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

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 ≲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}≲0.5  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}∼2-5  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.