Discovery of a Black-hole Mass - Period Correlation in Soft X-ray Transients and its Implication for Gamma-Ray Burst and Hypernova Mechanisms

We investigate the soft X-ray transients with black hole primaries which may have been the sources of gamma-ray bursts and hypernovae earlier in their evolution. For systems with evolved donors we are able to reconstruct the pre-explosion periods and find that the black-hole mass increases with the orbital period of the binary. This correlation can be understood in terms of angular-momentum support in the helium star progenitor of the black hole, if the systems with shorter periods had more rapidly rotating primaries prior to their explosion; centrifugal support will then prevent more of its mass from collapsing into the black hole on a dynamical time. This trend of more rapidly rotating stars in closer binaries is usual in close binaries, and in the present case can be understood in terms of spin-up during spiral in and subsequent tidal coupling. We investigate the relation quantitatively and obtain reasonable agreement with the observed mass-period correlation. An important ingredient is the fact that the rapidly rotating new black hole powers both a GRB and the hypernova explosion of the remaining envelope, so that the material initially prevented from falling into the black hole will be expelled rather than accreted. For systems in which the donor is now, and will remain, in main sequence we cannot reconstruct the pre-explosion period in detail, because some of their history has been erased by angular momentum loss through magnetic braking and gravitational waves. We can, however, show that their periods at the time of black hole formation were most likely 0.4–0.7 day, somewhat greater than their present periods. Furthermore, their black holes would have been expected to accrete ∼ 1M⊙ of material from the donor during their previous