ARlogo Annu. Rev. Astron. Astrophys. 2013. 51: 207-268
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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 XCO. 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 XCO as a function of metallicity and other local ISM properties. Here we review the techniques available to derive XCO in "normal" galaxies, meaning star-forming dwarf, spiral, or elliptical galaxies. We discuss specific efforts to understand the behavior of XCO 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 XCO in galaxies at high redshift.

Only a subset of the techniques used to determine XCO 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. XCO From Extragalactic Virial Mass Analyses

Broadly, virial mass measurements across a wide range of environments yield XCO,20 approx 1-4, consistent with Milky Way results and very similar to XCO derived from dust-based techniques applied to high mass nearby galaxies. Bolatto et al. (2008) find XCO,20 approx 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 XCO,20 approx 4. Considering NGC 6946, one of the nearest molecule-rich spiral galaxies, Donovan Meyer et al. (2012) report XCO,20 approx 1.2 and Rebolledo et al. (2012) find XCO,20 ~ 2. In M 33, Rosolowsky et al. (2003) show XCO,20 ~ 2 independent of radius and metallicity. In M 31, Rosolowsky (2007) calculate XCO,20 approx 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 XCO,20 = 2.9 with 0.4 dex scatter (slightly larger than a factor of 2).

Figure 6

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 approx 1-2.

Surprisingly at first, these "Galactic" XCO values obtained from virial masses extend to low metallicity, irregular galaxies. In the low metallicity Small Magellanic Cloud (SMC, with 12 + log[O/H] approx 8.0, Dufour, Shields & Talbot 1982), Bolatto et al. (2003) and Israel et al. (2003) find XCO,20 approx 4, consistent with the Milky Way value. Rosolowsky et al. (2003) find no dependence of XCO on metallicity in M 33. Leroy et al. (2006) find an approximately Galactic XCO in the Local Group dwarf IC 10 ([12 + log[O/H] approx 8.17, Lequeux et al. 1979). Wilson (1994) found XCO,20 ltapprox 6.6 in NGC 6822 (12 + log[O/H] approx 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 XCO 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 XCO 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 XCO,20 ~ 3 and XCO,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 XCO Estimates

As we will see in Section 5.2, the approximately constant Galactic XCO 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 XCO 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 XCO in the CO-bright region.

The range of values discussed above, XCO,20 ~ 1-4, is significant. Does it indicate real variations in XCO? 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 XCO 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 XCO 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 XCO 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 XCO than coarser resolution studies. For example, Hughes et al. (2010) find XCO,20 approx 4 in the LMC (as do Israel et al. 2003, Pineda et al. 2009, Wong et al. 2011) compared to XCO,20 approx 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 XCO,20 approx 14, while higher resolution studies find XCO as low as XCO,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 XCO in the SMC as a function of spatial scale, finding XCO propto R0.7 (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 XCO. 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 AV 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 XCO 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 XCO

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 XCO. Modeling infrared or millimeter emission yields an estimate of the dust optical depth, taud. Using Eq. 23, XCO can be estimated from taud, HI, CO, and the dust emissivity per H atom (Eq. 22). Conventions in the literature vary, with taud sometimes combined with a dust mass absorption coefficient and used as a dust mass, and deltaDGR 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 XCO study. He considers individual regions in eight (mostly irregular) galaxies and derives taud from a combination of 60 and 100µm continuum data. Israel (1997b) estimates deltaDGR, the dust emissivity per H atom, from comparison of taud 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 deltaDGR represents a key strength of the approach: deltaDGR is derived self-consistently from comparison of HI and taud, 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 deltaDGR and taud within the target to affect the determination of XCO 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 XCO,20 approx 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 XCO,20 approx 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 XCO finding XCO,20 approx 2 in M 31.

Other dust tracers such as mm-wave continuum emission and visual extinction have been used to arrive at XCO 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 XCO,20 ~ 1. Both Nakai & Kuno (1995) and Guelin et al. (1995) study XCO in M 51, the first using extinction estimates from Halpha / Hbeta, the second millimeter-wave continuum emission. Nakai & Kuno (1995) arrive at XCO,20 approx 0.9 ± 0.1 with a factor of ~ 2 variation with galactocentric radius, while Guelin et al. (1995) finds XCO,20 ~ 0.6. Zhu et al. (2009) employs 850 µm data to check the XCO derived from spectral line modeling in NGC 3310 and NGC 157, finding good agreement with XCO,20 approx 1.3-3.0 in the disks of their targets and a much lower XCO in the center of NGC 157.

Sandstrom et al. (2012) carry out the most comprehensive extragalactic study of XCO 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 deltaDGR and XCO. This yields resolved, self-consistent XCO measurements across 22 galaxy disks. Their methodology requires good S/N CO detections and so restricts robust XCO measurements to reasonably CO-bright parts of galaxies, typically half of the optical disks. There, the authors find XCO,20 approx 1.4-1.8 2 with a 1sigma scatter among individual solutions of 0.4 dex.

The top panel of Fig. 7 shows XCO derived by Sandstrom et al. (2012) as a function of galactocentric radius for their whole sample. The bottom panel shows XCO for each region normalized to the average value for the galaxy, highlighting the internal radial structure. This study finds clear central XCO depressions for a number galaxies. The value of XCO 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 XCO 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

Figure 7. Dust-based alphaCO 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 approx 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 XCO,20 approx 1-4 on kpc scales. For comparison, in the Milky Way extinction yields XCO,20 approx 1.7-2.3 and dust emission yields XCO,20 approx 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 XCO 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 XCO 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 XCO,20 approx 120 ± 20. Boselli, Lequeux & Gavazzi (2002) carry out a similar calculation and also find systematically higher XCO 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 XCO,20 approx 40-120 using measurements that isolate individual clouds and estimate deltaDGR locally. Gratier et al. (2010) considers NGC 6822 using a similar technique, also finding high XCO,20 approx 40 on large scales. Attempting to minimize systematics and making very conservative assumptions, Leroy et al. (2011) still find XCO,20 approx 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 XCO 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 XCO estimates indicate high conversion factors in low metallicity, irregular systems. This agrees with some other methods of estimating XCO 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 XCO 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 XCO 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 XCO 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 XCO determinations. Nonetheless, the close agreement between XCO 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, deltaDGR. 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 XCO determinations, deltaDGR 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 XCO is estimated. This makes self-consistent determinations very robust. Even the most robust analyses, however, still assume deltaDGR to be constant over some region of a galaxy and along a line of sight, and between the atomic and molecular phases. The deltaDGR, 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 deltaDGR depends on metallicity (Draine et al. 2007, Muñoz-Mateos et al. 2009). Large scale ISM density may also be important; deltaDGR 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 deltaDGR 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 deltaDGR 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 XCO, 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 XCO 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 XCO 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 XCO in bright regions with very different systematics than either virial or dust-based techniques.

Generally, these results indicate that XCO lower than XCO,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 XCO,20 approx 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 XCO,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 XCO, 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 XCO,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 XCO much closer to Galactic in the arms of M 51, XCO,20 approx 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 XCO 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 XCO 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: XCO in Normal Galaxies

Taken together, the picture offered by extragalactic XCO 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 XCO,20 approx 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" XCO = 2 × 1020 cm-2(K km s-1)-1 with an uncertainty of approx 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 XCO increases sharply in systems with metallicities below 12 + log[O/H] approx 8.4 (approximately one-half solar, Asplund et al. 2009). High spatial resolution virial estimates find approximately "Galactic" XCO 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 XCO 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 XCO 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 XCO 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 XCO. We expand on this topic when we consider starbursts in Section 7.

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

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