _{\rm CO}$, implying an artificially high $L_{\rm IR}/L_{\rm CO}^\prime$ unless the AGN contribution is accounted for (e.g., by considering $L_{\rm IR}^{\rm SF}$). As the AGN becomes less enshrouded, the PAH and cold dust emission from the host become less prominent because the dust heated by the AGN is outshining the dust in star forming regions, and/or because feedback from the AGN is quenching the star formation. If the AGN is quenching the star formation, this will produce lower $L_{\rm IR}^{\rm SF}$ values and hence lower $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$, unless feedback from the AGN expels CO on the same timescales.

As yet, no study has attempted to quantify the effect of the AGN on $L_{\rm IR}/L_{\rm CO}^\prime$ individually in galaxies due to the difficulty in measuring the amount of L_IR attributable to an AGN. The 5MUSES sample has mid-IR spectra that exhibit both PAH features and a strong underlying continuum, allowing us to cleanly separate out the AGN luminosity and calculate $L_{\rm IR}^{\rm SF}$. Figure 4 shows the relationship between $L_{\rm IR}^{\rm SF}$ and $L^\prime _{\rm CO}$, and the points are colored according to f_{AGN, IR}. We overplot the relations between $L_{\rm IR}^{\rm SF}$ and $L^\prime _{\rm CO}$ determined for SFGs (dashed line; gray region indicates one standard deviation) and starbursts (dotted line) in Genzel et al. (2010). These relations were robustly determined using large samples of normal SFGs and starbursts from z ∼ 0–3, and we are interested in testing how removing the AGN component in our galaxies changes their position relative to these relations. The presence of two separate relations is discussed in depth in Carilli & Walter (2013), where the authors also present a single relation fitting all available L_IR and L_CO measurements in the literature. We compare to the separate starburst and SFG relations to investigate any difference in $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$ according to IR power source or starburstiness.

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Genzel et al. (2010) determined the relations for SFGs and starbursts using the FIR luminosity (50–300 μm) as opposed to L_IR, so we scale the relationships according to L_IR/FIR = 1.63, a ratio determined using the LIRG and ULIRG templates from Kirkpatrick et al. (2012). We overplot the 1σ scatter from Genzel et al. (2010) as the gray shaded region. We plot the main-sequence galaxies (determined by Equation (3)) as filled circles and starbursts as filled stars. The starbursts on average have a factor of two higher $L_{\rm IR}^{\rm SF}$ and $L^\prime _{\rm CO}$ than the main-sequence galaxies. We find that both the main sequence and starbursts are consistent with the SFG relationship from Genzel et al. (2010), and there is no strong separation according to IR power source.

We can look at this more simply by considering the ratio $L_{\rm IR}^{\rm SF}/L^\prime _{\rm CO}$. In Figure 5, we plot $L_{\rm IR}^{\rm SF}/L^\prime _{\rm CO}$ as a function of f_{AGN, IR}. We also include $L_{\rm IR}^{\rm tot}/L_{\rm CO}^\prime$ as the unfilled circles and stars. The gray shaded regions illustrate the standard deviation around the average $L_{\rm IR}/L_{\rm CO}^\prime$ calculated for starbursts and SFGs in Genzel et al. (2010). The standard deviation for the SFG region is 0.33 dex, slightly larger than the standard deviation illustrated in Figure 4. This is due to the fact that the relation between L_IR and $L_{\rm CO}^\prime$ is nonlinear, so the standard deviation relative to the mean $L_{\rm IR}/L_{\rm CO}^\prime$ is larger.

