Updated Constraints on the Injection Energy of Positrons Generating the Galactic 511 keV $\gamma$-ray line

Abstract

Even 50 years after the discovery of a positron annihilation line from the inner Galaxy, no class of astrophysical sources has emerged as a definitive explanation for both the emission morphology and flux. Positrons produced by dark matter annihilation or decay have been proposed, but the mass of any such candidate is constrained by continuum $\gamma$-ray emission at energies $>511$ keV. Earlier analyses have claimed that this emission requires that the positrons have kinetic energies less than a few MeV at injection, disfavoring both much of the dark matter parameter space and many potential compact astrophysical source classes such as pulsars. However, these constraints were not based on a full forward model of the absolute flux of the $\gamma$-ray line and continuum data, and did not marginalize over uncertainties about the relative angular distributions of the line and continuum. Here we describe an improved analysis that overcomes these limitations, and show that constraints on the injection energy are much weaker than previously claimed; even under conservative assumptions the data are consistent with initial energies up to $\sim 110$ MeV from INTEGRAL/SPI data alone, and up to $\sim 55$ MeV when including COMPTEL and EGRET data, subject to cross-normalization between them and INTEGRAL.