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

5. X_CO IN NORMAL GALAXIES

The distance of even the nearest galaxies renders CO the primary tracer of molecular gas outside the Milky Way, a situation that will improve but not reverse with ALMA. Other galaxies therefore represent the key application of X_CO. They also offer a wider range of environments than the Milky Way and a simpler mapping between local ISM conditions, especially metallicity, and line of sight. As a result, for more than two decades observations of the nearest galaxies have been used to test and extend calibrations of X_CO as a function of metallicity and other local ISM properties. Here we review the techniques available to derive X_CO in "normal" galaxies, meaning star-forming dwarf, spiral, or elliptical galaxies. We discuss specific efforts to understand the behavior of X_CO as a function of metallicity in Section 6 and the special case of overwhelmingly molecular starburst galaxies, such as the local luminous and ultraluminous infrared galaxies, in Section 7. Section 8 considers X_CO in galaxies at high redshift.

Only a subset of the techniques used to determine X_CO in the Milky Way can be applied to other galaxies. In each case, the limited sensitivity and resolution of millimeter, submillimeter, and infrared facilities complicate the calculation. Direct estimates rely almost exclusively on the use of virial mass measurements (Section 4.1), dust emission employed as an optically thin tracer of the total gas reservoir (Section 4.2), or modeling of multiple CO lines. Ideally such modeling includes optically thin isotopologues, but studies of high redshift systems must often make due with a few, or only one, ¹²CO line ratios (Section 8).

5.1. Extragalactic Virial Mass Estimates

Since the late 1980s, millimeter telescopes have been able to resolve CO emission from nearby galaxies into discrete molecular clouds. From such observations, one can estimate the line width, size, and luminosity of these objects and proceed as in Section 4.1 (see the recent review by Fukui & Kawamura 2010).

Resolution and sensitivity have limited virial mass measurements to the nearest galaxies, those in the Local Group and its immediate environs. The Magellanic Clouds (d ~ 50 kpc) are close enough that single dish telescopes resolve individual clouds (e.g., Rubio, Lequeux & Boulanger 1993, Israel et al. 2003, Mizuno et al. 2001, Fukui et al. 2008, Hughes et al. 2010, Wong et al. 2011). Millimeter-wave interferometers resolve populations of GMCs in other Local Group galaxies — M 31, M 33, NGC 6822, and IC 10 (d ~ 1 Mpc, e.g., Vogel, Boulanger & Ball 1987, Wilson & Scoville 1990, Wilson 1995, Rosolowsky et al. 2003, Leroy et al. 2006, Blitz et al. 2007, Fukui & Kawamura 2010).

Early measurements beyond the Local Group focused on very nearby dwarf galaxies (d ~ 3 Mpc, Taylor et al. 1999, Walter et al. 2001, Walter et al. 2002, Bolatto et al. 2008) or considered structures more massive than GMCs in more distant galaxies (Giant Molecular Associations, or GMAs, e.g., Vogel, Kulkarni & Scoville 1988, Rand & Kulkarni 1990). The nearest spiral galaxies tend to be more distant (d ~ 6 Mpc), so that ~ 1 resolution is required to resolve massive GMCs. Only recently mm-wave interferometers have begun to achieve this resolution with the requisite sensitivity, by investing large amounts of time into dedicated observations of bright regions of the nearest massive spiral galaxies (Donovan Meyer et al. 2012, Donovan Meyer et al. 2013, Rebolledo et al. 2012). This has allowed the first cloud-scale virial mass measurements of populations of clouds in spiral galaxies beyond the Local Group.

