Astron. Astrophys. 357, 75-83 (2000)

4. Discussion and conclusion

4.1. The diverse nature of HVCs

It is still difficult to tackle the problem of the origin of HVCs, since they may be diverse in nature, with possibly different formation histories. The first idea that they are clouds infalling towards the Milky Way (Oort 1966) was proposed since only negative velocities clouds were discovered at this epoch. However, since differential galactic rotation makes an important contribution to those velocities and the tangential velocity of the HVCs is also unknown, it is difficult to ascertain their true three dimensional motion. Now that almost an equal number of clouds are detected with positive high velocities, and that is also true in the various reference frames (e.g. Wakker 1991), it is believed there must be other explanations for at least some of them. Some HVC complexes have been proven to be associated with the Galaxy, in being very close (less than 10 kpc) due to absorption detected in front of Galactic halo stars (e.g. Danly et al. 1993; van Woerden et al. 1999). This supported a Galactic origin for some of the HVCs and more specifically the Galactic fountain model, where gas is ejected in the halo by the star formation feedback mechanisms. The main problems with this scenario are the low metallicity observed in most lines of sight (even though it could explain why clouds have nearly solar metallicity, e.g. Richter et al. 1999), and the extreme velocities sometimes reached (up to -450 km s^-1 in the negative side). Alternatively, HVCs could be transient structures, now becoming bound to the Galaxy: an ensemble or complex of HVCs has been identified as tidal debris from the Magellanic Clouds (Mathewson et al. 1974), and is called the Magellanic Stream. Few of them could come from tidal debris from interactions with other dwarf galaxies but the corresponding dwarf galaxies either have not been identified yet, or they have been already dispersed (e.g. Mirabel & Cohen 1979).

A key point is to consider whether HVCs are transient structures or coherent and self-gravitating. With only their column density observed in HI, to be self-gravitating they should be at least at 1 Mpc distance, and in average at 10 Mpc, therefore outside the Local Group (Oort 1966). This distance can be reduced by a factor 10, if the total mass of HVC is taken to be 10 times their HI mass, composed mostly of dark matter (Blitz et al. 1999). Since the specific kinetic energy is in M/R Distance, then the clouds would have to be only at about 1 Mpc, and would consequently be part of the Local Group. The main difficulty with this model of mini-haloes merging with our Galaxy, is that other high-velocity clouds should have been observed around or in between external galaxies, which is not the case (Giovanelli 1981; Zwaan et al. 1997; Banks et al. 1999). Moreover, the derived typical dimensions and mass of these systems do not correspond to any observed object or any extrapolation of mass ranges (they have dwarf masses, but are very extended in size).

Another possibility, however, could be that HVCs represent gas left over from the formation of the Galaxy: they form a system out of equilibrium, but bound to the Galaxy, and are now raining down to the Galactic disk. This would explain several observed characteristics, such as the 4-10 kpc distance determined for some complexes, and the low metallicity of many of them (e.g. Wakker et al. 1999).

4.2. How many molecular absorptions could be expected?

Given the low HI column densities reported in Table 2, it could seem hopeless to detect molecular absorption, with the present sensitivities. But this is true only if the HVC gas is homogeneous. In fact, from previous HI observations, we expect that like the gas in the galactic disk,the HVC gas is also composed of several components, with clumps of much higher column densities, only detectable at higher spatial resolution. This information can be deduced from existing HI observations in emission and absorption, towards HVCs. The optical thickness is related to the column density N(HI) (cm^-2), the spin temperature T_s(K) and the FWHM velocity width (km s^-1) by

Since the profile extends at least over 20 km s^-1 in emission, and the spin temperature has been determined to be at least 50 K, if there was only one component, the derived optical depth would have to be very low, . Absorption and emission studies in the Galactic plane have shown though that there is indeed more than one component. If there was only one, both emission and absorption profiles would look similar, which is not what is observed. In fact, there are at least two components; a warm diffuse inter-clump component with cloudlets which are cold, narrow in velocity, and more optically thick (Garwood & Dickey 1989). If the surface filling factor of the two components are f₁ and f₂, for spin temperatures T₁ and T₂, and optical depths and , the observed ratio between the absorption depth and the antenna temperature of the emission is

In this formula, it is obvious that each component is weighted according to its mass if it is optically thin (i.e. weight ), but considerably less if . Therefore, if the cold component is optically thick, the derived spin temperature will be overestimated ¹.

