The 1991 ROSAT PSPC M31 X-ray point source catalog has been screened in order to set up a sample of candidate supersoft sources in this galaxy , additional to the 16 supersoft sources already known in M31 ( Supper et al .
1997 ) .
Selection criteria used were based on hardness ratios ( “ X-ray colors ” ) , as developed in an earlier paper ( Kahabka 1998 ) .
An additional criterion to be fulfilled was that the observed count rate is in agreement with the expected steady-state luminosity for a source with these hardness ratios .
This condition constrained mainly the hydrogen absorbing column towards the source .
26 candidates not correlating with foreground stars and M31 supernova remnants have been found to fulfil one of the selection criteria .
They can be considered to be candidate supersoft sources in M31 .
This comprises 6 % of all point sources in this galaxy .
For these candidates absorbing hydrogen column densities , effective temperatures and white dwarf masses ( assuming the sources are on the stability line of surface nuclear burning ) are derived .
An observed white dwarf mass distribution is derived which indicates that the masses are constrained to M \mbox { $ { } ^ { > } \hskip { -6.828661 pt } _ { \sim } $ } 0.90 M _ { \odot } .

The entire population of supersoft sources in M31 is estimated taking a theoretical white dwarf mass distribution into account and under the assumption that the observationally derived sample is restricted to white dwarf masses above 0.90 M _ { \odot } .
Taking into account that the gas and the source population have different scale heights a total number of at least 200-500 and at most 6,000-15,000 sources is deduced ( depending on the used galaxy N _ { H } model ) , making use of the population synthesis calculation of Yungelson ( 1996 ) .

The spatial distribution favors a disk ( or spiral-arm ) dominated young stellar population with a ratio of 1/ ( 4-7 ) of bulge/disk systems , very similar to what has been found for novae in the Milky Way but lower than favored for novae in M31 ( \sim 1/2 ) .
Supersoft sources and Cepheids both show association with the M31 spiral arms and may belong to a younger stellar population .
A mean space density of \sim ( 0.1 - 5 ) \times 10 ^ { -8 } { pc ^ { -3 } } is inferred for the supersoft sources .
Assuming that all supersoft sources with masses in excess of 0.5 M _ { \odot } are progenitors of supernovae of type Ia , a SN Ia rate of ( 0.8 - 7 ) \times 10 ^ { -3 } { yr ^ { -1 } } is derived for M31 based on these progenitors .
Supersoft sources might be able to account for 20-100 % of the total SN Ia rate in a galaxy like M31 .