5.1.1. X_CO From Extragalactic Virial Mass Analyses

Broadly, virial mass measurements across a wide range of environments yield X_CO,20 1-4, consistent with Milky Way results and very similar to X_CO derived from dust-based techniques applied to high mass nearby galaxies. Bolatto et al. (2008) find X_CO,20 3.5_-1.2^+1.8 in 12 nearby systems. In the highest resolution studies of the Large Magellanic Cloud (LMC) to date, Israel et al. (2003), Hughes et al. (2010), Wong et al. (2011), and Pineda et al. (2010) all find X_CO,20 4. Considering NGC 6946, one of the nearest molecule-rich spiral galaxies, Donovan Meyer et al. (2012) report X_CO,20 1.2 and Rebolledo et al. (2012) find X_CO,20 ~ 2. In M 33, Rosolowsky et al. (2003) show X_CO,20 ~ 2 independent of radius and metallicity. In M 31, Rosolowsky (2007) calculate X_CO,20 4 assuming virial equilibrium.

Figure 6 shows the relationship between virial mass and CO luminosity for a subset of these measurements. A good correlation extends across three orders magnitude in luminosity and roughly a dozen systems. As in the Milky way, there may be evidence for a slightly sub-linear slope (see Section 2.1 and Section 4.1 and Figure 2), though this may also reflect methodological or environmental differences among the galaxies studied. Across the ensemble of points we plot the median X_CO,20 = 2.9 with 0.4 dex scatter (slightly larger than a factor of 2).

Figure 6. Relation between virial mass (y-axis) and CO luminosity (x-axis) for extragalactic GMCs. We show virial masses measured from selected high spatial resolution CO observations of nearby galaxies: the compilation of Bolatto et al. (2008), including M 31, M 33, and nine dwarf galaxies), high resolution studies of the LMC by Pineda et al. (2009) and Wong et al. (2011), and high resolution studies of the nearby spiral NGC 6946 by Donovan Meyer et al. (2012) and Rebolledo et al. (2012), as well as NGC 4826 and NGC 4736 by Donovan Meyer et al. (2013). Dashed lines show fixed XCO, with the typical Milky Way value XCO,20 = 2 and ± 30% indicated by the gray region. Virial mass correlates with luminosity, albeit with large scatter, across more than three orders of magnitude in extragalactic systems. The median across all displayed data is XCO,20 = 2.8 with 0.4 dex scatter and the best fit relation has a power law index 0.90 ± 0.05, reflecting that most Local Group clouds show XCO,20 ~ 4 while both studies of the bright spiral NGC 6946 find a lower XCO,20 1-2.

Surprisingly at first, these "Galactic" X_CO values obtained from virial masses extend to low metallicity, irregular galaxies. In the low metallicity Small Magellanic Cloud (SMC, with 12 + log[O/H] 8.0, Dufour, Shields & Talbot 1982), Bolatto et al. (2003) and Israel et al. (2003) find X_CO,20 4, consistent with the Milky Way value. Rosolowsky et al. (2003) find no dependence of X_CO on metallicity in M 33. Leroy et al. (2006) find an approximately Galactic X_CO in the Local Group dwarf IC 10 ([12 + log[O/H] 8.17, Lequeux et al. 1979). Wilson (1994) found X_CO,20 6.6 in NGC 6822 (12 + log[O/H] 8.20, Lequeux et al. 1979). Most of the galaxies studied by the aforementioned (Bolatto et al. 2008) are dwarf irregulars with subsolar metallicity. In each case we highlight the results for the highest resolution study of the galaxy in question. We discuss the effects of varying spatial resolution in the next section. Overall, these studies show that high spatial resolution virial mass measurements suggest roughly Galactic X_CO irrespective of metallicity.

