Updated Constraints on Self-Interacting Dark Matter from Supernova 1987A
  We revisit SN1987A constraints on light, hidden sector gauge bosons ("dark
photons") that are coupled to the standard model through kinetic mixing with
the photon. These constraints are realized because excessive bremsstrahlung
radiation of the dark photon can lead to rapid cooling of the SN1987A
progenitor core, in contradiction to the observed neutrinos from that event.
The models we consider are of interest as phenomenological models of strongly
self-interacting dark matter. We clarify several possible ambiguities in the
literature and identify errors in prior analyses. We find constraints on the
dark photon mixing parameter that are in rough agreement with the early
estimates of Dent et al., but only because significant errors in their analyses
fortuitously canceled. Our constraints are in good agreement with subsequent
analyses by Rrapaj & Reddy and Hardy & Lasenby. We estimate the dark photon
bremsstrahlung rate using one-pion exchange (OPE), while Rrapaj & Reddy use a
soft radiation approximation (SRA) to exploit measured nuclear scattering cross
sections. We find that the differences between mixing parameter constraints
obtained through the OPE approximation or the SRA approximation are roughly a
factor of $\sim 2-3$. Hardy & Laseby include plasma effects in their
calculations finding significantly weaker constraints on dark photon mixing for
dark photon masses below $\sim 10\, \mathrm{MeV}$. We do not consider plasma
effects. Lastly, we point out that the properties of the SN1987A progenitor
core remain somewhat uncertain and that this uncertainty alone causes
uncertainty of at least a factor of $\sim 2-3$ in the excluded values of the
dark photon mixing parameter. Further refinement of these estimates is
unwarranted until either the interior of the SN1987A progenitor is more well
understood or additional, large, and heretofore neglected effects, are
identified.
