Gravitational radiation and the formation of neutron star thermo-elastic mountains

Abstract

Advancing sensitivity of LIGO-Virgo-KAGRA gravitational-wave instruments has led to much anticipation for the first detection of quasi-monochromatic continuous gravitational radiation from single, rapidly rotating neutron stars. This thesis is concerned with one specific scenario to facilitate gravitational radiation from such stars: the development of a non-axisymmetric quadrupolar deformation of the solid crust. In accreting systems in particular, deformations may manifest as so-called ‘thermal mountains'; whereby the mass distortion is supported by elastic strains sourced via large-scale non-axisymmetric temperature gradients misaligned from the star’s rotation axis. In this work we present for the first time a fully self-consistent calculation of the size of neutron star thermal mountains. In doing so, we will introduce a new class of deformations that we term `thermo-elastic' mountains, in which we consider different sources of temperature-dependence in the crustal equation of state than the conventional picture of the so-called `wavy electron capture layer'. Over the course of this thesis, we shall present a scheme to develop a mechanism to source a temperature perturbation in the accreted crust, compute the associated density perturbations, and calculate the resultant mass quadrupole moment. Models of the hydrostatic structure of spherically-symmetric accreting neutron stars are constructed using realistic equations of state. The thermal structure of these stars is then computed, assuming them to be accreting steadily. Temperature perturbations are subsequently introduced onto the homogeneous background via the insertion of a weak internal quadrupolar magnetic field, restricting the flow of heat orthogonal to the field lines and establishing a non-axisymmetric temperature distribution within the star. Such a calculation requires a detailed description of relevant heat generation, neutrino cooling, and heat transport mechanisms, each of which are discussed. The elastic readjustment of the crust in response to the aforementioned temperature asymmetry is then calculated. A piece of the crustal pressure that is generated by the ionic lattice is identified and shown to have some temperature dependence. Perturbations of this ‘thermal lattice pressure’ are necessarily tied to the star’s elastic phase, and not easily convected away. We find that the mountains sustained by the lattice in response to anisotropic heat conduction are small, and unlikely to be dictating the spin-equilibrium of rapidly rotating neutron stars but may still be playing a contributory role in determining the long-term spin-evolution of accreting systems.

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Identifiers

ORCID for Thomas James Hutchins: orcid.org/0000-0001-8185-665X

ORCID for Ian Jones: orcid.org/0000-0002-0117-7567

ORCID for Nils Andersson: orcid.org/0000-0001-8550-3843

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