Solar Constraints on Heavy Neutral Leptons with $\nu_\tau$ Mixing
The mixing of heavy neutral leptons (HNLs) with tau neutrinos remains largely unconstrained compared to their mixing with electron and muon neutrinos. In this work, we investigate the potential of solar neutrinos to improve constraints on HNL-$\nu_\tau$ mixing in the MeV mass range. Due to neutrino oscillations, the Sun is a copious source of neutrinos of all flavors, and the partial conversion of electron neutrinos into muon and tau neutrinos occurs already during their propagation through the solar interior. Tau neutrinos can produce HNLs through scattering with protons in the Sun, provided nonzero HNL-$\nu_\tau$ mixing is present. The HNLs escape the Sun and subsequently decay through the same interaction. For $\mathcal{O}(10)$ MeV HNL masses, the dominant visible decay yields electrons and positrons that can be detected by space-based solar observatories. Using data from the Solar and Heliospheric Observatory (SOHO), we search for such signals and derive constraints on the squared HNL-$\nu_\tau$ mixing matrix element, $|U_{\tau N}|^2$, reaching below the $10^{-2}$ level for HNL masses of $\sim 5$ MeV. These constraints improve upon existing terrestrial limits in this mass range by more than an order of magnitude.