What can quasi-periodic oscillations tell us about the structure of the corresponding compact objects?

TL;DR

This paper proposes a method to infer the multipole moments of compact objects like neutron stars and black holes from observed quasi-periodic oscillations, enabling tests of their structure and fundamental physics.

Contribution

It introduces a novel approach to estimate space-time multipole moments from QPO data, linking observations to the physical properties and equations of state of compact objects.

Findings

Method to fit QPO frequencies to multipole expansions

Constraints on neutron star equations of state

Tests of the no-hair theorem for black holes

Abstract

We show how one can estimate the multipole moments of the space-time, assuming that the quasi-periodic modulations of the X-ray flux (quasi-periodic oscillations), observed from accreting neutron stars or black holes, are due to orbital and precession frequencies (relativistic precession model). The precession frequencies $\Omega_{\rho}$ and $\Omega_z$ can be expressed as expansions on the orbital frequency $\Omega$, in which the moments enter the coefficients in a prescribed form. Thus, observations can be fitted to these expressions in order to evaluate the moments. If the compact object is a neutron star, constrains can be imposed on the equation of state. The same analysis can be used for black holes as a test for the validity of the no-hair theorem. Alternatively, instead of fitting for the moments, observations can be matched to frequencies calculated from analytic models that are produced so as to correspond to realistic neutron stars described by various equations of state. Observations can thus be used to constrain the equation of state and possibly other physical parameters (mass, rotation, quadrupole, etc.) Some distinctive features of the frequencies, which become evident by using the analytic models, are discussed.