Effects of light-mass fermionic dark matter on the equilibrium and stability of white dwarfs

TL;DR

We address how light fermionic dark matter (DM) affects white dwarfs (WDs) by developing a two-fluid general-relativistic model that treats normal matter and DM as gravitating, non-interacting fluids. The study solves full TOV-like hydrostatic equilibrium with NM rest-mass energy included and analyzes radial stability via a Sturm-Liouville formulation for oscillation frequencies, using DM masses in $0.1-10$ GeV. Key findings show that DM admixture makes WDs more compact, with typical DM-admixed configurations around $M\approx1.3\,M_\odot$ and $R\approx500$ km for $m_{\rm DM}=1$ GeV, and that DM can shift fundamental radial modes by up to $\sim20\%$ (especially for lighter DM, $m_f=0.1$ GeV). These results imply observable signatures in surface gravity, gravitational redshift, and gravitational-wave phasing, offering a pathway to constrain sub-GeV DM properties through WD observations and future multi-messenger measurements.

Abstract

White dwarfs (WDs) can be used as laboratories to test strong gravity and high-density regimes, once their equation of state is not so uncertain as the one of neutron stars. This makes them also a useful tool to constrain dark-matter models. In this work, we study dark matter white dwarfs (DMWD) composed of white dwarf matter admixed with fermionic dark matter in a two-fluid general relativistic framework. Dark matter particles are considered to have masses between $0.1-10$ GeV. The equilibrium configurations and stability are derived, showing that the DMWD can be more compact, with masses around 1.3 $M\odot$ and radii around 500 km. The increasing compactness leads to changes in the fundamental modes of radial oscillations ($\sim20\%$ for 0.1 GeV DM), which produce detectable shifts in GW frequencies. The interplay between dark matter and normal matter thus provides a compelling avenue for interpreting deviations in observed WD properties and for placing constraints on DM characteristics through astrophysical observations.

Figures (4)

• Figure 1: Pressure and energy density ratio as a function of the dimensionless Fermi momentum for both normal and dark matter equations of state.
• Figure 2: Panel a): Total mass versus normal matter central density. Panel. b): Dark matter component of the star's mass as a function of normal matter central density. Panel c): Normal matter component of the mass of the star as a function of normal matter central density. Panel d): Total mass versus total radius of the DMWD stars. Panel e): Dark matter central energy density versus total mass. In all panels, we consider $m_{\rm DM}=1$ GeV and different values of central Fermi momentum for the dark matter content.
• Figure 3: Same as Fig. \ref{['mr1']}, but for $m_{\rm DM}=0.1$ GeV.
• Figure 4: Radial oscillation frequencies as a function of the normal matter central density. The curves correspond to different values of central Fermi momentum for the dark matter content. Two values of dark matter particles are considered as displayed in each graph.