The relative frequency of type II and Ib,c supernovae and the birth rate of double compact star binaries

Using a population number synthesis code, we estimate the relative rates of different type (II and Ib,c) of supernovae for regions of constant star formation. We combine a large set of massive single star and massive close binary evolutionary computations and allow for black hole formation. If a neutron star forms, the binary system is followed through a supernova explosion where we account for asymmetries needed to explain the observed space velocity distribution of a large sample of pulsars. We also predict the theoretical formation rate and period distribution at birth of double compact star binaries. Finally we give the distribution of the binary parameters of the progenitors of the double neutron star systems. Our calculations reveal that the number ratio (II/Ib,c) strongly depends on the massive binary formation rate, on the binary mass ratio and period distribution. As consequence when average relative rates, obtained from observed supernova events in a sample of different galaxies, are used to predict the relative rates in a particular galaxy, this is meaningful only if the massive binary formation rate, the binary mass ratio and period distribution are the same in all these galaxies. Interestingly, the observed average number ratio from 2461 galaxies of different types can be reproduced assuming an average (cosmological) massive binary formation rate of ∼40-50% which may differ by a factor two from the massive binary formation rate in one particular galaxy. The theoretically predicted formation rate of close double neutron star systems in the galaxy, (10−6-10−5)/year, is in agreement with the observed values. Taking 40 M as limiting mass for black hole formation in binaries, we find that double black hole systems form at a very high rate.