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None of our galaxies lie in the starburst region. Genzel et al. (2010) find a mean $L_{\rm IR}/L^\prime _{\rm CO}$ of 44. We calculate that the mean $L_{\rm IR}^{\rm tot}/L_{\rm CO}^\prime$ is 59, but when we remove the AGN contribution to $L_{\rm IR}^{\rm tot}$, we calculate a mean $L_{\rm IR}^{\rm SF}/L^\prime _{\rm CO}$ of 52, closer to the mean measured by Genzel et al. (2010). Removing the AGN component only mildly reduces the scatter about the mean $L_{\rm IR}^{\rm SF}/L^\prime _{\rm CO}$. Two galaxies, 5MUSES-179 and 5MUSES-275, lie below the SFG region. The galaxy with the lowest $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$, 5MUSES-179, also lies decidedly below the main-sequence region in Figure 3, further indicating that its star formation is highly inefficient, and this galaxy could be transitioning to a quiescent phase. We find no relationship between $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$ and f_{AGN, IR}. For this small sample, the SFGs exhibit less scatter in $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$ than the composite galaxies, although both groups have the same average $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$. The AGNs have a lower average $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$ indicating that these galaxies are not converting gas to stars at the same rate as the composite or SF galaxies; this hints that the star formation might be beginning to quench in these AGN sources.

It is interesting to note that two galaxies with very high $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$ lower limits (5MUSES-249 and 5MUSES-294) show no trace of an AGN according to their mid-IR spectra. This could be illustrative of the different timescales that AGN signatures, starburst signatures, and enhanced $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$ ratios are visible. Mid-IR spectroscopy and Chandra X-ray observations provide evidence that the majority of local ULIRGs and high-redshift submillimeter galaxies, which have a high merger (and hence, starburst) fraction and enhanced $L_{\rm IR}/L_{\rm CO}^\prime$, are predominately powered by star formation in the mid-IR (e.g., Alexander et al. 2005; Pope et al. 2008; Veilleux et al. 2009; Elbaz et al. 2011). A non-negligible fraction of LIRGs and ULIRGs host a mid-IR luminous AGN, although optical morphologies of local LIRGs reveal that mid-IR AGN signatures are predominately found either in isolated disk galaxies or coalesced nuclei at the end of a merger (Petric et al. 2011). We expect, then, that if the AGN and starburst phase do not overlap completely, AGNs should have lower $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$ ratios, and Figure 5 shows that they do, for this small sample, once the AGN contribution to $L_{\rm IR}^{\rm tot}$ has been accounted for.

Also of interest is that we do not observe any dichotomy in $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$ either as a function of mid-IR power source or along the main-sequence/starburst classification. Saintonge et al. (2011b) observe a clear relationship between the gas depletion timescale and the sSFR in a large, complete, sample of local galaxies as part of the COLD GASS survey. We compare our sources with the COLD GASS galaxies in Figure 6. Saintonge et al. (2011b) calculate the depletion timescale as $t_{\rm dep} =M_{{\rm H}_2}/{\rm SFR}$, but to avoid any uncertainties due to converting $L_{\rm CO}^\prime$ to $M_{\rm H_2}$ (see Section 3.3), we simply use the ratio SFR/$L_{\rm CO}^\prime \propto t_{\rm dep}^{-1}$. We have calculated the SFRs for our galaxies using $L_{\rm IR}^{\rm SF}$. Figure 6 also includes the z = 1–3 galaxies from Genzel et al. (2010), where we have corrected the SFRs, calculated using the conversion in Kennicutt (1998), to be on the same scale as ours. The SFRs from Saintonge et al. (2011b) are calculated by fitting the SED from the UV out to 70 μm. We do not further correct for differing cosmologies as the intrinsic scatter in Figure 6 is larger than any shift introduced in this manner.

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When looking at just our 5MUSES sample in Figure 6, there is no strong correlation between SFR/$L_{\rm CO}^\prime$ and sSFR, just as we observed no separation according to sSFR in Figure 5. However, when we extend the dynamical range of the plot by considering the local galaxies from Saintonge et al. (2011b) and the z = 1–3 galaxies from Genzel et al. (2010), there is a strong correlation (a Spearman's rank test gives a correlation coefficient of ρ = 0.72 with a two-sided significance equal to 0.0). Our sample lies in the range expected. This suggests that we are not observing any differences between our starburst and main-sequence galaxies in Figures 4 and 5 simply because we are not probing a large enough range of $L_{\rm CO}^\prime$ and L_IR.

