Tidal deformations of general-relativistic multifluid compact stars

TL;DR

This paper develops a general-relativistic multifluid model for compact stars to analyze how mutual entrainment affects their tidal deformabilities, with implications for gravitational-wave observations.

Contribution

It introduces a comprehensive multifluid framework for tidal deformations, extending beyond perfect-fluid models, and assesses the impact of entrainment on gravitational-wave signals.

Findings

Entrainment does not alter adiabatic tidal responses.

Tidal deformabilities remain unaffected by mutual entrainment.

The model applies to superfluid neutron stars and dark matter admixed stars.

Abstract

Over the past decade, gravitational-wave astronomy has opened a new window onto the extreme states of matter inside compact stars. At some point during the inspiral of a binary system, each star starts to experience adiabatic tides, characterized by tidal deformabilities. The dominant tidal deformability, first measured with the GW170817 event, has already constrained the dense-matter equation of state. With the advent of third-generation detectors, tidal deformabilities are expected to be inferred with much higher precision, potentially revealing subleading tidal contributions. This motivates the development of more accurate compact-star models that incorporate richer microphysics. With this in mind, we move beyond the commonly adopted perfect-fluid approximation and model compact stars through a multifluid framework. In this work, we present the fully general-relativistic description of adiabatic tidal deformations of compact stars composed of an arbitrary number of interacting fluids, using Carter's multifluid variational formalism. A distinctive feature of this approach is the presence of nondissipative mutual entrainment between fluid species. We derive the hydrostatic equilibrium equations for multifluid configurations, along with the perturbed equations governing stationary gravitoelectric and gravitomagnetic tidal responses of arbitrary order. We then investigate how entrainment modifies the corresponding tidal deformabilities. Using an analytical representation of the multifluid equation of state, we show that entrainment leaves adiabatic tidal responses unchanged and therefore produces no measurable effect on the gravitational-wave signal emitted during the inspiral long before the excitation of internal mode resonances. We subsequently discuss two specific applications: superfluid neutron stars and dark matter admixed compact stars.