Trace-anomaly decomposition and universal dark matter scaling in compact stars

Abstract: We investigate how dark matter (DM) admixture modifies the conformal properties and phase structure of dense neutron-star matter within a self-consistent single-fluid framework, with the global DM fraction $F_χ=N_χ/N_B$ fixing the local relation $n_χ=F_χn_B$. We derive an exact decomposition of the total trace anomaly, $Δ<em>{\rm tot}$, into microscopic contributions. For collider-motivated Higgs-portal benchmarks, explicit Higgs, vector-mediator, and contact-interaction contributions are negligible, while heavy nonrelativistic DM has an intrinsic trace anomaly close to the nonrelativistic limit, $Δ</em>χ\simeq1/3$. Consequently, the DM rest-mass energy fraction dominates the DM-induced modification of $Δ<em>{\rm tot}$, producing a smooth upward shift of up to $\sim0.1$ for $F</em>χ\sim0.2\%$. In the pressureless, comoving heavy-WIMP regime, we further identify a universal dark-sector scaling governed by the mass-loading parameter $λ=F_χm_χ/m_N$: numerical calculations with different $(F_χ,m_χ)$ pairs at fixed $λ$ exhibit overlapping trace-anomaly, sound-speed, and mass--radius responses for a given baryonic equation of state. In hybrid stars, DM leaves the coexistence pressure and chemical potential essentially unchanged, whereas first-order hadron--quark deconfinement produces sharp discontinuities in the squared sound speed $c_s<sup>2$, $Δ<em>{\rm tot}$, and $Δ</em>{\rm tot}-Δ<em>B$. The combined softening substantially reduces the maximum stellar mass, placing $F</em>χ\sim0.2\%$ in tension with the observed $2\,M_\odot$ neutron stars. These results show that the trace anomaly and its density evolution provide a sensitive diagnostic for distinguishing smooth DM-induced modifications of dense matter from genuine first-order deconfinement.