Monitoring stellar orbits around the Massive Black Hole in the Galactic Center

TL;DR

The Galactic Center is probed through 16 years of precise stellar astrometry and spectroscopy to test whether a single point-mass MBH governs stellar orbits. By refining cross-instrument astrometric frames and incorporating relativistic and extended-mass modeling, the study delivers a tight measurement of the MBH mass and the distance to the GC, with R$_0$ ≈ 8.33 kpc and M$_ ext{MBH}$ ≈ 4.3 × 10^6 M$_$ (scaling ∝ R$_0^{2.19}$). The analysis confirms six late-type stars in close orbits and six young stars in the clockwise disk, while most other orbits appear randomly oriented; it also places stringent limits on any extended mass within the S2 orbit (η ≲ 0.04 at 1σ). These results solidify the Schwarzschild–Keplerian description of GC dynamics, constrain the possible dark-matter/dark-cluster content, and pave the way for future tests of general relativity with closer pericenter passages. The work demonstrates the critical role of robust error budgeting and cross-epoch calibration in exploiting long-baseline observations for Galactic-scale gravitational tests.

Abstract

We present the results of 16 years of monitoring stellar orbits around the massive black hole in center of the Milky Way using high resolution NIR techniques. This work refines our previous analysis mainly by greatly improving the definition of the coordinate system, which reaches a long-term astrometric accuracy of 300 microarcsecond, and by investigating in detail the individual systematic error contributions. The combination of a long time baseline and the excellent astrometric accuracy of adaptive optics data allow us to determine orbits of 28 stars, including the star S2, which has completed a full revolution since our monitoring began. Our main results are: all stellar orbits are fit extremely well by a single point mass potential to within the astrometric uncertainties, which are now 6 times better than in previous studies. The central object mass is (4.31 +- 0.06|stat +- 0.36|R0) * 10^6 M_sun where the fractional statistical error of 1.5 percent is nearly independent from R0 and the main uncertainty is due to the uncertainty in R0. Our current best estimate for the distance to the Galactic Center is R0 = 8.33 +- 0.35 kpc. The dominant errors in this value is systematic. The mass scales with distance as (3.95 +- 0.06) * 10^6 M_sun * (R0/8kpc)^2.19. The orientations of orbital angular momenta for stars in the central arcsecond are random. We identify six of the stars with orbital solutions as late type stars, and six early-type stars as members of the clockwise rotating disk system, as was previously proposed. We constrain the extended dark mass enclosed between the pericenter and apocenter of S2 at less than 0.066, at the 99% confidence level, of the mass of Sgr A*. This is two orders of magnitudes larger than what one would expect from other theoretical and observational estimates.

Figures (21)

• Figure 1: Finding chart of the S-star cluster. This figure is based on a natural guide star adaptive optics image obtained as part of this study, using NACO at UT4 (Yepun) of the VLT on July 20, 2007 in the H-band. The original image with a FWHM of $\approx 75\,$mas was deconvolved with the Lucy-Richardson algorithm and beam restored with a Gaussian beam with FWHM$\,=2\,$pix=$26.5\,$mas. Stars as faint as $m_H=19.2$ (corresponding roughly to $m_K=17.7$) are detected at the $5\sigma$ level. Only stars that are unambiguously identified in several images have designated names, ranging from S1 to S112. Blue labels indicate early-type stars, red labels late-type stars. Stars with unknown spectral type are labelled in black. At the position of Sgr A* some light is seen, which could be either due to Sgr A* itself or due to a faint, so far unrecognized star being confused with Sgr A*.
• Figure 2: The open symbols mark the sample of 91 reference stars which are used to define the astrometric frame for the S-stars. The underlying image was obtained on April 3, 2007 in H-band, deconvolved and beam-restored with a beam of $2\,$pix. North is up, East is left. The field is 9.3"$\times\,$9.3".
• Figure 3: The statistical errors of the pixel positions for the NACO K-band data as a function of arbitrary detector units of flux. The thin lines show the respective error model for each epoch; the thick dashed line is the mean for the data. The mean has a floor at $99\,\mu$as, the median (not shown) at $84\,\mu$as.
• Figure 4: The measured distribution of the statistical errors of the pixel positions for the NACO data. The characteristic statistical error (defined as the peak of the distribution) is $108\,\mu$as, the systematic error terms have to be added to this to come to a fair estimate of the true uncertainty.
• Figure 5: Determination of residual image distortions for the NACO H-band data from September 8, 2007, $13\,$mas/pix. The histograms show the differences of detector distances for a set of bona fide stars as measured in the four pointing positions with a dither offset of 7". Left: Using the raw frames. Middle: After application of a distortion model, Right: After transforming the raw positions with a cubic transformation onto a common grid. The corresponding 1D coordinate errors are determined from Gaussian fits to the distributions and are quoted at the top of each panel.