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Astron. Astrophys. 354, 787-801 (2000)

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4. Discussion

4.1. Spectrum integrals: the cool gas fraction

To study the mixture of the warm and cool phases of the interstellar medium along the lines of sight, we have to calculate the velocity integrals of the H I emission and absorption spectra. Results are shown in Table 2. Column 1 gives the source number. The H I column density of the emission and the "equivalent width" of the absorption profile at each line of sight for the entire velocity range (108 to 438 km s-1) are given in Columns 2 and 3. [FORMULA] is computed from the velocity integral of the brightness temperature, [FORMULA] (v), assuming optically thin emission:

[EQUATION]


[TABLE]

Table 2. Spectrum integrals


The equivalent width of the absorption profile is defined as the velocity integral

[EQUATION]

The error is calculated from [FORMULA], where [FORMULA] is the noise in the optical depth (Table 1, Column 7), [FORMULA] is the velocity resolution (1.65 km s-1) and n=200 is the number of channels included in the integral. In Columns 4 and 5 the column density of the warm gas and the equivalent width of the cool gas are recomputed by integrating only over velocities with [FORMULA] (v) [FORMULA] 2 K ([FORMULA], [FORMULA]). This is to separate the contribution to the column density by the warm halo from that by the atomic gas in the LMC proper as discussed in Dickey et al. (1994). As typically fewer than 10 or 15 channels contribute to this sum, the noise in the value of EW is about [FORMULA]. Column 6 gives for each line of sight the sum of the equivalent widths of the individual absorption lines (see Table 4, Column 2) for which the optical depth is above the threshold of 3 [FORMULA] (these values are sketched in Fig. 1). The values of the equivalent width in Columns 3 and 5 also include the contribution from broad, weak absorption components which are below the detection threshold in individual channels, but detectable if the spectrum is heavily smoothed. These marginally-detected contributions make up the bulk of the absorption in our sample, since the background sources are so weak that typically only features with [FORMULA] are securely detected. This is in contrast to most surveys of HI absorption in the Milky Way interstellar medium, which generally use much stronger background sources, allowing detection of lines as faint as [FORMULA] 0.05 to 0.1. It is premature to consider the abundance of lines vs. optical depth in the Magellanic Clouds, but our results do not indicate significant differences from the Milky Way result (Garwood & Dickey 1989, Fig. 4).

From the values of EW and [FORMULA] we can compute the average cool gas fraction by

[EQUATION]

If no absorption is detected we multiply by the upper limit for EW, which is taken to be 3 [FORMULA] (Column 5). [FORMULA] and [FORMULA] are the column densities of cool and warm gas. [FORMULA] is the assumed cloud temperature. Because of the uncertainties in the spin temperature of individual cool clouds, derived in Sect. 4.2, we calculate the fraction of cool gas in the LMC for two mean cloud temperatures, a value of 27 K, implied by the LMC studies (see Sect. 4.2) and a mean cloud temperature of 60 K as found for the Milky Way (Kalberla et al. 1985). The lower value has been confirmed by the study of cloud temperatures in the vicinity of 30 Doradus by Mebold et al. (1997) using high resolution emission- and absorption spectra obtained by combining ATCA and Parkes data. Mebold et al. find values of 30 K to 40 K for the cool diffuse clouds, but we cannot infer from this analysis that all of our cool atomic gas clouds show such low temperatures. The values for [FORMULA] assuming [FORMULA] = 60 K, the typical value for cool gas clouds in the Milky Way, are given in Table 2, Column 7, the values for [FORMULA] = 27 K are given in Column 8. Fig. 4a shows the fraction of cool gas over the face of the LMC for survey 2&3 using the values of Column 7. Fig. 4b and c present the distribution of the total absorption and the fraction of cool H I with distance from the gravitational centre (Luks & Rohlfs 1992). The angles from the gravitational centre are measured in the rectangular coordinate grid defined by Isserstedt (1975), i.e. [FORMULA] (for the projected distance from the gravitational centre we assume a distance to the LMC of 50 kpc). The lines of sight toward different regions (LMC 4, 30 Doradus complex, eastern H I boundary and the reference group) are distinguished with different symbols.

