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

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2. Method and data

2.1. Estimating N(H2) from [FORMULA] and N(HI)

[FORMULA] column densities are derived in the manner used on NGC 6822 by Israel 1997. At locations well away from star-forming regions and CO clouds, the ratio of neutral hydrogen column density to far-infrared surface brightness [FORMULA] is determined. In the absence of molecular gas, [FORMULA] equals [FORMULA] / [FORMULA] , which is a measure for the ambient gas-to-dust ratio. The observed [FORMULA] values at locations that contain [FORMULA], as betrayed by CO emission, reduced to the reference dust temperature [FORMULA] and then multiplied by [FORMULA] thus provide the total hydrogen column density [FORMULA]. The actual gas-to-dust ratio, which depends on poorly known dust particle properties, does not need to be known as long as it does not change from source to reference position. In the small irregular galaxies considered here, abundance gradients are negligible (cf. Vila-Costas & Edmunds 1992), so that we may safely assume no change in gas-to-dust ratio as a function of position in the galaxy. When [FORMULA] is known, [FORMULA] is found by subtracting the local N(HI) value:

2 [FORMULA] - N(HI) (2)

In Eq. 2, f(T) is a function which corrects [FORMULA] for the emissivity difference due to the (generally small) difference of [FORMULA] from [FORMULA] ; for small temperature differences f(T) is close to ([FORMULA] / [FORMULA])6. Temperatures [FORMULA] are derived from the IRAS 60µm/100µm flux ratio assuming a wavelength dependence for emission [FORMULA] [FORMULA] [FORMULA]. Here and in the following we will assume n = 2. The temperature correction assumes that the number distribution of dust particles emitting at varying temperatures does not differ significantly from one location to another. This is a reasonable assumption for values of f(T) not too far from unity, but may introduce significant errors for very large or very small values of f(T). The CO to [FORMULA] conversion factor X follows from the observed CO strength: X = [FORMULA].

This method of estimating [FORMULA] column densities depends on observed quantities independent of the actual spatial or kinematical distribution of the molecular material. It has this property in common with the methods used by Bloemen et al. (1986) and Bloemen et al. (1990) to estimate the same quantities in the Milky Way galaxy. It avoids the major weakness of the virial method discussed above, as there is no need to determine the structure of the molecular cloud complexes, to separate unrelated clouds in the same line of sight, or even to resolve the molecular clouds. It is important to emphasize that in this method, the absolute gas-to-dust ratio plays no role, nor does the actual dust mass. We thus avoid a major uncertainty associated with other infrared-derived [FORMULA] estimates, where the infrared flux is used to calculate a dust mass, which is then converted into a gas mass. Likewise, our results are independent of CO measurements, and as we will show below, the observational uncertainties are no worse than those associated with the traditional methods and probably better.

The column densities [FORMULA], and consequently X, determined in this paper are properly lower limits (Israel 1997). (i). If some [FORMULA] were to be present at the null positions where we assumed none, the total hydrogen column density corresponding to unit infrared luminosity is underestimated, implying higher actual [FORMULA] values than derived. (ii). If, unexpectedly, the hotter infrared sources were to be relatively rich in cooler dust, the observed infrared emission does not sample the total amount of gas, hence [FORMULA], will be higher than estimated. (iii). If, in regions of bright infrared emission, higher radiation densities would cause increased dust depletion, these regions will be characterized by a higher gas-to-dust ratio than assumed, again leading to higher than derived actual [FORMULA] values. This is expected only to be important for HII regions filling a significant fraction of the beam.

Errors in the assumptions would thus cause [FORMULA] and X to be higher rather than lower. Although these errors are hard to quantify, we consider it unlikely that their effect will exceed a factor of two. The calculated total hydrogen column densities [FORMULA] carry with them the combined uncertainty in the determinations of [FORMULA], f(T) and [FORMULA]. Because these quantities are compared in a relative rather than an absolute sense, the uncertainty [FORMULA] is of the order of 20 [FORMULA] - 30 [FORMULA] for the cases discussed below. The uncertainty in the calculated values of [FORMULA] is larger. Since the N(HI) determinations are considered to be rather accurate, it depends on the molecular to atomic hydrogen ratio: [FORMULA] = [FORMULA] (1 + 0.5 N(HI) /N(H2))

Thus, for [FORMULA] column densities equal to or higher than those observed in HI, the relative [FORMULA] uncertainty is typically less than 50 [FORMULA]. For HI column densities substantially higher than the derived [FORMULA] column density, the relative uncertainty may become considerable. However, this situation almost exclusively occurs at low absolute N([FORMULA]) values where a relatively large uncertainty still corresponds to an acceptable uncertainty in the absolute value. The uncertainty in the derived value of X, in turn, includes both the uncertainty in N(H2) and in I(CO). Since the latter is usually much smaller than the former, the uncertainty in X is actually dominated by that in N(H2). The combined effect of uncertainties in the observational values and in the assumptions implies a rough overall uncertainty of about a factor of two for individual determinations.

