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 (∼106~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 104~K. Thus, most of the
positrons annihilate only after the gas has cooled down to ∼105~K,
giving rise to annihilation emission characteristic of a warm, ionized ISM.Comment: 19 pages, 15 figures. Accepted by MNRA