[FIGURE] Fig. 4a-c. The fraction of cool gas, [FORMULA] = 60 K), compared to the warm for H I absorption survey 2&3 is shown on the left over the face of the LMC. The unphysically high value at the west side of the LMC (J0456-702) is due to a very low temperature of the gas in this direction (Paper II). On the right, the absorption integral and the fraction of cool gas is plotted against the projected distance from the gravitational centre, except the value of [FORMULA] for J0456-702.

Obviously, there is no clear decrease in [FORMULA] with distance from the gravitational centre. A decreasing value of [FORMULA] could e.g. indicate a pressure gradient gravitationally determined. The fraction of cool gas seems to be rather determined locally by the characteristics of the surrounding objects (e.g. H II regions, SNRs). Cloud formation is most efficient in the star-forming region 30 Doradus and in the direction of LMC 4.

All lines of sight near 30 Doradus show unusually high absorption integrals and a high fraction of cool gas compared to warm. The compact H II region, source No. 8, which is located in the 30 Doradus complex, shows the highest value, [FORMULA] @ 1, in the present survey. The high amount of cool gas toward the giant star-forming region, 30 Doradus, is consistent with H I emission/absorption studies toward galactic H II regions (Kuchar & Bania 1989), which show that cool atomic gas is very abundent toward star forming regions. Probably the ISM pressure generated by shock fronts is highest toward the 30 Doradus complex. While the heating rate is only proportional to the number density [FORMULA], the cooling rate is given by [FORMULA], where [FORMULA] denotes the interstellar cooling function. Local enhanced pressures might increase the density of the gas and force a higher cooling rate.

The high number of cool H I clouds and the high fraction of cool gas compared to warm toward LMC 4 (note that [FORMULA] [FORMULA]60[FORMULA] in the direction of J0526-658 and J0526-678 [survey 2]), also suggest a high cooling rate of gas caused by a high density near the supernova driven shock of LMC 4. The inhomogenity of the distribution of warm and cool gas near LMC 4 suggests a strong clumpiness of the ISM into which the shock wave of LMC 4 propagates.

Cool H I clouds are not frequently detected near the eastern steep H I boundary. Cool gas has only been observed in two directions toward the leading edge, which show high column densities and which are near the region, discussed as a possible impact with a High Velocity Cloud by Braun (1996). The fraction of cool H I in these directions is similar to that of empty fields. In contrast to these two directions with detected absorption, the other lines of sight toward the east show a separation of the H I emission into several lines of lower brightness, indicating lower densities and therefore a lower cooling rate.

Table 3 presents a comparison of the fraction of cool gas for the different regions of the LMC as well as the results of averaging over the entire sample of LMC spectra. We add the spectrum integrals, [FORMULA] and EW, using the values of survey 2 & 3 with the brightness temperature threshold of 2 K (see Table 2, Columns 4 and 5 for survey 3), and thus get totals for the entire sample, [FORMULA] and [FORMULA] (Table 3, Columns 3 and 4). We find [FORMULA] = 35[FORMULA] if intrinsic continuum sources are included, and [FORMULA] = 32[FORMULA] if they are excluded. In the 30 Doradus complex about half of the neutral hydrogen seems to be in the cool phase. Toward LMC 4 we find 40 per cent cool gas versus 60 per cent warm. This same approach has been used to interpret H I absorption results for disks of other galaxies (Dickey & Brinks 1993), including the Milky Way. Results for high galactic latitude clouds are shown on the bottom of Table 3. From this comparison we find that assuming [FORMULA] = 60 K the interstellar H I of the LMC contains a larger fraction of cool gas than the Milky Way (solar neighborhood). Excluding the nine lines of sight in the direction of the 30 Doradus complex, we find about the same fraction ([FORMULA] = 27 [FORMULA]) of atomic hydrogen in the cool phase as in the solar neighborhood. The values of [FORMULA] computed here depend, however, on the assumed cool phase temperature [FORMULA]. The value of 60 K used above is a good estimate of [FORMULA] in clouds at high latitudes in the solar neighborhood, but it may well be that the cool H I in the LMC is colder. For example, if [FORMULA] were 40 K, we would find [FORMULA] = 0.24[FORMULA] as in the Milky Way. In the extreme case, if [FORMULA] were as low as 27 K (i.e. mean [FORMULA] for both surveys), then the fraction of cool gas would be less than in the Milky Way; [FORMULA] would be only 0.16.


