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

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, $P_b\lesssim 0.5\mathrm{yr}$. 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, $P_b\sim 2-5\mathrm{yr}$, 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.

5 pages, 3 figures; accepted by PRL

References in corpus (11)

• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• The Milky Way's nuclear star cluster: Old, metal-rich, and cuspy
• Discovery of two pulsars towards the Galactic Centre
• A measurement of the Galactic plane mass density from binary pulsar accelerations
• Prospects for Constraining the Yukawa Gravity with Pulsars around Sagittarius A*
• Rotation measure variations in Galactic Centre pulsars
• Probing the vector charge of Sagittarius A* with pulsar timing
• Prospects for probing small-scale dark matter models with pulsars around Sagittarius A*
• BlackHoleCam -- Testing general relativity with pulsars orbiting Sagittarius A*

Cited by in corpus (3)

• Nethotrons: exploring the possibility of measuring relativistic spin precessions, from Earth's satellites to the Galactic Centre
• Timing Gravity with Pulsars in the Strong Field
• A survey for radio pulsars and transients in the 10 pc region around Sgr A*