  We show that the pulsar mass depends on the environment, and that it
decreases going towards the center of the Milky Way. This is due to two
combined effects, the capture and accumulation of self-interacting,
non-annihilating dark matter by pulsars, and the increase of the dark matter
density going towards the galactic center. We show that mass decrease depends
both on the density profile of dark matter, steeper profiles producing a faster
and larger decrease of the pulsar mass, and on the strength of
self-interaction. Once future observations will provide the pulsar mass in a
dark matter rich environment, close to the galactic center, the present result
will be able to put constraints on the characteristics of our Galaxy halo dark
matter profile, on the nature of dark matter, namely on its annihilating or
non-annihilating nature, on its strength of self-interaction, and on the
particle mass.