2.2. Data and results

All data were taken from the literature or existing databases. The CO, HI and far-infrared data included in the comparison are selected to have similar resolutions. This resolution is determined by the lowermost resolution to which the other data are degraded, if necessary.

2.2.1. LMC

The far-infrared data are from Schwering 1988, who conveniently produced maps of infrared luminosity over HI mass at [FORMULA] resolution (corresponding to 235 pc) and dust temperature at [FORMULA] resolution (Fig. 1). The HI data (resolution [FORMULA]) are from Rohlfs et al. (1984). The average of six positions in the main body of the LMC, well away from CO clouds and bright HII regions is [FORMULA] = 2.25 [FORMULA] 1027 cm-2 / [FORMULA] (corresponding to L /M = 1.7 [FORMULA] / [FORMULA]) at a reference temperature [FORMULA] = 25.5 K. From the internal variation, we estimate its uncertainty to be about 10 [FORMULA]. The uncertainty in f(T) is about 20 [FORMULA] and that in [FORMULA] about 10 [FORMULA].

[FIGURE] Fig. 1a and b. LMC. Top: ratio of far-infrared luminosity to neutral hydrogen column density at [FORMULA] resolution. Contours are at 5.3, 13, 26, 52, 105 [FORMULA] 10-28 W m-2 sr-1 cm2. Bottom: dust temperature [FORMULA] at [FORMULA] resolution. Contours are at 23, 28, 32 and 36 K.

In Table 1 we have listed data for several of the CO cloud complexes detected by Cohen et al. (1988) convolved to a resolution of [FORMULA] (e.g. Meinert, 1992). Except for cloud 31, all CO clouds considered have diameters larger than [FORMULA]). Weaker CO sources are included only if identification with an HII region complex support their validity. In Table 1, the first column identifies the CO cloud by its number in Table 1 of Cohen et al. (1988). Column 2 lists the far-infrared surface brightness at the peak CO position, column 3 the value of f(T) based on the dust temperature derived from the [FORMULA] / [FORMULA] flux ratio and column 4 the HI column density. Column 5 gives the molecular hydrogen column densities calculated according to Eq. 2, while columns 6 and 7 give the resulting ratios of molecular hydrogen to atomic hydrogen and total gas (including helium) respectively. Column 8 gives the integrated CO intensity and column 9 the resulting value of X. In column 10 we give the ratio of the observed infrared surface brightness (not reduced in temperature) over total hydrogen column density [FORMULA] = 2N(H2) + N(HI). This ratio is a measure of the ambient radiation field strength per H nucleon. Finally, column 11 lists HII region(s) associated with the molecular cloud. In most cases the HII region extent is much less than the [FORMULA] scale relevant to the data used.


[TABLE]

Table 1. LMC data (unit area 0.043 kpc2)


Some further comments are in order. Clouds 34, 35 and 36 are located south of the bright HII regions associated with the Doradus complex. Major CO emission occurs with little or no optical counterpart. There is relatively strong HI emission, but the far-infrared surface brightness decreases smoothly. The results for N157B and N159 (clouds 32 and 33) are uncertain, as both are at steep far-infrared gradients. N159 is also on a steep CO emission gradient in the opposite direction. Consequently, the resulting value of [FORMULA] depends critically on the precise (within a fraction of the resolution) position used. The mean value of the CO to [FORMULA] conversion ratio (excluding 30 Doradus) is X = 13([FORMULA] 2) [FORMULA]. Its uncertainty is determined by that in [FORMULA], which does not decrease with increasing sample size, whereas all other errors do.

2.2.2. SMC

The far-infrared data are from Schwering's (1988) maps of dust temperature and of far-infrared luminosity over HI mass (Fig. 2). The HI data at the same resolution are from McGee & Newton (1981). For the SMC we find an average [FORMULA] = 1.65([FORMULA] 0.25) [FORMULA] 1028 cm-2 / [FORMULA] (corresponding to L /M = 0.23 [FORMULA] / [FORMULA]) for various positions in and near the bar, at a reference temperature [FORMULA] = 28 K. In Table 2 we list the SMC data for several of the CO cloud complexes detected by Rubio et al. (1991) in the same format as Table 1.

[FIGURE] Fig. 2a and b. SMC. Top: ratio of far-infrared luminosity to neutral hydrogen column density at [FORMULA] resolution. Contours are at 2.6, 5.2, 10.5, 15.7, 21, 26 [FORMULA] 10-29 W m-2 sr-1 cm2. Bottom: dust temperature [FORMULA] at [FORMULA] resolution. Contours are at 28, 32 and 36 K.


[TABLE]

Table 2. SMC data (unit area 0.061 kpc2)


The mean value of the CO to [FORMULA] conversion ratio is X = 120([FORMULA] 30) [FORMULA]. The uncertainty in the null determination again dominates, but less decisively because of the relatively small sample size in Table 2.

