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Gravitational waves from pulsars: emission by the magnetic field induced distortion

The gravitational wave emission by a distorted rotating fluid star is computed. The distortion is supposed to be symmetric around some axis inclined with respect to the rotation axis. In the general case, the gravitational radiation is emitted at two frequencies: $Ω$ and $2Ω$, where $Ω$ is the rotation frequency. The obtained formulæ are applied to the specific case of a neutron star distorted by its own magnetic field. Assuming that the period derivative $\dot P$ of pulsars is a measure of their magnetic dipole moment, the gravitational wave amplitude can be related to the observable parameters $P$ and $\dot P$ and to a factor $β$ which measures the efficiency of a given magnetic dipole moment in distorting the star. $β$ depends on the nuclear matter equation of state and on the magnetic field distribution. The amplitude at the frequency $2Ω$, expressed in terms of $P$, $\dot P$ and $β$, is independent of the angle $α$ between the magnetic axis and the rotation axis, whereas at the frequency $Ω$, the amplitude increases as $α$ decreases. The value of $β$ for specific models of magnetic field distributions has been computed by means of a numerical code giving self-consistent models of magnetized neutron stars within general relativity. It is found that the distortion at fixed magnetic dipole moment is very dependent of the magnetic field distribution; a stochastic magnetic field or a superconductor stellar interior greatly increases $β$ with respect to the uniformly magnetized perfect conductor case and might lead to gravitational waves detectable by the VIRGO or LIGO interferometers. The amplitude modulation of the signal induced by the daily rotation of the Earth has been computed and specified to the case of the Crab pulsar and VIRGO