Virial masses have also been measured for very large structures, GMAs or superclouds (Vogel, Kulkarni & Scoville 1988, Wilson et al. 2003), although it is unclear the degree to which they are virialized or even bound. Wilson et al. (2003) consider ~ 500 pc-scale structures in the Antennae Galaxies and find the X_CO to be approximately Galactic (see also Ueda et al. 2012, Wei, Keto & Ho 2012), but this conflicts with results from spectral line modeling (see Section 7). Phrasing their results largely in terms of boundedness, Rand & Kulkarni (1990) and Adler et al. (1992) find X_CO,20 ~ 3 and X_CO,20 ~ 1.2 to be needed for virialized GMAs in M 51. Studies of other galaxies, for example M 83 (Rand, Lord & Higdon 1999), suggest that not all GMAs are gravitationally bound and that the mass spectrum of GMAs varies systematically from galaxy to galaxy or between arm and interarm regions (Rand & Kulkarni 1990, Rand, Lord & Higdon 1999, Wilson et al. 2003), complicating the interpretation of these large-scale measurements.

5.1.2. Caveats on Virial Mass-Based X_CO Estimates

As we will see in Section 5.2, the approximately constant Galactic X_CO implied by virial masses on small scales at low metallicity appears to contradict the finding from dust-based measurements and other scaling arguments (for example Blanc et al. 2013), which consistently indicate that X_CO increases with decreasing metallicity. This discrepancy most likely arises because virial mass measurements sample the gas that is bright in CO, while dust-based measurements include all H₂ along the line-of-sight. As discussed below (Section 6), decreasing dust shielding at low metallicities causes CO to be preferentially photodissociated relative to H₂, creating a massive reservoir of H₂ in which C⁺ and C rather than CO represent the dominant forms of gas-phase carbon. Because this reservoir is external to the CO emitting surface it will not be reflected in the CO size or its line width (unless the surface pressure term is important). Thus, we expect that high resolution virial mass measurements preferentially probe X_CO in the CO-bright region.

The range of values discussed above, X_CO,20 ~ 1-4, is significant. Does it indicate real variations in X_CO? Measuring cloud properties involves several methodological choices (Section 4.1). Different methods applied to the same Milky Way data shift results by ~ 30%, and biases of ~ 40% are common in extragalactic data (e.g., Rosolowsky & Leroy 2006). As we discuss below, the X_CO obtained by virial mass analysis seems to depend on the physical resolution of the observations. Ideally, results will be compared to "control" measurements that have been extracted and analyzed in an identical way, ideally at matched spectral and spatial resolution and sensitivity (e.g., Pineda et al. 2009). Many studies now employ the CPROPS algorithm (Rosolowsky & Leroy 2006), which is designed to account for sensitivity and resolution biases in a systematic way, allowing ready cross-comparison among data sets. This is not a perfect substitute, however, for matched analyses. Our assessment is that in lieu of such careful comparison, differences of ± 50% in X_CO should still be viewed as qualitatively similar.

We raised the issue of spatial scale in the discussion of systematics and implicitly in the discussion of GMAs. Virial mass-based X_CO exhibit a complex dependence on the spatial scale of the observations. For dwarf galaxies it seems that even using similar methodology and accounting for resolution biases, studies with finer spatial resolution systematically return lower X_CO than coarser resolution studies. For example, Hughes et al. (2010) find X_CO,20 4 in the LMC (as do Israel et al. 2003, Pineda et al. 2009, Wong et al. 2011) compared to X_CO,20 7 found by Fukui et al. (2008) using similar methodology but with ~ 3 times coarser linear resolution. In the SMC, Mizuno et al. (2001) find X_CO,20 14, while higher resolution studies find X_CO as low as X_CO,20 ~ 2-4 for the smallest resolved objects (Israel et al. 2003, Bolatto et al. 2003). Contrasting the interferometer measurements of Wilson (1994) and the coarser single-dish observations of Gratier et al. (2010) reveals a similar discrepancy in NGC 6822. In one of the first studies to consider this effect, Rubio, Lequeux & Boulanger (1993) explicitly fit a dependence for X_CO in the SMC as a function of spatial scale, finding X_CO R^0.7 (see also the multiscale analyses in Bolatto et al. 2003, Leroy et al. 2009).

