Measuring the Spin of the Galactic Center Supermassive Black Hole with Two Pulsars

TL;DR

This paper proposes a novel method to measure the spin of the Galactic Center supermassive black hole using timing observations of two or more pulsars in relatively wide orbits, improving measurement precision significantly.

Contribution

It introduces a new approach for determining Sgr A*'s spin with multiple pulsars in wider orbits, extending beyond the previously considered very tight orbit scenario.

Findings

Combining two pulsars enhances spin measurement accuracy by 2-3 orders of magnitude.

The method is effective with pulsars in orbits of 2-5 years, which are more realistic to find.

Simulations show the potential to achieve sub-percent precision in spin measurement.

Abstract

As a key science project of the Square Kilometre Array (SKA), the discovery and timing observations of radio pulsars in the Galactic Center would provide high-precision measurements of the spacetime around the supermassive black hole, Sagittarius A* (Sgr A*), and initiate novel tests of general relativity. The spin of Sgr A* could be measured with a relative error of $\lesssim 1\%$ by timing one pulsar with timing precision that is achievable for the SKA. However, the real measurements depend on the discovery of a pulsar in a very compact orbit, $P_b\lesssim0.5\,{\rm yr}$. Here for the first time we propose and investigate the possibility of probing the spin of Sgr A* with two or more pulsars that are in orbits with larger orbital periods, $P_b\sim 2- 5\,{\rm yr}$, which represents a more realistic situation from population estimates. We develop a novel method for directly determining the spin of Sgr A* from the timing observables of two pulsars and it can be readily extended for combining more pulsars. With extensive mock data simulations, we show that combining a second pulsar improves the spin measurement by $2-3$ orders of magnitude in some situations, which is comparable to timing a pulsar in a very tight orbit.