4 Comparisons with other source catalogues

For all correlations with other catalogues described in this section, the final source list of Table 6 was used. Table 1 summarises the results of the correlation analysis for different catalogues and these are discussed in more detail in the following subsections. From the description (in S97) of the correlation process itself, we simply summarise here that it yields not only the total number of correlating sources ( $N_{\rm total}$) but also the amount of expected accidental correlations ( $N_{\rm acc.}$) within a $1\sigma$confidence level.

 

 

Table 1: Summary of the correlation analysis. $N_{\rm total}$ gives the number of all possible correlations within a distance of $2\sigma$ of the combined positional error, $N_{\rm acc.}$ gives the number of statistically expected accidental correlations, and $N_{\rm fin.}$ gives the final accepted correlations. For a detailed explanation see Sect. 4.2.

Type	Databases	$N_{\rm total}$	$N_{\rm acc.}$	$N_{\rm fin.}$
X-ray	Einstein (TF)	82	12.7	69
GC	BA87, BA93, MA94a	43	11.6	33
Extragalactic	NED	10	0.6	10
Foreground	MA92, SIMBAD	72	40.4	55
SNR	DO80, BW93, MA95	22	4.1	16
Novae	SA91, SA92	0	0.8	-

4.1 Comparisons with previous X-ray source catalogues

   
4.1.1 Comparison with the first ROSAT survey of M 31

The source list of the second M 31 survey was merged with that of the first to obtain the final ROSAT PSPC X-ray source list of M 31 (Table 6). For this purpose the above-mentioned correlation process was applied to both lists to identify common sources. The "radius of acceptance'' ($r_{\rm a}$) - the important correlation parameter - was iteratively determined as follows: the correlation procedure was repeatly carried out, with $r_{\rm a}$ increasing successively from $r_{\rm a} = \sigma_{\rm comb.}$ (here, $\sigma_{\rm comb.} = \sqrt{\sigma_{\rm 1}^2 + \sigma_{\rm 2}^2}$, the combined positional error of the correlating sources, where the single positional error of each source is given by the maximum likelihood detect algorithm). This iterative process was stopped just before the occurrence of multi-identifications (one source in one catalogue correlating with more than one source in the other catalogue) for sources with likelihood $\ge$20 (to exclude sources near the detection threshold), and outside confused regions. In this way, most potential common sources have been uncovered, without risking having to accept multi-identifications for bright isolated point sources.

This process yielded 239 correlations (with $r_{\rm a} = 4 \sigma_{\rm comb.}$, corresponding to a 99.99% probability of all real identifications having been found) with an expected number of 23 chance coincidences ($1\sigma$-value). A few multi-correlations were accepted (see below) because they either occur within confused regions or have likelihoods <20 or at least one of the correlating sources is covered by the PSPC rib structure.

For sources correlated within the two surveys, the one with the better quality of detection (i.e. with the lowest classification parameter listed in Col. 10 of Table 6, class "4'' of the second survey being considered the same as classes "2'' and "3'' of the first) was taken and the other was rejected as being identical with the first. In cases where the correlating sources were of the same class, the one with the higher likelihood was taken and, if the likelihood was also the same, the source from the second survey was taken because of its better positional accuracy. The same procedure was applied to the few multi-correlations to clarify their situation. With this only one multi-correlation remained: source #379 of the first survey (see Table 5 in S97) correlates with sources #380 and #384 of the second survey (see Table 5 in this paper). Applying the rules mentioned above for both correlations we would have to accept source #379 from the first survey and would have to reject both sources from the second survey. Here we decided only to accept the correlation with the least distance as a true identification and left source #384 as a new one.

Conversely, 158 sources from the first survey and 163 from the second do not correlate with any other source (and we extend to 164 for the second survey due to the reasons mentioned above). To consider all these sources as transients would ignore the different spatial sensitivity distributions and different sky coverage of the two surveys. Therefore, a more explicit investigation of transients is presented in Sect. 5.