Are HVC clouds of the same nature than normal low-velocity galactic clouds, and have they similar small-scale structure? For normal HI clouds, Payne et al. (1983) have determined (from absorption/emission comparisons) that the weighted average spin temperature is decreasing as the optical depth increases (cf line in Fig. 4). There is only a small scatter in this relation, which means that if the cold and thick component is made of cloudlets, their size must be smaller than that of their background continuum sources, i.e. a fraction of an arcmin, and their number must be large accordingly (N 100). We do not see the situation where absorption features are deep and rare (statistically the T_s- relation will still hold, but with large scatter). The data favor a model, in which the cloudlets are quite small ( 0.1 pc) and numerous, and they are weighted according to their surface filling factor f both in emission and in absorption for any line of sight. The existence of such small scale structure is also confirmed by VLBI HI absorption (Faison et al. 1998), where sizes down to 20 AU are detected. It is also very likely that the structure, apart from these smallest fragments, has no particular scale. If it is a fractal, statistically, there is a correlation between the optical depth between scales with a limited scatter. This would explain the observed correlation between emission and absorption at different scales. When the emission/absorption measurements for HVCs are considered (cf Fig. 4) the lower limits on derived spin temperature are compatible with the detections on the normal low-velocity gas and their T_s- relation. The spin temperature of HVCs is a weighted mean of the warm and cold components, with the same mixtures as the one observed in normal low-velocity clouds of the galactic plane. The difficulty to find HI in absorption in HVCs corresponds then only to their low average column density, and not to a different physical structure.

Fig. 4. Spin temperature Ts of the HI in HVCs derived from absorption/emission measurements, as a function of the optical depth of the absorption. Positive detections are from Payne et al. 1980 (filled stars) and Wakker et al. 1991 (unfilled circles). Upper limits in HI absorption lead to lower limits in Ts and are plotted by vertical bars (Payne et al. 1980; Wakker et al. 1991; Akeson & Blitz 1999). The line is that fitted to the detections of low-velocity gas (Payne et al. 1983).

As for molecular absorptions, the column densities to which a detection is possible is even larger. The corresponding scales must be smaller, and consequently the corresponding line-widths narrower. This is observed for low-velocity absorptions, where the detected line-widths are as narrow as 0.6 km s^-1 (LL96). The detected optical depths are larger on average, and the probability to underestimate the column density is higher, because of saturation. (One should note though that the apparent optical depth is low because of spatial and velocity dilutions.) The probability of detection of the HCO⁺(1-0) absorption has been estimated to be 30% as large as the 21cm absorption for galactic clouds (LL96). The presently observed low probability to find an HCO⁺(1-0) absorption is therefore expected. In addition, there could be a column density threshold for self-shielding against photo-dissociation, that hampers molecular observations. This threshold has been estimated for CO emission to N(H₂) 410²⁰ cm^-2 (or equivalently of the order of 10¹² cm^-2 for HCO⁺). If our tentative detection is confirmed, given the low metallicity of the HVCs, this will support the existence of clumps of high column densities in this medium. The fact that molecular absorption is more frequent with respect to emission than atomic absorption is related to the excitation mechanism. Large volumic critical densities are required to excite molecules above the cosmic background, and this is in particularly true for HCO⁺. This makes absorption techniques the more promising to probe the molecular content of HVCs in the future.

