5. Distribution of the thermal 3/4 keV XRB
In Sect. 4 we found evidence that the observed intensity variation of the keV XRB radiation is a function of galactic longitude. Since the differential photoelectric absorption cannot cause the apparent intensity variation between the galactic center and anticenter we conclude that the distant galactic XRB plasma component is the source of the intensity variation.
It is important to establish the distribution of the distant X-ray plasma located beyond the bulk of the galactic neutral hydrogen layer. Nousek et al. (1982) confronted three different models with keV observations which had been obtained on Aerobee rocket flights:
2) A layer parallel to the galactic plane plus an extragalactic isotropic component , both absorbed by neutral matter in the Galaxy:
3) A spherical galactic halo model as an uniformly emitting sphere affected by absorption:
where is the radius of the halo in units of the solar galactocentric distance and .
Nousek et al. (1982) found that their models 1 and 2 gave acceptable fits to the X-ray data available at that time. They concluded in favor of a disk-like galactic halo (model 2), mainly because such a model is easier to understand in a physical context.
In the following we perform an analysis similar to that of Nousek et al. (1982) using the RASS and the Leiden/Dwingeloo H I data. With the new H I and X-ray data it is possible to constrain the models more strongly.
5.1. Modeling the 3/4 keV XRB
We start the analysis with model 1. Based on the results given in Sect. 3 and Sect. 4, we assume that the 3/4 keV foreground component is . The extragalactic XRB component is and the distant galactic XRB plasma count rate is in the direction of .
Using these values we calculate the expected count rate distribution using Eq. (5) and compare the count rates with the observations (thin lines in Fig. 4). On small angular scales of , the keV intensity distribution can be reproduced. For example, the deep X-ray absorption minima near , , and close to the Orion-Eridanus Bubble can be modelled, demonstrating that the fraction of the H I column to the total absorbing column density is sufficient to model the absorption of the 3/4 keV radiation even in this molecular-gas-rich area. Even the humps in Fig. 5 between and at and are predicted by the model. This demonstrates that Eq. (4) is meaningful in describing the observed keV count rate distribution on angular scales of towards the high-latitude sky.
Nevertheless, deviations of the observed count rates from the modelled keV count rates exist on larger angular scales. All keV latitude slices reveal a count rate minimum in the direction of the galactic anticenter (e.g. Fig. 4, ). The intensity contrast between the galactic anticenter region and the neighbouring longitudes decreases with increasing latitude.
Such a behaviour cannot be reproduced by the isotropic model (model 1), nor can it be reproduced by a plane-parallel galactic halo (model 2) (see e.g. Fig. 5, and ). To overcome this problem we introduce a galactic-longitude dependence to the model. We demonstrate that this is necessary by modeling the observations first with a simple linear dependence of the keV intensity on galactic longitude, assuming a linear decrease of the keV distant galactic component between and .
Furthermore, we have to take into account that the amplitude of the intensity modulation decreases as latitude increases from the galactic equator to the galactic poles. As is obvious in Fig. 5, such a linear dependence of the keV intensities on galactic longitude (thick lines in Fig. 4) reproduces the observed keV count-rate distribution better than the models discussed above. It is also relevant that the dependence of the keV radiation on galactic longitude is the same for both galactic hemispheres. This indicates that the brightness of the distant galactic XRB plasma is the same on both sides of the Galaxy.
Hence we conclude that a thermal X-ray halo model must fulfill the following conditions:
Recently Freyberg (1994, 1997) analyzed the keV RASS data and came to the conclusion that a spherical-halo model (model 3) with gives the best fit to the data. Indeed such a model (see Fig. 5 right) is consistent with the conditions mentioned above.
Another model which also accounts for the above conditions follows from analysis of the Leiden/Dwingeloo survey and describes the distribution of H I gas at large z distances. We explain this model first before comparing it with the spherical galactic halo model.
5.2. A halo hydrostatic-equilibrium model
Recent investigations by Kalberla et al. (1997) tentatively suggest the existence of H I at large z distances which can be described by hydrostatic equilibrium conditions between gravitation, gas pressure, and magnetic pressure. H I gas with a velocity dispersion of was found to be consistent with model assumptions of a turbulent gas layer with a scale height of 2 kpc or more. Such a high-dispersion H I halo agrees with the predictions of Boulares & Cox (1990) but is apparently in disagreement with models proposed by Spitzer (1956), Bloemen (1987), and Wolfire et al. (1995).
In the following, we assume that the galactic X-ray halo may be caused by a hot gas at a temperature of k which is in hydrostatic equilibrium with the gravitational potential of the Galaxy. The pressure is assumed to balance the gravitational potential :
The function according to Taylor & Cordes (1993) defines a volume-density gradient as function of galactocentric radius, R:
where is the radial scale length and . Taylor & Cordes (1993) assumed a scale length of for the Reynolds (1991) layer. We used the potential derived by Kuijken & Gilmore (1989) which is in agreement with the potential derived by Bienaymé et al. (1987). Such a potential implies a low fraction of hidden mass in the Galactic disk (see Boulares & Cox 1990 and Crézé 1991). The normalization of the density is determined by the emission measure, at , taken from the spectral-fitting results described in Sect. 3.