This scale dependence may reflect one of several scenarios. First, low resolution observations can associate physically distinct clouds that are not bound, causing a virial mass analysis to overpredict X_CO. Alternatively, the ensemble of clouds conflated by a coarser beam may indeed be bound. In the case of a heavily molecular interstellar medium like the Antennae Galaxies or the arm regions of M 51, most of the material in the larger bound structure may be molecular and a virial mass measurement may yield a meaningful, nearly Galactic conversion factor for objects much bigger than standard GMCs. For a low metallicity irregular galaxy, the best case for low resolution virial mass measurements is that large complexes are virialized and that the low A_V gas between the bright clouds is H₂ associated with [CII]. We caution, however, that this is only one of many possible scenarios.

We suggest that the sensitivity of virial mass measurements to extended CO-free envelopes of H₂ is ambiguous at best. In that sense, the uniformity in X_CO derived from virial masses probably reflects fairly uniform conditions in CO-bright regions of molecular clouds (Bolatto et al. 2008). The spatial scale at which virialized structures emerge in galaxies is unclear. Given these ambiguities and the assumptions involved in the calculation of virial masses, we emphasize the need for careful comparison to matched data to interpret virial results.

5.2. Extragalactic Dust-Based Estimates of X_CO

Dust is expected and observed to be well-mixed with gas, and dust emission remains optically thin over most regions of normal galaxies. Following the approach outlined in Section 4.2, dust emission offers a tool to estimate X_CO. Modeling infrared or millimeter emission yields an estimate of the dust optical depth, _d. Using Eq. 23, X_CO can be estimated from _d, HI, CO, and the dust emissivity per H atom (Eq. 22). Conventions in the literature vary, with _d sometimes combined with a dust mass absorption coefficient and used as a dust mass, and _DGR alternately cast as the emissivity per H atom or a dust-to-gas mass ratio. Regardless of convention, the critical elements are a linear tracer of the dust surface density and a calibration of the relation between this tracer and gas column density.

Thronson et al. (1988) and Thronson (1988b) first suggest and apply variations on this technique to nearby galaxies. Israel (1997) uses data from IRAS to carry out the first comprehensive dust-based extragalactic X_CO study. He considers individual regions in eight (mostly irregular) galaxies and derives _d from a combination of 60 and 100µm continuum data. Israel (1997b) estimates _DGR, the dust emissivity per H atom, from comparison of _d and HI in regions within the galaxy of interest but chosen to lie well away from areas of active star formation, thus assumed to be atomic-dominated. This internally derived estimate of _DGR represents a key strength of the approach: _DGR is derived self-consistently from comparison of HI and _d, and does not rely on assuming a dust-to-gas ratio. This leads to the cancellation of many systematic errors (e.g., see Israel 1997b, Leroy et al. 2007), leaving only variations in _DGR and _d within the target to affect the determination of X_CO in Eq. 23.

5.2.1. Dust-Based Estimates in Normal Disk Galaxies

Spitzer and Herschel allowed the extension of the dust approach to more massive, more distant, and more "normal" galaxies. Draine et al. (2007) compare galaxy-integrated infrared spectral energy distribution (SED) modeling to CO and HI luminosities for a large sample. They argue that X_CO,20 4 (over entire galaxies) yields the most sensible gas-to-dust ratio results in their sample. Leroy et al. (2011) perform a self-consistent treatment of the Local Group galaxies M 31, M 33, LMC, NGC 6822, and SMC. They find X_CO,20 1-4.5 for regions of M 31, M 33, and the LMC (the higher metallicity galaxies in the sample). Smith et al. (2012) use Herschel observations to solve for X_CO finding X_CO,20 2 in M 31.

