3 Analysis

For the analysis, the ROSAT energy range from 0.1 to 2.4 keV was divided into five energy bands: a soft band (S: 0.1-0.4 keV), two hard bands (H1: 0.5-0.9 keV and H2: 0.9-2.0 keV), and two combined bands (hard H: 0.5-2.0 keV and broad B: 0.1-2.0 keV). This energy band splitting was used previously in the analysis of the first M 31 survey (S97), except that an upper limit of 2.4 keV was used for the B-band. The change from 2.4 keV to 2.0 keV makes no significant difference due to the drastic drop in effective area for the ROSAT telescope + PSPC instrumentation between 2.0 and 2.4 keV (the count rate in the 0.1-2.0 keV energy band is 2% less than in the 0.1-2.4 keV band, when applying a power law with photon index $\Gamma = -2.0$ and $N_{\rm H} = 9\times 10^{20}~\mbox{ cm}^{-2}$ as a spectral model - typical for M 31 sources). Therefore the count rates of the two survey analyses are directly comparable.

Parts of the following analysis are based on the Extended Scientific Analysis System (EXSAS; Zimmermann et al. 1993) developed at the Max-Planck-Institute für extraterrestrische Physik.

   
3.1 Data preparation and images

All the data were inspected for contamination by solar scattered X-rays and particle background. The first originate from Thomson and fluorescent scattering of solar X-ray photons with atoms and molecules in the upper atmosphere along the line of sight. For the ROSAT orbit, these are mainly oxygen, nitrogen, argon, helium, and hydrogen (Jacchia 1972). For the integral solar scatter, the illuminated column density of the atomic oxygen can be used because of the well known fixed ratio of scatter contribution of the other components, as discussed in detail by Snowden & Freyberg (1993). Therefore, for each pointing, the column density of atomic oxygen was calculated from the orientation of the telescope and the sun position during the whole observation. All time intervals with oxygen column densities above $1\times 10^{15}~\mbox{cm}^{-2}$ (see Snowden & Freyberg 1993 for an explanation of this threshold) were rejected.

Snowden et al. (1992) found a strong correlation between the Master Veto Rate of the ROSAT onboard electronics and the residual particle background not rejected by the veto electronics. Therefore, all time intervals with a Master Veto Rate of more than $170~\mbox{ct~s}^{-1}$ were additionally rejected. Applying these procedures, the rest of the scattered X-rays and residual particle background within the screened intervals was estimated to be less than $1\%$.

For the following analysis, the photon events of all 94 observations representing the survey were merged into one single event file. This increased the photon statistics and allowed us to make use of the homogeneity of the raster survey. A slight random offset and rotation of each pointing was corrected for by first correlating bright point sources in neighbouring pointings detected by the Standard Analysis Software System (SASS) and delivered with the data. For this purpose, only sources within the inner PSPC region ( $20\hbox {$^\prime $ }$ radius) were used where the telescope has its highest spatial resolution. The final source position was calculated as the weighted mean position from the individual source positions in each contributing pointing, with the signal to noise ratio as the weighting factor. In a last step, each contributing pointing was shifted and rotated to fit best this mean source position. The distribution of the shift and rotation offsets over all 94 pointings was found to be Gaussian-like, with $\sigma = 5.2\hbox{$^{\prime\prime}$ }$ in shift and $\sigma = 0.21\hbox{$^\circ$ }$ in rotation. These corrected data were then ready to be merged.

Figure 2 shows a photon image in the B-band from the merged inner PSPC regions of the 94 pointings with a pixel size of $21.5\hbox {$^{\prime \prime }$ }\times 21.5\hbox {$^{\prime \prime }$ }$. Just from this image, the high homogeneity and the narrow (center of detector) point spread function (PSF; Hasinger et al. 1992) of the second ROSAT M 31 survey across the whole galaxy (indicated by the $D_{\rm 25}$-ellipse) can be seen, especially when compared to the image of the first survey (Fig. 2 in S97). Some bright identified sources are also indicated in Fig. 2. Most of them are not members of the M 31 system. The bulge region is severely crowded by point sources and confused by an additional diffuse component.

