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Astron. Astrophys. 342, 213-232 (1999)

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5. Discussion

5.1. The radiation transfer of [FORMULA] keV photons

We discuss here the accuracy of our solution of the radiation transfer in confirming the detections of enhanced soft X-ray radiation close to HVCs, and some general properties of the distant soft X-ray sources. The compelling similarity between the observed and the modelled SXRB intensity distributions, based only on H I data, supports several conclusions. It argues for a smooth intensity distribution of the SXRB sources, at greater distances than the galactic H I . Moreover, the smoothness of the SXRB source distribution is emphasized by the success of a constant intensity background distribution in fitting the ROSAT data well across several tens of degrees as suggested by Pietz et al. (1998b). This situation does not rule out that there may be large-scale intensity gradients across the entire galactic sky. Also, the averaged variations plotted against galactic l and b do not suggest that, there are no intensity gradients in the SXRB, but they do indicate that within the fields considered, the distant X-ray sources do not show significant intensity variations.

Table 2 summarizes the derived intensities of the [FORMULA] and the distant X-ray component, [FORMULA], in order of increasing angular distance of the map center from the galactic center. The variation of the galactic halo intensity noted in Table 2 and plotted in Fig. 7 suggests that towards the inner Galaxy the distant soft X-ray source reaches a local maximum. Because we avoid the area of the North Polar Spur (Egger & Aschenbach 1995), this variation is probably due to the distant SXRB source component. Moreover, the distant SXRB source intensities tend to decrease in the direction away from the galactic center (see Fig. 7 and the discussion below). This variation with l implies that we indeed observe galactic soft X-ray emission, confirming the findings of Pietz et al. (1998a; 1998b).


Table 2. Summary of the derived [FORMULA] keV X-ray intensities, in units of [FORMULA]. The HVC complexes investigated by Herbstmeier et al. (1995) and by Kerp et al. (1996) are indicated by asterisks. The fields are ordered according to the angular distance of each map center from the galactic center (see Fig. 7). The righthand column gives the [FORMULA] value of the difference between the modelled and observed X-ray map. Using a significance level of 0.05 the acceptable [FORMULA] is 120 with 96 degrees of freedom.

[FIGURE] Fig. 7. Dependence of [FORMULA] (dots) derived from our analysis on angular distance from the galactic center. The data point without an error bar corresponds to an averaged value extracted from the analysis of Herbstmeier et al. (1995). With the exception of this point, all [FORMULA] intensities are towards comparable b. The horizontal solid and dashed lines represent the [FORMULA] intensity level based on Barber et al. (1996) and Cui et al. (1996), respectively. [FORMULA] shows a continuous decrease with increasing angular distance from the galactic center and is significantly larger than [FORMULA] towards all analyzed fields.

A similar intensity variation of the galactic X-ray halo component with b cannot be claimed from our data because all the X-ray maps analyzed are at roughly the same latitude, near [FORMULA]. Our data suggest, however, that the derived galactic X-ray halo intensity shows the same brightness in the northern and southern sky (Pietz et al. 1998b; Wang 1998). We note further that the derived LHB intensities are proportional to the extent of the local cavity and in agreement with the shape of the LHB derived from absorption-line measurements (e.g. Egger et al. 1996).

The variations of the observed SXRB intensity, averaged over l and b, indicate that, on large angular scales, the observed SXRB intensity variation is determined, in detail, by the distribution of the absorbing interstellar medium. The similarity between the observed and modelled SXRB maps shows that small-scale intensity variations [FORMULA] of the observed SXRB can also be attributed to photoelectric absorption. The soft X-ray absorption is well traced by H I in the velocity range [FORMULA]. This range covers the conventional galactic gas as well as the IVCs. Because the chosen velocity range includes low-velocity as well as intermediate-velocity H I , and because in some cases the H I column from the IVC gas exceeds that of the conventional-velocity gas, the X-rays have to originate beyond the IVCs studied by Kuntz & Danly (1996). From the soft X-ray shadow cast by HVC complex M (Herbstmeier et al. 1995), we conclude that at least a minor fraction of the galactic distant X-ray emission originates at distances larger that of HVC complex M. We conclude that nearly all galactic H I absorbs the X-ray halo radiation, because the vertical extent of the galactic H I is entirely located within this distance range (Lockman & Gehman 1991).

Our analysis suggests that H I alone predominantly traces the X-ray absorption, because otherwise the modelled X-ray intensities would not fit the observational data as well as they do. H2 certainly absorbs the SXRB radiation along some lines of sight, but is not diffusely distributed over scales of several tens of degrees, and is rare at the higher galactic latitudes considered here (Magnani et al. 1997). Furthermore, the SXRB source intensity absorption traced by [FORMULA] occurs within regions of high [FORMULA], for instance as shown by our data towards the Polaris Flare (Sect. 4.1.2; Meyerdierks & Heithausen 1996). Otherwise we would have detected deep soft X-ray absorption features not traced by the [FORMULA] distribution, because [FORMULA].