   
4.1.2 Comparison with the ${\mathsfsl {Einstein}}$ catalogue

The 560 X-ray sources in the merged source list of the two ROSAT PSPC surveys exceeds the number of X-ray sources detected with the Einstein observatory in this region of sky by a factor of more than 5. On the one hand, it is the result of the $\sim$10 times higher sensitivity of ROSAT and the larger exposure of the disk region in the second ROSAT survey. On the other hand, both ROSAT surveys covered a more complete and therefore larger portion of the M 31 field than the Einstein observations did. The number of sources detected with the ROSAT PSPC in the M 31 bulge region (within 1 kpc from the centre) increased from 22 in the first survey to 31 using the data from both surveys. The fact that this is still less than the 48 sources found with the Einstein observatory in this region, as listed by Trinchieri & Fabbiano (1991, hereafter TF), is due to the large fraction of sources in TF's list which were detected with the higher spatial resolution Einstein HRI. Primini et al. (1993) reported 45 sources found with the ROSAT HRI within the bulge region of M 31 and Immler (2000), again using the ROSAT HRI observations, counted 63 sources within a $5\hbox{$^\prime$ }$ circle around the centre.

As already described in S97, the list of Einstein X-ray sources in the field of M 31 reported by TF contains 108 sources, with 81 sources taken from the Einstein HRI data with an assumed positional error of 3 $^{\prime\prime}$ (reported by Crampton et al. 1984), and 27 sources based on Einstein IPC data with a 45 $^{\prime\prime}$ positional error. Applying the above mentioned correlation procedure to the 560 ROSAT sources and the 108 Einstein sources reported by TF yields $N_{\rm total} = 82$ correlations with a probable contamination of $N_{\rm acc.} = 12.7$ chance coincidences, here accepting a source separation of up to twice the combined positional error ($2\sigma$). 12 ROSAT sources each correlated with several Einstein sources, due mainly to the large positional error of the Einstein IPC. To clarify their situation, only the correlation with the smallest separation (between the correlating counterparts) was taken into account. This reduced the number of finally accepted correlations to 69, which is in good agreement with the number of statistically expected true correlations (i.e. $N_{\rm total} - N_{\rm acc.} = 69.3$).

All 69 identifications are listed in Table 7. Column 1 gives the ROSAT RXJ-number (ref. Table 6), Col. 2 gives the fluxes and $1\sigma$ errors of the ROSAT sources using the spectral model of TF (thermal bremsstrahlung with $kT = 5 \mbox{ keV}$ and $N_{\rm H} = 7\times 10^{20}~\mbox{cm}^{-2}$ in the 0.2-4.0 keV energy band), Col. 3 lists the Einstein source numbers (ref. Table 2A of TF), Col. 4 the fluxes and $1\sigma$ errors given by TF, and Cols. 5 and 6 the distances between the ROSAT source positions and the Einstein source positions in arcseconds and in units of their combined positional errors ($\sigma$) respectively. The last column shows the ratio between the fluxes obtained with ROSAT and Einstein and can be considered as a long term variability check between the epochs of the two observations. More detailed investigations into long time variabilities are described in Sect. 5.

Comparing this correlation list to the one using only ROSAT sources found in the first survey as published in S97 (Table 6), a few remarks should be made. Using only the data of the first survey we had to manually extend the correlation list by one entry (ROSAT source #67 correlating with Einstein source #3) as mentioned in S97. This had been necessary because of the poorly-known PSF and the therefore uncertain positioning at the source position. The second PSPC survey now gave us the opportunity to determine much more precisely the position of this source (RX J0040.2+4050), turning out in fact to be only $3.6\hbox{$^{\prime\prime}$ }$ away from the position of the Einstein HRI source #3. Therefore no manual extension of the correlation list had to be made in this paper.

