Positron annihilation spectrum from the Galactic Centre region observed by SPI/INTEGRAL, revisited: annihilation in a cooling ISM?

We analyse SPI/INTEGRAL data on the 511 keV line from the Galactic Centre, accumulated over ~6 years of observations. We decompose the X-ray and soft gamma-ray emission of the central part of the Milky Way into a relatively compact "Bulge" and a more extended "Disk" components and report their spectral properties. The Bulge component shows a prominent 511 keV line and essentially no flux at 1.8 MeV, while the Disk component on the contrary contains a prominent 1.8 MeV line and a very weak annihilation line. We show that the spectral shape of the annihilation radiation (the narrow 511 keV line and the associated othro-positronium continuum) is surprisingly well described by a model of annihilation of hot positrons in a radiatively cooling interstellar medium (ISM). The model assumes that positrons are initially injected into a hot ($\sim 10^6$~K), volume filling ISM, which is allowed to freely cool via radiative losses. The annihilation time in such a medium is longer than the cooling time for temperatures higher than a few $10^{4}$~K. Thus, most of the positrons annihilate only after the gas has cooled down to $\sim 10^5$~K, giving rise to annihilation emission characteristic of a warm, ionized ISM.