Soft X-ray absorption associated with diffusely distributed ionized hydrogen (Reynolds 1991) is also not obvious in our data. If the H+ layer has a column density distribution similar to that of the H I layer, we would anticipate a constant scaling factor for the brightness of the galactic halo X-ray component. On the other hand, if the distribution of [FORMULA] is patchy within the analyzed fields, its soft X-ray absorbing column density would be about [FORMULA].

The low SXRB source intensity towards the galactic anticenter can be used to separate the contribution from galactic halo emission and that from unresolved extragalactic point sources. Barber et al. (1996) determined [FORMULA], while Cui et al. (1996) derived [FORMULA]. Our minimum [FORMULA] keV count rate is about [FORMULA]. In the extreme cases [FORMULA] and [FORMULA], the extragalactic X-ray background contribution is about equal to the soft X-ray intensity of the galactic halo. We plotted the [FORMULA] values as a function of angular distance from the inner Galaxy in Fig. 7. The horizontal lines in the lower part of Fig. 7 indicate the extragalactic background level determined by Barber et al. (1996) and Cui et al. (1996). [FORMULA] increases towards the galactic center. This leads us to conclude that the bulk of the distant soft X-ray emission is of galactic origin and that the extragalactic background radiation gives only a constant X-ray intensity offset.

5.2. X-ray enhancements near HVCs

We have shown that the general radiation transfer of the SXRB photons is well represented by our modelling of the diffuse X-ray background. Our analysis of the ROSAT all-sky data reveals no evidence for soft X-ray shadows attributable to HVCs. This is in some respect surprising because our analysis is biased towards the detection of HVC soft X-ray shadows and, consequently, against the detection of soft X-ray enhancements of HVCs (see Sect. 3.5.2). Certainly, HVCs attenuate the extragalactic background radiation. As shown above, the maximum extragalactic background intensity is [FORMULA] = 4.4[FORMULA] (Cui et al. 1996) and an HVC with [FORMULA] attenuates this radiation by about 60%. If some HVCs are located at large distances from the galactic disk (see Blitz et al. 1998) this only HVC absorbed X-ray radiation is additionally attenuated by the diffuse galactic H I layer. This layer may be characterized by a typical [FORMULA] of about [FORMULA]. On the HVC we observe a count rate of about [FORMULA] whereas off the HVC the count rate is [FORMULA]. The difference [FORMULA] is undetectable in the ROSAT data analyzed at the current angular resolution.


Table 3. Properties of the soft X-ray enhancements towards HVC complexes C, D and GCN. The l and b extent is determined by the distribution of the [FORMULA] and [FORMULA] contour lines, plotted in the individual maps of the fields of interest. [FORMULA] denotes the total energy detected by the ROSAT PSPC integrated across the extent of the excess soft X-ray emitting area. [FORMULA] gives the mean significance level, while [FORMULA] gives the maximum significance level within the extent of the excess emission area. To evaluate the emission measure [FORMULA] as well as the electron volume density [FORMULA], we assumed [FORMULA] (Kerp et al. 1998) and a "normalized" distance of D = 1 kpc to the HVCs. For a different distance of the HVCs the radiated 1/4 keV energy [FORMULA] has to be scaled by [FORMULA] [kpc] and the corresponding electron density by [FORMULA] [kpc]. The last two columns give the field-averaged significance level of the [FORMULA] keV excess emission and the peak significance level.

For the HVC complexes C, GCN, and D we found significant soft X-ray emission close to or towards the HVCs. In case of the higher-l end of HVC complex C, soft X-ray enhancements up to the 11-[FORMULA] level were detected. The X-ray enhancements generally follow the orientation of the HVCs, for instance in the case of HVC complex C (Fig. 4d), but not always in detail. In case of HVC complex C, large parts of the complex are located close to intermediate-velocity gas (Kuntz & Danly 1996). Depending on the origin of the excess soft X-ray radiation, IVCs may also be X-ray bright. To investigate this, we mosaicked the X-ray and H I data of the entire HVC complex C. Fig. 8 shows a mosaic, where the excess soft X-ray emission is displayed in colour and the [FORMULA] distribution of the HVCs [FORMULA] and IVCs [FORMULA] are superposed as contours. Contours of the HVC [FORMULA] distribution encompass areas of excess X-ray emission (Fig. 8, top ).

