Trace Anomaly and Effective Topological Sources in Neutron Stars

Abstract

This work investigates whether the trace anomaly can diagnose the stellar response to a topological scalar field in tensor multi-scalar gravity. Eleven cold tabulated equations of state (EoSs) were examined, with six retained after general relativistic (GR) thermodynamic and causality checks. Their fiducial topological configurations were compared with the corresponding GR models under complementary matching prescriptions. After controlling for stellar mass and EoS dependence, the GR trace source strength $S_T$ remained strongly correlated with the topological mass response, with a partial Spearman coefficient $ρ=0.975$. Near $1.4\,M_\odot$, the topological configurations were systematically more compact, with Jordan frame radius reductions of $6.7$--$8.7\%$ at fixed baryonic mass and $0.87$--$1.29\,\mathrm{km}$ at fixed gravitational mass. These shifts are comparable to current uncertainties from the Neutron Star Interior Composition Explorer (NICER) and produce source dependent observational effects. Despite the global deformation, the interior effective source remained matter dominated, with a median topological contribution of about $0.8\%$. The GR matter trace therefore emerges as a useful diagnostic of the fiducial topological stellar response.