Astron. Astrophys. 344, 333-341 (1999)

3. Data analysis

PSPC spectral data were extracted from a region of radius 0^o.2 and binned at 50 eV intervals. Procedures recommended by Plucinsky et al. (1993) for accepting valid event data were followed. Care was taken to ensure that the region selected was free from all obvious X-ray sources. The extracted data were then further corrected for the effects of vignetting, exposure and detector dead time.

3.1. Galactic latitude survey for different lines of galactic longitude

We extracted as many available ROSAT PSPC observations from the archive as possible, ensuring a fairly uniform sampling interval in galactic latitude for longitudes 40^o, 60^o, 90^o, 120^o and 145^o. The slab model was then applied to each observation using the appropriate H I column density for each region. Values for the three free parameters (viz. foreground EM, halo temperature and EM) were obtained from the best spectral fits. The complete results of this investigation are presented in Table 1. The best fit halo temperature is not included in this table as it was found to lie in the rather narrow range of log T = 6.30.1 for all directions. In general the low galactic latitude regions in our sample provided the poorer fits to the model and are therefore excluded from the table. This is not a surprising result as the observer's line of sight passes through more of the complex Galactic disk structure with decreasing latitude. Satisfactory spectral fits were however obtained for the majority of observations at  b 35^o.

Table 1. Results of fitting three component models to PSPC observations of all galactic longitude strips. The last entry is for the deep observation in the Lockman hole region.

Table 1. (continued)

The results for all the regions are summarised in Figs. 1 to 3 using the Hammer-Aitoff projection of the sky in galactic coordinates. The fitted halo EM for each direction is shown as an open circle. The diameter of each circle is proportional to the halo emission component at that point. The labelled contours represent the expected EM variation if the hot gas is associated with the spiral arms and calculated from the following expression (see Sidher et al. 1996)

where A is a factor associated with the local halo density in the solar neighbourhood, z₀ is the disk height above the galactic plane marking the start of the halo, b is the galactic latitude, h is the scale height above the plane of the disk, l is the distance along the line of sight, p determines the radial halo mass distribution in the Galaxy and r _l is the radial distance from the Galactic centre given by

R ₀, the distance of the Sun from the Galactic centre, is taken to be 8 kpc. The halo emission contours in Fig. 1 show no longitude structure; the reason for this is apparent from Eq. 1 as the term in the denominator becomes unity for no radial dependence (p =0). Figs. 2 and 3 show the same set of fitted halo emission measures, except that the contours now denote a radial mass distribution following dark matter (p =2) and luminous matter (p =3) respectively. In all three cases a disk thickness of 3 kpc and a halo scale height of 12 kpc are assumed following the model proposed by Bloemen (1987) for stability at log T = 6.3. The maximum halo path-length, or the halo cut-off, is set at 50 kpc and the electron density is fixed at 0.0025 cm^-3.

Fig. 1. Halo EM plotted as a function of galactic coordinates. The open circles represent the fitted halo EM, the diameter of each symbol being proportional to the emission. The contours represent the EM variation for a hot gas associated with the Galactic spiral arms (p =0).

Fig. 2. Same as Fig. 1 but here the contours represent the EM variation following a radial mass distribution of dark matter (p =2).

Fig. 3. Same as Fig. 1 but here the contours represent the EM variation following a radial mass distribution of luminous matter (p =3).

Fig. 4 shows the best fit  values for the fitted halo emission measures as plotted in each of the previous three figures. In general there appears to be no significant pattern between the map of Fig. 4 and any of the maps of Figs. 1, 2 and 3, for example the high  points do not belong to a group with high emission components.

Fig. 4. Variation of , the goodness of fit parameter for the regions fitted in Figs. 1-3. The diameter of each circle is proportional to , i.e. the smaller the circle the better the spectral fit.

The mean value of our fitted halo emission measures (excluding the three very high values) is 0.020 cm^-6 pc. The standard deviation (see Fig. 5) is 60% of this value (again excluding the three very high values) at 0.012 cm^-6 pc. Although our halo emission measures compare favourably with the range 0-0.017 cm^-6 pc derived by Snowden et al. (1998) from their detailed analysis of keV band data, the foreground emission measures in our sample do not support their conclusion that the bulk of the SXRB originates inside the LHB. Our results are in broader agreement with those of Pietz et al. (1998).

Fig. 5. Frequency distribution of the fitted halo emission measures (in units of 0.0032 cm-6 pc) as given in Table 1.

