Do the sources of the 511 keV excess explain the anomalous CMZ ionization?

The anomalous rate of molecules ionization observed at the Central Molecular zone (CMZ) challenges known mechanisms of ionization observed in molecular clouds across the Galaxy, due to the exceptionally high levels of ionization measured (orders of magnitude above what cosmic rays can explain) and its uniform spatial distribution within the CMZ. Recent studies suggest that the source of the $511$~keV excess can be correlated with this anomalous ionization rate or contribute significantly to the ionization in the Galactic Centre (GC). One of the leading hypotheses attributes the $511$~keV signal to positron injection from radionuclides or pulsars distributed following the stellar bulge, which is rather flat around the GC and, hence, could help explaining the uniform ionization profile. In this work, we investigate whether such a population of sources, injecting MeV positrons at rates consistent with the $511$~keV observations, can account for the ionization levels and distribution observed in the CMZ. Our results indicate that positron injection alone falls short at explaining the anomaly, although their expected ionization is larger than expected from any previously studied candidates.