I-Love-Q Relations of Fermion-Boson Stars

TL;DR

This paper explores how fermion-boson stars, which include dark matter, deviate from universal neutron star relations, revealing that dark matter properties significantly influence these deviations and can set bounds on boson particle mass.

Contribution

The study extends I-Love-Q relations to fermion-boson stars with a nonrotating bosonic component, analyzing the impact of dark matter parameters on these universal relations.

Findings

Deviations up to 5% for certain dark matter parameters.

Universal relations hold within 1% for boson mass ≥ 26.8×10^{-10} eV.

Higher dark matter content increases deviations.

Abstract

We investigate the properties of fermion-boson stars (FBSs), which can be viewed as neutron stars with a bosonic dark matter (DM) admixture. A challenge in studying the impact of DM on neutron stars is the absence of a universally accepted nuclear-matter equation of state (EOS), making it difficult to distinguish between the effects of DM and various EOS models. To address this issue, we extend the study of the I-Love-Q universal relations of neutron stars to FBSs with a nonrotating bosonic component by solving the Einstein-Klein-Gordon system. We study how DM parameters, such as the boson particle mass and self-interaction strength, would affect the structure of FBSs and explore the parameter space that leads to deviations from the I-Love-Q relations. The properties of FBSs and the level of deviations in general depend sensitively on the DM parameters. For boson particle mass within the range of $\mathcal{O}(10^{-10} \ \mathrm{eV})$, where the Compton wavelength is comparable to the Schwarzschild radius of a $1 M_\odot$ star, the deviation is up to about 5% level if the star contains a few percent of DM admixture. The deviation increases significantly with a higher amount of DM. We also find that the universal relations are still valid to within a 1% deviation level for boson particle mass $m_b \geq 26.8\times10^{-10} \ \mathrm{eV}$. This effectively sets an upper bound on the boson particle mass, beyond which it becomes not feasible to probe the properties of FBSs by investigating the I-Love-Q relation violations.