Phenomenological constraints on accretion of non-annihilating dark matter on the PSR B1257+12 pulsar from orbital dynamics of its planets

TL;DR

This paper derives analytical constraints on non-annihilating dark matter accretion onto pulsars by examining its effects on pulsar timing and planetary orbital dynamics, applied specifically to PSR B1257+12.

Contribution

It provides the first analytical framework linking dark matter accretion rates to observable pulsar timing and orbital changes, constraining dark matter properties.

Findings

Constraints on dark matter accretion rates derived from pulsar timing.

Limits on dark matter density around PSR B1257+12.

Analytical expressions relating mass variation to orbital changes.

Abstract

We analytically compute the effects that a mass variation rate \dot M/M of a pulsar may have on the changes \Delta\tau in the times of arrival of its pulses due to test particle companions, and on their orbital dynamics. We apply our results to the planetary system of the PSR B1257+12 pulsar, located in the Galaxy at 600 pc from us, to phenomenologically constrain a putative accretion of non-annihilating dark matter on the hosting neutron star. (Abridged)