Annu. Rev. Astron. Astrophys. 2013. 51: 207-268 Copyright © 2013 by Annual Reviews. All rights reserved

7. X_CO IN STARBURSTS AND OTHER LUMINOUS GALAXIES

Molecular gas in starbursts exists under conditions very different from those found in most normal galaxies. Observations of starbursts suggest widespread gas volume and column densities much higher than those typical of normal disks (e.g., Jackson et al. 1995, Iono et al. 2007). Molecular gas in starbursts is also warmer, exciting higher rotational transitions than those found in less active objects (e.g., Bradford et al. 2003, Ward et al. 2003, Rangwala et al. 2011). In fact, a negative correlation is observed between molecular gas depletion time (a parameter that characterizes how long a galaxy can maintain its current star formation rate), and excitation (e.g., Paglione, Jackson & Ishizuki 1997). Similarly, a positive correlation exists between gas density and star formation rate (e.g., Gao & Solomon 2004). These observations show that there is a fundamental relation between the density and temperature of the molecular gas and the existence of starburst activity, such that the gas present in starbursting galaxies or regions has higher densities and temperatures than those prevalent in quiescent systems.

What are the effects of higher temperatures, densities, and column densities on X_CO ? To first order, higher gas temperatures yield brighter CO emission, decreasing X_CO. Note, however, that while increasing the temperature decreases X_CO, increasing the density and surface density of the self-gravitating clouds of gas has the opposite effect, increasing X_CO (see Eqs. 11, 12, and 15). Therefore we expect a certain level of compensation to occur, lessening the impact of environment on the conversion factor as long as most of the CO emission arises from GMCs. In regions where the average gas density is comparable to that of a GMC, however, the entire medium will turn molecular and CO emission will originate from an extended warm phase. These conditions are thought to be prevalent throughout the active regions of the brightest starbursts, such as ULIRGs. Adding to this fact, many of these luminous galaxies are mergers, or the starbursts occur in regions such as galaxy centers. The gas correspondingly experiences motions in excess of the velocity dispersion due to its self-gravity. The large column densities conspire to make the medium globally optically thick, thus setting up the conditions discussed in Section 2.3. In this situation the CO emission will be disproportionally luminous, driving X_CO to lower values.

We can quantitatively explore this scenario with PDR model calculations (adapted from Wolfire, Hollenbach & McKee 2010), which incorporate self-consistently the chemistry, heating, and radiative transfer. Setting up a "typical" Milky Way GMC (a virialized structure of size ~ 30 pc with _mol 170 M pc^-2 and M 1 × 10⁵ M) we reproduce a Galactic X_CO. In a ~ 160 pc virialized cloud with _mol 10⁴ M pc^-2 and M 2 × 10⁸ M (representing the molecular structures observed in existing high-resolution observations of ULIRGs) under the same Galactic conditions, we obtain X_CO,20 ~ 80 in rough agreement with Eq. 11. Increasing the gas velocity dispersion to include 2 × 10⁹ M of stars (see Section 2.3), and increasing the UV and cosmic ray fluxes by 10³ to account for the larger SFR, decreases the conversion factor to X_CO,20 ~ 0.6. Most of this effect is due to the velocity dispersion: increasing the UV and cosmic ray fluxes by only 10 with respect to the Galactic case yields X_CO,20 ~ 2, still much lower than the starting value of 80.

Narayanan et al. (2011) explore these effects in detail using a series of computational models of disks and merging galaxies. They find that X_CO drops throughout the actively star-forming area in merger-driven starbursts due to increased gas temperatures (caused in part by collisional thermal coupling between dust and gas, which occurs at high densities), and the very large velocity dispersion in the gas (in excess of self-gravity) which persists for at least a dynamical time after the burst. The magnitude of the drop in X_CO depends on the parameters of the merger, with large X_CO corresponding to low peak SFR. Thus, the large drop in X_CO occurs in massive mergers during the starburst phase, and X_CO settles to normal values when the star formation activity and the conditions that caused it subside. The simulated normal disk galaxies experience less extreme conditions of density and turbulence, and accordingly possess higher values of X_CO except in their centers. The mean values of the CO-to-H₂ factor for the simulated mergers and disks are X_CO,20 0.6 and 4 respectively, with a very broad distribution for the mergers. In a follow-up study Narayanan et al. (2012) introduce a calibration of X_CO where it becomes a function of W(CO), as well as metallicity, Z. This calibration captures the fact that the factors that cause a drop in X_CO occur increasingly at higher surface densities. Note, however, that because X_CO is a non-linear function of W(CO) obtained from luminosity-weighted simulations, the calibration must be applied carefully to observations. The observed CO intensity corresponds to the intrinsic intensity multiplied by a filling factor f_beam < 1, while the luminosity-weighted W(CO) employed by the model-derived calibration is much closer to the intrinsic CO intensity, which is not directly observed because observations do not completely resolve the source.