Other dust tracers such as mm-wave continuum emission and visual extinction have been used to arrive at X_CO estimates, although usually by assuming or scaling a Galactic calibration with the associated systematic uncertainties. Guelin et al. (1993) use 1.2 mm continuum observations of the edge-on spiral NGC 891 to estimate X_CO,20 ~ 1. Both Nakai & Kuno (1995) and Guelin et al. (1995) study X_CO in M 51, the first using extinction estimates from H / H, the second millimeter-wave continuum emission. Nakai & Kuno (1995) arrive at X_CO,20 0.9 ± 0.1 with a factor of ~ 2 variation with galactocentric radius, while Guelin et al. (1995) finds X_CO,20 ~ 0.6. Zhu et al. (2009) employs 850 µm data to check the X_CO derived from spectral line modeling in NGC 3310 and NGC 157, finding good agreement with X_CO,20 1.3-3.0 in the disks of their targets and a much lower X_CO in the center of NGC 157.

Sandstrom et al. (2012) carry out the most comprehensive extragalactic study of X_CO to date. They combine high-quality CO J = 2 → 1 maps with Herschel and Spitzer dust continuum, and high-resolution HI data. Building on the method of Leroy et al. (2011), they break apart galaxies into regions several kpc² in size and within each region they simultaneously solve for _DGR and X_CO. This yields resolved, self-consistent X_CO measurements across 22 galaxy disks. Their methodology requires good S/N CO detections and so restricts robust X_CO measurements to reasonably CO-bright parts of galaxies, typically half of the optical disks. There, the authors find X_CO,20 1.4-1.8 ² with a 1 scatter among individual solutions of 0.4 dex.

The top panel of Fig. 7 shows X_CO derived by Sandstrom et al. (2012) as a function of galactocentric radius for their whole sample. The bottom panel shows X_CO for each region normalized to the average value for the galaxy, highlighting the internal radial structure. This study finds clear central X_CO depressions for a number galaxies. The value of X_CO in galaxy centers relative to their disks spans a range from no change to a factor of five below the galaxy average. The authors note that these low central X_CO values tend to coincide with high stellar masses and enhanced CO brightness, suggesting that the effects discussed for starbursts in Section 7 may also be at play in the central parts of many galaxies, including the Milky Way (Section 4).

Figure 7. Dust-based CO determination across the disks of 22 galaxies (Sandstrom et al. 2012). The top panel shows the results for the individual regions (gray points), averages in radial bins for each galaxy (color lines), and the average trend for all data as a function of radius (black circles with error bars showing the scatter in that bin). The black solid line in the top panel corresponds to XCO,20 = 2, and the dotted line shows the average, weighting all solution pixels equally (XCO,20 = 1.2). Weighting by galaxy or CO intensity rather than line of sight, the mean is XCO,20 1.4-1.8 for low inclination galaxies. The bottom panel shows each galaxy normalized by its mean XCO to highlight the fact that many galaxies exhibit low XCO in their centers.

Thus in the disks of normal star-forming galaxies, a dust-based approach yields X_CO,20 1-4 on kpc scales. For comparison, in the Milky Way extinction yields X_CO,20 1.7-2.3 and dust emission yields X_CO,20 1.8-2.5 (Section 4.2, Table 1). Thus, broadly dust analyses strongly support a Milky Way conversion factor in the disks of normal, massive disk galaxies but methodological differences and, presumably, real changes in X_CO with environment produce a factor of 2 spread among studies and galaxies.

5.2.2. Dust-Based Estimates in Dwarf Irregular Galaxies

Dust-based determinations of X_CO in low metallicity dwarf irregular galaxies consistently yield values much higher than Galactic, and also generally higher than virial estimates. Israel (1997) finds in the SMC, the lowest metallicity target, a notably high X_CO,20 120 ± 20. Boselli, Lequeux & Gavazzi (2002) carry out a similar calculation and also find systematically higher X_CO at low metallicity. Subsequent studies leveraging the sensitivity, resolution, and wavelength coverage of Spitzer and Herschel qualitatively support this conclusion. Leroy et al. (2007, 2009), and Bolatto et al. (2011) follow Israel (1997) and Stanimirovic et al. (2000) in analyzing the SMC. They find X_CO,20 40-120 using measurements that isolate individual clouds and estimate _DGR locally. Gratier et al. (2010) considers NGC 6822 using a similar technique, also finding high X_CO,20 40 on large scales. Attempting to minimize systematics and making very conservative assumptions, Leroy et al. (2011) still find X_CO,20 10 and 40 for NGC 6822 and the SMC, significantly higher than they find for the higher metallicity M 31, M 33, and the LMC.

