General-relativistic structure of two-component quantum dark fermion stars

Abstract

We develop a general-relativistic framework for two-component quantum dark fermion stars: equilibrium configurations of two degenerate fermion species governed by gravity, a Yukawa-mediated dark fifth force and a globally relevant Bohm quantum-pressure correction. The treatment retains the full covariant form of the nonlinear Klein--Gordon equation in the Schwarzschild interior, with closure relations valid at arbitrary compactness, from the ultralight baseline up to densities of order $0.16\,\mathrm{fm}^{-3}$ at which relativistic scalar densities and self-consistent effective fermion masses become unavoidable. Two Lagrangian parameters, the dark-fermion mass and the dimensionless ratio between the Yukawa channel and gravity, together fix the equilibrium structure; a joint measurement of mass and radius therefore constrains the dark-sector microphysics directly from gravitational-wave observables. For particle masses in the band $10^{-11}$--$10^{-10}$ eV, the configurations exhibit radii of $3$-$24\,\mathrm{km}$ and compactness in the range $0.14$-$0.34$, behaving as dual mimickers: at moderate compactness they overlap with neutron stars in mass, radius, and inspiral frequency; at the most compact end ($κ\sim 0.34$, $R_T/R_S\simeq 1.5$) they cross the photon sphere and could masquerade as low-mass black holes in the mass-gap region. Tidal-deformability measurements discriminate against both populations: the dimensionless tidal deformability is measurably smaller than the neutron-star value yet remains non-zero, unlike that of a genuine black hole. These objects populate the sensitivity bands of LISA, the Einstein Telescope, and Cosmic Explorer, producing astrometric microlensing signatures individually resolvable by \textit{Gaia}. The framework thus provides a reproducible and falsifiable template for constraining dark-sector properties through multi-messenger observations.