# Constraining light fermionic dark matter with binary pulsars

## TL;DR

This paper investigates how binary pulsar systems can be used to detect or constrain light fermionic dark matter by analyzing orbital period changes caused by dynamical friction in a dark matter background.

## Contribution

It introduces a method to constrain light fermionic dark matter properties using orbital period measurements of binary pulsars, especially in extragalactic systems.

## Key findings

- Orbital period decay is more sensitive to fermions with masses >50 eV.
- Large orbital period binaries (P_b > 100 days) show larger decay effects.
- Current pulsar data constrain fermion mass to less than about 1 keV.

## Abstract

A binary system embedded in a Dark Matter (DM) background may experience a change in its orbital period due to dynamical friction as the binary moves through a wind of DM particles. We compute such a perturbative effect on the binary evolution considering that DM is constituted of degenerate gas of free fermions. The analysis point out that the secular change of the orbital period is more sensitive, and likely measurable, to degenerate fermions with masses $\gtrsim50$ eV, depending slightly, but still being distinguishable, on the binary star configuration (e.g. NS-NS, NS-WD and WD-WD). Interestingly, we find that NS-NS binary systems with large orbital periods, $P_{b}\gtrsim100$ days, experience larger orbital period decays. We also show that this effect is clearly increased, under the former conditions, in binaries orbiting small DM halos, which correspond to extragalactic pulsars. This situation represents the best astrophysical scenario to test such effects of light fermionic DM. We use some available measurements of the orbital period time-derivative for long-period binaries in the Milky-Way to quantify more realistically this effect. For instance, measurements of the J1713+0747 pulsar set an upper bound on the fermion mass of $m_{f}\lesssim 1$ keV. This bound can be considerably improved by using pulsar timing observations of extragalactic pulsars. Under this perspective, high precision of timing pulsar observations will reveal whether DM dynamical friction effect may be tested with the upcoming generation of surveys leading to the possibility of constraining more strongly the properties of light fermionic DM.