[TABLE]

Table 3. Comparison of [FORMULA] and [FORMULA] with the Milky Way


The LMC differs from the Milky Way also in the overall absorptivity, [FORMULA], which is calculated in Column 5 (Table 3) by:

[EQUATION]

where i=33o is the inclination of the disk, [FORMULA] is the number of background sources and [FORMULA] is the number of intrinsic sources (for the Milky Way the corresponding value is the equivalent width times sin[FORMULA]). Even if we exclude lines of sight near the unusual 30 Doradus region, the LMC shows a higher value for [FORMULA] than the Milky Way. No other system known shows a value for [FORMULA] as high as 1 km s-1. Assuming a thickness of the gas disk of the LMC, h, of 300 pc (Kim priv. comm.) we can determine the mean opacity of the H I [FORMULA] = 6 km s-1 kpc-1. Values for [FORMULA] in the Milky Way, M31 and M33 are in the range 2 to 5 km s-1 kpc-1 (Dickey & Brinks 1993).

4.2. Individual absorption lines: comparison of cloud properties for different regions of the LMC

Nine of the twenty lines of sight show absorption above the 3 [FORMULA] detection threshold. 20 cool atomic clouds are detected. The cloud properties as derived from the individual absorption features and from the comparison with the H I emission data are shown in Table 4. Column 1 gives the source number, Column 2 the equivalent width of the absorption line. Column 3 shows the peak optical depth, [FORMULA], and Column 4 gives the centre velocity, [FORMULA], of the absorption line relative to the LSR. In Column 5 the column density of the emission, [FORMULA], is listed. We have integrated over just the velocity range of the line component for which the optical depth is above the 3 [FORMULA] absorption threshold. The absorption line width, [FORMULA], is given in Column 6. It is calculated by dividing the equivalent width in Column 2 by [FORMULA]. The upper limits of [FORMULA] of 0.6 km s-1 are determined by the velocity resolution of 1.6 km s-1. Column 7 shows the velocity difference, [FORMULA], between [FORMULA] and [FORMULA], the velocity of the disk component "D" in direction of the background source: [FORMULA]. Values for [FORMULA] are from the PhD thesis of Luks (1991) and are listed in Column 8. In some cases the absorption component can be identified with the secondary gas system at lower velocity, the "L" component. We used this term in analogy to Dickey et al. (1994) for all absorption components with [FORMULA] km s-1, even if the emission spectra do not show the "L" component (marked with "L" in Column 9). Lines which are tentative detections near the noise threshold are marked with "?", their velocities are ill-determined. The distribution of the velocity difference [FORMULA] is shown in Fig. 5 for all 62 absorption components detected in survey 2 & 3. The different populations ("L" and "D" component) are shown by different shading. The distribution shows a nearly symmetric shape with a mean velocity of [FORMULA] = -0.3 [FORMULA] 1.6 km s-1 and a dispersion in velocity of [FORMULA] = 12.4 km s-1. Considering only the 35 lines marked "D", we find a mean value [FORMULA] = 3.1 [FORMULA] 1.2 km s-1 and a dispersion in velocity of 7.3 km s-1. This value does not significantly differ from the one found by Dickey et al. (1994) and is close to the true random velocity dispersion of the cloud population in the LMC disk.

[FIGURE] Fig. 5. For the absorption survey 2 & 3 the distribution of the deviations ([FORMULA]) of velocities of absorption components from the disk velocity is shown. The shading distinguishes between the low velocity component "L", the disk component "D" and tentative lines "?". The velocity dispersion of the entire set of lines is 12.4 km s-1, for the "D" population alone it is 7.3 km s-1.


