Dark Matter Admixed White Dwarfs: A Single-Fluid Approach
In this study, we investigate the influence of an admixed fermionic dark matter (DM) component on the equilibrium structure of white dwarfs (WDs), with particular emphasis on the effects of varying the DM particle mass ($m_{\rm DM}$) and DM fraction ($f_{\rm DM}$). Notably, we employ a single-fluid approximation for the first time in this context, wherein the baryonic and DM contributions to the total energy density and pressure are treated within a unified framework, assuming non-interacting fermionic DM in hydrostatic equilibrium with baryons. We examine how variations in $m_{\mathrm{DM}}$ and $f_\mathrm{DM}$ modify the equation of state (EoS), the mass-radius relationship, and the internal mass and pressure distributions of WDs. Our results show that the presence of DM softens the EoS, with lighter DM particles providing stronger pressure support and leading to more extended stellar structures. Increasing the DM mass fraction leads to a more compact configuration, reducing both the radius and maximum mass of the WD. We further demonstrate that heavier DM particles enhance stellar compactness and can eventually drive the star toward gravitational instability. Moreover, the analysis of mass-radius relationships reveals that while small fractions of DM are consistent with observed WD masses, the radii predicted by our models are smaller than observations, suggesting additional influences such as rotation or magnetic fields. Our stability analysis confirms that the inclusion of dark matter does not lead to instability within the expected parameter space, indicating that white dwarfs admixed with dark matter can remain dynamically stable under certain conditions. These findings show that even a small admixture of DM can modify the structural properties and stability limits of WDs, providing a potential indirect astrophysical probe of DM particle properties.