Dark Matter Admixed White Dwarfs: A Single-Fluid Approach

TL;DR

The paper addresses how a fermionic dark matter component, via a Higgs-portal coupling, modifies white dwarf structure by formulating a unified single-fluid EoS and solving the TOV equations. It finds that DM softens the EoS, with lighter DM providing more pressure support and larger radii, while higher DM fractions and heavier DM masses yield more compact stars and smaller maximum masses; radii tend to be smaller than some observations, suggesting additional physics may be needed. The work demonstrates that even modest DM admixtures can alter WD stability and global properties, offering a potential astrophysical avenue to constrain DM particle properties. The approach and results have implications for WD cooling, electron-capture thresholds, and compact-object formation, and motivate future extensions to multi-fluid treatments and inclusion of rotation or magnetic fields.

Abstract

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.

Figures (9)

• Figure 1: Variation of the equation of state (EoS) for dark matter-admixed white dwarfs. Left panel: Total pressure $P_{T}$ as a function of total energy density $\epsilon_{T}$ for a fixed dark matter particle mass $m_\mathrm{DM}=10\,\mathrm{GeV}$. The arrows mark the curves corresponding to $f_\mathrm{DM}=0.01$ and $f_\mathrm{DM}=0.1$, while the intermediate curves represent the other dark matter fractions $f_\mathrm{DM}= [0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09]$. Right panel: The variation of the EoS for a fixed dark matter fraction $f_\mathrm{DM}=0.05$. The arrows indicate the curves corresponding to $m_\mathrm{DM}=0.1\,\mathrm{GeV}$ and $m_\mathrm{DM}=10\,\mathrm{GeV}$, with the intermediate curves showing the results for $m_\mathrm{DM}=[1,2,3,4,5,6,7,8,9]\,\mathrm{GeV}$. In both panels, the dashed black line represents the standard Chandrasekhar white dwarf without dark matter.
• Figure 2: Radial mass profile $m(r)$ of dark matter-admixed white dwarfs. Left panel: The mass distribution for a fixed dark matter particle mass $m_\mathrm{DM}$=10 GeV. The arrows indicate the curves corresponding to $f_\mathrm{{DM}}=0.01$ and $f_\mathrm{{DM}}=0.1$, while the intermediate curves represent other dark matter mass fractions $f_\mathrm{{DM}}=[0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09]$. Right panel: The radial mass profile for a fixed dark matter mass fraction $f_\mathrm{{DM}}=0.05$. The arrows mark the curves corresponding to $m_\mathrm{{DM}}=0.1\;\mathrm{GeV}$ and $m_\mathrm{{DM}}=10\;\mathrm{GeV}$, with the intermediate curves corresponding to other dark matter particle masses $m_\mathrm{{DM}}=\mathrm{[1,2,3,4,5,6,7,8,9]\;GeV}$. In both panels, the dashed black line represents the standard Chandrasekhar white dwarf without dark matter.
• Figure 3: Radial pressure profile $P_{T}(r)$ of dark matter-admixed white dwarfs. Left panel: The pressure distribution for a fixed dark matter particle mass $m_\mathrm{{DM}}=\mathrm{10\;GeV}$. The arrows indicate the curves corresponding to $f_\mathrm{{DM}}=0.01$, $f_\mathrm{{DM}}=0.05$, and $f_\mathrm{{DM}}=0.1$. Right panel: The pressure profile for a fixed dark matter mass fraction $f_\mathrm{{DM}}=0.05$. The arrows mark the curves corresponding to $m_\mathrm{{DM}}=\mathrm{0.1\;GeV}$, $m_\mathrm{{DM}}=\mathrm{5\;GeV}$, and $m_\mathrm{{DM}}=\mathrm{10\;GeV}$. In both panels, the dashed black line denotes the standard Chandrasekhar white dwarf without dark matter.
• Figure 4: Mass-radius relationship of dark matter-admixed white dwarfs. Left panel: The mass-radius curves for a fixed dark matter particle mass $m_\mathrm{{DM}}=\mathrm{10\;GeV}$, where the arrows indicate the curves corresponding to $f_\mathrm{DM}=0.01$ and $f_\mathrm{DM}=0.1$; the intermediate curves correspond to other dark matter mass fractions $f_\mathrm{DM}=[0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09]$. Right panel: The mass-radius relationship for a fixed dark matter mass fraction $f_\mathrm{DM}=0.05$, with arrows marking the curves for $m_\mathrm{{DM}}=\mathrm{0.1\;GeV}$ and $m_\mathrm{{DM}}=\mathrm{10\;GeV}$; the intermediate curves correspond to other dark matter particle masses $m_\mathrm{{DM}}=\mathrm{[1,2,3,4,5,6,7,8,9]\;GeV}$. In both plots, the dashed black line represents the standard Chandrasekhar white dwarf without dark matter, and no legend is displayed. Shaded horizontal bands indicate recent observational mass constraints from $\mathrm{ZTF\;1901+1458}$ (wheat), $\mathrm{Sirius\;B}$ (plum), $\mathrm{Stein\; 2051\;B}$ (light blue), $\mathrm{40\;Eridani\;B}$ (light green), and $\mathrm{GK\;Vir}$ (light pink), representing the range of astrophysically viable stellar configurations.
• Figure 5: Mass variation of dark matter-admixed white dwarfs. Left panel: The variation of stellar mass with central white dwarf energy density $\epsilon_{0WD}$ (in log scale) for a fixed dark matter particle mass $m_\mathrm{{DM}}=\mathrm{10\;GeV}$. The arrows mark the curves corresponding to $f_\mathrm{{DM}}=0.01$ and $f_\mathrm{{DM}}=0.1$, while the intermediate curves correspond to other dark matter mass fractions $f_\mathrm{{DM}}=\mathrm{[0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09]}$. Right panel: The variation of stellar mass with total central number density $n_{T0}$ (in log scale) for a fixed dark matter mass fraction $f_\mathrm{{DM}}=0.05$. The arrows indicate the curves corresponding to $m_\mathrm{{DM}}=\mathrm{0.1\;GeV}$ and $m_\mathrm{{DM}}=\mathrm{10\;GeV}$ with intermediate curves representing other dark matter particle masses $m_\mathrm{{DM}}=\mathrm{[1,2,3,4,5,6,7,8,9]\;GeV}$. In both panels, the dashed black line represents the standard white dwarf without dark matter, and no legend is displayed.