A unified thermodynamic framework for coextensive dark matter admixed strange stars

Abstract We investigate the structural and physical properties of a strange star admixed with self-interacting bosonic dark matter within a unified thermodynamic framework. The total energy density is modelled as a weighted combination of quark matter and dark matter components regulated by a fixed local volume fraction, corresponding to the frozen coextensive limit in which both the components share the same spacetime geometry and extend to a common radius ( $$R_D = R_Q=R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>D</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>Q</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> ). The quark component is described by a linear equation of state (EOS), while the dark matter follows a mean-field EOS with repulsive self-interactions. By combining these EOSs into a barotropic effective EOS derived from a unified thermodynamic potential, the two-fluid system is reformulated as a thermodynamically closed and mechanically equilibrated configuration. The construction preserves the dynamical distinction between the quark and dark sectors but treats them as a macroscopically unified mixture governed by a single hydrostatic equilibrium equation. This framework identifies the fully coextensive limit of two-fluid models as a physically meaningful and thermodynamically closed configuration and provides a coherent macroscopic closure linking dark matter-strange matter microphysics to stellar observables. Using the effective EOS, we solve the Tolman–Oppenheimer–Volkoff (TOV) equations to obtain the mass–radius relationship by varying the fixed local dark matter fraction, dark matter particle mass and self-coupling constant. Our results reveal distinct modifications to the $$M-R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>-</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> profiles, suggesting observable signatures that could offer insights into the impacts of dark matter in extreme astrophysical environments. We note that even a modest dark matter admixture softens the equation of state, thereby shrinking the maximum mass limit and hence can explain a wide range of ultra-compact stars. In particular, our study provides a possible explanation and a radius estimate for ultra-compact stars with small radii, such as XTE J1814-338, as well as for heavier pulsars like PSR J0348+0432, PSR J0740+6620, and PSR J0952-0607.