Dark Matter in White Dwarfs: Implications for Their Structure

TL;DR

The paper investigates whether ambient dark matter (DM) can alter white dwarf (WD) structure in DM-rich environments such as galactic halos. It develops a hybrid equation of state (EoS) that smoothly interpolates between hot dense plasma and cold DM using a tanh-based mixing function $f(ε)$ and a self-consistent coupling $P_{DM}=α ε_{DM}$. Solving the Tolman–Oppenheimer–Volkoff equations yields WD mass–radius sequences showing a ~12% increase in radius and ~0.7% increase in mass due to DM in the envelope, with the DM fraction depending on central temperature and stellar mass. The results align with halo WD observations and suggest WDs as indirect probes of DM properties in galactic halos, highlighting the importance of including DM components in stellar modeling for high-DM-density environments.

Abstract

White Dwarfs (WDs), the final evolutionary stage of most stars, are frequently modeled considering only a dense plasma matter. However, their potential interaction with dark matter (DM), especially in galactic halos where DM is expected to be prevalent, may lead to significant consequences. This work proposes a novel EoS (EoS) that consistently incorporates both hot dense plasma and cold dark matter (CDM) contributions in hot WDs. The hot dense plasma EoS is extended to include thermal and radiative contributions. At the same time, the CDM component is modeled as a linear fluid, with the coupling constant $α$ determined self-consistently within the star. A smooth phase transition between hot dense plasma and CDM regimes is introduced via a hyperbolic mixing function that depends on local energy density and stellar temperature. Our results show that the inclusion of CDM leads to an increase in the WD radius by approximately $12\%$ and a total mass enhancement of $0.7\%$, compared to standard hot WD models without lattice effects. These results highlight the importance of considering CDM in stellar modeling and suggest that WDs may serve as indirect probes for the astrophysical properties of dark matter.

Figures (6)

• Figure 1: Log-log plot of the pressure as a function of energy density for different equations of state (EoS). The blue dashed curve represents a typical WD composed of ions, electrons, and photons at a central temperature of $T = 10^7\,[\rm K]$. The red dashed curve corresponds to CDM. The black curve shows the proposed EoS, which interpolates the standard WD EoS at high densities and the CDM behavior at low densities, incorporating a mixed-phase regime. Temperature effects are also considered, with CDM contributing to the system's cooling, driving it toward $T = 0\,[\rm K]$ at low densities.
• Figure 2: Hyperbolic transition function $f(\varepsilon)$ plotted as a function of energy density for four different central temperatures. The function interpolates smoothly between $f(\varepsilon) = 0$, representing a typical WD EoS, and $f(\varepsilon) = 1$, corresponding to a regime dominated by CDM. The transition region reflects a mixed phase where both components coexist.
• Figure 3: The pressure, energy density, and mass in their normalized form against the radial coordinate are respectively presented on the top, middle, and bottom panels for four different central temperatures. The central pressure and central energy density of normalization are respectively $P_c=9.6\times10^{25} \,[\rm erg/cm^3]$ and $\varepsilon_c=3.0\times10^8\,[\rm g/cm^3]$.
• Figure 4: Mass as a function of radius for four different central temperatures. Pink triangles indicate the maximum mass configurations, corresponding to the stability limit for each case
• Figure 5: The fraction of DM in the WD radius as a function of stellar mass.