CO SPECTRAL LINE ENERGY DISTRIBUTIONS OF INFRARED-LUMINOUS GALAXIES AND ACTIVE GALACTIC NUCLEI

We conducted the CO J = 6–5 measurements as part of our multi-J CO and HCN line survey of LIRGs in the local universe. The first CO J = 6–5 (691.473 GHz) line measurements with the JCMT atop Mauna Kea (Hawaii) were conducted for the luminous ULIRG/QSO Mrk 231 and the LIRG Arp 193, using the old W/D band (620–710 GHz) receiver (operating in the SSB mode) on 2005 February 20 and April 22, respectively, under very dry conditions (τ_220 GHz ≲ 0.035). The typical system temperatures were T_sys ∼ (3700–5500) K (including atmospheric absorption). The DAS spectrometer was used at its widest mode of 1.8 GHz (∼780 km s⁻¹ at 690 GHz), and rapid beam switching at ν_chop = 2 Hz with azimuthal throws of 60'' resulted in remarkably flat baselines. The beam size at 691 GHz is Θ_HPBW = 8''. Good pointing with such narrow beams is crucial and was checked every 45–60 minutes using differential pointing with receiver B3 (350 GHz). The latter technique can access many more compact sources in the sky in order to conduct pointing checks than can direct pointing with the W/D receiver, and was found accurate to within σ_r ∼ 26 (rms). The aperture efficiency for these periods was found to be η*_a = 0.25.⁶

The main set of CO J = 6–5 observations were conducted during several periods in 2009 January, February, March, and May with the upgraded W/D receiver and its new SIS mixers (effectively the same type that will equip the ALMA telescopes at this waveband) that dramatically enhance its performance. The resulting low receiver temperatures allowed very sensitive observations with typical T_sys ∼ (1500–3000) K (including atmospheric transmission) for $\rm \tau _{220\,GHz} \sim 0.035$–0.06. Dual channel operation (two polarization channels aligned within ≲1'') further enhanced the W/D band observing capability of the JCMT. The new ACSIS spectrometer was used at its widest mode of 1.8 GHz (∼780 km s⁻¹ at 690 GHz), and in a few cases (e.g., Arp 220) two separate tunings per object with an effective bandwidth of ∼3.2 GHz (∼1390 km s⁻¹) ensured adequate coverage of CO lines with FWZI ∼ 800–1000 km s⁻¹. Rapid beam switching at ν_chop = 4 Hz (continuum mode) with a throw of 30'' (in azimuth) yielded flat baselines under most circumstances. Finally the pointing was checked every 45–60 minutes by observing compact sources with the W/D receiver itself, and differential pointing with the A 3 receiver (230 GHz), yielding rms residual error radius of σ_r ∼ 22 (see Figure 1). The aperture efficiency for these periods is η*_a = 0.32, and a flux calibration uncertainty of ∼25% (encompassing η*_a variations and three-load calibration uncertainties) was estimated from observations of several strong spectral line standards at ∼690 GHz.

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A final set of CO J = 6–5 observations were obtained recently during several days between 2010 January 12 and 23, and 2010 February 5–6 under dry weather conditions (τ_220 GHz ≲ 0.05) that yielded typical system temperatures of T_sys ∼ (1400–2800) K. The spectrometer setup was identical to that used in our 2009 observations with two separate tunings used to cover a wide line in a few objects (e.g., Mrk 273, NGC 6240). Observations of Mars yielded an aperture efficiency of η*_a = 0.35, while the overall calibration uncertainty remained within ∼25%. The same beam switching scheme was employed while pointing was checked every hour and its accuracy remained within the range shown in Figure 1.

We inspected each 10 minute spectrum for baseline ripples and intensity "spikes" in individual channels. The edited CO J = 6–5 spectra were then co-added and are shown in Figure 2, overlaid (mostly) with CO J = 3–2 lines. The velocity-integrated line flux densities were then estimated from those spectra, after subtraction of linear baselines, using

$$\begin{eqnarray} S_{{\rm line}} &=& \int _{\Delta V} S_{\nu } dV = \frac{8 k_B}{\eta ^{*} _a \pi D^2} K_c (x)\int _{\Delta V} T^* _A dV\nonumber\\ &=& \frac{\Gamma ({\rm Jy\;K^{-1}})}{\eta ^{*} _a} K_c(x) \int _{\Delta V} T^* _A dV, \end{eqnarray} \tag{ 1 }$$

where Γ_JCMT = 15.62 and η*_a is the aperture efficiency. The factor $K_c (x)=x^2/(1-e^{-x^2})$, with x = θ_CO/(1.2θ_HPBW) and θ_CO = (source diameter) accounts for the geometric coupling of a Gaussian main beam to a finite-sized disk-like source when θ_CO is available.

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2.2.1. Observing Compact Sources with Narrow Beams: A Bias

For point-like sources, even with the accurate tracking and pointing achievable by enclosed telescopes such as the JCMT, the residual rms pointing errors and the narrow beams of large millimeter/submillimeter telescopes at high frequencies can lead to a substantial systematic reduction of the measured fluxes of compact sources. In Papadopoulos et al. (2010) this is shown to be

$$\begin{equation} G(\sigma _r)=1+8\ln 2\left(\frac{\sigma _r}{\sqrt{2}\, \Theta _{{\rm HPBW}}}\right)^2, \end{equation} \tag{ 2 }$$

(see also Condon 2001) where $\sigma _r/\sqrt{2}$ is the rms pointing error per direction (for identical error distributions per coordinate). Thus in Equation (1), when θ_CO ⩽ 2σ_r, K_c(x) → G(σ_r), since the geometric coupling correction is then overtaken by the pointing error correction.