In the following sections we will discuss the observational findings in starburst galaxies in the local universe.

7.1. Luminous Infrared Galaxies

One of the earliest comprehensive studies of the state of the molecular gas and the value of X_CO in a luminous infrared galaxy (LIRG) was performed on the prototypical starburst M 82. Wild et al. (1992) use multi-transition observations and detailed excitation calculations to determine the proportionality between the optically thin C¹⁸O emission and the H₂ column density. Bootstrapping from this result, they find that X_CO varies across the disk of M 82, and is in the range X_CO,20 0.5-1. They attribute this low X_CO mostly to high temperatures, as they estimate T_kin > 40 K for the bulk of the gas from their modeling. Using a similar technique, Papadopoulos & Seaquist (1999) analyze the inner region of NGC 1068, a well known starburst with a Seyfert 2 nucleus. They conclude that a diffuse, warm, molecular phase dominates the ¹²CO emission, while the mass is dominated by a denser phase that is better observed in the C¹⁸O isotopologue. The ¹²CO J = 1 → 0 emission from the diffuse phase has low optical depth (₁ ~ 1-2) and is not virialized, and is thus overluminous with respect to its mass. They argue that the CO-to-H₂ conversion factor in the nuclear region is X_CO,20 ~ 0.2-0.4, although the precise value depends critically on the assumed CO abundance.

Along similar lines, Zhu, Seaquist & Kuno (2003) perform a multi-transition excitation study of molecular gas in the Antennae pair of interacting galaxies (NGC 4038 / 9). They find that the H₂ gas mass in their analysis depends critically on the ¹²CO/H₂ abundance ratio, which is an input to their model. They conclude that ¹²CO/H₂ ~ 0.5-1 × 10^-4, and consequently X_CO,20 ~ 0.2-0.4 for the center of NGC 4038 and X_CO,20 ~ 0.5-1 for the "overlap" region between both galaxies. They argue that the adoption of this smaller-than-standard X_CO is consistent with the gas distribution, including HI, in the interacting pair, while the very large mass for the "overlap" region that would result from adopting a standard X_CO would be very difficult to reconcile with the gas dynamics. The authors find that their excitation analysis points to gas with high velocity dispersion, large filling fraction, and low optical depth as the reason why CO is overluminous in the Antennae. Recently, Sliwa et al. (2012) find also a low X_CO in their excitation and dynamical analysis of Arp 299 using interferometric data, X_CO,20 0.2-0.6.

The broad conclusions of these in-depth studies are in agreement with findings from studies carried over large samples. Yao et al. (2003) survey 60 local infrared-luminous (starburst) galaxies spanning FIR luminosities L_FIR ~ 10⁹ - 10¹² L, analyzing their ¹²CO J = 1 → 0 and J = 3 → 2 emission. Using the dust temperature as a proxy for the gas temperature, and assuming coextensive emission and a CO/H₂ abundance ratio similar to what would be expected if all the gas phase carbon was locked in CO molecules for Milky Way abundances, they conclude that X_CO,20 ~ 0.3-0.8 is consistent with the available data.

Papadopoulos et al. (2012) perform a detailed analysis on another large sample of luminous infrared galaxies, with L_FIR 10¹¹ L. They find that one-phase radiative transfer models generally match the observations for the lower J transitions of CO with a typical X_CO,20 ~ 0.3 (_CO 0.6 ± 0.2 M (K km s^-1 pc²)^-1), a value compatible with previous studies (e.g., Downes & Solomon 1998). The authors conclude that although the gas temperature is partially responsible for the lower X_CO, the most important factor is the gas velocity dispersion. They also point to a caveat with this result, which has to do with the possible existence of a dense, bound phase with lower velocity dispersion and a much higher X_CO. This phase is associated with dense gas tracers such as high-J CO or heavy rotor molecules (HCN, CS, HCO⁺). It has the potential to dominate the molecular mass of the system, and raise the conversion factor to X_CO,20 ~ 2-6. Because the uniqueness of this explanation for the observed excitation is unclear, and the derived masses conflict in some cases with dynamical mass estimates, we consider the results of multi-component models an interesting topic for further research. Papadopoulos et al. (2012) also point out that although the global CO J = 1 → 0 luminosity is dominated by the warm, low X_CO component, it is possible to hide a cold, normal X_CO component that could add a significant contribution to the molecular mass of the system. This component would most likely be spatially distinct, for example an extended molecular disk, and thus could be separated in high spatial resolution studies with interferometers.

