Annu. Rev. Astron. Astrophys. 1994. 32:
531-590
Copyright © 1994 by . All rights reserved |

**8.4. Gravitational Radiation from Black Holes**

The formation of a population of black holes of mass *M* at
redshift *z*_{B} would
be expected to generate bursts of gravitational radiation with a
characteristic period and duration:

(8.4) |

One can show that the expected time between bursts (as seen today) is less
than their characteristic duration provided that
_{B} >
10^{-2}^{-2}, where
is the
total density parameter.
(Bertotti & Carr 1980).
If the holes make up galactic
halos, one would therefore expect the burst to form a background of waves
with present density
_{g} =
_{g}_{B}(1 +
*z*_{B})^{-1}, where
_{g} is the
efficiency with which the collapsing matter generates gravity waves. If
_{g} were as
high as 0.1,
the background could be detectable by ground-based laser interferometers
(e.g. LIGO) for *M* below 10^{3}
*M*_{}, by
Doppler tracking of interplanetary spacecraft
(e.g. *Cassini*) for *M* in the range
10^{5}-10^{10}
*M*_{}, and by
pulsar timing for *M* above 10^{9}
*M*_{}. The
observable domains are indicated in Figure 7 and
the dotted
lines indicate how the predicated backgrounds depend on *M* and
*z*_{B}. Note that the value of
_{g} is very
uncertain and it is probably well below 0.1 for isolated collapse.

The prospects of detecting the gravitational radiation would be much better
if the holes formed in binaries
(Bond & Carr 1984).
This is because two sorts of
radiation would then be generated: (*a*) continuous waves as the
binaries spiral
inward due to quadrupole emission; and (*b*) a final burst of waves
when the
components finally merge. The burst would have the same characteristics as
that associated with isolated holes but it would be postponed to a lower
redshift and
_{g} would
be larger (~ 0.08) because of the larger asymmetry; both factors
would increase
_{g}. The
continuous waves would also be interesting since they
would extend the spectrum to longer periods, thus making the waves
detectable
by a wider variety of techniques. Over most wavebands, the spectrum of the
waves would be dominated by binaries whose initial separation is such that
they are coalescing at the present epoch. This corresponds to a separation
*a*_{crit} = 10^{2} (*M*/10^{2}
*M*_{})^{3/4}
*R*_{}. The
total background generated by the binaries is also shown in
Figure 7: For each value of *M*,
_{g}(P) goes
as *P*^{-2/3}, as
indicated by the broken lines. Providing the fraction of binaries
*f*_{crit} with around
the critical separation is not too small, the background should be
detectable by LIGO for *M* < 10^{3}
*M*_{}, by
*Cassini* for 10^{5}
*M*_{} <
*M* < 10^{10}
*M*_{}, by
LISA for
*M*_{} <
*M* < 10^{10}
*M*_{}, and by
pulsar timing for *M* > 10^{6}
*M*_{}.

One could also hope to observe coalescences occurring at the present epoch.
For our own halo, the average time *t*_{burst} between
bursts and their expected amplitude *h*_{burst} would be

(8.5) |

Although the time would be uncomfortably long, one could also detect bursts
from the Virgo cluster every 4(*M* / 10^{2}
*M*_{}) days
with somewhat improved sensitivity.
Haehnelt (1994)
has argued that LISA could detect coalescence bursts
throughout the Universe for *M* in the range
10^{3}-10^{6}
*M*_{}.