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Astron. Astrophys. 328, 471-482 (1997)

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1. Introduction

1.1. [FORMULA] content of galaxies

The existence of molecular hydrogen ([FORMULA]) in interstellar space was suggested as early as 60 years ago by Eddington (1937) and Strömgren (1939). Thirty years later, Gould & Salpeter (1963) and Hollenbach et al. (1971) predicted that it could be a large fraction of all hydrogen. However, [FORMULA] is difficult to observe directly, because it is a symmetrical molecule lacking a dipole moment. Nevertheless, it has been observed in absorption at UV wavelengths and in emission at infrared wavelengths. Because the emission arises mostly in warm or hot molecular gas, it has been virtually impossible to deduce total amounts of [FORMULA] which is expected to be present mostly at low temperatures.

As [FORMULA] is an abundant and important constituent of the interstellar medium in galaxies, there has been great interest in determining its presence and properties. Because it is commonly assumed that star formation requires interstellar clouds to pass through a cool, high-density phase in which most of the hydrogen is in molecular form, studies of star formation in external galaxies also seek to determine [FORMULA] amounts in such galaxies.

Emission from the tracer CO molecule has been and still is widely used to determine the distribution and amount of molecular hydrogen in our own Milky Way and other galaxies. Although the usually optically thick 12 CO emission does not provide direct information on column densities, empirical relations between CO luminosities and virial masses of molecular clouds in the Galaxy suggest that circumstances nevertheless allow its use in an indirect manner. The underlying thought is that CO is distributed in a very clumpy manner, and that clumps are not self-shadowing. The strength of the signal received from many clumps in a single observing beam thus provides a measure for their total projected area weighted by brightness temperature. If the clumps are statistically similar from one line of sight to the other, we thus have a measure for the number of clumps per beam area, hence for the total amount of molecular material. In fact, the high optical depth of 12 CO emission is then a boon, as it makes such determinations to first approximation independent of the actual [CO]/[ [FORMULA] ] abundance.

1.2. Problems with CO-based methods

The most commonly used methods to estimate molecular hydrogen contents of extragalactic objects are either application of a `standard' CO to H2 conversion factor X (defined as the ratio of molecular hydrogen column density N(H2) to velocity-integrated CO intensity I(CO)) derived from Milky Way observations, or application of the virial theorem to observed CO clouds. The first method assumes similarity of extragalactic molecular clouds and Galactic clouds, or at least that the effects of different physical conditions cancel one another. In environments that are very different from those in the Galaxy, such as those found in galaxy central regions or in low-metallicity dwarf galaxies, this method must be considered unreliable (cf. Elmegreen et al. 1980; Israel 1988; Maloney & Black 1988; Elmegreen 1989; Maloney 1990a). For instance, application of this method to the very low CO luminosities commonly observed for irregular dwarf galaxies would suggest negligible amounts of [FORMULA] (Israel et al. 1995) and consequently unusually high star formation efficiencies (Israel 1997). In contrast, direct evidence for X factors varying by more than an order of magnitude, probably as a function of local conditions, has been presented for Galactic clouds by Magnani & Onello (1995). We thus agree with Roberts & Haynes (1994): `values of the molecular hydrogen content in late-type systems derived in this manner are uncertain and possibly too low by up to an order of magnitude'

The second method frequently used estimates total molecular cloud mass from observed parameters such as CO extent R(CO) and velocity dispersion dv(CO). Although this method, not assuming similarity between Galactic and extragalactic clouds, is preferable, it is likewise beset by problems, as it requires correct determination of the structure and dynamics of the observed clouds. For instance, the value of the virial constant used to convert observed parameters into mass may vary by a factor of four depending on the assumed condition of the system (see e.g. McLaren et al. 1988; McKee & Zweibel 1992), while it is not clear that the virial theorem is in fact relevant. If one considers the morphology of molecular complexes such as the ones in Orion (Bally et al. 1987), Taurus (Ungerechts & Thaddeus 1987) or indeed in the LMC (Israel & de Graauw 1991; Kutner et al. 1997) it is hard to imagine that these very elongated structures with little systematic velocity structure actually represent virialized complexes. Maloney (1990b) has shown that the correlation between CO luminosities and virial masses of Galactic molecular clouds follows directly from the size-linewidth relationship exhibited by molecular clouds and does not require virial equilibrium at all. Molecular hydrogen masses have also been determined applying X -factors scaled from [FORMULA] by L(CO) as a function of dv (e.g. LMC - Cohen et al. 1988; SMC - Rubio et al. 1991).

Especially in the large linear beamsizes typical of extragalactic observations, actually unrelated clouds at somewhat different velocities may blend together, leading to unrealistical values of both cloud complex radius R and velocity dispersion dv. The derived (virial) masses may then either overestimate or underestimate the actual mass, depending on circumstances. For instance, consider an area mapped with a large beam blending together N unrelated clouds, each having a true mass [FORMULA] = a r d [FORMULA]. Here, [FORMULA] is the diameter of a single cloud and d [FORMULA] its velocity dispersion. The true total mass is thus N a [FORMULA] d [FORMULA]. Cloud emission is measured over an area with radius R = [FORMULA] b [FORMULA] in which b [FORMULA] is the projected separation between cloud centers. Unjustified application of the virial theorem on this observation suggests a total mass [FORMULA] = a [FORMULA] b [FORMULA] d [FORMULA], where d [FORMULA] now is the dispersion derived from the velocity width of the sum profile of all clouds within radius R. The ratio of the derived mass over the true mass is thus:

[FORMULA] / [FORMULA] = b [FORMULA] (d [FORMULA] /d [FORMULA])2 (1)

If N [FORMULA] [FORMULA] and d [FORMULA] [FORMULA] d [FORMULA], this will result in a potentially large overestimate of the mass. However, if instead the unrelated clouds are at more or less identical radial velocities, d [FORMULA] [FORMULA] d [FORMULA], the true mass is underestimated if N [FORMULA] [FORMULA]. Such a situation may occur in low-metallicity dwarf galaxies with relatively small velocity gradients. It occurs if we have a large number of clouds with small projected distances; a more physical equivalent is a very filamentary structure of the molecular material.

A further problem in estimating H2 masses from CO observations is the need to assume virtually identical distributions for both. If CO is significantly depleted, [FORMULA] may well occur outside the area delineated by CO emission and its amount is underestimated by the CO measurements. This effect appears to lie at the base of the size dependence of N(H2) /I(CO) ratio, noted by Rubio et al. (1993) and Verter & Hodge (1995). In low-metallicity galaxies suffering CO depletion, this results in a lack of CO emission in complexes observed on large angular scales. Observations on small angular scales selectively concentrate on the densest molecular components, that have resisted CO depletion most effectively, so that the N(H2)/I(CO) ratio looks progressively more `normal' notwithstanding the lack of CO in most of the complex.

Thus, in order to estimate H2 content of such galaxies, it is desirable to use a method that does not require specific assumptions on or knowledge of the detailed structure and dynamics of the molecular clouds involved. Use of far-infrared data in principle provides such a method (e.g. Thronson et al. 1987, 1988; Israel 1997).

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© European Southern Observatory (ESO) 1997

Online publication: March 26, 1998

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