In the Magellanic Clouds, Herschel and millimeter-wave bolometer cameras have mapped individual molecular clouds. Roman-Duval et al. (2010) find an increase in X_CO in the poorly shielded outer regions of LMC clouds. Rubio et al. (2004), Bot et al. (2007), and Bot et al. (2010) find unexpectedly bright millimeter-wave emission in SMC clouds. Bot et al. (2010) show that the emission suggests a factor of four higher masses than returned by a virial analysis, even on very small scales and even assuming a very conservative rescaled Milky Way dust mass emissivity coefficient.

Therefore, dust-based X_CO estimates indicate high conversion factors in low metallicity, irregular systems. This agrees with some other methods of estimating X_CO but not with virial mass results, particularly on small scales, as already discussed (Section 5.1). We discuss the discrepancy further below (Section 6). The simplest explanation is that virial masses based on CO emission do not sample the full potential well of the cloud in low metallicity systems, where CO is selectively photodissociated relative to H₂ at low extinctions.

5.2.3. Caveats on Dust-Based X_CO Estimates

Because dust traces the total gas in the system with little bias (at least compared to molecules), this technique represents potentially the most direct way to estimate X_CO in other galaxies. We highlight two important caveats: the possibility of other "invisible" gas components and variations in the emissivity.

As described, the method will trace all gas not accounted for by HI 21 cm observations and assign it to H₂. The good qualitative and quantitative association between H₂ derived in this manner and CO emission suggests that H₂ does represent the dominant component (e.g., Dame, Hartmann & Thaddeus 2001, Leroy et al. 2009), but opaque HI and ionized gas may still host dust that masquerades as "H₂" using Eq. 23. Both components could potentially represent significant mass reservoirs. Their impact on dust-based X_CO estimates depends on the methodology. Any smooth component evenly mixed with the rest of the ISM will "divide out" of a self-consistent analysis. Moreover, the warm ionized medium exhibits a large scale height compared to the cooler gas discussed here and may be subject to dust destruction without replenishment (e.g., see Draine 2009). Planck Collaboration et al. (2011b) find that dust associated with their ionized gas template represents a minor source of emission. On the other hand, absorption line experiments from our galaxy and others suggest that ~ 20% HI may be missed due to opacity effects (Heiles & Troland 2003) and observations of M 31 suggest that it may lie in a filamentary, dense component (Braun et al. 2009), making it perhaps a more likely contaminant in X_CO determinations. Nonetheless, the close agreement between X_CO derived from dust and other determinations in our Galaxy strongly suggests that contamination from dust mixed with other "invisible" components, particularly the ionized gas, represents a minor correction.

Concerning the second caveat, the methodology relies on either blindly assuming or self-consistently determining the dust emissivity per hydrogen, _DGR. This is a combination of the dust-to-gas mass ratio, and the mass absorption coefficient of dust at IR wavelengths. In blind determinations, a linear scaling of Eq. 22 with metallicity is usually assumed. In self-consistent X_CO determinations, _DGR is measured locally through the ratio of the dust tracer to HI somewhere within the galaxy (for example, in an HI-dominated region), and ideally close to or inside the region where X_CO is estimated. This makes self-consistent determinations very robust. Even the most robust analyses, however, still assume _DGR to be constant over some region of a galaxy and along a line of sight, and between the atomic and molecular phases. The _DGR, however, may change across galaxies and between phases due to metallicity gradients, varying balance of dust creation and destruction, or changes in dust grain properties.