The archetypal starburst Arp 220 has been reobserved during our 2010 observing campaign, and a significantly larger (∼2.6 times) integrated line flux has been measured, along with a different line profile. The latter now agrees well with those from high-density gas tracers such as HCN J = 3–2 (see Figure 3) which places the highest density gas at the high-velocity component corresponding to emission from the eastern nucleus (see Greve et al. 2009, and references therein). We thus conclude that the first CO J = 6–5 measurement of Arp 220 reported by Papadopoulos et al. (2010) has likely been affected by a pointing offset on the order of σ_r ∼ 47 (∼33 per direction). This is clearly an outlier of the distributions shown in Figure 1 but is certainly possible and also accounts for the different CO J = 6–5 line profile shown in Papadopoulos et al. (2010) (σ_r ∼ 47 in this system of two CO-bright nuclei ∼1'' apart can yield a maximum apparent emission asymmetry of S(V₁)/S(V₂) ∼ 0.54 between two intrinsically equal emission contributions at the velocity centers V₁ and V₂ of the two nuclei). Finally our fast-switching scheme allows an independent estimate of the adjacent dust continuum from the line-free part of the spectrum, which we find to be S_434 μm = (6.0 ± 1.5) Jy, in good agreement with the value given by Dunne & Eales (2001) rather than that in the JCMT calibrator database. The ramifications from this revision are discussed in Section 3.2.

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The sources, their coordinates, and CO J = 6–5 line flux densities (using Equation (1)) are tabulated in Table 1. The corresponding line luminosities are estimated using

$$\begin{equation} L^{^{\prime }} _{{{\rm CO}}} = \int _{\Delta V} \int _{A_s} \Delta T_{b}\,da\,dV = \frac{c^2}{2 k_B \nu ^2 _{{{\rm co,rest}}}} \left(\frac{D^2 _L}{1+z}\right) \int _{\Delta V} S_{\nu }\,dV, \end{equation} \tag{ 3 }$$

where ΔT_b is the continuum-subtracted line brightness temperature emerging at the source frame, ΔV and A_s are the total linewidth and line-emitting source area, D_L is the luminosity distance, and ν_co,rest the line rest-frame frequency. Substituting and converting to astrophysical units yields

$$\begin{eqnarray} L^{^{\prime }} _{{{\rm CO}}} &=& 3.25\times 10^7\,(1+z)^{-1} \left(\frac{\nu _{{{\rm co,rest}}}}{{\rm GHz}}\right)^{-2} \left(\frac{D_L}{{\rm Mpc}}\right)^2 \nonumber\\ &&\times\left(\frac{\int _{\Delta V} S_{\nu }\,dV}{{\rm Jy\,km\,s^{-1}}}\right)\, {\rm K\, km\,s^{-1}}\,{\rm pc^2}, \end{eqnarray} \tag{ 4 }$$

while the conversion to ordinary luminosity units (L_☉), used for the CO SLEDs, is

$$\begin{eqnarray} L_{{{\rm CO}}}&=&\frac{8\pi k_B\nu ^3 _{{\rm co,rest}}}{c^3}\,L^{^{\prime }} _{{{\rm CO}}}= 3.18\times 10^4\left(\frac{\nu _{{\rm co,rest}}}{100\,{\rm GHz}}\right)^3\nonumber\\ &&\times\left[\frac{L^{^{\prime }} _{{{\rm CO}}}}{10^{9}\,{\rm K\,km\,s^{-1}\,pc^2}}\right]L_{\odot }. \end{eqnarray} \tag{ 5 }$$

In Table 2, we tabulate the total IR luminosity L_IR of each system, with any contribution from a warm AGN-heated dust-subtracted when possible. In this table we also list the IR luminosity due to SF, L^(SF)_IR (see Section 4), as well as the $R_{{\rm HCN/CO}}=L^{^{\prime }} _{{\rm HCN}(1\hbox{--}0)}/L^{^{\prime }} _{{{\rm CO}}(1\hbox{--}0)}$ and $R_{65/32}=L^{^{\prime }}_{{\rm CO}(6\hbox{--}5)}/L^{^{\prime }} _{{\rm CO}(3\hbox{--}2)}$ line ratios. The latter is currently the most widely available one for conducting comparisons between the excitation conditions in our local LIRG sample and high-z starbursts, though for some high-z systems the "neighboring" J = 7–6 transition rather than J = 6–5 is the one available (Tacconi et al. 2006).

In Figure 4, the R_65/32 ratio is plotted versus L_IR for all the LIRGs in Table 1, and any local or distant galaxies for which this or a similar (high-J)/(low-J) global CO line ratio is available. The lightly shaded area marks the range of R_65/32 values expected for the dense and warm gas phase that fuels SF in starbursts, determined using our Large Velocity Gradient (LVG) molecular line radiative transfer code for: 〈n(H₂)〉 = (10⁴–10⁶) cm⁻³ and T_kin = (30–100) K, which encompasses the conditions of star-forming molecular gas. In this determination of the R_65/32 range we consider only self-gravitating gas, as appropriate for any star-forming gas phase, where

$$\begin{equation} K_{{\rm vir}}=\frac{\left(dV/dr\right)_{{\rm obs}}}{\left(dV/dr\right)_{{\rm virial}}}\sim 1.54\frac{[{\rm CO/H}_2]}{\sqrt{\alpha }\Lambda _{{{\rm CO}}}}\left[\frac{\langle n({\rm H}_2)\rangle }{10^3\,{\rm cm^{-3}}}\right]^{-1/2}\sim 1, \end{equation} \tag{ 6 }$$

(e.g., Goldsmith 2001; Greve et al. 2009). Values of K_vir ≫ 1 correspond to unbound gas motions (α ∼ 1–2.5 depending on the assumed cloud density profile). The parameter Λ_CO = [CO/H₂]/(dV/dr) along with T_k and 〈n(H₂)〉 classify the LVG solutions (we assume a Galactic abundance [CO/H₂] = 10⁻⁴).