7.2. Ultraluminous Infrared Galaxies

Ultra-luminous infrared galaxies (ULIRGs) are extreme cases of dust-enshrouded stabursts and active galactic nuclei, with far-infrared luminosities in excess of L_FIR ~ 10¹² L. These objects are the products of gas-rich major mergers, and possess very large CO luminosities (Mirabel & Sanders 1988, Sanders & Mirabel 1996). Despite that, their L_FIR / L_CO ratios frequently exceed those found in spiral galaxies, including interacting pairs, and Milky Way GMCs. The fundamental question is how those CO luminosities relate to their molecular gas masses. Understanding X_CO in ULIRGs is particularly interesting because they likely provide the best local templates for the most luminous high-redshift submillimeter galaxies, which have very high star formation rates compared to other galaxies of similar stellar mass at their redshift (i.e., are off the main sequence, Tacconi et al. 2006, Narayanan et al. 2010).

Studies presented in a series of papers (Downes, Solomon & Radford 1993, Solomon et al. 1997, Downes & Solomon 1998, Bryant & Scoville 1996, Bryant & Scoville 1999) show that the molecular gas masses obtained for ULIRGs using the Galactic disk CO-to-H₂ conversion factor are uncomfortably close to (or exceed) their dynamical masses, suggesting that the Galactic X_CO overestimates their total molecular mass. These authors develop a consistent one-component model that explains the high-resolution observations as rotating, highly turbulent remnants of the merging process. The CO emission is dominated by low density gas, and although it is optically thick it is only moderately so (for example, see also Iono et al. 2007). This lower molecular mass is consistent with the observed (optically thin) millimeter dust continuum emission for Galactic dust-to-gas ratio. The "typical" X_CO they derive is X_CO,20 ~ 0.4, approximately a factor of 5 lower than in the Milky Way disk (_CO ~ 0.8 M (K km s^-1 pc²)^-1, with individual results ranging between 0.3 and 1.3 in Table 9; Downes & Solomon 1998).

Detailed high resolution studies of individual ULIRGs find similar results. Bryant & Scoville (1996, 1999) study the kinematics of seven LIRGs and ULIRGs, determining interferometric sizes and dynamical masses. They conclude that the use of a Milky Way conversion factor results in molecular masses larger than the dynamical mass of the system in the cores of all seven objects, although in some cases that can be explained away assuming a face on orientation. They find X_CO,20 < 0.7 and X_CO,20 < 1.5 for Mrk 231 and NGC 6240 respectively. Modeling the CO kinematics of Arp 220, including the effects of the stellar components in the dynamics of the nuclear disk, Scoville, Yun & Bryant (1997) find X_CO,20 ~ 1. These estimates are comparable with those from one-component radiative models for the same galaxies, and typically much lower than the two-component results (Downes & Solomon 1998, Papadopoulos et al. 2012).

7.3. Synthesis: X_CO in Starbursts

There has been much recent progress, through both observations and modeling, on the determination of X_CO in starbursts. Studies of CO excitation in large samples, as well as detailed studies of individual cases, strongly point to lower than Galactic values of X_CO, particularly in extreme starbursts such as ULIRGs. These low values of X_CO are driven by a globally molecular medium coupled with high gas temperatures and, more importantly, very high velocity dispersions in the CO emitting gas due to a combination of merger activity and the stellar potential (Narayanan et al. 2011, Papadopoulos et al. 2012). The standard practice has been to adopt _CO 0.8 M (K km s^-1 pc²)^-1 (Downes & Solomon 1998), a value similar to the _CO 0.6 ± 0.2 M (K km s^-1 pc²)^-1 resulting from recent one-component modeling in a large sample (Papadopoulos et al. 2012). Note, however, that this is an average value and there are likely large galaxy-to-galaxy variations (Narayanan et al. 2011). To first order these variations should be mostly related to the total surface density of the galaxy, if the gas is bound and experiencing the global gravitational potential (c.f., Eq. 16). We will use this to suggest a tentative X_CO correction in Section 9.

Large uncertainties exist in the estimates from observations, stemming from assumptions about ¹²CO / H₂ and ¹²CO / ¹³CO ratios, coextensive emission in the different transitions, and the general need for simplifications in excitation models. Note also, as a persistent caveat, the possibility of hiding significant molecular mass in ULIRGs in a low velocity dispersion, dense component. This posibility, however, seems disfavored in some cases where high quality dynamical estimates are available.