3.2 Gravitational wave bursts from gravitational collapse

Neutron stars and black holes are formed from the gravitational collapse of a highly evolved star or the core collapse of an accreting white dwarf. In either case, if the collapse is nonspherical, perhaps induced by strong rotation, then gravitational waves could carry away some of the binding energy and angular momentum depending on the geometry of the collapse. Collapse events are thought to produce supernovae of various types, and increasingly there is evidence that they also produce most of the observed gamma-ray bursts [193] in hypernovae and collapsars [397251]. Supernovae of Type II are believed to occur at a rate of between 0.1 and 0.01 per year in a milky-way equivalent galaxy (MWEG); thus, within the Virgo supercluster, we might expect an event rate of about 30 per year. Hypernova events are considerably rarer and might only contribute observable gravitational-wave events in current and near-future detectors if they involve so much rotation that strong non-axisymmetric instabilities are triggered.

Simulating gravitational collapse is a very active area of numerical astrophysics, and most simulations also predict the energy and spectral characteristics of the emitted gravitational waves [167]. However, it is still beyond the capabilities of computers to simulate a gravitational collapse event with all the physics that might be necessary to give reliable predictions: three-dimensional hydrodynamics, neutrino transport, realistic nuclear physics, magnetic fields, rotation. In fact, it is still by no means clear why Type II supernovae explode at all: simulations typically have great difficulty reversing the inflow and producing an explosion with the observed light-curves and energetics. It may be that the answer lies in some of the physics that has to be oversimplified in order to be used in current simulations, or in some neutrino physics that we do not yet know, or in some unexplored hydrodynamic mechanism [277]. In a typical supernova, simulations suggest that gravitational waves might extract between about 10–7 and 10–5 of the total available mass-energy [266148Jump To The Next Citation Point149], and the waves could come off in a burst whose frequency might lie in the range of ∼ 200 – 1000 Hz.

We can use Equation (18View Equation) to make a rough estimate of the amplitude, if the emitted energy and timescale are known. Using representative values for a supernova in our galaxy, lying at 10 kpc, emitting the energy equivalent of −7 10 M ⊙ at a frequency of 1 kHz, and lasting for 1 ms, the received amplitude would be

( E )1 ∕2( 1 ms )1∕2( 1 kHz ) ( 10 kpc ) h ∼ 6 × 10−21 --−-7--- ----- ------ ------- . (21 ) 10 M ⊙ T f r
The upper bound in Equation (11View Equation) would give the same amplitude for a source 60 times further away, which reflects the fact that simulations find it difficult to put significant energy into gravitational waves. This amplitude is large enough for current ground-based detectors to observe with a reasonably high confidence, but of course the event rate within 10 kpc is expected to be far too small to make an early detection likely.
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