How far do Galactic positrons travel before annihilating?

In plain words

If positrons made in the disk can drift into the bulge before annihilating, ordinary disk sources could explain the bulge glow.

Precise statement

Determine the distribution of propagation distances of positrons born at energies below a few MeV in the warm, hot and neutral phases of the interstellar medium, with slowing-down times of $\sim 10^{5}\text{ to }10^{7}\,\mathrm{yr}$ and realistic magnetic turbulence. Answer: the fraction of disk-born positrons that annihilate in the bulge, compared with the observed bulge-to-disk ratio and line width.

What would settle it

Transport calculations with measured interstellar turbulence spectra, validated against the line width and positronium fraction.

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