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

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 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 χ 1/3. Consequently, the DM rest-mass energy fraction dominates the DM-induced modification of Δ tot, producing a smooth upward shift of up to about0.1 for F χ about0.2%. 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 squared, Δ tot, and Δ tot-Δ B. The combined softening substantially reduces the maximum stellar mass, placing F χ about0.2% in tension with the observed 2,M 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.