Comment on "Tidal Love numbers of neutron and self-bound quark stars"

TL;DR

This paper discusses a correction to the calculation of tidal Love numbers of neutron stars when a phase transition occurs, providing a modified formula to improve accuracy in such cases.

Contribution

It introduces a modified formula for tidal Love numbers accounting for phase transitions at non-zero pressure, improving previous calculations.

Findings

The original formula's error approaches zero as pressure approaches zero.

Maximum relative error is estimated at around 5% for high-density discontinuities.

The correction is significant for accurate modeling of neutron star properties.

Abstract

We comment on the paper of S. Postnikov et al. in Phys. Rev. D 82, 024016 (2010) and give a modified formula that needs to be taken into account when calculating the tidal Love number of neutron stars in case a first order phase-transition occurs at non-zero pressure. We show that the error made when using the original formula tends to zero as $p \rightarrow 0$ and we estimate the maximum relative error to be $\sim 5\%$ if the density discontinuity is at larger densities.