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From Figure 4 it is clear that for several LIRGs the R_65/32 ratio falls well below the range expected for star-forming gas, and this happens in some of the most extreme starbursts in the local (e.g., Arp 220: R_65/32 ∼ 0.2) or the distant (e.g., HR 10: R_65/32 ∼ 0.053–0.08) universe.⁷ On the other hand all nearby galaxies clearly segregate into two groups with the star-forming ones exhibiting consistently high R_65/32 ratios (∼0.8–0.9), while the SF-quiescent ones have much lower CO ratios (∼0.12–0.24) reflecting a much less excited state of their molecular gas. Thus in some local LIRGs as well as some of their high-z counterparts, R_65/32 can be as low or even lower than in SF-quiescent systems. This contradiction between the excitation conditions of the star-forming molecular gas and the emergent faint CO J = 6–5 line emission (and thus low R_65/32) found in some LIRGs becomes even more acute when additional information from other transitions tracing the same phase as CO J = 6–5 (e.g., those of HCN) is used to further narrow the expected range of R_65/32. The (U)LIRGs Arp 220 and NGC 6240 are excellent such examples, with a multi-J line survey of several heavy rotor molecules available to constraint the R_65/32 ratio (see Section 3.2). For all other local LIRGs much less such information is available (and is virtually non-existent for their high-redshift counterparts), with only two small surveys of HCN J = 1–0, 3–2 (Graciá-Carpio et al. 2008; Krips et al. 2008) currently providing the most uniform line data sets probing the star-forming phase locally. These yield an average HCN (3–2)/(1–0) brightness temperature ratio of 〈R_32/10(HCN)〉 ∼ 0.55, reaching up to ∼0.8–0.9 for the dense gas found in starbursts such as M 82 (Krips et al. 2008) and Arp 220, NGC 6240 (Greve et al. 2009). Adopting R_32/10(HCN) = 0.55 and K_vir(HCN) ∼ 1 (implemented for an assumed $\rm [HCN/H_2]=2\times 10^{-8}$) as constraints on our LVG code yields T_kin = (35–65) K and 〈n(H₂)〉 = (3 × 10⁴–10⁵) cm⁻³, conditions that are indeed typical for the dense star-forming molecular gas (e.g., Güsten et al. 1993; Mao et al. 2000) and corresponding to an even narrower range of R_65/32 ∼ 0.70–0.85 (cross-hatched area in Figure 4), excluding several more LIRGs.

In the absence of dominant low-excitation molecular gas mass in LIRGs (a real possibility which is discussed in Section 5.1), non-negligible dust optical depths at short submillimeter wavelengths provide the only other mechanism that can suppress the large CO J = 6–5 line luminosities expected from their star-forming molecular gas. This has been recently demonstrated in the archetypal ULIRG Arp 220, where its average dust optical depth of τ_860 μm ∼ 1 (Sakamoto et al. 2008) has been shown to be responsible for its very faint CO J = 6–5 line (Papadopoulos et al. 2010). Our current results indicate that such ISM conditions may occur often in extreme starburst systems throughout the universe.

A recent multi-J HCN, HCO⁺, and CS line survey of these two archetypal ULIRGs by Greve et al. (2009) allows placing their CO J = 6–5 line luminosities in the best context currently possible for such systems. Moreover the significantly higher CO J = 6–5 luminosity we measured for Arp 220 than that reported by Papadopoulos et al. (2010) necessitates a revisit of the analysis for this ULIRG. From the findings of the aforementioned line survey it is immediately obvious that for the dense and warm gas phase of 〈n(H₂)〉 ∼ (10⁵–10⁶) cm⁻³ and T_k ∼ (50–120) K dominating the gaseous ISM in these two starbursts: R_65/32 ∼ 0.85–0.93. This confines it well into the upper (cross-hatched) range of R_65/32 values in Figure 4, and well above the observed values for both systems. For Arp 220 the new higher value of R_65/32 = 0.21 ± 0.06 remains ∼3–6 smaller than that expected for its dense gas phase, and thus the evidence for significant dust optical depths at short submillimeter wavelengths quenching its CO J = 6–5 line emission (Papadopoulos et al. 2010) remains strong. Regarding the dust emission itself, even for the larger value of S_434 μm ∼ 6 Jy and S_860 μm = (0.55 ± 0.082) Jy (Sakamoto et al. 2008), the same analysis as in Papadopoulos et al. (2010) yields τ_860 μm ∼ 0.27. The latter is smaller than that deduced by Sakamoto et al. (2008), but remains more than enough (with a corresponding τ_434 μm ∼ 1) to quench the CO J = 6–5 line emission in Arp 220 by immersing it into a nearly blackbody continuum at short submillimeter wavelengths. For NGC 6240 a similar discordance between the R_65/32 expected for its HCN/CS-bright gas and its measured R_65/32 = 0.26 (Table 2) exists.

