Stellar limits on scalars from electron-nucleus bremsstrahlung

We revisit stellar energy-loss bounds on the Yukawa couplings $g_{\rm B,L}$ of baryophilic and leptophilic scalars $\phi$. The white-dwarf luminosity function yields $g_{\rm B}\lesssim 7 \times 10^{-13}$ and $g_{\rm L}\lesssim 4 \times 10^{-16}$, based on bremsstrahlung from ${}^{12}{\rm C}$ and ${}^{16}{\rm O}$ collisions with electrons. In models with a Higgs portal, this also implies a bound on the scalar-Higgs mixing angle $\sin \theta \lesssim 2 \times 10^{-10}$. Our new bounds apply for $m_\phi\lesssim {\rm 1~keV}$ and are among the most restrictive ones, whereas for $m_\phi\lesssim 0.5\,{\rm eV}$ long-range force measurements dominate. Besides a detailed calculation of the bremsstrahlung rate for degenerate and semi-relativistic electrons, we prove with a simple argument that non-relativistic bremsstrahlung by the heavy partner is suppressed relative to that by the light one by their squared-mass ratio. This large reduction was overlooked in previous much stronger bounds on $g_{\rm B}$. In an Appendix, we provide fitting formulas (few percent precision) for the bremsstrahlung emission of baryophilic and leptophilic scalars as well as axions for white-dwarf conditions, i.e., degenerate, semi-relativistic electrons and ion-ion correlations in the ``liquid'' phase.