Astron. Astrophys. 332, 189-193 (1998)

2. The sample of supersoft sources in M 31

16 firm candidate supersoft sources have been found in M 31 with ROSAT PSPC (Supper et al. 1997, Greiner, Supper & Magnier 1997). The spectral parameters of the M 31 supersoft sources can be further constrained if the ROSAT PSPC hardness ratios HR1 and HR2 as given in Greiner, Supper & Magnier (1997) are taken into account. These hardness ratios should be compared with theoretical hardness ratios derived using white dwarf atmosphere spectra.

These hardness ratios have been calculated (cf. Kahabka 1997) for model M4 (NLTE, LMC abundance, log g=9) for the temperature grid available from the model atmosphere spectra (cf. Heise et al. 1994, van Teeseling et al. 1996, Hartmann & Heise 1997) and for Hydrogen column density 0 and in the range 2 to making use of the X-ray spectroscopy package described in Kahabka (1997). In Fig. 1 and Fig. 2 these hardness ratios are presented for these models and in Fig. 3 the ROSAT PSPC count rate is given for a steadily nuclear burning source. Greiner, Supper & Magnier (1997) give for the 16 M 31 supersoft sources hardness ratios HR1 and HR2. Selection as a supersoft source was according to the criterion . If one assumes that the hydrogen column extends over the range one finds making use of the M4 model and combining the HR1, HR2 and the count rate information of the sources given in Table 1 that the effective temperature is constrained to the range . The lower bound of the temperature has been derived from the - plane of individual sources (cf. the example given for the recurrent transient RX J0045.4+4154 (White et al. 1994) in Fig. 5) by extrapolating the parameter confidence regions below the lower bound of the presently used temperature grid of . The range of white dwarf masses derived from this temperature range (assuming the stability line relation given in Fig. 4) is consistent with the properties found for the galactic supersoft sources: Massive ( ) white dwarfs are found which undergo steady nuclear burning and which can be found in the Hertzsprung-Russell diagram of hot steady nuclear burning white dwarfs (cf. Iben 1982, Fig. 2 and this Fig. 4) close to the stability line. The stability line is the location where the plateau and the cooling track join for different white dwarf masses (Fig. 4).

Fig. 1. Hardness ratio HR1 for ROSAT PSPC and model M4 (NLTE, log g=9, LMC opacitiy). Isolines are given for H-columns of (from bottom to top).

Fig. 2. Hardness ratio HR2 for ROSAT PSPC and model M4 (NLTE, log g=9, LMC opacitiy). Isolines are given for H-columns of (from bottom to top).

Fig. 3. Count rates [1/s] for ROSAT PSPC and model M4 (lower panel) for a distance of 700 kpc (M 31). Isolines are given for H-columns of (from top to bottom).

Table 1. ROSAT PSPC count rates, hardness ratios HR1, from NLTE white dwarf atmosphere model M4 derived absorbing hydrogen columns ), effective temperatures and white dwarf masses for the 16 supersoft sources in M 31 (sample of Greiner, Supper & Magnier 1997).

Fig. 4. Stability line of steady nuclear burning in the Hertzsprung- Russell diagram ( - L plane) of supersoft sources as deduced from Iben (1982), Fig. 2. Circles mark values for white dwarf masses in the range .

Fig. 5. Effective temperature - absorbing column density plane for the recurrent supersoft source RX J0045.4+4154 (White et al. 1994). Solid band gives the HR1 constraint, dotted band the HR2 constraint and dashed band the count rate constraint.

The question arises where are the less hot (and most probably less massive) steady nuclear burning white dwarfs? They have according to Fig. 1 a hardness ratio HR1 very close to HR1=-1 and more importantly they are faint. They cannot be easily detected in a galaxy like M 31. The important conclusion which can be drawn from this is that there are 15 massive () white dwarfs in M 31 undergoing steady nuclear burning. Widening the upper bound to would not affect this mass constraint at all. Another point to mention is that the supersoft transient source RX J0045.4+4154 must indeed be connected with a very massive white dwarf. For HR2=-0.6 one finds with Fig. 2 a temperature assuming (cf. Fig. 5 for the - parameter plane).

This temperature is similarly high as for CAL 87 (Parmar et al 1997) or RX J0925.7-4758 (Ebisawa et al. 1996). It corresponds assuming that the source is on the stability line to a white dwarf mass . Taking this important mass constraint into account and assuming that about 4.6% of the supersoft sources have white dwarf masses , which follows from the population synthesis calculations of Yungelson et al. (1996), one expects that there are at least about 650 supersoft sources in M 31. This number increases accordingly if one widens the hardness ratio criterion as then about 30 candidates are found (Hasinger 1994). Due to selection effects (obscuration due to absorption in M 31) not all massive supersoft sources are expected to be seen. Thus the number of 650 supersoft sources is a lower limit on the total number. From the number / count rate diagram shown in Fig. 6, upper panel, investigation of the isoline shows that a detection limit of  counts/sec corresponds to a white dwarf mass of . This means only supersoft sources with masses in excess of are expected to be seen which is consistent with the lower mass bound of derived from the spectral properties of the sources. Also it can be seen from this figure that sources seen with an absorption in excess of will fall below the detection limit in agreement with the range of values derived for the individual sources in Table 1. This result is consistent with the distribution of white dwarf masses derived by Di Stefano (1996) for the M 31 supersoft sources. The fact that only one supersoft source is found for the mass range can be explained due to the selection criteria applied by Greiner, Supper & Magnier. From Fig. 1 one finds that a much wider range in HR1, , has to be considered to cover the complete sample with temperatures 3-13 K, equivalent to masses . A fraction of these candidates may be contained in the sample of 30 sources mentioned in Hasinger (1994).

© European Southern Observatory (ESO) 1998

Online publication: March 10, 1998
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