AI 中文总结
本文建立双组分量子暗费米子星的广义相对论框架，其平衡结构由两个拉格朗日参数确定，可通过多信使观测约束暗区性质，且其可作为中子星或低质量黑洞的模仿体，可通过潮汐可变形性区分。
AI 中文摘要
我们建立了双组分量子暗费米子星的广义相对论框架：该结构是两种简并费米子物种的平衡构型，受引力、Yukawa介导的暗第五力以及全局相关的Bohm量子压强修正共同支配。该处理保留了Schwarzschild内部非线性Klein-Gordon方程的完整协变形式，以及适用于任意致密性的闭合关系，覆盖从超轻基线到约0.16 fm⁻³密度的范围，在该密度下相对论标量密度和自洽有效费米子质量变得不可避免。两个拉格朗日参数——暗费米子质量和Yukawa通道与引力的无量纲比值——共同确定平衡结构；因此，质量与半径的联合测量可直接通过引力波观测量约束暗区微观物理。对于10⁻¹¹至10⁻¹⁰ eV范围内的粒子质量，这些构型表现出3至24 km的半径和0.14至0.34的致密性，具有双重模仿特性：中等致密性时，它们在质量、半径和并合频率上与中子星重叠；在最致密端（κ≈0.34，R_T/R_S≈1.5），它们穿过光子球，可能在质量间隙区域伪装成低质量黑洞。潮汐可变形性测量可区分这两类天体：无量纲潮汐可变形性明显小于中子星的值但仍非零，与真实黑洞不同。这些天体分布在LISA、Einstein Telescope和Cosmic Explorer的敏感带中，产生可被Gaia单独分辨的天体测量微引力透镜信号。因此，该框架为通过多信使观测约束暗区性质提供了可重复且可证伪的模板。
英文摘要
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.
Comments19 pages, 10 figures and 3 tables. Accepted for publication in Phys. Rev. D 114, 035032, Published 25 August, 2026
Journal refPhys. Rev. D 114, 035032, 25 August, 2026
