Stability analysis of the spin evolution fix points in inspiraling compact binaries with black hole, neutron star, gravastar, or boson star components

TL;DR

This paper analyzes the stability of spin configurations in inspiraling compact binaries with various exotic and standard components, revealing how stability depends on spin alignment, mass ratio, and quadrupolar parameters.

Contribution

It provides a detailed dynamical system analysis of spin fix points and their stability across different binary compositions and parameters, including new insights into transitional instabilities.

Findings

Aligned and coplanar spin configurations can be stable or marginally stable depending on parameters.

Transitions from stability to instability can occur during inspiral for certain configurations.

Stability regions vary significantly among different binary types and are influenced by quadrupolar parameters.

Abstract

Based on the secular spin evolution of black holes, neutron stars, gravastars, or boson stars in precessing compact binaries on eccentric orbit, we identify the aligned and more generic coplanar configurations of the spins and orbital angular momentum as fix points. Through a dynamical system analysis, we investigate their linear stability as function of the mass quadrupole parameter. Marginal stability holds for the binary configurations with both spins antialigned to the orbital angular momentum, for both spins aligned to the orbital angular momentum (with the exception of certain quadrupolar parameter ranges of neutron stars and boson stars), and for the extremal mass ratio. For equal masses, the configurations of one of the spins aligned and the other antialigned is stable for gravastar binaries, for neutron star binaries in the high quadrupolar parameter range, and for boson star binaries. For some unequal mass gravastar binaries, black hole binaries or neutron star binaries, a transition from stability to instability can occur during the inspiral, when one of the spins is aligned, while the other is antialigned to the orbital angular momentum. We discover a transitional instability regime during the inspiral of certain gravastar, neutron star, or boson star binaries with opposing spins. For coplanar configurations we find instabilities only for the gravastar - gravastar, boson star - boson star and black hole - boson star binaries. For a given spin configuration, marginal stability strongly depends on the value of the quadrupolar parameters. The stability region is larger for neutron star binaries than for black hole binaries, while the mixed systems have a restricted stability parameter region.