Reconstructing the Dark Matter Equation of State with Compact Object Inspirals

RESUMO

We investigate the gravitational wave (GW) signatures of compact binaries embedded in extended dark matter (DM) configurations in hydrostatic equilibrium. If a neutron star is surrounded by a sufficiently massive and extended envelope, an inspiraling companion experiences dynamical friction (DF) in addition to the standard GW energy loss. We show that this environmental effect can be isolated through a GW observable, the $D$-function, which directly characterizes the additional dissipative power induced by the surrounding medium. Since the density of the envelope is directly determined by the DM equation of state together with the stellar boundary conditions, the frequency dependence of the $D$-function provides direct information about the macroscopic properties of the dark sector. We develop a regression-based framework to reconstruct both the density profile and the DM equation of state over the density range probed by observations of the GW inspiral. Using representative DM models as benchmarks, we demonstrate that the method accurately recovers the input equation of state while remaining largely independent of the microscopic realization of DM. Our results show that future GW observations of compact binaries can provide a probe of the equation of state of DM.