To check how much of the EM variation might be due to small-scale variability in the column density which would not be picked up by the Stark catalogue, column densities have also been recovered from the Leiden/Dwingeloo survey (Hartmann & Burton 1997). The Stark and Leiden/Dwingeloo column densities for all our pointing directions are compared in Fig. 6. As well as a random scatter of a few 10²⁰ cm^-2 there is a small systematic difference. To estimate the effect of this on the derived Galactic halo EM it is necessary to consider the effect on absorption in the 400-500 eV energy range where the halo has its most dominant effect on the spectrum (see Fig. 7). From Morrison & McCammon (1983) the absorption cross section in this region is 7.4 . 10^-22 cm^-2. The solid line in Fig. 8 shows how the difference in column density between the Leiden/Dwingeloo survey values and the Stark values would affect the halo EM. The symbols on the figure show the difference between the actual fitted value and the mean. The scatter shown in the plot is far in excess of that expected on the basis of column density uncertainties, from which we conclude that the scatter reflects a real intrinsic variation in the halo EM. The fact that the Leiden/Dwingeloo column density values are about 8% lower than from Stark has a neglible effect on our results.

Fig. 6. Scatter plot of the Leiden/Dwingeloo H I survey data vs. the data from the Stark H I survey for all the directions in our sample.

Fig. 7. Spectral fit for a typical SXRB direction. The overall fit is shown together with contributions of the individual components.

Fig. 8. Scatter plot of the deviation from the mean of each fitted halo EM (in units of 0.0032 cm-6 pc) and the H I column density difference between the Stark and Leiden/Dwingeloo surveys. The solid line represents the expected halo EM variation as a result of this column density difference.

An additional source of Galactic and nearby halo absorption, not taken into account in the modelling of Sect. 2, is the warm, diffuse H⁺ component of the ISM. This gas, believed to be at 10⁴ K, constitutes a quarter of the interstellar hydrogen. It extends out into the halo region with a scale height of about 900 pc. Detailed measurements of the latitude and longitude distribution are not available for H⁺, but we can use some figures supplied by Reynolds (1991) to estimate the additional error in our determination of the halo EM variability likely to arise from this lack of knowledge. From Table 1 of Reynolds (1991) we notice that the H⁺ column is both less than the H I column and less variable than the neutral hydrogen. However, there seems to be some correlation of the variability. While values range from 0.74 . 10²⁰ cm^-2 to 2.1 . 10²⁰ cm^-2, values range from 1.5 . 10²⁰ cm^-2 to 6.2 . 10²⁰ cm^-2. Now the peak contribution to the counting rate (Fig. 7) from the halo occurs at about 200 eV. At this energy we assume that the absorption cross section per H⁺ within an H II region of an O star is a reasonable approximation to the H⁺ cross section in a warm ISM gas. From Cruddace et al. (1974) we take this cross section to be 5 . 10^-21 cm^-2. For cold gas we estimate the H I cross section to be 9 . 10^-21 cm^-2 (Morrison & McCammon 1983). We find a range of attenuations between 0.7 and 0.35 for the H⁺ column and between 0.2 and 0.004 for the H I column, based on the Reynolds data. Thus the H I column variability dominates that of the warm gas and the latter is likely at the most to contribute a factor of two to the halo EM variability. In view of the fact that we find a halo emission varying by a factor 10 or more and also since we find this variability to be uncorrelated with likely errors in the cold gas column, we conclude it to be unlikely that the additional warm gas absorption can significantly affect our conclusions.

Fig. 7, which shows a typical fitted spectrum for a SXRB direction, clearly demonstrates that at 1 keV the halo component is about 10% of the extragalactic power law component. This suggests that at 1 keV the SXRB fluctuations can only be studied at the 10% level. Likewise, at 2 keV, it appears that fluctuations at just the 1% level can be examined.

3.2. Possibility of a Local Group halo

It can be argued that the component of emission attributed to the Galactic halo is in fact related to the hot gas associated with the LG of galaxies (see Suto et al. 1996). To investigate this possibility we took the coordinates of the Andromeda nebula as being representative of the origin of the coordinate system for the LG. Doing the necessary coordinate transformations for all the regions in our sample we show in Fig. 9 the Hammer-Aitoff projection map in "Local Group" coordinates, with the fitted halo component now being associated with the LG. The contours represent the expected fall-off in the EM from the centre of the group assuming a simple 1/r² (i.e. p =2) spherically-symmetric halo mass distribution. The actual expression used for EM variation as a function of LG coordinates is similar to Eq. 2 but without the term in the numerator for the disk dependence. For consistency with Suto et al. (1996) the distance from the LG centre to our Galaxy is maintained at 350 kpc.

Fig. 9. LG halo EM variation as a function of LG coordinates (centred on the Andromeda nebula). The contours denote the expected EM for a p =2 density decrease from the centre.

There is no striking pattern apparent here and it is difficult to argue in favour of the conclusions drawn by Suto et al. (1996). It is unlikely that the emission originates from the LG, principally because of the large variations observed in the halo emission. For all the analyzed directions the data were arranged in the LG longitude bands of 30^o width. The best fit value for the electron density is estimated to be 0.00040.0003 cm^-3. This value is an order of magnitude smaller than the one corresponding to the Galactic halo.

© European Southern Observatory (ESO) 1999

Online publication: March 10, 1999
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