Revisiting Stellar Orbits and the Sgr A$^*$ Quadrupole Moment

TL;DR

This paper explores how to test the no-hair theorem at the Milky Way's center using stellar orbit precession, addressing observational challenges, stellar spin effects, and noise mitigation strategies for measuring Sgr A$^*$'s quadrupole moment.

Contribution

It demonstrates that the no-hair theorem can be tested with a single star's orbit over half a period and develops methods to mitigate various noise sources affecting quadrupole measurements.

Findings

Precession measurements over half an orbit are sufficient for testing the no-hair theorem.

Stellar spin can introduce errors of a few percentage points in quadrupole measurements.

Optimal observable combinations can reduce noise from mass precession, stellar spin, and transient quadrupole moments.

Abstract

The "no-hair" theorem can, in principle, be tested at the center of the Milky Way by measuring the spin and the quadrupole moment of Sgr A$^*$ with the orbital precession of S-stars, measured over their full periods. Contrary to the original method, we show why it is possible to test the no-hair theorem using observations from only a single star, by measuring precession angles over a half-orbit. There are observational and theoretical reasons to expect S-stars to spin rapidly, and we have quantified the effect of stellar spin, via spin-curvature coupling (the leading-order manifestation of the Mathisson-Papapetrou-Dixon equations), on future quadrupole measurements. We find that they will typically suffer from errors of order a few percentage points, but for some orbital parameters, the error can be much higher. We re-examine the more general problem of astrophysical noise sources that may impede future quadrupole measurements, and find that a judicious choice of measurable precession angles can often eliminate individual noise sources. We have derived optimal combinations of observables to eliminate the large noise source of mass precession, the novel noise of spin-curvature coupling due to stellar spin, and the more complicated noise source arising from transient quadrupole moments in the stellar potential.