Given the large impact that high dust optical depths at short submillimeter wavelengths will have to a large number of issues (see discussion in Sections 4.3 and 5), it is worth asking whether a large "boost" of the CO J = 3–2 rather than a suppression of the CO J = 6–5 line luminosity by dust can be responsible for the low R_65/32 ratios in some ULIRGs. This can happen only if the diffuse non-self-gravitating gas phase found in these systems contributes substantially to the CO J = 3–2 emission (but not to CO J = 6–5). For Arp 220 the detailed study by Greve et al. yields a diffuse phase with n(H₂) ∼ (1–3) × 10² cm⁻³, T_k ≳ 40 K, and Λ_CO ∼ (1–3) × 10⁻⁵ (km s⁻¹ pc⁻¹)⁻¹, with negligible CO J = 3–2 line emission. This is also obvious from the fact that even the CO J = 2–1 transition appears globally subthermally excited in this system. Thus a diffuse gas phase cannot be responsible for the very low R_65/32 value in Arp 220. For NGC 6240 this is less clear since its diffuse phase: n(H₂) ∼ (1–3) × 10³ cm⁻³, T_k ≳ 40 K and $\rm \Lambda _{CO}$ ∼ (1–3) × 10⁻⁶ (km s⁻¹ pc⁻¹)⁻¹ can contribute to CO J = 3–2 while having negligible CO J = 6–5 line luminosity. This demonstrates the "degeneracy" between dust-affected and genuinely low-excitation CO SLEDs, and the need for multi-J and multi-species molecular line observations with excitation characteristics spanning the entire range of molecular gas physical conditions in LIRGs. For an earlier such study, conducted for the archetypal ULIRG/QSO Mrk 231, that finds luminous CO J = 6–5, 4–3 line emission from the same gas phase as that emitting HCN lines see Papadopoulos et al. (2007).

From Table 3 it becomes apparent that cold dust mass obtained from typical multi-component SED fits always contains most of the mass in LIRGs with M_d,c/M_d,SF ∼ 5–100, even in extreme starbursts such as Arp 220 and Mrk 231. This is a direct result of the far-IR/submillimeter "excess" found in their SEDs once submillimeter data became available (Lisenfeld et al. 2000; Dunne & Eales 2001), and was suspected even when only IR data were available because of the high gas/dust ratios deduced with respect to the Milky Way (Devereux & Young 1990). Sensitive submillimeter imaging has conclusively demonstrated the presence of massive and extended cold dust mass in some LIRGs by spatially separating its emission from that of a more luminous SF-heated dust in nuclear regions (e.g., Papadopoulos & Seaquist 1999; Thomas et al. 2001). From Figure 5 it would then seem that the cold dust mass dominates across the entire L_IR range of our sample and up to ULIRGs. Nevertheless there are some serious problems with this scenario, at least in extreme starburst systems.

• 1.  
  The bulk of the molecular gas mass in most ULIRGs is in a dense, warm, and presumably star-forming phase (i.e., n(H₂) ≳ 10⁵ cm⁻³, T_dust ≳ 40 K), and thus most of the concomitant dust also should be warm (at such high densities T_k ∼ T_dust).
• 2.  
  The M(H₂)/M_dust ratio obtained from classical dust SED fits of such objects can be very low: ∼4–20 (Table 3), thus requiring most of the gas in ULIRGs to be atomic (with a presumably Galactic gas/dust ratio) so that the global gas/dust ratio can attain Galactic values (∼140–190; Sodroski et al. 1994). However, ULIRGs are found to be exceptionally H₂-rich with ≲30% of the gas in atomic form (Mirabel & Sanders 1989, for the X_CO factor used in our work).
• 3.  
  Submillimeter imaging of ULIRGs with the Submillimeter Array (Sakamoto et al. 2008; Wilson et al. 2008) found most of the dust emission emanating from very compact regions (≲100–150 pc), of hot dust (∼100–140 K), and with M(H₂)/M_dust close to the Galactic value.

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These issues could be resolved if the far-IR/submillimeter "excess" found in the dust SEDs of most LIRGs is, in some of them, of different origin rather than cold dust emission. Indeed such "excess" also can be generated by emission that is optically thick at far-IR and even short submillimeter wavelengths. Recently this has been shown for the compact molecular gas disks in Arp 220 (e.g., Sakamoto et al. 2008; Matsushita et al. 2009), and is indeed expected if most of the molecular gas in ULIRGs is in a very dense state. For 〈n(H₂)〉 ∼ (10⁵–10⁶) cm⁻³ (e.g., Solomon et al. 1990; Greve et al. 2009), solar metallicities, and thickness of h ∼ (40–60) pc (e.g., Downes & Solomon 1998) such molecular gas disks, if not very clumpy, will have dust optical depths of

$$\begin{eqnarray} \tau _{d}(\lambda) &\sim & 1.66\left(\frac{\lambda }{400\;\mu {\rm m}}\right)^{-2} \left[\frac{h \langle n({\rm H}_2)\rangle (\cos \theta)^{-1}}{10^{25}\,{\rm cm^{-2}}}\right]\nonumber\\ &\sim & (2.05\hbox{--}30.7)\times \left(\frac{\lambda }{400\;\mu {\rm m}}\right)^{-2} (\cos \theta)^{-1}, \end{eqnarray} \tag{ 8 }$$

(θ is the inclination angle, θ = 0: face-on). Such extreme gas configurations are the results of mergers and/or strong dynamical interactions found in all ULIRGs (Sanders & Ishida 2004), essentially packing the entire molecular gas supply of two gas-rich spirals within a few hundred parsecs. Their emergent IR luminosities will then be less than proportional to their dust mass reservoirs, and can be further absorbed by outer dust distributions that are optically thick at IR/far-IR wavelengths (Condon et al. 1991; Solomon et al. 1997). For such very dense gas disks the dust mass estimates using submillimeter fluxes and temperatures obtained from global SED fits (e.g., Dunne et al. 2000) can be significant overestimates since an outer cooler dust distribution, while not containing the bulk of the mass, dominates most of the observed SED (see also Section 4.2). This may explain why submillimeter interferometric imaging can recover a Galactic value for M(H₂)/M_dust in ULIRGs (e.g., Wilson et al. 2008) while global SED fits can yield significantly lower ones (Table 3; Dunne & Eales 2001).⁸

