4.2 Formation rate
The fraction of massive stars collapsing to black holes can be estimated theoretically and lies between
5 - 40% [89]. But it is much more difficult to determine the fraction of these black-hole forming stars that
also have enough rotation to produce a GRB. Likewise, the wide-field monitoring of the night
sky of GRBs produces an accurate observed rate of GRBs, but this rate must be corrected by
beaming factors to get a true long-duration GRB rate. Observations of supernova remnants have
allowed GRB observers to place some constraints on the GRB rate relative to the Type Ib/c
supernova rate:
[22]. This predicts a Galactic rate that is below
and the true value is likely to lie between
. Correlating the
observed GRB rate to the rate of black hole accretion disks formed in stellar collapse is not
straightforward. First, it may be that long-duration GRBs are not formed from stellar collapse, but
from stellar mergers [93, 94]. If this is the case, then we do not expect any GW signal from
the collapse itself, but any disk instabilities may still produce GW signals. Second, there may
be a number of black hole accretion disk systems produced that do not produce gamma-ray
bursts because they can not achieve the high relativistic flows, increasing the total rate of GW
sources.