3. Analysis and discussion
3.1. The CO to H2 conversion factor
In the sample galaxies, we find CO to conversion factor X values much higher than the range 0.2-0.4 1021 ()-1 commonly adopted for Milky Way objects. In the LMC, we find a mean value X = 1.3 1021 ()-1, or 3 - 7 times higher than in the Milky Way. We may compare this result to that obtained by Cohen et al. (1988). Comparing CO luminosities L(CO) to velocity width , they conclude that on average = 6 . They adopt = 0.28 1021 ()-1 resulting in a value for 30 higher than ours. However, if = 0.20 1021 ()-1 (Bloemen 1989), their result is identical to ours. Satisfactory as this may seem, the situation is more complex.
First, Cohen et al. (1988) estimated their value of X from the mean ratio / , but their Fig. 2 shows this ratio to be a function of . At the smallest velocity widths, their implied is only 3 , but at the largest widths it is 10 . The figure exhibits a large scatter around the mean, covering an equivalent range in of 2 - 20 . Part of this scatter is undoubtedly due to the low signal-to-noise ratio of the CO measurements, but part of it is real. For instance, Garay et al. (1993) studied seven CO clouds in the 30 Doradus halo and found those to have / ratios implying a much higher value = 20 than the mean found by Cohen et al. (1988). We note that the values tabulated in our Table 2 also define a large range in X, from close to the Galactic value to more than an order of magnitude higher. For 30 Doradus itself we derive an even higher X value. We will discuss this variation in X in Sect. 3.2.
Second, we differ in individual cases, even though the mean values agree. For instance, Cohen et al. (1988) obtain very high and virial masses (and their Fig. 2 implies a high value for X) in cloud 35. In this cloud, we find a low X value. The result by Cohen et al. (1988) follows from the high = 28 km s-1 they found for this cloud. They list similarly large velocity widths for e.g. clouds 13, 19 and 23. Yet, the higher resolution SEST survey yields velocity widths typically a factor of two less (Israel et al. 1993; Kutner et al., 1997). At least in the case of cloud 35, the anomalously high velocity width appears to be the result of CO clouds at two distinct velocities blended together in the large beam used by Cohen et al. (1988). Reduction of the large velocity widths to the more modest SEST values, yields X values in much better agreement with those in Table 2. Similar comments apply to the SMC results by Rubio et al. (1991), except that here we find a larger value of X, although both results have significant uncertainties associated with them. It is nevertheless clear that is much higher than either or .
For the objects listed in Table 3, X estimates can be obtained from the literature (Table 4). These are mostly rough estimates based on comparison of CO luminosities and virial masses, and are very uncertain. Nevertheless, we see reasonably good agreement in Table 4 for NGC 55, NGC 4214, NGC 4449 and for NGC 5461. There is also good agreement for NGC 595 and NGC 604 if we disregard the estimates derived from the high resolution observations which apply to individual cloud components rather than whole complexes. It has been noted before (Rubio et al. 1993; Verter & Hodge, 1995) that such observations always yield X values much lower than the global values derived from observations covering the whole complex (see als Sect. 1.2). Our results for NGC 6822, and especially for NGC 1569, are higher than the other published estimates.
Table 4. Comparison of X values
3.2. Dependence of X on environment
3.2.1. Dependence on radiation field
Compared to the Milky Way, the galaxies studied here have lower metallicities, and are found to have higher X ratios. This is not a new result: several authors have suggested a more or less inverse linear dependence between X and metallicity as measured by the oxygen abundance (cf. Dettmar & Heithausen, 1989; Rubio et al. 1991; Verter & Hodge 1995; Arimoto 1996, Sakamoto 1996). Arnault et al. (1988) found the ratio of CO to HI emission in a sample of 19 late-type galaxies to vary roughly as [O]/[H]2.2. Sage et al. (1992) failed to reproduce such a relation, but our sample suggests the CO to HI ratio to be proportional to [O]/[H]2.6, within the errors identical to the result obtained by Arnault et al. (1988). The latter conclude that CO must be deficient relative to as a function of metallicity, but could not determine a functional dependence for the CO/ ratio, hence X, on metallicity. Their result nevertheless suggests a dependence with a coefficient larger than unity, as there is no reason to assume vastly different /HI ratios in low-metallicity galaxies. The present data provide an excellent basis to pursue this question, as they have been obtained in a consistent manner. Much of the previously published discussions were based on a compilation of data (notably X -values) from different sources, and obtained in different manners.