Optically thick dust emission in ULIRGs at far-IR wavelengths has been first noticed by Condon et al. (1991) using interferometric radio continuum imaging to identify the true sizes of their starburst regions. To explore its effect on emergent dust emission we follow Lisenfeld et al. (2000) and replace the SF-heated and cold dust components inside the brackets of Equation (7) with

$$\begin{equation} L_{\nu }=\kappa _d(\nu) B_{\nu }(T_{d,\tau })\times \left(\frac{1-e^{-\tau (\nu)}}{\tau (\nu)}\right) M_{d,\tau }, \end{equation} \tag{ 9 }$$

where $\rm \tau (\nu) = \tau _{\circ } (\nu /\nu _{\circ })^2$. In Table 3, we list the results of these dust SED fits, and in Figure 6 show the distribution of the deduced optical depths for all the LIRGs with available submillimeter data from the literature. Substantial dust optical depths are found at 100 μm (∼4–21) for most LIRGs, in accord with earlier results (e.g., Solomon et al. 1997; Lisenfeld et al. 2000). Even NGC 1068, a vigorously star-forming LIRG where a massive and extended cold dust reservoir with T_d ∼ (10–15) K is revealed via submillimeter imaging (Papadopoulos & Seaquist 1999), can have its non-AGN global dust emission fitted equally well with a single-temperature but optically thick SED. The latter would then erroneously interpret its cold dust as optically thick emission with τ_100 μm ∼ 4.6. Thus the SED fits using Equations (7) and (9) are degenerate, with both cold and optically thick dust emission capable of producing a far-IR/submillimeter emission "excess." This $\rm \tau _{IR}$–T_d degeneracy can lead to a misinterpretation of the true state of the dust in LIRGs, and cannot be broken even for well-sampled SEDs such as those of Mrk 231 and Arp 220 (Figure 7). Only sensitive millimeter/submillimeter imaging can overcome it by: (1) spatially separating the cold from the warm and much more luminous SF-heated dust, and (2) identifying any warm compact dust/gas regions (with potentially significant submillimeter optical depths) "nested" inside more extended cooler dust distributions that are optically thick at far-IR wavelengths. In Arp 220 such submillimeter imaging has identified hot and spatially extended (i.e., starburst-heated) dust reservoirs, with 2r∼100 pc, T_h ∼ (100–180) K, and τ_h(850 μm) ∼ 1 (Downes & Eckart 2007; Sakamoto et al. 2008), within its extended cooler dust distribution with T_w ∼ (45–60) K and significant optical depths at the far-IR (τ_w(100 μm) ∼ 10; Lisenfeld et al. 2000). A simple expression for the emergent SED of such a dust configuration

$$\begin{eqnarray} S_{\nu } &=& \frac{1+z}{4\pi D^2 _L}\left[1+\frac{B_{\nu }(T_h)}{B_{\nu }(T_w)} \frac{M_{d,h}}{M_{d,w}}\frac{F[\tau _h(\nu)]}{F[\tau _w(\nu)]}e^{-\tau _w(\nu)/2}\right]\nonumber\\ &&\times k_{d}(\nu)M_{d,w} B_{\nu }(T_{w}) F[\tau _w(\nu)], \end{eqnarray} \tag{ 10 }$$

where F(τ) = (1 − e^−τ)/τ, τ(ν) = τ_°(ν/ν_°)², can easily show the inadequacy of global dust emission SEDs in disentangling the true dust components. In Figure 8, after setting T_w = 40 K, T_h = 120 K τ_°,h(850 μm) ∼ 1, and τ_°,w(100 μm) ∼ 10, M_d,w = 10⁸ M_☉ we plot the aforementioned SED which makes apparent that hot and compact starburst regions can remain inconspicuous in the global dust emission SED, apart from an emission contribution in the millimeter/submillimeter domain where a cold dust reservoir would also contribute (and thus the τ_IR–T_d degeneracy). This is a result of the high dust temperatures in the compact regions (which makes their emission peak at wavelengths where the outer dust distribution remains very absorptive, i.e., at IR/far-IR wavelengths), and their high dust optical depths over almost the entire observed range of a typical SED. The latter diminishes the emission contribution of those compact and warm starburst regions well below from being proportional to their dust mass content.

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One of the most unexpected discoveries made by ISO was the so-called [C ii] line luminosity deficit for some of the most extreme starbursts in the local universe (Malhotra et al. 1997; Luhman et al. 1998, 2003). This was deemed all the more perplexing for ULIRGs since the [C ii] fine structure line at 157.74 μm is the major ISM cooling line and would thus be expected to be particularly bright in such extreme star-forming systems. Various explanations have been offered for this such as: (1) absorption by a cooler dust foreground "screen," (2) saturation of the [C ii] line luminosity (while the IR continuum rises unabated) predicted for high-density photon-dominated regions (PDRs) or PDRs in which the local UV radiation field is high and the gas density is low, (3) soft far-UV radiation fields (see Malhotra et al. 1997; Luhman et al. 1998 for a review). Significant submillimeter dust optical depths for the bulk of the dust mass suggests a simple and common cause for the [C ii] and the high-J CO lines luminosity deficiency in some ULIRGs since in an almost featureless blackbody dust continuum, no lines are expected from a concomitant isothermal gas reservoir. In particular, the weakness of the CO J = 6–5 line argues against the most prominent alternative explanation given for the [C ii] line luminosity deficit: the dense and/or strongly far-UV illuminated PDRs where in fact such high-J CO lines ought to be very luminous. Finally even modest submillimeter dust optical depths such as τ_400 μm ∼ 0.2 (from Equation (8) and 〈n(H₂)〉 = 10⁴ cm⁻³, h = 40 pc) correspond to τ^(c)_158 μm ∼ 1.3 (for β = 2) for the dust continuum at the rest frequency of the [C ii] line, yielding a F(τ) = (1 − e^−τ)/τ = 0.56 reduction in line strength with respect to the optically thin case.

