Astron. Astrophys. 321, 207-212 (1997)

4. Galactic formation rates

The formation rate of binaries that reach Roche-lobe contact and survive the spiral-in can be estimated by computing the birth rate of binaries with suitable initial parameters; primary mass, mass ratio and semi-major axis. For simplicity we neglect the eccentricity. For the initial mass function for the primary we use a Salpeter function (Salpeter 1964) integrated over the Galaxy:

This normalization gives a supernova rate in agreement with the observed rate. The initial semi-major axis distribution is taken flat in (Kraicheva et al. 1978). We assume a flat initial mass-ratio distribution, . For a given mass of the primary M the fraction of binaries with a mass of the secondary between and is then proportional to .

Primaries with an initial mass between 10 and 40  are assumed to leave a neutron star after the supernova, progenitors with a mass between 40 and 100  form black holes. The mass of the secondary is taken to be . The minima and maxima for the initial semi-major axis are computed as described in the previous section. We integrate the initial distribution functions for the primary mass, the mass ratio and the semi-major axis between the mass limits and and the corresponding limits for the semi-major axis and (see Fig. 3):

With , with a binary fraction of 50% of high mass stars, and with the lower limit to set by the main-sequence star, the galactic formation rate of binaries that reach Roche-lobe contact and survive the spiral-in is for the binaries with a neutron star and for the black-hole binaries. The formation rate thus calculated for the low-mass X-ray binaries with a neutron star is compatible (within the rather wide uncertainties) with the rate derived from the observed numbers of such binaries. The formation rate of low-mass X-ray binaries with a black hole is about 1% of the formation rate of low-mass X-ray binaries with a neutron star, whereas the observations indicate equal formation rates for these two types of binaries.

© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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