[FIGURE] Fig. 8. Mosaic showing the positional correlation of excess [FORMULA] keV emission and the HVC and IVC [FORMULA] distributions towards the entire HVC complex C. The images present the areas of excess soft X-ray emission in the significance range 4[FORMULA] (dark colour) to 10[FORMULA] (bright colour). Top: The HVC [FORMULA] distribution [FORMULA] superposed as contours with [FORMULA] in steps of [FORMULA]. Bottom: The IVC [FORMULA] distribution [FORMULA] superposed as contours with [FORMULA] in steps of [FORMULA]. The HVC [FORMULA] distribution follows the orientation of the soft X-ray enhancements. The IVCs reach [FORMULA] maxima not positionally coincident with excess X-ray emitting areas, except near [FORMULA], [FORMULA], close to the Draco nebula, and near [FORMULA], [FORMULA]. Both IVCs are located close to HVCs. In particular, the cloud at [FORMULA], [FORMULA] is close to an H I velocity bridge (VB 111+35, Pietz et al. 1996) which was not detectable in the higher l and b portion of HVC complex C (Sect. 4.1.2). A further investigation of the connection of IVCs and HVCs is mandatory.

IVCs show a lower degree of correlation with the soft X-ray enhancements (Fig. 8, bottom ) than shown by the HVCs (Fig. 8, top ). Their H I emission maxima coincide positionally with minima in the X-ray emission, indicating that IVCs absorb the constant [FORMULA] intensity distribution. Most probably, they are located nearer than the sources of the excess soft X-rays. Thus, HVCs remain as the most probable candidate for the association with the excess soft X-ray emission, while the role of the IVCs remains unclear. Especially the presence of the "velocity bridges" (Pietz et al. 1996) linking some HVCs with the excess X-ray emission with the intermediate-velocity gas deserves further investigation, especially in regard to the Blitz et al. (1998) predictions.

The difference in location between the H I clouds and the soft X-ray emission is not surprising if we assume that the X-ray emitting plasma and the HVCs are spatially close. Under this hypothesis, the neutral HVC boundaries are ionized by the radiation from the X-ray plasma. This can cause the apparent positional shift between the neutral gas and the X-ray radiation. In consequence, [FORMULA] radiation should be detectable from this interface region; in particular, it has to originate close to [FORMULA] gradients. Towards complexes M, A, and C, Tufte et al. (1998) detected H[FORMULA] radiation. In these cases the soft X-ray enhancements reveal the presence of collisionally ionized gas.

These findings can be interpreted in two general ways. First, an H I gradient is caused by the ionizing radiation from the X-ray plasma alone (conductive interfaces). Second, an H I gradient is caused by the interaction of the HVC with the ambient ISM.

For HVC complex C (higher-l end, Sect. 4.1.2), we can estimate the energy budget of the apparent interaction process. Assuming that complex C has a total mass of about [FORMULA] to [FORMULA] and a bulk velocity of [FORMULA] (Wakker & van Woerden 1991), the kinetic energy of the complex is [FORMULA]-[FORMULA] erg. In the ROSAT [FORMULA] keV band we detect at maximum [FORMULA]. Thus, the observed X-rays require only a very small fraction of the available kinetic energy. This implies that we need, from the energy point of view, only a weakly-efficient process which converts the HVC bulk motion into thermal energy. If the excess soft X-ray emission is caused by heating of the HVC and the surrounding medium, we have to investigate the physical conditions of the interaction scenario. At a vertical distance of [FORMULA] kpc, the temperatures are about [FORMULA]-[FORMULA] K, the volume densities [FORMULA] (Kalberla & Kerp 1998), and the sound speed [FORMULA]-[FORMULA]. It is difficult to account for a strong shock if the absolute value of the complete HVC velocity vector is [FORMULA]. Two other possibilities are open to overcome this distance discrepancy, namely the galactic wind scenario (Kahn 1991), in which a wind encounters the HVCs, and the magnetic reconnection process (Kahn & Brett 1993, Zimmer et al. 1997), in which turbulent motions within and close to the HVC disturb the magnetic lines of force. The field lines find a new configuration of minimum energy during the reconnection process. As Zimmer et al. (1997) pointed out, the magnetic reconnection can heat the ISM to several million degrees.

A remaining problem concerns the large angular extent of the areas of excess soft X-ray emission. As Fig. 4d shows, the angular extent of the soft X-ray excess emission and the extent of HVC complex C are about equal. Assuming a distance of at least 2 kpc for complex C, this corresponds to a linear size of at least 150 pc. Heating such a volume via atomic collisions would require [FORMULA] years. This time is comparable to the cooling time of the detected X-ray plasma. This may indicate that the thermal expansion of hot gas heated by a single event may not be the source of the observed X-ray radiation. We note that the Alfvén velocity is much higher than the sound speed: [FORMULA], where B denotes the magnetic field strength and [FORMULA] the volume density of the medium. If [FORMULA] (Beuermann et al. 1985) and [FORMULA], then [FORMULA]. This indicates that the magnetic lines of force transfer information about the motion of the HVCs in the halo some five times more rapidly than the particle collisions do. Understanding the role played by magnetic fields may be important to understanding the HVC excess X-ray emission scenario.

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Online publication: December 22, 1998