An underabundance of CO with respect to hydrogen is expected to result from low carbon and oxygen abundances. It will be enhanced by photodissociation of CO since low metal abundances imply both lower selfshielding and lower dust shielding of CO against the ambient radiation field. The LMC and SMC samples allow us to first investigate the effect of the radiation field. In Fig. 3 we have plotted the ratio N(H2)/I(CO) = X as a function of the energy available per H nucleon, represented by the quantity / . Straight lines indicate the linear regression lines. In case of the LMC, we did not include 30 Doradus in determining the regression line, because its very high values would dominate the result. Nevertheless, extrapolation of the regression line to the / value of 30 Doradus predicts it to have X = 7 ()-1, or 85 of the value derived directly in Table 1. The SMC sample, although much smaller, shows a similar behaviour. Further analysis suggests that the dependence of X on radiation field is indeed very close to linear: X ( / ) .
The increase of X, i.e. the decrease of CO relative to N(H2), as more energy per nucleon is available is the result of two processes, as is illustrated by the SEST results obtained for the LMC. High-resolution maps (linear beamsize corresponding to 10 pc) were obtained of clouds 35/36 (south of 30 Doradus - Kutner et al. 1997), cloud 6 (N11 - see Israel & de Graauw 1991) and cloud 32 (30 Doradus - Johansson et al., in preparation). The map of cloud 35/36 shows numerous clumps embedded in extended interclump gas; the average peak-to-diffuse CO contrast ratio is about 3. Bright clumps (i.e. those having a CO strength of more than 5 per SEST beam area) are numerous, but contribute only about a quarter to a third of the CO luminosity of the whole complex. This is similar to Galactic giant molecular clouds, where e.g. Heyer et al. (1996) find most of the molecular mass to be in extended, low column-density regions. Cloud 6 is embedded in a four times stronger radiation field (Table 1) and contains a very similar number of clumps per unit area. Two thirds of these are bright with I(CO) 5 per SEST beam, but cloud 6 lacks the extended diffuse gas seen in cloud 35/36. In this complex, the contrast ratio is of order ten. Apparently, the fourfold increase in radiation density has resulted in the removal of virtually all the low column density CO gas. As the high column density hydrogen gas will be practically unaffected, the value of X has increased in cloud 6 more or less commensurate with the increase in radiation density and CO removal.
Cloud 32 experiences a radiation density a factor of three over that in cloud 6, i.e. over an order of magnitude more than that of Cloud 35/36. There is no trace of interclump gas. The number of clumps per unit area is still very similar, but the fraction of bright clumps is only a third, down by more a factor of two from Cloud 6. Many of the weaker clumps are hardly discernible. We conclude that the further increase in radiation density in cloud 32 is eroding even the dense CO clumps that are surviving reasonably well in cloud 6, resulting in a further decrease of the I(CO) /N(H2) ratio, i.e. a further increase in X.
It is of interest that the low-excitation clouds south of N 159 have X values only a few times rather similar to the canonical value of X in the Milky Way. In these clouds, the lack of dissociating radiation apparently allows the CO to fill most of the volume, nothwithstanding the lower CO abundance.
3.2.2. Dependence on metallicity
The ratio of X to / for the objects in Tables 1, 2 and 3 can now be compared to the metallicities given in Table 5. We have included the Milky Way by using the Y and / values tabulated as R2 tot R5 by Bloemen et al. (1990 - their Table 3) and the metallicities from Shaver et al. (1983). We have determined linear regressions with and without the Milky Way points, and for X - / dependences with exponents 0.9 and 1.0. We find:
log X = 0.9 0.1
log() - 3.5 0.2 log
+ 34.6 2.2
Table 5. Adopted abundances
Inclusion of the Milky Way points changes this to:
log X = 0.9 0.1
log() - 3.2 0.1 log
+ 34.3 3.1
This is illustrated in Fig. 4a, which shows the dependence on [O]/[H] for a linear (exponent 1.0) dependence of X on / . As is clear from Fig.4a, there is almost perfect agreement of the Milky Way points with the relation determined for the sample galaxies alone. We have also empirically determined the dependence of X on metallicity, ignoring any dependence on radiation density. This yields (see also Fig. 4):
log X = -2.7 0.3 log
+ 11.6 1.0
Here, the nominal global Milky Way Y -point (Bloemen et al. 1990) is low compared to the relation defined by the sample galaxies, while the commonly used value X = 2.3 1020 cm provides a very good fit.
The dependence of X on [O]/[H] alone, ignoring / effects, found here is significantly steeper than the result log X 1.5 log [O]/[H] found by Sakamoto (1996) from modelling radiative transfer and excitation of CO in clumpy molecular clouds. However, that result did not take into account the full effects of photodissociation of CO especially on the interclump gas.
