Measuring Distance and Properties of the Milky Way's Central Supermassive Black Hole with Stellar Orbits

TL;DR

This work uses 1995–2007 Keck astrometry and radial velocities of S0-2 to measure the Milky Way's central black hole mass and the Sun–Galactic center distance. A 13-parameter Keplerian orbit model is fitted to 38 astrometric points and 5 radial velocities, with a Monte Carlo approach to quantify uncertainties and parameter degeneracies. The results yield $M_{bh}=4.1\pm0.6\times10^{6} M_{\odot}$ and $R_0=8.0\pm0.6$ kpc when line-of-sight BH motion is allowed to vary, and $M_{bh}=4.5\pm0.4\times10^{6} M_{\odot}$ and $R_0=8.4\pm0.4$ kpc if $V_z=0$ is assumed; a robust upper limit on an extended mass within 0.01 pc is $M_{ext}(<0.01\mathrm{pc})\lesssim(3-4)\times10^{5} M_{\odot}$. The study identifies key systematics—source confusion, BH motion relative to the reference frame, and bias in faint sources like SgrA*-IR—that must be accounted for in orbital fits. These precise measurements support consistency with other methods for the Galactic constants and imply an updated placement of the Milky Way on the $M_{bh}-\sigma$ relation, with important implications for relativistic effects and the dynamical environment near the BH.

Abstract

We report new precision measurements of the properties of our Galaxy's supermassive black hole. Based on astrometric (1995-2007) and radial velocity (2000-2007) measurements from the W. M. Keck 10-meter telescopes, a fully unconstrained Keplerian orbit for the short period star S0-2 provides values for Ro of 8.0+-0.6 kpc, M_bh of 4.1+-0.6x10^6 Mo, and the black hole's radial velocity, which is consistent with zero with 30 km/s uncertainty. If the black hole is assumed to be at rest with respect to the Galaxy, we can further constrain the fit and obtain Ro = 8.4+-0.4 kpc and M_bh = 4.5+-0.4x10^6 Mo. More complex models constrain the extended dark mass distribution to be less than 3-4x10^5 Mo within 0.01 pc, ~100x higher than predictions from stellar and stellar remnant models. For all models, we identify transient astrometric shifts from source confusion and the assumptions regarding the black hole's radial motion as previously unrecognized limitations on orbital accuracy and the usefulness of fainter stars. Future astrometric and RV observations will remedy these effects. Our estimates of Ro and the Galaxy's local rotation speed, which it is derived from combining Ro with the apparent proper motion of Sgr A*, (theta0 = 229+-18 km/s), are compatible with measurements made using other methods. The increased black hole mass found in this study, compared to that determined using projected mass estimators, implies a longer period for the innermost stable orbit, longer resonant relaxation timescales for stars in the vicinity of the black hole and a better agreement with the M_bh-sigma relation.