R-mode frequencies of slowly rotating relativistic neutron stars with realistic equations of state

TL;DR

This paper extends the relativistic r-mode frequency calculations of neutron stars to realistic equations of state, providing results crucial for gravitational wave detection and understanding neutron star interiors.

Contribution

It develops a formalism for calculating relativistic r-mode frequencies with realistic equations of state, improving upon previous polytropic models.

Findings

R-mode frequency ranges from 1.39 to 1.57 times the star's spin frequency.

Relativistic corrections are significant for realistic neutron star models.

Results aid gravitational wave searches and constrain dense matter equations of state.

Abstract

The frequencies of r-mode oscillations of rotating neutron stars can be useful for guiding and interpreting gravitational wave and electromagnetic observations. The frequencies of slowly rotating, barotropic, and non-magnetic Newtonian stars are well known, but subject to various corrections. After making simple estimates of the relative strengths of these corrections we conclude that relativistic corrections are likely to be the most important. For this reason we extend the formalism of K. H. Lockitch, J. L. Friedman, and N. Andersson [Phys. Rev. D 68, 124010 (2003)], who consider relativistic polytropes, to the case of realistic equations of state. This formulation results in perturbation equations which are solved using a spectral method. We find that for realistic equations of state the r-mode frequency ranges from 1.39 to 1.57 times the spin frequency of the star when the relativistic compactness parameter (M/R) is varied over the astrophysically motivated interval 0.11 to 0.31. The results presented here are relevant to the design of gravitational wave and electromagnetic r-mode searches, and following a successful r-mode detection could help constrain the high density equation of state.