In the light of recent observations in which short \gamma -ray bursts are interpreted as arising from black-hole ( BH ) , neutron-star ( NS ) or NS-NS mergings we would like to review our research on the evolution of compact binaries , especially those containing NS ’ s .
These were carried out with predictions for LIGO in mind , but are directly applicable to short \gamma -ray bursts in the interpretation above .

Most important in our review is that we show that the standard scenario for evolving NS-NS binaries always ends up with a low-mass BH ( LMBH ) , NS binary .
Bethe and Brown ( 1998 ) showed that this fate could be avoided if the two giants in the progenitor binary burned He at the same time , and that in this way the binary could avoid the common envelope evolution of the NS with red giant companion which sends the first born NS into a BH in the standard scenario .
The burning of He at the same time requires , for the more massive giants such as the progenitors of the Hulse-Taylor binary NS that the two giants be within 4 % of each other in ZAMS mass .
Applying this criterion to all binaries results in a factor \sim 5 of LMBH-NS binaries as compared with NS-NS binaries .

Although this factor is substantially less than the originally claimed factor of 20 which Bethe and Brown ( 1998 ) estimated , largely because a careful evolution has been carried through here , our factor 5 is augmented by a factor of \sim 8 arising from the higher rate of star formation in the earlier Galaxy from which the BH-NS binaries came from .
Furthermore , here we calculate the mergers for short-hard gamma-ray bursts , whereas Bethe and Brown ’ s factor 20 included a factor of 2 for the higher chirp masses in a BH-NS binary as compared with NS-NS one .
In short , we end up with an estimate of factor \sim 40 over that calculated with NS-NS binary mergers in our Galaxy alone .
Our total rate is estimated to be about one merging of compact objects per year .

Our scenario of NS-NS binaries as having been preceded by a double He-star binary is collecting observational support in terms of the nearly equal NS masses within a given close binary .

We review our work on population synthesis of compact binaries , pointing out that it is in excellent agreement with the much more detailed synthesis carried out by Portegies Zwart .
This is currently of interest because the recent discovery of the double pulsar has substantially increased the number of binary NS ’ s that will merge gravitationally , giving signals to LIGO .
This discovery brings in the low ZAMS mass main sequence progenitors that can evolve into a NS binary , adding importantly to the “ visible ” binaries that can merge .
However it does not affect the factor \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ > $ } } 40 increase , mostly from the much greater number of LMBH-NS binaries , which have only a small probability of being observed before they merge .

We develop the phenomenology which suggests that NS ’ s evolve from ZAMS mass \sim 10 - 18 \mbox { $M _ { \odot } $ } star , LMBH ’ s from 18 - 20 \mbox { $M _ { \odot } $ } , and high-mass BH ’ s from 20 - 30 \mbox { $M _ { \odot } $ } .
These brackets follow from Woosley ’ s ^ { 12 } C ( \alpha, \gamma ) ^ { 16 } O rate of 170 MeV barns at 300 keV .

We discuss the observed violation of our previous maximum NS mass M _ { NS } ^ { max } = 1.5 \mbox { $M _ { \odot } $ } , raising our M _ { NS } ^ { max } to 1.7 \mbox { $M _ { \odot } $ } and comment on how our scenario would change if the maximum NS mass is greater than 1.7 \mbox { $M _ { \odot } $ } .