Prospects for constraining the spin of the massive black hole at the Galactic center via the relativistic motion of a surrounding star

TL;DR

This study explores how precise measurements of a star's relativistic orbit around the Galactic center's black hole can constrain the black hole's spin, revealing potential for future observational tests of black hole properties.

Contribution

It provides a detailed analysis of the observational requirements and orbital parameters needed to accurately determine the black hole's spin using relativistic stellar motion simulations.

Findings

Astrometric precision has a greater impact on spin constraints than velocity precision.

High-precision measurements can constrain the black hole spin with errors less than 0.1.

Stars with semimajor axes less than 300 AU and eccentricities above 0.95 are ideal for spin measurement.

Abstract

In this paper, we investigate the quality of constraining the spin of the massive black hole (MBH) at the Galactic center (GC) by using full general relativistic simulations of the motion of a surrounding star. We obtain the dependence mapping of the spin-induced signals on any spin direction of the MBH for given example stars, which indicates the feasibility to test whether the spin direction is the same as the normal of the young stellar disk located at the GC, and, further to provide insights into the assembly history of the MBH. We demonstrate the quality of constraining the MBH spin that may be achieved, given any set of the astrometric and the redshift precisions of observational facilities. We find that in the ranges of the astrometric and the velocity precisions with 1--30$\mu$as and 0.1--10 km/s, an improvement in astrometric precision would be more effective at improving the quality of constraining the spin than an improvement in velocity precision. We obtain the parameter space of the semimajor axis and the eccentricity for the orbit of the target star that a high-precision constraint on the GC MBH spin can be obtained via the motion of the star. Our results show that the spin of the GC MBH can be constrained with 1-sigma error <~0.1 or even >~0.02 by monitoring the orbital motion of a star, if existing as expected, with semimajor axis <~300AU and eccentricity >~0.95 over a period shorter than a decade through future facilities.