The physical conditions of star-forming molecular gas used to deduce its "intrinsic" CO SLED in LIRGs (Section 3.1) are typical, however significant deviations do exist. Arp 193 with a star-formation-related IR luminosity of L^(SF)_IR = 2.2 × 10¹¹ L_☉ is notable in having the lowest (4–3)/(1–0), (3–2)/(1–0) HCN line ratios: r₄₃(HCN) ≲ 0.08 (2σ), r₃₂(HCN) = 0.22 (Papadopoulos 2007; Krips et al. 2008), as well as a faint CO J = 6–5 line with R_65/32 ≲ 0.08. These are indicative of very low excitation conditions for the bulk of its molecular gas reservoir while by comparison NGC 6240, a galaxy with a similar L^(SF)_IR ∼ 3.8 × 10¹¹ L_☉, has r₄₃(HCN) = 0.6 and r₃₂(HCN) = 0.8 (Greve et al. 2009), indicative of a much denser and warmer gas phase. Radiative transfer LVG modeling of HCN and CO (6–5)/(3–2) line ratios in Arp 193 (constrained also by K_vir ∼ 1) are consistent only with low-density n(H₂) ∼ 100 cm⁻³ and warm T_k = (85–110) K gas. These are highly atypical conditions for either vigorously star-forming LIRGs (where the ISM is usually dominated by dense and warm molecular gas), or quiescent galaxies (where molecular gas has similarly low densities but is much colder, T_kin ∼ 15 K), and demonstrate that even vigorously star-forming systems can have low high-J CO line excitation for the bulk of their gas. The corresponding CO SLED for the dense gas in Arp 193 already turns over at CO J = 3–2, in contrast to the HCN-bright star-forming phase of NGC 6240 which is expected to emit copiously up to CO J = 10–9 (Figure 10). It should be noted that besides similar L^(SF)_IR, these LIRGs both have M(H₂) ∼ (0.5–1) × 10¹⁰ M_☉ (for the CO–H₂ conversion factor of Downes & Solomon 1998), global SF efficiencies L^(SF)_IR/M(H₂) ∼ 50 L_☉/M_☉, and similar dense gas mass fractions as indicated by $R_{{\rm HCN/CO}}=L^{^{\prime }}_{{\rm HCN}(1\hbox{--}0)}/L^{^{\prime }}_{{\rm CO}(1\hbox{--}0)}$ (∼0.05 for Arp 193, and ∼0.08 for NGC 6240). This shows that observables commonly available for LIRGs such as IR luminosity, CO J = 1–0, and HCN J = 1–0 lines, may provide no indication of very different molecular gas excitation conditions and CO SLEDs, at least on an individual object basis.

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The rapid evolution of starburst events can in principle have short periods during which a (U)LIRG stays IR-luminous while its dense gas phase is strongly dispersed and/or depleted, by the formation of stars and their concentrated and coherent mechanical feedback (Loenen 2009). This could place LIRGs such as NGC 6240 and Arp 193 at the two ends of such a short evolutionary track, but observations of similar objects are needed to decide such issues. Finally we note that a population of near-IR-selected gas-rich galaxies with ULIRG-levels of star formation (∼100–150 M_☉ yr⁻¹) but very low (comparable to the Milky Way) levels of global molecular gas excitation, and star formation efficiency similar to Arp 193, has been recently revealed at high redshifts (Daddi et al. 2008; Dannerbauer et al. 2009).

Once both possibilities of large dust optical depths at short submillimeter wavelengths and low gas excitation have been recognized as affecting emergent CO SLEDs, they can be hard to tell apart without additional information from other lines tracing the dense star-forming phase. These are low-J transitions (thus not affected by dust) of HCN or CS, but can be difficult to detect on a routine basis, even in bright nearby LIRGs, since the brightest such line: HCN J = 1–0, typically has $L^{^{\prime }} _{{{\rm HCN}}(1\hbox{--}0)}$ ∼ (1/5–1/30) × $L^{^{\prime }}_{{\rm CO}(1\hbox{--}0)}$ (e.g., Gao & Solomon 2004). An insidious aspect of the aforementioned degeneracy is that some of the most extreme starbursts in the universe can show "cold" CO SLEDs despite hosting intense star-forming activity simply because their low CO (high-J)/(low-J) line ratios are attributed to low-excitation (i.e., non-star-forming) molecular gas rather than dust absorption. As already discussed in Sections 4.1 and 4.2, global dust emission cannot provide a definitive distinction either, even with well-sampled dust SEDs in the crucial IR/submillimeter range.

