Decoding Dark Matter Admixed Neutron Stars: From Static Structure to Rotational Deformation

In this study, we investigate the impacts of dark matter (DM) on the properties of both static and rotating neutron stars utilizing a self-interacting DM model, motivated by the neutron decay anomaly. DM-admixed NSs are modeled by assuming chemical equilibrium between ordinary matter and the dark sector, treating a single-fluid Tolman-Oppenheimer-Volkoff (TOV) framework. By treating the DM interaction strength ($G$) as a free parameter, we explore its influence on NS properties, considering a broad range of equations of state (EoSs). Using the mass-radius constraints from NICER pulsar measurements, we constrain the DM interaction strength for each EoS via a likelihood analysis. Extending this model to rotating NSs, we analyze how centrifugal forces associated with increasing angular velocity ($\mathrm{\Omega }$) enhance both mass and radius, causing deformation. We assess the impact of DM on rotational deformation by calculating the eccentricity, highlighting the interplay between DM and rotational forces. Since both DM and rotation simultaneously influence NS properties, we compute the relative changes in mass and radius across varying $G$ and $\mathrm{\Omega }$ values to quantify their combined effects.