Testing bosonic dark matter through white dwarf mass measurements

TL;DR

This work proposes that a gravitationally coupled, electromagnetically invisible scalar-field component (dark matter) can reside in white dwarfs, forming mixed fermion–boson star configurations that shift the total gravitational mass without altering atmospheric signatures. By solving the coupled Einstein–Klein–Gordon–hydrodynamics system with a polytropic WD and a tiny but non-negligible scalar field, the authors reproduce the observed discrepancies between gravitational redshift and electromagnetic mass estimates, with a scalar-field mass fraction $f_{\rm DM}$ in the $5-15\%$ range. A Bayesian model comparison favors the presence of a scalar field with ultralight boson mass $\mu$ around $10^{-10}$ eV, while allowing for a range of configurations (compact DM cores to extended halos) that preserve WD radii and mass–radius relations. The results provide a physically motivated probe of ultralight DM in compact stars and offer testable predictions for future WD observations, asteroseismology, and environmental DM correlations, thereby linking stellar astrophysics to particle DM properties.

Abstract

Mass estimates of white dwarfs via electromagnetic methods, often differ from those obtained through gravitational redshift measurements, in some cases with discrepancies ranging in $5-15\%$ across independent datasets. Although many of the discrepancies reported in large spectroscopic surveys and confirmed by high-precision techniques such as astrometric microlensing and wide-binary analyses may be attributable to thermal effects, model uncertainties or measurement errors prevent a complete description of some of the observations. Here, we explore an alternative explanation based on the presence of a gravitationally coupled bosonic scalar field that contributes to the stellar mass while remaining electromagnetically invisible. We construct stationary, static mixed configurations consisting of a white dwarf that presents a bosonic scalar field (dark matter) component, forming a composite white dwarf-boson star system. We explore families of solutions showing that a scalar field fraction $f_{\rm DM} \sim 5-15\%$ to the mass contribution can account for the observed redshift excess. Our models provide a physically motivated explanation for the mass bias, might offer new observational signatures, and allow us to place preliminary constraints on the mass and compactness of the scalar field configuration. Finally, using our theoretical framework in combination with Bayesian model selection we provide plausible bounds for the mass of the constituent (ultralight) bosonic particle.

Figures (5)

• Figure 1: Sample of WDs for which pairs of observational mass measurements are available. Small black circles correspond to the EM measurement, while big blue circles indicate the GRS counterpart. Each measurement is accompanied by its corresponding uncertainty. In ascending order of radii, the stars reported are: Sirius B joyce2018gravitationalbond2017sirius, DB falcon2012gravitational2011ApJ...737...28B, DBA falcon2012gravitational2011ApJ...737...28B, Hyades WD 2019AA...627L...8Ptremblay2012spectroscopic, DBs falcon2012gravitational2011ApJ...743..138G, Chandra 2020ApJ...899..146Carseneau2024measuring, El-Badry arseneau2024measuringarseneau2024measuring, DA 2010ApJ...712..585F2011ApJ...730..128T, DAs 2010ApJ...712..585F2011ApJ...730..128T, Koester koester1987gravitational2011ApJ...743..138G, Procyon B Onofrio:2014txa2000AJ....119.2428G and 40 Eridani B popper1954redbond2017sirius. The $x$-axis is broken in the value indicated by the vertical dotted line to facilitate the visualisation of the data points.
• Figure 2: Top row: scalar field profiles of the models presented in Table \ref{['table1']}. Bottom row: pressure profiles for the same configurations. Each column shows the profiles for the different boson masses, as indicated in the titles of the figures. The legends indicate the model names $M_i$, with $i=1,2,3,4$. These numbers correspond to equilibrium models that can be respectively identified with the following observational WDs: 1 for Sirius B, 2 for DB, 3 for DBA, and 4 for Chandra. On the other hand, MpWD refers to pure WD models (with no scalar field component). Only equilibrium solutions with label numbers $1$, $2$, and $4$ are displayed in this case, since the pure WD configurations for cases $2$ and $3$ are identical.
• Figure 3: Comparison between the observational data and the equilibrium configurations for $\mu = 1 \times 10^{-10}$ eV (top) and $\mu = 1.68 \times 10^{-11}$ eV (bottom). The left column displays the GRS mass estimates while the right column shows the EM estimates alongside the fermionic mass components of the mixed configurations. The colormap represents the percentage of bosonic (or DM) content relative to the total mass in each model. This visual representation enables us to evaluate the contribution of the scalar field across various mass regimes and model configurations.
• Figure 4: Comparison of the percent mass difference between the observational results ($\Delta M\%$) and our theoretical models ($\Delta M\%_{\rm{T}}$). The top panel corresponds to $\mu = 1 \times 10^{-10}\,\mathrm{eV}$ and the bottom one to $\mu = 1.68\times 10^{-11}\,\rm eV$.
• Figure 5: Posterior probability for the boson-mass values $\mu$ evaluated considered in this work. We assume a uniform prior probability $p(\mu)$. Thus, the y-axis of the plot is directly proportional to the likelihood $p(d|\mu)$. We have restricted the x-axis to $\mu \geq 1.68\times 10^{-12}$ eV to ease visualization.