[TABLE]

Table 4. Individual absorption lines


Column 10 of Table 4 lists the values for the spin temperatures calculated for the individual line components at their centre velocity:

[EQUATION]

We find a mean cloud temperature of 29 K in agreement with the value of 25 K derived from survey 2. The calculated spin temperatures are apparent ones, because we assume the H I emission to be distributed homogeneously over the entire 15´ Parkes beam and we do not take into account mixing of gas at different temperatures in each velocity channel. From the present data, we can not isolate discrete emission features at the velocities of the absorption features. Most of the emission observed with Parkes must come from the warm gas. The presence of emission fringes on the shortest baselines of the ATCA (77 m to 800 m) indicates that there is structure in the 21 cm emission on scales of 9´ to 54" ([FORMULA]131 to 13 pc) (K. Rucker 1995). A comparison with the ATCA-H I -Mosaic of the LMC (Kim et al. 1997) also reveals small emission structures for several lines of sight with cool H I gas.

The last column shows the values of the "Doppler temperature", i.e. the equivalent temperature for which the line width would result from thermal broadening alone

[EQUATION]

where m is the hydrogen mass and k is Boltzmann's constant. [FORMULA] is a weak upper limit on the kinetic temperature of the gas seen in absorption (see Dickey et al. 1994). The limit of 43 K for the "Doppler temperatures" is the result of the velocity resolution.

The difference in cloud parameters among the 30 Doradus complex, LMC 4, the eastern H I boundary and the reference sample are illustrated in Fig. 6. The values of the equivalent width (Fig. 6a), the optical depth (Fig. 6b) and the spin temperatures (Fig. 6c) from survey 2&3 are plotted against the projected distance from the gravitational centre. Lines of sight toward different regions are distinguished with different symbols. Mean values per distance interval of 250 km s-1 are shown by dotted lines, mean values of the four different groups are plotted on the right margin. We do not find a dependence of the mean values of [FORMULA] or EW on the distance from the gravitational centre. The mean temperature (dotted line in Fig. 6c) increases over the face of the LMC, which is consistent with the non-detection of cool gas in the halo of the LMC. Atomic clouds toward the 30 Doradus complex show the highest values of EW, [FORMULA] and [FORMULA], but also a striking scatter of all cloud parameters. Unusually high values of EW, above 13 km s-1 are detected toward J0540-697 (survey 2) and source No. 8. Both sources are associated with regions of recent star formation. The high value of EW seems to be due to a high number of unresolved clouds with similar velocities. Clouds in the direction of LMC 4 and the leading edge of the LMC also differ from atomic clouds at the reference positions by higher values of EW and [FORMULA]. Their mean optical depths are not significantly different from that of the 30 Doradus complex. About half of the cool clouds near 30 Doradus, near LMC 4 and near the eastern steep H I boundary are optically thick, whereas most clouds in other regions show low values of [FORMULA]. This implies higher densities of the cool atomic gas toward 30 Doradus, LMC 4 and the eastern H I boundary compared to other regions of the LMC.

[FIGURE] Fig. 6a-c. Equivalent widths, optical depth and spin temperature of detected absorption lines on the individual lines of sight versus the projected distance from the gravitational centre. Values for lines of sight near 30 Doradus, near LMC 4 and toward the eastern steep H I boundary are marked with different symbols. The dotted line shows mean values of EW per distance of 250 pc. The mean values for the four different groups are plotted on the right margin.

Comparing the cloud properties with those of galactic cool H I clouds (Dickey et al. 1978), we find that LMC clouds show higher values of EW and [FORMULA]. For all lines of sight the mean value of [FORMULA] is 2.39 km s-1, which is a factor of six higher than the mean value from high galactic latitude clouds ([FORMULA] 25o), [FORMULA] = 0.38 km s-1. Even the reference group has a higher value of [FORMULA]= 1.23 km s-1, which is similar to that of intermediate galactic latitude clouds ([FORMULA] 20o), [FORMULA] = 1.28 km s-1. The mean value of the optical depth, [FORMULA]= 1.01, is a factor of 6 higher than the value found for high latitude clouds in the Milky Way, [FORMULA]= 0.18, but is similar to that found for the inner Milky Way, [FORMULA]= 0.83 (Garwood & Dickey 1989). Clouds toward LMC 4, 30 Doradus and the leading edge show mean values of [FORMULA] above 1, the reference sample shows a value of 0.67.

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Online publication: February 25, 2000
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