Figure 3 shows an optical image (taken from the Mount Palomar Sky Survey) of M 31 in false colour representation. Size and orientation are as in Fig. 2 and the $D_{\rm 25}$-ellipse of M 31 is also marked. The white boxes mark the 560 X-ray source positions from the analyses of both ROSAT PSPC surveys of M 31 as described in Sect. 3.3 and listed in Table 6. The 4 box sizes indicate the logarithm of the X-ray luminosities below 36, between 36 and 37, between 37 and 38, and above 38 (from small to large). This corresponds to flux thresholds of $1.76\times 10^{(-14, -13, -12)}~\mbox{erg~cm}^{-2}~\mbox{s}^{-1}$. For flux calculations, a spectral model of a power law with photon index $\Gamma = -2.0$ and $N_{\rm H} = 9\times 10^{20}~\mbox{ cm}^{-2}$has been used which holds for M 31-sources but not for foreground or background objects. A distance of 690 kpc for M 31 is asumed for the resulting luminosity values.

3.2 Source detection

To make use of the high homogeneity of the second PSPC M 31 survey, the source detection was performed on the merged data of the inner PSPC regions of all 94 observations. This guaranteed the best results for the determined source positions and covered approximately the whole $D_{\rm 25}$-area of M 31. For detections of sources outside this region, the following source detection procedure was repeated using the merged data of the total FOV. The source detection technique used is similar to the one previously used for the analysis of the first survey and described in detail in S97. Hence, only a brief description will be given here, with emphasis on the differences employed.

The computations can be divided into three steps: a local, a map, and a maximum likelihood detection algorithm. For the local detect algorithm, the merged photon event tables were split into a northern, middle and southern part and for each part, images were created with a pixel size of $15\hbox{$^{\prime\prime}$ } \times 15\hbox{$^{\prime\prime}$ }$ for each of the five energy bands. This led to $3 \times 5 = 15$ images for the three regions and the five energy bands. With a sliding window technique ( $3 \times 3$ pixel box), the images were searched for a significant count excess within the box compared with the surroundings. Only source candidates with a likelihood of existence $\ge$8 were listed, where the likelihood $L = -{\rm ln}(P),~P$ being the probability that the measured number of photons in the box originate from Poissonian background fluctuations.

In the following map detect algorithm, the same procedure was applied to the 15 images, but this time the photon number within the box was compared with the number of photons within a box of equivalent area and position in a background map. These background maps were computed from the photon images by punching out holes at the source positions determined by the local detect algorithm, and applying smoothing procedures before and afterwards as described in S97. The radius of the holes was set to twice the FWHM of the PSF computed for a $20\hbox {$^\prime $ }$ off-axis angle and for the lowest energy value within the considered energy band (a $40\hbox{$^\prime$ }$ off-axis angle was used for the merged total FOV data). This resulted in a second list of source candidates (also with $L \ge 8$).

For the third step, the local and map source candidate lists were merged into one list (separately for each of the five energy bands) and used as input for a maximum likelihood detection procedure (Cruddace et al. 1988). Here only sources with a likelihood $L \ge 10$ were accepted and the background maps described above were used. All resulting lists were merged into one final list such that sources separated by less than $2\sigma$ of the PSF (referring to the lowest energy value within the considered energy band) were substituted by one single source, its position set to the position of the original source with the highest likelihood. This list was used as input for a repeated maximum likelihood process to compute upper limits in the energy bands where a source was below our detection threshold (but above in any of the other energy bands).

