Adamu Issifu, Constança Providência, Franciele M. da Silva, Débora P. Menezes, Tobias Frederico

We develop a self-consistent framework based on a contact vector current-current interaction that couples the chemical potentials of both sectors through mutual mean-field shifts, with the dark matter (DM) fraction $F_D = N_D/N_B$ fixed as a global input parameter. This formulation provides a physically motivated alternative to fixed-density prescriptions, allowing the local DM density to follow the baryonic matter (BM) density throughout the stellar interior. As an application, we consider a mirror-DM scenario with exact symmetry between the dark and visible sectors and investigate NS matter using the NL3$ωρ$, FSU2R, NL3, and DDME2 equations of state (EOSs). We find that the DM--BM interaction weakens the binding of dense matter, reduces its incompressibility, and softens the EOS. Consequently, DM increases the central density and compactness of NSs, lowers their maximum masses, and shifts the onset of the direct Urca process to higher stellar densities. As a consequence, the onset of rapid cooling is shifted to more massive stars for models with a stiff symmetry energy and to less massive stars for models with a soft symmetry energy, depending on the extra compactness that results from the DM admixture. These results demonstrate that mirror-DM admixtures modify both the microscopic composition and macroscopic structure of NSs, with potential implications for their thermal evolution and multimessenger observational signatures.