$φ$-Dwarfs: White Dwarfs probe Quadratically Coupled Scalars

TL;DR

The paper studies ultralight spin-0 fields with quadratic couplings to SM fermions and shows that white dwarfs can source these scalars, altering fermion masses and potentially creating a new ground state of matter. By deriving the effective EOS modifications in the negligible-gradient limit and solving the TOV equations, the authors predict observable features in the white-dwarf mass-radius relation, including a forbidden radius gap and distinct shape distortions, which depend on whether electrons or nucleons couple to the scalar. They develop an EFT framework with quadratic couplings, address quantum corrections, and systematically map the allowed and excluded regions of parameter space against precise WD data (Sirius B, Procyon B) and the WD population, while comparing to axion benchmarks and laboratory constraints. The results show that WD observations provide strong, largely assumption-free constraints on a broad class of ultralight scalars, offering complementary coverage to laboratory searches and to astrophysical probes in neutron stars and black holes.

Abstract

We study ultralight scalar fields with quadratic couplings to Standard-Model fermions and derive strong constraints from white-dwarf mass-radius data. Such couplings source scalar profiles inside compact stars, shift fermion masses, and can produce a new ground state of matter. We analyze couplings to electrons and to nucleons, incorporating composition and finite-temperature effects in white dwarf structure and equations of state. We identify two robust observables: (i) forbidden gaps - ranges of radii with no stable configurations - and (ii) characteristic shape distortions that drive white dwarf masses toward the Chandrasekhar limit (electron couplings) or shift the maximum mass (nucleon couplings). Confronting these predictions with precise measurements for Sirius B and Procyon B, together with the global white dwarf population, excludes large regions of unexplored parameter space and extends earlier QCD-axion-specific bounds to a broader class of scalar theories. Our stellar constraints rely only on sourcing and do not assume the scalar constitutes dark matter; where mass reductions are small, precision laboratory searches remain competitive. White-dwarf astrophysics thus provides a powerful, largely assumption-minimal probe of ultralight, quadratically coupled scalars.

Figures (23)

• Figure 1: Generation of higher order scalar fermion couplings due to a quartic scalar self-interaction
• Figure 2: Fermion Loop contribution to the scalar mass
• Figure 3: Radiative generation of additional interactions. Left: A single electron loop converts the primary $\phi^2\bar{\psi}_e\psi_e$ vertex into a one‑loop coupling to photons. Right: Inserting an extra photon rung yields a two‑loop diagram that induces a coupling to protons.
• Figure 4: Mass–radius relation for white dwarfs in the free Fermi‑gas model with a radiative, He‑dominated envelope. The gray band shows the expected spread of the mass-radius curve, obtained by varying the composition from Helium/Carbon ($Y=2$), to Iron ($Y=2.15$), as well as the central temperature from $T_0 = 0$ up to $T_0=e8K$. Colored curves illustrate specific choices to isolate these effects: warmer cores (blue $\to$ orange) push the high‑radius portion of the curve to larger masses, while a higher neutron excess (dashed vs. solid) lowers the maximum mass at large radii. Observed white dwarf mass-radius data is shown in blue B_dard_2017tremblay_gaia_20162018MNRAS.479.1612JBond_2015Bond_201710.1093/mnras/stx1522Brown_2020. The two closest white dwarfs, Sirius B and Procyon B, are highlighted in red (Bond_2015Bond_2017). Note that the errors on mass and radius measurements of those nearby stars are too small to be visible in the plot.
• Figure 5: Energy per particle with (blue and orange) and without (black) a light, sourced scalar field. The lower value of $n_c$ for the new ground state (blue) compared to that of the phase transition (orange) originates from a different choice of the scalar potential, in particular, a smaller $c_{m_\psi}$ for the new ground state. Dashed segments mark unstable regions ($p<0$). On the new ground state curve (blue), we also distinguish the metastable and stable parts.