As discussed in Section 4.2, recent Planck results suggest only mild localized variations in the emissivity per H nucleon across the Milky Way. Observations of other galaxies do show that _DGR depends on metallicity (Draine et al. 2007, Muñoz-Mateos et al. 2009). Large scale ISM density may also be important; _DGR appears depressed in the low-density SMC Wing and the outer envelopes of dwarf galaxies (Bot et al. 2004, Leroy et al. 2007, Draine et al. 2007). The balance of the dust production and destruction mechanisms is complex: basic accounting implies that most dust mass buildup occurs in the ISM (Dwek 1998, Draine 2009 and references therein), suggesting an increase in _DGR in denser regions of the ISM where this accumulation must take place. Independent of dust mass buildup, if grains become more efficient emitters for their mass at moderate densities (through the formation of fluffy aggregates, for example) then the effective _DGR will be higher at high densities. Though not strongly favored by the overall Planck results, which suggest that emissivity variations are localized, a number of authors point to evidence for an environmental dependency of the dust emissivity (e.g., Cambrésy, Jarrett & Beichman 2005, Bot et al. 2007).

In our opinion these caveats concerning emissivity will lead a dust-based approach to preferentially overpredict the amount of H₂ present and consequently X_CO, as dust associated with the molecular ISM will have a higher dust-to-gas ratio or be better at emitting in the far-infrared. Nonetheless, we still see the dust-based approach as the most reliable way of producing extragalactic X_CO estimates. Placing stronger quantitative constraints on these systematics requires further work. The Planck results noted above, and the close agreement in the Milky Way of dust-based X_CO with other techniques, suggests that emissivity variations are not a major concern.

5.3. Extragalactic Spectral Line Modeling

Observations of multiple CO lines or a combination of CO and other chemical species allow one to constrain the physical conditions that give rise to CO emission. When these observations include optically thinner tracers like ¹³CO, these constraints can be particularly powerful. Due to sensitivity considerations, most multi-line data sets have been assembled for bright regions like galaxy centers (or starbursts, Section 7). From these data we have constraints on X_CO in bright regions with very different systematics than either virial or dust-based techniques.

Generally, these results indicate that X_CO lower than X_CO,20 = 2 is common but not ubiquitous in the bright, central regions of galaxies. This is in qualitative agreement with the independent (Sandstrom et al. 2012) dust-based results already mentioned. For example, Israel, Tilanus & Baas (2006) use large velocity gradient (LVG) modeling of multiple ¹²CO, ¹³CO, and [CI] lines in the central region of M 51. They find X_CO,20 0.25-0.75 in the central regions, in good agreement with earlier work by Garcia-Burillo, Combes & Gerin (1993). Israel (2009) and Israel (2009b) extend this work to the centers of ten bright and starburst galaxies, finding X_CO,20 ~ 0.1-0.3 (see also Israel et al. 2003, Israel & Baas 2001), again significantly lower than Galactic. Based on maps of the ¹²CO/¹³CO ratio across NGC 3627, Watanabe et al. (2011) argue for a similar central depression in X_CO, with dynamical effects associated with a galactic bar leading to broader line widths and optically thinner ¹²CO emission. Using optically thin tracers and dust emission, Meier & Turner (2001, 2004) find that X_CO,20 ~ 1-0.5 in the centers of IC 345 and NGC 6946. Lower conversion factors are not a universal result, however. Utilizing high resolution data, Schinnerer et al. (2010) found X_CO much closer to Galactic in the arms of M 51, X_CO,20 1.3-2.0. They attribute the difference with previous studies to the implicit emphasis on GMCs in their high resolution data, speculating that it removes a diffuse CO-bright component that would drive X_CO to lower values.