4.3. Physical nature and distance of the gas

Since the HVCs appear to follow in projection the same fractal properties as the normal low-velocity gas (Vogelaar & Wakker 1994), it could be interesting to develop an insight in their distance from their size-linewidth relation. It is now well established that clouds in the interstellar medium (either molecular or atomic) are distributed according to a self-similar hierarchical structure, characteristic of a fractal structure (Falgarone et al. 1991; Stanimirovic et al. 1999; Westpfahl et al. 1999). Such a scaling relation between mass and size, can also lead to a relation between size and line-width, provided that the structures are virialized. In particular, various clouds at all scales obey a power-law relation between sizes R and line-widths or velocity dispersion :

with q between 0.35 and 0.5 (e.g. Larson 1981; Scalo 1985; Solomon et al. 1987). We have plotted this latter relation, together with the sizes and line-widths of the 65 well defined isolated HVCs, catalogued by Braun & Burton (1999). This catalog is expected to be free from galactic contamination as well as from blending along the line of sight, because of the isolation criterium imposed for their selection. To compute their sizes, two distances were assumed, either 20 kpc, or 1 Mpc, and the geometrical mean between major and minor axis was calculated. At a distance of 20 kpc, the clouds fall on the relation corresponding to Giant Clouds in the Galaxy. Note that the large scatter is due to the fact that this choice of distance is only one order of magnitude, and the HVCs are certainly not all at the same distance. This set of clouds has been determined with a spatial resolution of half a degree. The clouds determined at higher spatial resolution have correspondingly narrower line-widths. In Fig. 5, we have also plotted the characteristics of clouds determined with the Westerbork interferometer, at 1 arcmin resolution (Wakker & Schwarz 1991). They also fit the galactic clouds relation on average, if their distance is chosen to be 20 kpc, with large scatter since individual distances are also not known. In fact, HI observations at different spatial resolutions emphasize a particular scale of the hierarchical structure (see e.g the 10' resolution observations by Giovanelli & Haynes 1977). This hierarchical structure is similar to what is observed for "normal" galactic clouds, in the sense that the same fraction 20-30% of the single dish flux is retrieved in the interferometer data (Wakker & Schwarz 1991).

Fig. 5. Size-linewidth plot for HVCs, observed with two spatial resolutions. The first set is the compact isolated HVCs from the Braun & Burton (1999) catalog, with two assumed distances, 20 kpc (filled stars), and 1 Mpc (open circles). The second set is the clouds identified by Wakker & Schwarz (1991) with the Westerbork interferometer, with the same two assumed distances, 20 kpc (filled triangles), and 1 Mpc (open triangles). The line is the relation derived for clouds in the Milky Way (Solomon et al. 1987).

The size-linewidth relation has been widely observed up to 100pc in size, the largest size for self-gravitating clouds in the Galaxy, but it might appear questionable to extend it to higher scales, where the gas would not be self-gravitating. At these scales, the gas is bound into largest self-gravitating structures, including stars or dark matter. However, even at these scales, the gas should trace the gravitational potential of the bound structure it is embedded in, and share the corresponding velocity dispersion; such a relation is observed for instance in the form of the Tully-Fisher relation in galaxies. The main point is that the gas should reveal velocity profiles in emission that should grow wider with the distance, if it belongs to an assumed self-gravitating remote system. The observed profile width is therefore a distance indicator.

4.4. Conclusion

We have searched for HCO⁺(1-0) absorption towards 27 high velocity clouds, in front of remote radio-loud quasars. The technique is efficient, since we detect the existing absorption due to low velocity galactic clouds, for our low latitude sources. Only one tentative HVC detection is reported. If confirmed, this indicates the presence of small scale cloudlets, at low excitation and high column densities, prolonging the hierarchical structure already observed in the atomic component at larger scale. When this hierarchical structure is compared to the one observed for low-velocity galactic clouds, a good fit is obtained for the self-similar relation between sizes and line-widths, if the HVCs are on average at 20 kpc distance. Since mm molecular absorptions are expected to be more frequent than emission for these low column density HVCs, this absorption technique appears promising to probe the molecular component of HVCs, already directly detected by UV H₂ absorption lines (Richter et al. 1999).

© European Southern Observatory (ESO) 2000

Online publication: May 3, 2000
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