Effect of positron-alkali metal atom interactions in the diffuse interstellar medium

In the Milky Way galaxy, positrons, which are responsible for the diffuse 511 keV gamma ray emission observed by space-based gamma ray observatories, are thought to annihilate predominantly through charge exchange interactions with neutral hydrogen. These charge exchange interactions can only take place if positrons have energies greater than 6.8 eV, the minimum energy required to liberate the electron bound to the hydrogen atom and then form positronium, a short-lived bound state composed of a positron-electron pair. Here we demonstrate the importance of positron interactions with neutral alkali metals in the warm interstellar medium (ISM). Positrons may undergo charge exchange with these atoms at any energy. In particular, we show that including positron interactions with sodium at solar abundance in the warm ISM can significantly reduce the annihilation timescale of positrons with energies below 6.8 eV by at least an order of magnitude. We show that including these interactions in our understanding of positron annihilation in the Milky Way rules out the idea that the number of positrons in the Galactic ISM could be maintained in steady state by injection events occurring at a typical periodicity $>\mathrm{Myr}$.

Figure 1

Positronium formation and charge-exchange (CX) cross section for positron annihilation through various channels as a function of incident positron energy. Hydrogen and helium CX cross sections based on fits to available data, radiative recombination with free electrons from R. Sutherland [53] lithium and sodium CX cross sections from [51] and potassium CX cross sections from [52]. Direct annihilation cross sections for positron interactions with free and bound electrons are shown in red. The black dashed line shows the average energy of positrons that have thermalized in the WPIM.

Figure 2

Annihilation timescale for thermalized positrons as a function of positron energy. Including the effect of positron interactions with alkali metal atoms, even at solar metallicity, substantially decreases the annihilation timescale for positrons that thermalize with energies $<6.8\mathrm{eV}$. The black dashed line shows the average energy of positrons that have thermalized in the WPIM.

Figure 3

Comparison of annihilation timescales for thermalized positrons in the HIM (top left), WIM (top right), WNM (bottom left) and WPIM (bottom right). Vertical dashed lines indicate the average energy of positrons thermalizing in each phase. Horizontal lines show the energy loss timescale for MeV positrons in each phase. In the case of the HIM (top left), the energy loss timescale for MeV positrons is $\sim {10}^{11}\mathrm{yr}$