Probing the spinning of the massive black hole in the Galactic Center via pulsar timing: A Full Relativistic Treatment

TL;DR

This study demonstrates that pulsar timing near the Galactic Center's massive black hole, modeled with full relativistic treatment, can tightly constrain the black hole's spin and other parameters within a decade, especially with combined timing and astrometric data.

Contribution

It provides a full relativistic framework for pulsar timing analysis around the MBH, showing the potential to accurately measure the black hole's spin and other properties using upcoming pulsar observations.

Findings

Relativistic signals in pulsar timing are significantly larger than measurement errors.

Constraints on MBH spin magnitude and orientation can reach high precision within 8 years.

Combining timing and astrometric data improves parameter constraints substantially.

Abstract

Pulsars around the Massive Black Hole (MBH) in the Galactic Center (GC) are expected to be revealed by the incoming facilities (e.g., the Square Kilometre Array). Under a full relativistic framework with the pulsar approximated as a test particle, we investigate the constraints on the spinning of the MBH by monitoring the timing of surrounding pulsars. For GC pulsars orbiting closely around the MBH (e.g., $\lesssim1000$AU), we find that full relativistic treatment in modeling accurately their timing signals can be necessary, as the relativistic signals are orders of magnitude larger than the time of arrival measurement accuracies. Although usually there are near-degeneracies among MBH spin parameters, the constraints on the spinning of the MBH are still very tight. By continuously monitoring a normal pulsar in orbits with a period of $\sim2.6$yr and an eccentricity of $0.3-0.9$ under timing precision of $1-5$ms, within $\sim 8$yr the spin magnitude and the orientations of the GC MBH can be constrained with $2\sigma$ error of $10^{-3}-10^{-2}$ and $10^{-1}-10^\circ$, respectively. Even for pulsars in orbits similar to the detected star S2/S0-2 or S0-102, we find that the spinning of the MBH can still be constrained within $4-8$yr, with the most significant constraints provided near the pericenter passage. If the proper motion of the pulsars with astrometric accuracy of $10\mu$as can also be collected along with the timing measurement, then the position, velocity, mass and the distance to the Solar System of the MBH can be constrained about $\sim10\mu$as, $\sim1\mu$as$/$yr, $\sim 10 M_\odot$ and $\sim1$pc, respectively.