Gravitational wave constraints on the shape of neutron stars

TL;DR

This paper establishes a direct relation between gravitational wave limits on neutron star quadrupole moments and their surface deformations, enabling new constraints on neutron star shapes from gravitational wave data.

Contribution

It derives a general relativistic relation linking quadrupole moments to surface deformations, applicable with minimal assumptions, and applies it to LIGO/Virgo data for neutron stars.

Findings

LIGO bounds constrain Crab pulsar's surface deformation to be smaller than rotational deformation.

The relation depends only on star's mass and radius, not detailed internal composition.

Gravitational wave data provides unique constraints not possible with electromagnetic observations.

Abstract

We show that there is a direct relation between upper limits on (or potential future measurements of) the m = 2 quadrupole moments of slowly rotating neutron stars and the l = m = 2 deformation of the star's surface, in full general relativity, to first order in the perturbation. This relation only depends on the star's structure through its mass and radius. All one has to assume about the star's constituents is that the stress-energy tensor at its surface is that of a perfect fluid, which will be true with good accuracy in almost all the situations of interest, and that the magnetic field configuration there is force-free, which is likely to be a good approximation. We then apply this relation to the stars which have direct LIGO/Virgo bounds on their m = 2 quadrupole moment, below the spin-down limit, and compare with the expected surface deformations due to rotation. In particular, we find that LIGO observations have constrained the Crab pulsar's l = m = 2 surface deformation to be smaller than its l = 2, m = 0 deformation due to rotation, for all the causal equations of state we consider, a statement that would not have been able to be made just using the upper bounds on the l = m = 2 deformation from electromagnetic observations.