The listed flux ratio ( $F_{\rm R}/F_{\rm E}$) between ROSAT and Einstein which can be used as a long term variability indicator should be inspected carefully for sources in the bulge region (marked with a $\star$ preceding the ROSAT source number). Because of the heavy confusion in this region, the flux determination of these sources is very uncertain.

With the help of the second PSPC survey, some positions of X-ray sources already found in the first survey could be improved. Therefore, the 69 identifications listed in Table 7 show a very good positional agreement between the PSPC source positions and the ones listed by TF, which were largely obtained with the Einstein HRI. In fact, the mean source separation of the 43 ROSAT PSPC-detected sources correlating with sources also found with the Einstein HRI is $5.9\hbox{$^{\prime\prime}$ }\pm3.2\hbox{$^{\prime\prime}$ }$.

Excluding the heavily confused bulge region and the sources therein, we found a good ROSAT confirmation (90%) of the sources detected with the Einstein observatory as, out of the 60 of the 108 Einstein sources outside the bulge region, 54 could be confirmed by ROSAT. For the 6 Einstein-only detected sources, we give ROSAT flux upper limits and discuss their transient nature in Sect. 5.1. Over and above this, 491 new sources have been found with ROSAT which were not detected with Einstein.

   
4.2 Correlations with optical and radio sources

To identify and classify individual sources, the merged ROSAT source list of both surveys (Table 6) was correlated with the same catalogues previously used for the sources of the first survey in S97. For completeness and to simplify the discussions, we summarise the public data bases and catalogues used as follows:

• globular clusters: the two lists of Battistini et al. (1987, 1993; hereafter BA87, BA93) and the lists of Magnier et al. (1994a; Table 2; hereafter MA94a);
• extragalactic objects: the NASA Extragalactic Database (version date: 30. Dec. 1992; hereafter NED);

• foreground stars: the catalogue of stellar photometry described by Magnier et al. (1992), hereafter MA92, and Haiman et al. (1994) and the SIMBAD catalogue (Centre de Données astronomiques de Strasbourg; version date: Dec. 1989; hereafter SIMBAD);

• supernova remnants: the lists of d'Odorico et al. (1980; hereafter DO80), Braun & Walterbos (1993; hereafter BW93), and Magnier et al. (1995; hereafter MA95);

• novae: the two lists of Sharov & Alksnis (1991, 1992; hereafter SA91, SA92).

Information regarding the characteristics of these catalogues, especially the individual positional errors used in the correlation processes, can be found in S97. We adopted them except for the SNR catalogues: D'Odorico et al. (1980) report general position errors of $8\hbox{$^{\prime\prime}$ }$ in declination and $15\hbox{$^{\prime\prime}$ }$in right ascension. In S97 we assumed a mean position error of $12\hbox{$^{\prime\prime}$ }$whereas in this paper we decided to use a geometric mean of $17\hbox{$^{\prime\prime}$ }$. For the SNR list of Braun & Walterbos (1993) and also for the list of Magnier et al. (1995) we used $5\hbox{$^{\prime\prime}$ }$ as a systematic position error for our correlations.

Table 8 shows the result of the correlations. The columns are defined as follows. Column 1 gives the ROSAT RXJ source number (ref. Table 6). Column 2 lists the object class, of which four exist: "Star'' for galactic foreground stars followed in brackets by their type if available, "EO'' for extragalactic objects, mainly background galaxies, "GC'' for sources belonging to globular clusters, and "SNR'' for supernova remnants. Column 3 lists the identification, using the abbreviations of the correlated catalogues as defined above. The number following in brackets gives the name/entry number of the object as listed in the relevant catalogue (for details see the remarks to the individual catalogues below). Finally, Cols. 4 and 5 give the distance between the ROSAT source position and the correlated object in the catalogue, both in arcseconds and in $\sigma$ units. For the distance expressed in sigma, the combined positional error of the ROSAT source and the correlated catalogue source was used.

