Discovery of a Black Hole Mass‐Period Correlation in Soft X‐Ray Transients and Its Implication for Gamma‐Ray Burst and Hypernova Mechanisms

Abstract

We investigate the soft X-ray transients with black hole primaries, which may have been the sources of gamma-ray bursts (GRBs) 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 days, somewhat greater than their present periods. Furthermore, their black holes would have been expected to accrete $1 M of material from the donor during their previous evolution. Comparison with predictions suggests that little mass will be lost in the explosion for the relatively high pre-explosion periods of these binaries. A natural consequence of the He star rotation is that black holes formed in the shorter period (before explosion) soft X-ray transients acquire significant Kerr parameters. This makes them good sources of power for GRBs and hypernovae, via the Blandford-Znajek mechanism, and thus supports our model for the origin of GRBs in soft X-ray transients.

The case for Case C mass transfer in the galactic evolution of black hole binaries

“…We use a rate of 3 per century, giving a formation rate of 2.1 × 10 −6 yr −1 . Although these live a Hubble time, we can observe these for 10 9 yrs (Lee & Brown 2002) so this would give 2100 presently observable in the Galaxy, of the same general number as Wijers' estimate of 3000 (Wijers 1996). PRH give ∼ > 10 −5 as the formation rate for binaries with m d < 15M .…”

“…We emphasized in Lee & Brown (2002) that in Case C mass transfer the orbital separations for the above progenitor binaries in Roche Lobe contact are at ∼ 1700R (± ∼ 10%), ∼ 8 AU, for ZAMS 20M black hole progenitor and 1M companion star. Progenitors with more massive companions and the larger initial separation necessary for Case C mass transfer could have removed the H-envelope of the giant with spiral-in to larger final separations a f , since their drop in gravitational energy of the more massive companion is then sufficient to remove the envelope, and we shall see that this is indeed what happens.…”

“…It is made clear in LBW and Lee & Brown (2002) that for Case C (or very late Case B) the radii of the relevant stars must have the following behavior, as shown in Fig. 1. (i) They must increase rapidly in radius with hydrogen shell burning and with the early He core burning, which begins while the hydrogen shell burning is still going on.…”

“…The probability (logarithmic distribution of initial binary separation) is given by P = log(a n+1 /a n )/7 where the initial binary separation a i,t=0 is between a n and a n+1 , and the logarithmic distribution is normalized by the total logarithmic interval "7" of Bethe & Brown (1998) effect by strong wind losses. As shown by Lee et al (2002) giant progenitors as massive as 30M are necessary as progenitors of some of the black holes in the SXTs, especially for the binaries with evolved companions, in order to furnish the high mass black hole masses. These authors reduce wind losses by hand, forcing the resulting curve of R vs burning stage to look like that for a ZAMS 20M shown in Fig.…”

“…In Table 1 of Lee, Brown, & Wijers (2002) (denoted as LBW), the seven SXTs with shortest periods had K-or M-star companions and the unclassified companion in XTE 1859+226 may also well be K or M because of its short period P = 0.380 days. The progenitor binaries of these would have involved ∼ 25M giants and ∼ 1 − 2M companions, the latter having had some mass stripped off by the black hole.…”