Prospects for probing small-scale dark matter models with pulsars around Sagittarius A*

TL;DR

Future pulsar observations near Sagittarius A* could provide a novel way to probe small-scale dark matter distributions and test general relativity in the strong gravity environment of the Galactic Center.

Contribution

This paper develops a numerical timing model for pulsar-supermassive black hole systems and explores their potential to constrain dark matter models through pulsar timing.

Findings

Dark matter density profile near Sgr A* can be constrained to about 20%.

Pulsar timing can reveal small-scale dark matter properties.

The method is comparable to large-scale measurements but focuses on the Galactic Center.

Abstract

Future observations with next-generation large-area radio telescopes are expected to discover radio pulsars (PSRs) closely orbiting around Sagittarius~A* (Sgr~A*), the supermassive black hole (SMBH) dwelling at our Galactic Center (GC). Such a system can provide a unique laboratory for testing General Relativity (GR), as well as the astrophysics around the GC. In this paper, we provide a numerical timing model for PSR-SMBH systems based on the post-Newtonian (PN) equation of motion, and use it to explore the prospects of measuring the black hole (BH) properties with pulsar timing. We further consider the perturbation caused by the dark matter (DM) distribution around Sgr~A*, and the possibility of constraining DM models with PSR-SMBH systems. Assuming a 5-year observation of a normal pulsar in an eccentric ($e=0.8$) orbit with an orbital period $P_b = 0.5\,$yr, we find that -- with weekly recorded times of arrival (TOAs) and a timing precision of 1 ms -- the power-law index of DM density distribution near the GC can be constrained to about 20%. Such a measurement is comparable to those measurements at the Galactic length scale but can reveal small-scale properties of the DM.