Gravitational waves from deformed rotating neutron stars

Abstract

This thesis is devoted to studying gravitational waves from “mountains” on neutron stars.  It is, in fact, well known that a non-axisymmetric deformation of a rotating neutron star will lead to a time varying quadrupole and thus to gravitational wave emission.  We shall consider first of all the case of the LMXBs, as it has been suggested that the spin equilibrium period of these systems cannot be explained by accretion physics alone, but is dictated by gravitational wave emission.  We present a more refined accretion model, which can explain the observations without gravitational waves.  This means that, to model the gravitational wave emission of these systems, one needs a more detailed picture of the emission mechanisms at work.  We, therefore, move on to discuss the “maximum mountain” that a neutron star can sustain.  To do these we develop a perturbation formalism to study a star with a fluid core and an elastic crust which is gradually deformed until the crust cracks.  We apply the formalism to the case of a neutron star, both with an accreted and a non accreted crust.  We find that a non accreted crust can support a slightly larger mountain. Finally we consider magnetic deformations of neutron stars.  It is, in fact, well known that a magnetic star cannot be spherical, and if the rotation and magnetic axis are not aligned we can, once again, have a time varying quadrupole.  We consider the case of a dipolar field which is compatible with a constant density star and with an n = 1 polytrope; in both cases one finds that it is impossible to have a purely toroidal field, but one must always have a dipolar component.  We then calculate the deformations due to the field and find that the star is oblate when the field is poloidal and becomes prolate as the toroidal component increases in strength.  Having determined the deformed configuration, we then use it as a background to write the equations for a general mode of oscillation.

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