IR, CO, and PAH luminosities are all commonly used as tracers of star formation in dusty galaxies. PAH emission arises from PDRs surrounding young stars and has been demonstrated locally to be largely cospatial with the molecular clouds traced by CO emission (Bendo et al. 2010). If star formation is continuously fueled for ≲ 1 Gyr, these tracers should all correlate.

For most SFGs, the ratio of L_PAH/L_IR is fairly constant, but there is an observed deficit of PAH emission relative to L_IR in local ULIRGs, possibly due to an increase in the hardness of the radiation field caused either by a major merger/starburst or an AGN (Tran et al. 2001; Desai et al. 2007). This same deficit does not hold for similarly luminous galaxies at high redshift, however, where the majority of ULIRGs are observed to have strong PAH emission (Pope et al. 2008; Menéndez-Delmestre et al. 2009; Kirkpatrick et al. 2012).

Pope et al. (2013) explored the evolution of L_6.2/L_IR with redshift for a sample of ULIRGs from z ∼ 1–4 as well as a sample of local ULIRGs. Specifically, the authors compare L_6.2/L_IR with L_IR and find that the deficit in L_6.2 relative to L_IR occurs at a higher L_IR for high-redshift galaxies than is seen in the local universe. Galaxies from z ∼ 1–3 typically have higher gas fractions than local counterparts (Daddi et al. 2010a; Tacconi et al. 2010). This increase in molecular gas could be linked to the relative increase in PAH emission, since both are largely cospatial. Indeed, when Pope et al. (2013) compare L_6.2/L_IR with $L_{\rm IR}/L^\prime _{\rm CO}$, they find a consistent relationship for both the local and high-redshift ULIRGs.

We now build on the analysis presented in Pope et al. (2013) by extending the parameter space explored to the lower luminosity 5MUSES sample. The 5MUSES galaxies combined with the local ULIRGs comprise a low-redshift sample for comparison with the high-redshift ULIRGs. We plot $L_{\rm 6.2}/L_{\rm IR}^{\rm SF}$ versus $L_{\rm IR}^{\rm SF}$ for our sample in the left panel of Figure 7. We also include the high-redshift and local ULIRGs from Pope et al. (2013) where we have calculated $L_{\rm IR}^{\rm SF}$ for all ULIRGs by scaling the mid-IR AGN strength, determined by decomposing the mid-IR spectra. There is a decreasing trend between the 5MUSES sample and the local ULIRGs, but the high-redshift ULIRGs are shifted from this relation. In the right panel, we plot $L_{\rm 6.2}/L_{\rm IR}^{\rm SF}$ versus $L_{\rm IR}^{\rm SF}/L^\prime _{\rm CO}$. $L_{\rm CO}^\prime$ is calculated using the estimated CO(1–0) luminosity for all galaxies (see Pope et al. 2013, for conversion details). In this panel, most galaxies follow the same decreasing trend, with a few obvious outliers. We overplot the best-fit relation for the 5MUSES sample and the local and high-redshift ULIRGs. The shaded region indicates one standard deviation above and below the fit. There is a decreasing correlation between $L_{\rm 6.2}/L_{\rm IR}^{\rm SF}$ and $L_{\rm IR}^{\rm SF}/L^\prime _{\rm CO}$ for most galaxies.

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Figure 7 suggests that the relative amount of emission from small dust grains is related to $L_{\rm IR}^{\rm SF}/L^\prime _{\rm CO}$ for dusty galaxies out to z ∼ 2. That is, weaker PAH emission is associated with a higher star formation efficiency and faster gas depletion timescales. The decrease in L_6.2 with increasing L_IR could indicate that PAH emission in general is suppressed for more luminous galaxies. We do not find significantly lower $L_{\rm 6.2}/L_{\rm IR}^{\rm SF}$ ratios for our AGNs or composite galaxies as compared to our SFGs, indicating that in our sample, the growing AGN is not affecting this ratio.

