New ultralight scalar particles and the mass-radius relation of white dwarfs -- the important role of Sirius B

TL;DR

White dwarfs provide a unique laboratory for testing ultralight scalar particles via their equation of state. The authors derive density‑dependent EOS modifications for two beyond‑the‑Standard‑Model scenarios—a scalar field with quadratic electron coupling and a $\mathbb{Z}_{\mathcal{N}}$ axion with nucleon coupling—and confront WD models with precise mass–radius measurements, notably Sirius B. They find that first‑order phase transitions predicted by the scalar model are incompatible with Sirius B across the explored parameter space, and the $\mathcal{N}=31$ axion cross‑over scenario is also excluded by Sirius B, yielding strong red regions in the corresponding parameter spaces. Overall, white‑dwarf MR data thus provide powerful, competitive constraints on dense‑matter physics and beyond‑the‑Standard‑Model particles, often surpassing laboratory bounds in large parameter regions.

Abstract

We present the equation of state for two classes of new ultralight particles, a scalar field coupling to electrons and a light $\mathbb{Z}_\mathcal{N}$ QCD axion field coupling to nucleons. Both are potential candidates for dark matter. Using the scalar modified equations of state, we calculate models for white dwarf stars and compare their radii and masses with observed mass-radius data. The comparison results in stringent constraints on the masses of the particles and the coupling parameters. For a wide range of particle masses and coupling parameters, constraints from the white dwarf equation of state surpass existing limits, outperforming also dedicated laboratory searches. The remarkable accuracy of modern white-dwarf mass-radius relation data, exemplified by Sirius B, now allows stringent tests of dense-matter physics and constraints on new particle scenarios.

Figures (10)

• Figure 1: Schematic description of a scalar field profile emerging in a white dwarf. The main panel sketches the scalar field as a function of radius $r$ in and around a white dwarf. The dashed line marks the radius of the white dwarf $r=R_\mathrm{WD}$. The insets show the scalar potential at their respective position. The minimum of the potential, which corresponds to the realized field values, is marked in red. See text for details.
• Figure 2: First-order phase transition behavior in the EOS. Top: Schematic sketch of the phase transition behavior, stable, metastable, and unstable branches, see text. Bottom: EOS in the presence of a quadratically coupled scalar field for different values of mass to coupling ratios $c_m$. The equation of state without a scalar field is shown in grey and the metastable branch in red. Note that for $c_m=0.01$, the phase transition happens at pressures and densities much lower than visible. The temperature is fixed at $T=10000~\mathrm{K}$ for this example.
• Figure 3: White Dwarf EOS in the presence of a $\mathbb{Z}_{31}$-Axion (blue). The free fermi gas EOS without any new physics is shown in grey for comparison. If the central density is below $\rho_c \approx 2.4 \cdot 10^7~\mathrm{g} \cdot \mathrm{cm}^{-3}$, as described in the Appendix, there is a metastable branch (red) tracking the SM EOS. The temperature is fixed at $T=10000~\mathrm{K}$ for this example.
• Figure 4: Mass-radius relations with the classical SM equation of state for the effective temperatures $5000, 15000, 25000, 35000, 60000\,\mathrm{K}$. Color codes different temperature ranges; red: $5000-20000\,\mathrm{K}$, green: $20000-40000\,\mathrm{K}$, blue: $>40000\,\mathrm{K}$. The crosses are the observed masses and radii described in the text. They use the same color coding as the theoretical relations, except for Sirius B, which we plot in magenta for better visibility. The dashed line is the $15000\,\mathrm{K}$ relation from the LaPlata group. The inset shows an enlarged plot around Sirius B.
• Figure 5: Mass-radius relations with Scalar equation of state for the effective temperatures $5000, 15000, 25000, 35000$ and $60000\,\mathrm{K}$ (from bottom) and $c_m =0.03$. The five upper curves are stable branches for low masses, extended by metastable branches depending on the central density (see Fig. \ref{['fig:FOPTPlot']}). The crosses are the observed masses and radii as in Fig. \ref{['mrrCHeHSM']}, which the theory with the new scalar field badly fails to explain. Coloring of objects and mass-radius relations as in Fig. \ref{['mrrCHeHSM']}.