In addition to degeneracy inherent in the modeling, these line ratio-based techniques suffer from the fundamental bias of the virial mass technique. They are only sensitive to regions where CO is bright and so may miss any component of "CO-faint" H₂. A handful of observations of low metallicity dwarf galaxies have attempted to address this directly by combining CO and [CII] observations, with [CII] employed as a tracer of the "CO-faint" molecular regime (Maloney & Black 1988, Stacey et al. 1991). Poglitsch et al. (1995) find that the [CII]-to-CO ratio in the 30 Doradus region of the LMC is ~ 60,000, roughly an order of magnitude higher than is observed in Milky Way star forming regions or other star-forming spirals (e.g., Stacey et al. 1991). Israel et al. (1996) and Israel & Maloney (2011) also find high values elsewhere in the LMC and SMC, with large scatter in the ratio. Madden et al. (1997) find that regions in the Local Group dwarf IC 10 also exhibit very high [CII] 158µm emission compared to CO, 2–10 times that found in the Milky Way. They argue that [CII] emission cannot be readily explained by the available ionized or HI gas, and is thus an indicator of H₂ where CO is photodissociated. Hunter et al. (2001) present ISO measurements for several more dwarf irregular galaxies, showing that at least three of these systems also exhibit very high [CII]-to-CO emission ratios. Cormier et al. (2010) present a Herschel map of the 158µm [CII] line in NGC 4214, again showing very high [CII]-to-CO ratios ( ~ 20,000-70,000) that cannot be explained by emission from [CII] associated with ionized gas. Inferring physical conditions from the [CII] line requires modeling. When such calculations are carried out generally imply a massive layer on the photodissociation region in which the dominant form of hydrogen is H₂, while carbon remains ionized as C⁺ (e.g., Madden et al. 1997, Pak et al. 1998).

Thus, detailed spectral line studies of CO-bright sources often, but not always, suggest lower X_CO in the bright central regions of galaxies. Meanwhile, at low metallicities, [CII] observations suggest an important reservoir of H₂ not traced by CO.

5.4. Synthesis: X_CO in Normal Galaxies

Taken together, the picture offered by extragalactic X_CO determinations in normal galaxy disks resembles that in the Milky Way writ large (Section 4.4). Virial masses, dust-based estimates, and spectral line modeling all suggest X_CO,20 1-4 in the disks of normal spiral galaxies. Systematics clearly still affect each determination at the 50% level, with physical effects likely adding to produce the factor-of-two dispersion. Given this, applying a "Milky Way" X_CO = 2 × 10²⁰ cm^-2(K km s^-1)^-1 with an uncertainty of 0.3 dex appears a good first-brush approach for normal star-forming galaxies. This applies to galaxies where the CO emission is dominated by self-gravitating clouds or cloud complexes with masses dominated by H₂.

Several very strong lines of evidence, as well as simple arguments, show that X_CO increases sharply in systems with metallicities below 12 + log[O/H] 8.4 (approximately one-half solar, Asplund et al. 2009). High spatial resolution virial estimates find approximately "Galactic" X_CO in low metallicity clouds, but they are not sensitive to extended "CO-faint" H₂ envelopes, only to CO-bright regions. We expand on the dependence of X_CO on metallicity in Section 6. We caution about the usefulness of virial estimates on large spatial scales, particularly in low metallicity galaxies. But even in normal galaxies, concerns exist about whether molecular cloud complexes and associations are bound and dominated by H₂ on large scales.

Finally, in the central parts of galaxies spectral line modeling suggests that X_CO is often, but not always, depressed in a manner similar to that seen in the Galactic center and in molecule-rich starbursts. Dust observations are consistent with this picture, revealing central depressions in X_CO in some galaxies. Broader line widths, increased excitation, and the emergence of a diffuse molecular medium likely contribute to more CO emission per unit mass, decreasing X_CO. We expand on this topic when we consider starbursts in Section 7.

² The weighting used to derive the average X_CO affects the mean value. Weighting all high quality solutions equally, Sandstrom et al. (2012) find mean X_CO,20 1.4, median X_CO,20 1.2. Weighting instead by CO intensity, they find X_CO,20 1.8. Back