Concerning this list, the following should be noted. If one ROSAT source correlates with more than one catalogue source of the same catalogue, only the correlation with the smallest positional separation is listed. If the correlating catalogue sources belong to different catalogues of the same source class then all correlations are listed, separated by commas. In a few cases, multi-correlations between one ROSAT source and catalogue sources of different source classes were found. Here, spectral considerations clarified the situation, especially for distinguishing between foreground stars and globular clusters. Rejections of a good spatial correlation in place of a poorer spatial correlation only took place when the more distant counterpart was spectrally consistent with the ROSAT source and the closer counterpart very inconsistent.

In contrast, no rejection was performed in cases of perfect positional single-correlations, even of moderate coincident spectral characteristics. Additionally, we did not accept identifications with supernova remnants for ROSAT sources with a hardness ratio $HR_{\rm 1} + \sigma_{HR_1} \le -0.80$, because we consider these sources as supersoft sources (see S97 and Greiner et al. 1996). The hardness ratio $HR_{\rm 1}$ is defined as $HR_{\rm 1} = (H - S) / (H + S)$, where Sand H stand for the source counts in the relevant energy bands calculated with the maximum likelihood algorithm (and listed in Table 6). With these criteria, 114 identifications with optical and radio sources were found, corresponding to an identification quota of 20.4%. Some quantitative comments on the various object classes are as follows:
Foreground Stars (Star): Among the $N_{\rm total} = 72$ correlations within the $2\sigma$ error level, 17 had to be rejected due to the above criteria, leading to $N_{\rm fin.} = 55$ finally accepted identifications. The high density of foreground stars within the HA94 catalogue yields a relatively high number of possible chance coincidences, $N_{\rm acc.} = 40.3$. The resulting statistically expected number of true identifications is $N_{\rm i} = 31.8\pm6.3$, which is too low when compared with the finally accepted 55 identifications. As already discussed in S97, from the Einstein and ROSAT medium and deep surveys we know the foreground source luminosity function, and this can be used to derive an upper limit of 54 expected foreground sources within the region covered by the HA94-catalogue. This value is in good agreement with our finally accepted number of identifications.
Background Galaxies (EO): None of the $N_{\rm total} = 10$ found correlations had to be rejected due to the above criteria. The remaining number of $N_{\rm fin.} = 10$ finally accepted identifications is in good agreement with the statistically expected number of $N_{\rm i} = 9.4\pm0.8$. The dwarf galaxy M 32 can be found among the identifications, correlating with ROSAT source RX J0042.6+4052.
Globular Clusters (GC): Within the $2\sigma$ error level we found $N_{\rm total} = 43$ correlations (with $N_{\rm acc.} = 11.6$ chance coincidences), from which 10 had to be rejected due to the above criteria. The remaining 33 finally accepted identifications are in good agreement with the statistically expected number of $N_{\rm i} = 31.4\pm3.4$ true identifications. Among the 10 rejected correlations, 2 accounted for double-correlations with globular clusters, while the remaining 8 were rejected on spectral grounds, showing soft spectral characteristics incompatible with the known relatively hard spectra of X-ray sources belonging to globular clusters.
Supernova Remnants (SNR): Among the $N_{\rm total} = 22$ correlations within the $2\sigma$ error level, 6 had to be rejected due to the above criteria, leading to $N_{\rm fin.} = 16$ finally accepted identifications. This is in good agreement with the statistically expected number of $N_{\rm i} = 17.9\pm2.0$ true identifications. One important comment concerning the SNR-correlations listed in S97: Due to a misuse of the SNR list of Magnier et al. (abbreviated as MA94b in S97) a few SNR miss-correlations are listed in S97. This is repaired in this paper.
Novae: The extension of the ROSAT source catalogue of the first M 31 survey (S97) with the sources found in the second survey does not uncover a single correlation with one of the known novae in M 31.