Waves from Neutron Stars

Rapidly rotating neutron stars (pulsars) tend to be axisym-metric however, they must break this symmetry in order to radiate gravitationally. Several mechanisms may lead to deformations of the star, or to precession of its rotation axis, and hence to gravitational wave emission. The characteristic amplitude of gravitational waves from neutron stars at 10 kpc distance scales as 

Neutron stars are thought to form in supernova explosions. The outer layers of the star crystallize as the newborn neutron star cools by neutrino emission. Estimates, based on the expected breaking strain of the crystal lattice, suggest that anisotropic stresses, which build up as the pulsar loses rotational energy, could lead to e 10 the exact value depends on the breaking strain of the neutron 

FIGURE 3 Sources of gravitational radiation and detector sensitivities. 

Large magnetic fields trapped inside the superfluid interior of a neutron star may also induce deformations of the star. Numerical simulations suggest that this effect is extremely small for standard neutron star models (e 10 ). 

Another plausible mechanism for the emission of gravitational radiation in very rapidly spinning stars is accretion-driven asymmetries. The principal axes of the moment of inertia can be driven away from the rotational axes by accretion from a companion star. Accretion can produce relatively strong radiation, since the amplitude is related to the accretion rate rather than to structural effects in the star. 

---

Black holes. One great achievement of gravitational wave astronomy would be the first detection of a signal coming directly from a black hole. Just like with neutron stars, black holes can emit gw either alone or in binary systems. 

The interaction of mass transfer, gravitational wave backreaction and the reaction of the neutron star radius to the mass loss leads to a very complicated accretion dynamics in a neutron star black hole system. We find in all of our simulations (apart from an extreme test case with mass ratio q = 0.93, i.e. a... 

Fig. 5.4. Schematic evolution of the internal structure of a star with 25 times the mass of the Sun. The figure shows the various combustion phases (shaded) and their main products. Between two combustion phases, the stellar core contracts and the central temperature rises. Combustion phases grow ever shorter. Before the explosion, the star has assumed a shell-like structure. The centre is occupied by iron and the outer layer by hydrogen, whilst intermediate elements are located between them. CoUapse followed by rebound from the core generates a shock wave that reignites nuclear reactions in the depths and propels the layers it traverses out into space. The collapsed core cools by neutrino emission to become a neutron star or even a black hole. Most of the gravitational energy liberated by implosion of the core (some 10 erg) is released in about 10 seconds in the form of neutrinos. (Courtesy of Marcel Amould, Universite Libre, Brussels.)...

However, according to Stan Woosley, there must be a whole range of masses in which a black hole is not immediately created, but only when a shock wave has blown the star apart. One would feel sure that the explosion had succeeded, and yet a certain fraction of the matter would fall back into the core, for it would have insufficient kinetic energy to resist the call of gravity from the central neutron star. The latter would be transformed into a black hole by the extra matter. This delayed delivery of a black hole may be much more common than the hasty birth described above. 

The supernova 1987A in the Large Magellanic Cloud has provided a new opportunity to study the evolution of a young neutron star right after its birth. A proto-neutron star first cools down by emitting neutrinos that diffuse out of the interior within a minutes. After the neutron star becomes transparent to neutrinos, the neutron star core with > 1014 g cm-3 cools predominantly by Urea neutrino emission. However, the surface layers remain hot because it takes at least 100 years before the cooling waves from the central core reach the surface layers (Nomoto and Tsuruta 1981, 1986, 1987). 

Type II supernovae are massive stars, ones that progress in their nuclear fuels well past the fusion of carbon and the fusion of oxygen at their centers. When their cores run out of nuclear fuel, those central regions collapse to form a neutron star, or in some cases a black hole. The incredibly intense emission of neutrinos from the newly born neutron star so heats the overlying layers, aided by an outward moving shock wave of pressure, that those layers pardy explode and are ejected. The last of these thatwas visible to the naked eye occurred in 1987, and demonstrated for the first time the correctness of the intense neutrino burst that is their main energy output. 

Rapidly spinning neutron stars are the main source of continuous waves in the HF band accessible to earth-based interferometers and resonant bar detectors. When the neutron star can be observed using radio (or other) telescopes, the expected gravitational waveform can be inferred (up to small uncertainties) from observations of the spin period. In this case, the optimal data analysis strategy is matched filtering. The implementation may be slightly different than for burst sources, but the idea is the same. Successful detection of waves from these sources will rely on direct interaction between the radio astronomers and gravitational astronomers. 

Compact binary systems with pairs of neutron stars have been observed using radio telescopes. The famous millisecond pulsar PSR 1913+16 discovered in radio data by Hulse and Taylor orbits with a (radio quiet) neutron star companion. Emission of gravitational waves from this system has been confirmed by measuring the decay of the orbit, and the loss of energy agrees with the predictions of general relativity to high precision. 

During the final few minutes before coalescence, the gravitational wave from a neutron star binary sweeps up in amplitude and frequency ( chirps ) through the HF band. When the binary system reaches a frequency of 1 kHz, the orbit will become unstable either due to the tidal interaction between the two stars or because of a dynamical instability of orbital motion in general relativity. At this stage, the details of the merger may depend on the internal properties and spins of the two neutron stars. 

Black holes in binary systems spiral together, as they emit gravitational waves, just as binary neutron stars do. The gravitational waves from, and the dynamics of, the coalescence will be quite different, however. 

Pulsars are rotating neutron stars with typical radii of 10 km and masses of 1.4 Mg, with rotation periods ranging from fractions of hertz to hundreds hertz. Pulsars can emit gravitational waves if deviating from axial symmetry. The emission is continuous at twice the rotation frequency, with an amplitude of... 

---