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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: RateGRB/RateSNIb/c < 3% [22]. This predicts a Galactic rate that is below ~ 10-4 yr-1 and the true value is likely to lie between ~ 10- 5-10 -4 yr- 1. 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 [9394]. 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.
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