As discussed in Pope et al. (2013), the PAH deficit could be similar to the observed deficit in [C ii] emission at high L_IR in local galaxies (e.g., Kaufman et al. 1999; Stacey et al. 2010; Graciá-Carpio et al. 2011). Díaz-Santos et al. (2013) probe the [C ii] deficit in local LIRGs and find that galaxies with compact mid-IR emission have a [C ii] deficit, regardless of the mid-IR power source. For our sample, follow-up observations are required to trace the compactness of the galaxies. If our galaxies have extended dust emission, this would explain the similar $L_{6.2}/L_{\rm IR}^{\rm SF}$ ratios for the 5MUSES galaxies and the high-redshift ULIRGs, since high-redshift ULIRGs are known to have extended dust emission (e.g., Chapman et al. 2004). Based on the relative strengths of the dust emission and CO(1–0) emission, the 5MUSES sources, primarily LIRGs, seem to be more accurate counterparts for the high-redshift ULIRGs than the local ULIRGs, evidencing the evolution of ISM properties with redshift. A morphological comparison of these sources could provide more insight into structure and compactness of the dust and gas emission.

The gas fraction is expressed as f_gas = M_gas/(M_gas + M_*), where $M_{\rm gas} = \alpha _{\rm CO} L^\prime _{\rm CO}$. α_CO = 4.6 is a commonly adopted value for normal SFGs, while in starbursts, the conversion α_CO = 0.8 has been measured (Bolatto et al. 2013 and references therein). We have two observational indicators of starburstiness: $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$ and sSFR. To calculate M_gas, we explore two scenarios. First, we apply α_CO = 4.6 to our entire sample (top panel of Figure 8). None of our galaxies have $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$ indicative of a starburst (Figure 5), so applying the same α_CO to the entire sample is a reasonable assumption. Second, we use α_CO = 0.8 to calculate the gas mass for those galaxies with an sSFR indicative of a starburst (bottom panel of Figure 8). We plot the gas fractions as a function of redshift We also plot gas fractions of normal SFGs from the literature, and we have corrected the individual α_CO values used to be 4.6. The average molecular gas fraction evolves with redshift, and we plot the measured relation, f_gas∝(1 + z)², determined from a stellar-mass-limited sample with log M_* > 10 (Geach et al. 2011), similar to the masses of our 5MUSES sample.

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Our gas fractions (in both panels) lie in the range expected when comparing with the best-fit line and the points from Leroy et al. (2009) and Geach et al. (2011). Our CO(1–0) detection rate is high (17 out of 24 sources), producing a large range of measured gas fractions. In the top panel, our starburst galaxies are systematically higher than the main-sequence galaxies, and the scatter about the (1 + z)² line is larger, which suggests that the lower α_CO = 0.8 conversion factor might be more appropriate for these sources if we expect similar gas fractions for main-sequence and starburst galaxies. Theoretically, the conversion factor depends on the geometry of the CO and H₂ distribution. When the CO emission is extended and not confined to molecular clouds, warm, and has a high surface density, as is the case in mergers, then the lower α_CO value is appropriate (Bolatto et al. 2013 and references therein). Magnelli et al. (2012) measure α_CO for a sample of high-redshift main-sequence and starburst galaxies and find an anti-correlation between α_CO and sSFR, which they interpret as evidence that the mechanisms responsible for raising a galaxy off the main sequence must also affect the physical conditions within the star forming regions. We also find that the gas fractions reproduce a similar separation between sources as the main-sequence criterion, linking α_CO with the sSFR. In contrast, neither $L_{\rm IR}^{\rm SF}/L_{\rm CO}^\prime$ nor $L_{\rm 6.2}/L_{\rm IR}^{\rm SF}$ shows any separation between the starburst and main-sequence galaxies, likely due to the limited range being probed. These ratios, then, are relatively stable for galaxies of a limited mass and luminosity range. Narayanan et al. (2012) argue against a bimodal α_CO conversion factor, and instead develop a fitting formula for the conversion factor that depends on the metallicity and CO line intensity. We currently lack metallicities for our sample, so we cannot directly apply the prescribed variable conversion factor. Given the continuous relationship between sSFR and SFR/$L_{\rm CO}^\prime$ evidenced in Figure 6, a continuous, rather than bimodal, conversion factor based on galactic environment may be the most appropriate choice and would mean that all galaxies in our sample obey a similar relationship between the molecular gas and the stellar mass.