   
3.3 The catalogue of detected X-ray sources

The source detection yielded the 396 sources listed in Table 5, which has the same structure as the first survey source list given in Table 5 of S97. Column 1 gives the source number. Columns 2-7 list the centroid position (epoch J2000) after correction for a systematic offset (see below) and Col. 8 shows the $1\sigma$ uncertainty of the source position in arcseconds. The calculation of this positional uncertainty is based on the maximum likelihood algorithm and incorporates the effects of statistical errors depending on the number of source counts, together with the blur radius of the PSF at the off-axis angle and the mean photon energy of the source. We also set a minimum threshold of $5\hbox{$^{\prime\prime}$ }$ to account for a systematic positional error. The parameter in Col. 9 represents a classification of the quality of the detection and is differently defined than for the first survey due to the different homogeneity and sensitivity of the second survey: class "1'' indicates sources detected in the inner PSPC region ( $20\hbox {$^\prime $ }$ radius) and class "4'' sources outside this region. Column 10 in Table 5 gives the highest likelihood of existence found in any of the five energy bands computed with the maximum likelihood method. Finally, Cols. 11 to 15 list the count rates with their $1\sigma$ errors (in counts per kilosecond) within the five energy bands (B, S, H, H1, and H2; see beginning of Sect. 3). The listed count rate errors are only statistical errors, whereas the systematical errors are expected to be less than $\pm15\%$. Because some faint sources were not detected in all energy bands (i.e., these sources had a likelihood below the threshold value of 10 in one or more energy bands), we present $1\sigma$ upper limits to their count rates. The upper limits are computed from the $1\sigma$ fluctuations (Poissonian statistics) of the background counts at the source position and are indicated by a preceding "<'' symbol.

The 396 X-ray sources found in the second PSPC survey underwent a correlation with a positionally accurate (optical) reference catalogue to determine a systematic offset in source position. This was done in the same manner as for the sources in the first survey, and is described in detail in S97. Here, for reference, we also used the optical globular cluster catalogue of Magnier et al. (1994a; Table 2) which revealed a slight systematic offset in our source positions of $\Delta {\rm RA} = 5.8\hbox{$^{\prime\prime}$ }$ and $\Delta {\rm Dec} = 1.2\hbox{$^{\prime\prime}$ }$. Table 5 lists the offset-corrected source positions.

The fact that the total number of detected sources in the second PSPC survey is identical with the total number of detected sources in the first PSPC survey (S97) is purely accidental. The source lists are different and contain only 239 common sources. The detection of common sources in the two surveys is due to the fact that approximately the same region of sky was observed over (in some areas) similar integrated exposure time. The differences in the source lists are mainly due to different sensitivity characteristics: the first survey has its highest sensitivity along a line following the main axis of the M 31 ellipse, whereas the second survey has an approximately constant and high sensitivity across the whole galaxy. Therefore, the detected sources are concentrated within different regions of each survey. Additionally, the slight differences in the source detection procedures and statistical fluctuations cause some departures close to the detection threshold.

Merging of the two survey lists (see Sect. 4.1.1 for details) yielded a final catalogue containing 560 PSPC detected X-ray sources in the field of M 31. This is presented in Table 6, which has a similar structure to Table 5 described above. The only differences are that Col. 1 gives the RXJ-number of the source and Col. 2 lists the source number of the first survey (as listed in Table 5 of S97) if a correlation was found. Here four possible cases are indicated; (i) number followed by "+'': source was found in both surveys and the listed data are from the first survey, (ii) number followed by "-'': source was found in both surveys and listed data are from the second survey, (iii) number without any additions: source was found only in the first survey, the listed data being from there, and (iv) no number at all: source was found only in the second survey, the listed data being from there. For the criteria of which data are listed in cases of correlation see Sect. 4.1.1. The following Cols. 3-16 are identical with Cols. 2-15 of Table 5, and have been described above. For sources found in the first survey, the classification parameter listed in Col. 10 is as follows: class "1'' identifies sources detected in the central region of the PSPC with off-axis angles $\le 20\hbox{$^\prime$ }$, class "2'' defines locations of sources found between $20\hbox {$^\prime $ }$ and $40\hbox{$^\prime$ }$, and class "3'' contains sources with off-axis angles $> 40\hbox{$^\prime$ }$. As mentioned in Sect. 2 of S97, the source position was derived from the pointing in which it appears at the lowest off-axis angle, i.e., the best class (though not under a PSPC rib). For sources in class "2'' and especially class "3'', any upper limit in count rate listed in Cols. 11-15 can even be an underestimation due to the wider PSF and the therefore higher possibility of rib influencies. For sources found in the second survey, the listed classification parameter for the quality of detection is defined as described above: class "1'' for sources detected in the inner PSPC region ( $20\hbox {$^\prime $ }$ radius) and class "4'' for sources outside this region.

The caveats for the first survey source catalogue mentioned in S97 are still valid where these sources are not substituted by second survey detections.