Tidal Love Numbers of Neutron Stars in Horndeski Theories

TL;DR

This paper develops methods to compute tidal Love numbers of neutron stars within Horndeski scalar-tensor theories, revealing potential ambiguities and quantifying deviations from General Relativity that impact gravitational wave analysis.

Contribution

It derives linear perturbation equations for static tidal Love numbers in Horndeski theories and addresses ambiguities in their extraction, extending previous work to more general scalar-tensor models.

Findings

Tidal Love numbers are influenced by additional contributions beyond the asymptotic expansion.

In scalar-tensor theories, Love numbers can differ by up to 10% if extra contributions are ignored.

The paper provides a framework for accurate Love number calculation in alternative gravity theories.

Abstract

Precision measurements of the gravitational wave signal from compact binary inspirals allow us to constrain the internal structure of those objects via physical parameters such as the tidal Love numbers. In scalar-tensor theories, one typically finds new types of Love numbers that are usually not considered or simply absent in General Relativity, which further allows us to constrain deviations from General Relativity. Building upon previous results, we present the linear perturbation equations necessary to calculate static and even-parity tidal Love numbers in Horndeski theories, the most general scalar-tensor theories with second-order field equations of motion. We further focus on the quadrupolar Love numbers and demonstrate how these can be extracted from the asymptotic expansion of the perturbation fields. We find that there is a potential ambiguity in extracting the Love numbers in this way, which we resolve by performing supplementary calculations in the effective field theory framework. We show that, in the case of scalar-tensor theories, the tidal Love numbers are not directly given by the $1/r^3$ term in the asymptotic expansion of the perturbation fields, as there is an additional contribution to this term independent of the Love numbers. We calculate such a contribution for a minimally coupled scalar field and also for the Damour-Esposito-Far\`ese model. For the latter, we find that the Love numbers can differ by $\mathcal{O}(1 \sim 10)\,\%$, if this additional contribution is not taken into account.