On the Formation of Low-Mass Black Holes in Massive Binary Stars

Abstract

Recently (Brown \& Bethe 1994) it was suggested that most stars with main sequence mass in the range of about $18 - 30 M_{\odot}$ explode, returning matter to the Galaxy, and then go into low-mass ($\geq 1.5 M_{\odot}$) black holes. Even more massive main-sequence stars would, presumably, chiefly g o into high-mass ($\sim 10 M_{\odot}$) black holes. The Brown-Bethe estimates gave approximately $5 \times {10}^{8}$ low-mass black holes in the Galaxy. A pressing question, which we attempt to answer here, is why, with the possible exception of the compact objects in SN1987A and 4U\,1700--37, none of these have been seen. We address this question in three parts. Firstly, black holes are generally ``seen'' only in binaries, by the accretion of matter from a companion star. High mass black holes are capable of accreting more matter than low-mass black holes, so there is a selection effect favoring them. This, in itself, would not be sufficient to show why low-mass black holes have not been seen, since neutron stars (of nearly the same mass) are seen in abundance. Secondly, and this is our main point, the primary star in a binary ---the first star to evolve--- loses its hydrogen envelope by transfer of matter to the secondary and loss into space, and the resulting ``naked'' helium star evolves differently than a helium core, which is at least initially covered by the hydrogen envelope in a massive main-sequence star. We show that primary stars in binaries can end up as neutron stars even if their initial mass substantially exceeds the mass limit for neutron star formation from single stars ($\sim 18 M_{\odot}$). An example is 4U\,1223--62, in which we suggest that the initial primary mass exceeded $35 M_{\odot}$, yet X-ray pulsations