Most of the H I gas is confined at pc (Dickey & Lockman 1990). Since in the spectral analysis the foreground plasma component is fit well by k keV (Sect. 3), no keV emission is expected from the foreground component. Taking this observational result into account, we assumed that the hot gas causing the XRB is located entirely beyond pc. Since our analysis is restricted to this assumption holds true for the local environment of the Sun and not for the entire galactic disk. Such an assumption affects the results of our modeling only to a minor degree, due to the necessary renormalization with respect to the observed emission measure towards the galactic poles. We found no evidence for any significant X-ray plasma temperature variation, hence we assume that the X-ray halo can be described by an isothermal distribution. In this case the X-ray halo temperature of k (Sect. 3) corresponds to a scale height of .
In summary, the parameters needed for our model are: a temperature, k ; a mid-plane density, , reproducing the observed emission measure, EM ; and a scale length, , which still has to be determined. The count rate dependence on galactic coordinates for a scale length of is drawn in Fig. 5 (left). Comparison with the count rate distribution of the spherical-halo model (Fig. 5, right) shows that both models reproduce the basic conditions mentioned in Sect. 5. The differences are found in the detailed l variations, as discussed in the following section.
5.3. Flattened-halo model versus spherical-halo model
To decide which model fits the keV X-ray data best, we calculated the rms deviations, , of the residual between observations and model for each smoothed galactic latitude strip (Fig. 6). For the flattened models we varied the scale-length parameter between and , while the spherical-halo parameter was varied between 1.5 and 5. The data-points with the largest deviations correspond to the latitude strips , where generally the largest deviations from our simple radiation transfer model are expected to occur in any case, because of the additional X-ray radiation from the galactic disk.
The spherical-halo models (Fig. 6) reveal in general a mean rms deviation (marked with diamonds in Fig. 6) larger than that of the flattened-halo models. Of the spherical-halo models, the one with a normalized radius of appears to fit the observations best. This is roughly consistent with the result of Freyberg (1994, 1997) who determined as best-fit value.
The flattened-halo models (Fig. 6, models 1-4) have, however, generally lower mean rms deviations; the scatter between the different latitude strips is also significantly lower, indicating a systematically better fit of the observations by the flattened-halo models than is realized by the spherical-halo ones. The best-fit scale length is , similar to the scale length found for the flattened H I halo suggested by Kalberla et al. (1997).
For the preferred flattened X-ray halo model with we obtain an emission measure EM at the galactic poles of
with a mid-plane density of (Eq. 8). The resulting variations with longitude and latitude, expressed as keV count rates, are shown in Fig. 5 (left).
5.4. Comparison of the best-fit flattened-halo model with the observations
In Fig. 7 we show data from all analyzed latitude strips, smoothed to an angular resolution of . The thin line within the upper part of each latitude panel represents the modelled keV count rate. The thick line in the lower half of the corresponding panel indicates the difference between model and observations. Especially the amplitude of the observed keV intensity variation is well reproduced in each latitude strip.
The largest deviations between observations and model, with , are located near the galactic plane () between and . Since is larger than zero, corresponding to too low predicted count rates, excess emission is located here.
Figs. 8 and 9, maps in Hammer-Aitoff projections centered on the galactic center and the galactic anticenter, respectively, demonstrate our results. These maps show the entire sky observed by the Leiden/Dwingeloo H I survey, but exclude the region of the galactic equator itself. The maps have been smoothed to an angular resolution of . Patterns of excess emission at low latitudes are visible in the difference maps, panels (e), representing the observed-minus-modelled keV distribution. The difference maps suggest that the excess emission X-ray features may be characteristically oriented perpendicular to the galactic plane, consistent with the existence of energetic events originating near the galactic disk and extending into the lower galactic halo. Certainly, one has to consider that the interstellar environment is more complex closer to the galactic plane. The radiation transport equation used, Eq. (11), may not represent this complex situation well.
Other enhanced residual-emission areas may be associated with X-ray features described in Sect. 4.2. The Orion-Eridanus Bubble is centered near ; the enhancements near the galactic center are associated with Loop I and the galactic bulge. Comparison of the keV and 1.5 keV RASS maps published by Snowden et al. (1995) reveal a rough correlation between keV and 1.5 keV enhancements, suggesting the existence of an additional hot plasma component (k ) towards both Loop I and the Orion-Eridanus Bubble, as well as generally towards the galactic plane.
Extended areas where the predicted count rates are too high are observed at a level of in the smoothed latitude strips, e.g. in the strip to at (Fig. 7). Comparing the residual maps in Figs. 8 and 9 with the survey exposure map shown by Snowden et al. (1995) indicates that these deviations may be attributed to the instrumental scanning direction of the RASS (see the keV map by Snowden et al., 1995).
In view of the above, we conclude that our flattened-halo model with and can reproduce the observed keV RASS data down to the present accuracy limit of the X-ray data. Additional emission close to the galactic plane may be caused by localized galactic features.
© European Southern Observatory (ESO) 1998
Online publication: March 10, 1998