I-Love-Q relations of fermion-boson stars

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 $\mathcal{O}({10}^{\ensuremath{-}10}\text{ }\text{ }\mathrm{eV})$, where the Compton wavelength is comparable to the Schwarzschild radius of a $1{M}_{\ensuremath{\bigodot}}$ 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 ${m}_{b}\ensuremath{\ge}26.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\text{ }\text{ }\mathrm{eV}$. 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.