2.2.3. NGC 55, NGC 1569, NGC 4214 and NGC 4449

Four other irregular galaxies have far-infrared, HI and CO data at similar resolutions (Table 3). For these galaxies, we used far-infrared data at a resolution of [FORMULA] obtained with IRAS CPC instrument at 50µm and 100µm (F. Sloff, unpublished; Van Driel et al. 1993). For consistency, we interpolated the CPC 50µm fluxes to 60µm; as the absolute calibration of the CPC is unreliable (Van Driel et al. 1993), we scaled all CPC fluxes by the IRAS survey fluxes. In the case of NGC 55 we verified the outcome by comparison with the IRAS survey image-sharpening (PME) result published by Bontekoe et al. (1994).


[TABLE]

Table 3. Other galaxies


NGC 55 was sampled at the CO cloud detected by Dettmar & Heithausen (1989) and at two reference positions [FORMULA] on either side of this peak. Using HI data from Hummel et al. (1986), we found for the reference value [FORMULA] = 1.4 [FORMULA] 0.2 [FORMULA] 1028 cm-2 / [FORMULA]. Dettmar & Heithausen (1989) give a CO surface brightness of 3 [FORMULA] and a source size of [FORMULA] 4 [FORMULA], so that I(CO) = 2 [FORMULA] in a [FORMULA] beam.

NGC 1569 was observed in CO by Greve et al. (1996) who detected a cloud with a peak I(CO) = 2.9 [FORMULA] and a size of [FORMULA], corresponding to a CO intensity of 0.37 [FORMULA] in a [FORMULA] beam. HI data at [FORMULA] resolution are from J. Stil (private communication; see also Israel & Van Driel 1990). At the reference position [FORMULA] to the southeast, where Greve et al. (1996) did not find CO emission, we determined [FORMULA] = 7.7 [FORMULA] 1028 cm-2 / [FORMULA]. Infrared emission gradients render this result uncertain by 25 [FORMULA]. As weak CO emission might be present outside the limited area mapped, the uncertainty in X may be as high as 65 [FORMULA]. If we take the Young et al. (1984) results (I(CO) = 1.1 [FORMULA] 0.3 [FORMULA] in a [FORMULA] beam), we would find an X -ratio only half the value in Table 3, which we take as indicative of the uncertainty in X.

NGC 4214 was observed in CO by Becker et al. (1995) who found a cloud complex of dimensions [FORMULA] with a peak I(CO) = 2.8 [FORMULA] in a [FORMULA] beam. After correction for beamsize, this is consistent with earlier and less accurate determinations by Tacconi & Young (1985) and Thronson et al. (1988). Weak CO was also detected by Ohta et al. (1993) in a [FORMULA] beam towards positions [FORMULA] southeast and [FORMULA] northwest of the reference position given by Becker et al. (1995). On the basis of all available data, we take I(CO) = 0.7([FORMULA] 0.15) [FORMULA] in a [FORMULA] beam. HI data at [FORMULA] resolution are from Allsop (1979). At two reference positions, we determined [FORMULA] = 1.2 [FORMULA] 0.2 [FORMULA] 1027 cm-2 / [FORMULA].

NGC 4449 was observed in CO by Hunter & Thronson 1996 ([FORMULA] beam) and by Sasaki et al. 1990 ([FORMULA] beam). Taking into account beam sizes and efficiencies, the data agree well. HI data at [FORMULA] resolution are from the WHISP database (J. Kamphuis, private communication). We obtained reasonably accurate infrared surface brightnesses for Hunter & Thronson's regions 1 through 4 only and determined [FORMULA] = 4.35 [FORMULA] 1.0 [FORMULA] 1027 cm-2 / [FORMULA]. Table 3 gives the mean of the individual results for the four positions, weighted by I(CO).

2.2.4. Extragalactic HII regions

In Table 3, we have also included the results obtained for NGC 6822 (Israel 1997). Two sets of entries are given: NGC 6822-HII represents the mean values towards the HII region complexes Hubble I/III, V and X, and NGC 6822-IR those towards the infrared sources 4 and 6 not associated with major HII regions.

We also included data for the bright HII regions NGC 604 and NGC 595 in M 33. The infrared data were taken from Rice et al. (1990), HI data at the same resolution from Deul (1988) and CO data from Blitz (1985). Note that the results for NGC 595 are rather uncertain, as a reliable flux at 100µm is hard to determine; we assumed essentially similar infrared flux distribtions for both NGC 604 and NGC 595. Finally, we also included NGC 5461, the brightest HII region in the galaxy M 101. Infrared data were taken from Bontekoe et al. (1994), HI data from van der Hulst & Sancisi (1988) and CO data from Blitz et al. (1981) and Kenney et al. (1991). In this case, we applied a correction factor of 1.3 to allow for the presence of significant amounts of HII; this effect is negligible for the M 33 objects. Because the parent galaxies M 33 and M 101 have radial abundance gradients, we selected null positions adjacent to the HII regions used.

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© European Southern Observatory (ESO) 1997

Online publication: March 26, 1998

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