With respect to steep dependences on metallicity, we note that Garnett et al. (1995) have shown that [C]/[O] , so that [C]/[H] should be proportional roughly to . If the CO abundance is solely determined by the carbon abundance, [CO]/[H] likewise will be proportional to ; if the oxygen abundance plays a role this may increase to . The strength of the radiation field experienced by CO is proportional to the photon flux diluted by dust extinction. To first order, we may equate the decrease in dust shielding with the decrease in dust abundance. As the dust-to-gas ratio in galaxies is about proportional to [O]/[H] (see e.g. Issa et al. 1990), we expect photodissociation alone to gain in importance as roughly [O]/[H]-3 when metallicity decreases. Because the effects of photo-dissociation are highly non-linear, and depend critically on the balance between ambient radiation field and local column densities, a more quantitative estimate of the effect of metallicity can only be obtained by detailed modelling, which should treat photodissociation more rigorously and take into account the structure and column density distribution of the molecular clouds experiencing the dissociating radiation (cf. Maloney 1990a). This is beyond the scope of this paper.
3.3. H2 masses
The results given in Tables 1 and 2 show the presence of significant amounts of molecular hydrogen in both the LMC and the SMC. At the (CO-selected) positions sampled, locally dominates the interstellar gas. Table 3 suggests that this is also true in the other galaxies.
Can we extrapolate the results obtained so far to estimate the total amount of in the sample galaxies? Application of the mean X value from Table 1 to the LMC CO results obtained by Cohen et al. (1988) yield = 0.8 108 . A more detailed treatment, applying the individual N(H2) values from Table 1 to the cloud complex sizes given by Cohen et al. (1988) and correcting for their CO sources not included in our Table 1, yields a higher value = 1.2 108 . This result is very similar to that obtained by Cohen et al. (1988) (but see Sect. 3.1). It corresponds to a global mass ratio of molecular-to-atomic hydrogen of 0.2, much lower than the mass ratio of 1.9 found for the individual CO clouds in Table 1. It implies that in the LMC, about 12 of all the interstellar gas, including helium, is in molecular form.
We have also applied Eq. (2) to the total far-infrared emission of the LMC, yielding a total hydrogen mass = 1.1 108 , much less than the observed total HI mass M(HI) = 5.4 108 (McGee & Milton 1966). Apparently, the LMC contains a significant fraction of relatively cool dust not significantly contributing to the total infrared luminosity. However, we may still estimate the total amount of associated with the warm dust by assuming the mean /HI mass ratio from Table 1 to apply to all sources of warm : we then find = 0.7 108 . This rougher method thus underestimates the actual amount of by about 30 .
Following the same procedures for the SMC, we find = 0.50 0.05 108 , implying /M(HI) = 0.1, or 7 of all interstellar gas in molecular form. This is a lower limit, since the CO observations by Rubio et al. (1991) cover only part of the SMC. Indeed, extrapolation to the total infrared luminosity of the SMC yields = 1.75 108 which nevertheless still falls short of the total HI mass M(HI) = 5 108 (Hindman 1967). Applying the mean /HI mass ratio from Table 2, we obtain = 1.0 108 .
The galaxies listed in Table 3 were not sampled extensively in CO, so that we can only extrapolate from the total infrared luminosity. However, the example of the LMC suggests that this extrapolation is accurate to about 30 . The results are given in Table 6, which also includes the global results for the Milky Way given by Bloemen et al. (1990). Table 6 shows that molecular hydrogen, although dominating the interstellar medium near star formation regions, occurs much less predominantly in irregular dwarf galaxies as a whole. Globally, the total mass of atomic hydrogen is typically five times higher than that of molecular hydrogen. On average, about one eigth of the interstellar gas mass is in molecular form. These fractions are surprisingly close to those of the Milky Way Galaxy as a whole, where the fraction of molecular gas reaches a peak of 0.46 in the `molecular ring' at R = 4 - 8 kpc, and drops to 0.11 in the outer galaxy (Bloemen et al. 1990). If is somewhat lower than assumed by Bloemen et al., as has been suggested by e.g. Bhat et al. (1986), the similarity of the Milky Way and irregular dwarf mean ratio is even more striking. Our result does not reproduce the apparent dependence of global molecular gas fraction on metallicity discussed by Tosi & Diaz (1990) and Vila-Costas & Edmunds (1992). We note that the latter expressed doubts on the physical significance of that result, and suggested that it might be an artifact of the CO to conversion used. Our result implies that this is indeed the case.
Table 6. Global mass estimates
The molecular hydrogen fraction in this admittedly small sample appears to be uncorrelated with metallicity, hence presumably dust-to-gas ratio. This is somewhat surprising as molecules form on dust grain surfaces, so that one would expect less in low metallicity environments poor in dust grains. Our result may thus indicate that the formation of is so efficient, that it is to first order independent of the dust abundance. Alternatively, it may reflect a selection effect. Higher metallicity environments provide more shielding and therefore may have a larger fraction of cold dust/molecular hydrogen than lower metallicity environments. In the presence of warm dust, IRAS fluxes poorly sample cold dust, so that we may increasingly have underestimated the total amount of for the higher metallicity galaxies.
© European Southern Observatory (ESO) 1997
Online publication: March 26, 1998