In Figure 11, we show a possible statistical distinction between these two possibilities using CO J = 1–0 (the main bulk molecular gas mass tracer), HCN J = 1–0 (the most widely used dense gas tracer), along with CO J = 6–5, 3–2. The $R_{{\rm HCN/CO}}=L^{^{\prime }}_{{\rm HCN}(1\hbox{--}0)}/L^{^{\prime }}_{{\rm CO}(1\hbox{--}0)}$ ratio (Table 2) is considered here as an approximate measure of the dense molecular gas mass fraction (since n_crit(CO) ∼ 410 cm⁻³ and n_crit(HCN) ∼ 2 × 10⁵ cm⁻³), with little sensitivity to temperature since for both CO and HCN J = 1–0: E₁₀/k_B ∼ 4–5 K. The low frequencies of ∼115 GHz (CO J = 1–0) and ∼87 GHz (HCN J = 1–0), ensure that R_HCN/CO remains unaffected by dust extinction. From Figure 11 it becomes apparent that several LIRGs have very high R_HCN/CO (≳0.15) and very low R_65/32 ≲ 0.2 ratios, quite unlike typical star-forming galaxies with much lower IR luminosities (and thus SFRs). Thus, unless one is willing to entertain the possibility of massive amounts of dense but otherwise SF-idle molecular gas in these (mostly) merger systems, such LIRGs are likely to be starbursts with dust-suppressed high-J CO lines.

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Considering SF as a process directly fueled by self-gravitating dense gas means that star formation switches on rapidly in the dense HCN-bright phase, with its typically short dynamical times t_dyn ∼ 10⁵ yr (much shorter than Giant Molecular Cloud (GMC) evolutionary timescales of ∼10⁶–10⁷ yr). This likely yields the tight L_IR–L_HCN(1–0) correlation in galaxies (Gao & Solomon 2004), extending "down" to individual GMCs and spanning 7–8 orders of magnitude in L_IR (Wu et al. 2005). It also provides the basis for our aforementioned CO–HCN line ratio diagnostic and its ability to "weed-out" dust-affected CO SLEDs from genuinely low-excitation ones. In the few cases where multi-J dense gas tracers (e.g., HCN, CS) and dust SEDs are available to constrain the state of the dense gas in LIRGs, it is always found in the warm and self-gravitating "corner" of the available parameter space, typical of star-forming gas (Mao et al. 2000; Papadopoulos et al. 2007; Greve et al. 2009), and where R_65/32 ≳ 0.45. Moreover for the lowest possible temperature of T_k ∼ 10 K in dense starless cores deep in GMCs (regulated by cosmic rays rather than photons), a minimum

$$\begin{equation} R_{65/32}=\frac{E_{65}}{E_{32}} \left(\frac{e^{E_{32}/k_BT_k}-1}{e^{E_{65}/k_BT_k}-1}\right)= 2\left(\frac{e^{16.6/T_k}-1}{e^{33.2/T_k}-1}\right) \sim 0.32, \end{equation} \tag{ 11 }$$

is expected for the optically thick CO emission (shown also in Figure 4 as a dotted line). Thus even for the unlikely case of a high R_HCN/CO ratio due to a massive and dense but otherwise SF-idle cold gas phase, this is the lowest R_65/32 value possible. Values of R_65/32 ≲ 0.3 would then imply either a dominant gas phase that necessarily has 〈n(H₂)〉 ≲ 10⁴ cm⁻³ (and thus also low R_HCN/CO), or dust suppression of the CO J = 6–5 line luminosity. In the second case such dust-affected LIRGs would then populate the area marked by R_65/32 ≲ 0.3 and R_HCN/CO ≳ 0.15, shown in Figure 11 to be containing several objects.

The brightest CO J = 6–5 lines in our sample are measured in the hosts of two powerful AGNs, the optically luminous QSO PG 1119+120 and the FR II radio galaxy 3C 293 known for a particularly powerful jet (Floyd et al. 2006). These are also the only two objects where R_65/32>1, possible only for CO line emission that is optically thin and remains well-excited up to J = 6–5, which requires very warm and dense molecular gas. This becomes apparent from its maximum value, achieved in the LTE optically thin limit,

$$\begin{eqnarray} R^{({\rm thin})} _{65/32}({\rm LTE}) &=& \frac{J(\nu _{65}, T_k)}{J(\nu _{32}, T_k)} \left(\frac{\tau _{65}}{\tau _{32}}\right)\nonumber\\ &=& \left(\frac{\nu _{65}}{\nu _{32}}\right)^2\,e^{-E_{52}/k_BT_k}=4\,e^{-66.35/T_k}, \end{eqnarray} \tag{ 12 }$$

where J(ν, T_k) = (hν/k_B)[exp(hν/k_BT_k) − 1]⁻¹ (the cosmic microwave background (CMB) has been omitted for simplicity). For PG 1119+120 even R_65/32 = 2 (i.e., ∼(the measured value)–σ) yields T_k = 96 K, which is rather high for the bulk of its molecular gas. Submillimeter interferometric imaging has recently uncovered such high brightness temperatures for the dust (and thus for the concomitant molecular gas since T_kin ≳ T_dust) in Arp 220, but its molecular gas reservoir consists of very dense gas with CO line optical depths that are nowhere near the optically thin limit (Greve et al. 2009). Comprehensive LVG radiative transfer modeling of such a high CO (6–5)/(3–2) ratio, made over a larger gas temperature range of T_k = (15–310) K (to allow the possibility of very warm gas) yields its best solutions for n(H₂) ∼ 10⁵ cm⁻³ and T_k ≳ 140 K (with solutions improving right up to 310 K). Such high gas temperatures could in principle be the result of bulk irradiation of the molecular gas by X-rays emanating from a central AGN creating giant X-ray-dominated regions (XDRs), rather than starburst-induced far-UV irradiated PDRs (see Meijerink & Spaans 2005). Very high CO line excitation in AGN hosts that could be attributed to X-ray luminous AGNs has been observed recently (Papadopoulos et al. 2008), but unfortunately no X-ray data are available for PG 1119+120 in particular, and the cause of its large CO J = 6–5 luminosity remains unknown.

Large amounts of molecular gas (∼10⁹–10¹⁰ M_☉) have been discovered in IR-luminous powerful radio galaxies locally as well as at high redshifts (e.g., Evans et al. 1999, 2005; De Breuck et al. 2005). In 3C 293, shocks emanating from a very strong jet–ISM interaction (Emonts et al. 2005) may be responsible for a galaxy-wide shock-induced CO line excitation (Papadopoulos et al. 2008). A "trademark" of this excitation mechanism could be its capability of producing highly excited mid-J and high-J CO lines, even in the absence of high SFRs, since the shock-induced turbulent heating would deposit most of its energy on the gas leaving the concomitant dust mass reservoir much less affected. The high luminosity CO J = 4–3 and J = 6–5 lines in 3C 293, with (4–3)/(3–2), (6–5)/(3–2) ratios of R_43/32 = 2.3 ± 0.91 and R_65/32 = 1.3 ± 0.54, seem to bear this out by representing some of the highest levels of global molecular gas excitation discovered in our sample but in a system whose low-level SF (SFR ≲ 4 M_☉ yr⁻¹) is insufficient to "power" them.

We extended our LVG modeling of the extraordinarily high R_43/32 and R_65/32 ratios in 3C 293 to cover a larger range of T_k = (15–310) K and allow also K_vir>1 rather than K_vir ∼ 1. We do so because turbulent heating can drive molecular gas temperatures well above those in star-forming regions (where typically T_kin ≲ 100 K), while K_vir ≳ 1 widens the LVG solution search to include non-self-gravitating gas phases. These are now more probable given the large kinetic energy injection from the powerful jets driving very impressive gas outflows in 3C 293 (Morganti et el. 2003; Emonts et al. 2005), and the fact that no massive star-forming (and thus self-gravitating) gas phase "powering" the luminous high-J CO lines is present in 3C 293. The characteristics of the various LVG solution groups are summarized in Table 4, where two facts immediately stand out: (1) the best solutions are provided by a very warm T_k ∼ (130–310) K and dense n(H₂) ∼ (10⁴–10⁵) $\rm cm^{-3}$ gas phase, and (2) most solutions with T_k ≲ 80 K are ruled out since they have K_vir ≪ 1 (marked with asterisk in Table 4). Such kinematic states are deemed unphysical since gas motions cannot be slower than those induced by gas self-gravity (only raising the $\rm [CO/H_2]$ abundance by factors of ≳10 could make K_vir ∼ 1). On the other hand almost all of the good solutions found have K_vir ∼ 15–49, indicating highly unbound gas states. We must also note that in all solutions listed in Table 4 the fit continues improving well past the T_k = 310 K limit of the LVG parameter grid, while gas densities remain high (∼(10⁴–10⁵) cm⁻³). On the other hand the non-AGN cool dust SED in 3C 293 carries little luminosity (L_IR ∼ 3 × 10¹⁰ L_☉) and is typical for quiescent ISM.

Thus in the powerful radio galaxy 3C 293 the molecular gas seems to be in a surprisingly hot, dense, and gravitationally unbound state, while the bulk of its concomitant dust reservoir maintains lower temperatures and has only a modest IR luminosity. Tellingly, similar ISM conditions have been reported for the turbulent molecular clouds in the Galactic Center (Rodrígez-Fernández et al. 2001) where very warm and dense H₂ is concomitant with cold dust (Pierce-Price et al. 2000), as well as in 3C 326, another FR II radio galaxy (Ogle et a. 2007). In the latter case jet-induced shocks are also suggested as the culprit for a LIRG-sized mass (∼10⁹ M_☉) of very warm molecular gas (T_k ∼ 125–1000 K), despite star formation levels even lower (∼0.1 M_☉ yr⁻¹) than those found in 3C 293.

In Figure 12, we show the range of CO SLEDs corresponding to the shocked-excited ISM environment of 3C 293. Clearly more observations of high-J CO lines, now possible with the spaceborne Herschel Space Observatory, are needed to better constrain them and verify shock-excited molecular gas over large scales in this powerful radio galaxy and other similar systems. The very large molecular gas reservoirs found around radio galaxies at high redshifts, and the potential feedback role of their energetic jets in inducing (Klamer et al. 2004) or hindering (Ogle et al. 2007) starbursts in galaxy formation events at early cosmic epochs, make a detailed study of shock-energized molecular gas even more important. Distinct and accessible "signatures" of shocked molecular gas states on SLEDs of various molecules would be particularly valuable in the upcoming era of ALMA.

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Extremely dense and compact gaseous disks able to attain significant dust optical depths at short submillimeter wavelengths in LIRG/AGN systems can have dramatic effects on their emergent ISM lines used as AGN-versus-starburst diagnostics. In the presence of such gas disks around AGNs, ISM line diagnostics using IR and even molecular lines at short submillimeter wavelengths (e.g., very high-J CO lines) to discriminate between dust-enshrouded AGN-excited XDRs versus starburst-excited PDRs can become difficult to employ. Relative line strengths may then be more indicative of relative dust optical depths rather than intrinsic gas excitation properties and their causes. Interestingly all four LIRGs with R_65/32 ≳ 0.5 (i.e., IRAS 02483+4302, VII Zw 31, PG 1119+120, and Mrk 231) have face-on or nearly face-on molecular gas disks, indicated either by high-resolution CO interferometry (Downes & Solomon 1998) and/or by their narrow CO line widths (3C 293 is the only exception). This would be expected for gas disks where the smaller dust optical depths in face-on than in highly inclined gas disks along the line of sight would enhance their (line)-(continuum) contrast. Nevertheless nearly face-on systems with low R_65/32 ratios do exist (e.g., IRAS 00057+4021), and systematic CO J = 6–5 observations of optically selected QSO samples (which will contain many more face-on gas disks) would be valuable in revealing such geometric effects.