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The center of the Milky Way hosts a massive black hole. The observational evidence for its existence is overwhelming. The compact radio source Sgr A* has been associated with a black hole since its discovery. In the last decade, high-resolution, near-infrared measurements of individual stellar orbits in the innermost region of the Galactic Center have shown that at the position of Sgr A* a highly concentrated mass of 4 x 10^6 M_sun is located. Assuming that general relativity is correct, the conclusion that Sgr A* is a massive black hole is inevitable. Without doubt this is the most important application of stellar orbits in the Galactic Center. Here, we discuss the possibilities going beyond the mass measurement offered by monitoring these orbits. They are an extremely useful tool for many scientific questions, such as a geometric distance estimate to the Galactic Center or the puzzle, how these stars reached their current orbits. Future improvements in the instrumentation will open up the route to testing relativistic effects in the gravitational potential of the black hole, allowing to take full advantage of this unique laboratory for celestial mechanics.
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Using 25 years of data from uninterrupted monitoring of stellar orbits in the Galactic Center, we present an update of the main results from this unique data set: A measurement of mass of and distance to SgrA*. Our progress is not only due to the eight year increase in time base, but also due to the improved definition of the coordinate system. The star S2 continues to yield the best constraints on the mass of and distance to SgrA*; the statistical errors of 0.13 x 10^6 M_sun and 0.12 kpc have halved compared to the previous study. The S2 orbit fit is robust and does not need any prior information. Using coordinate system priors, also the star S1 yields tight constraints on mass and distance. For a combined orbit fit, we use 17 stars, which yields our current best estimates for mass and distance: M = 4.28 +/- 0.10|stat. +/. 0.21|sys. x 10^6 M_sun and R_0 = 8.32 +/- 0.07|stat. +/- 0.14|sys. kpc. These numbers are in agreement with the recent determination of R_0 from the statistical cluster parallax. The positions of the mass, of the near-infrared flares from SgrA* and of the radio source SgrA* agree to within 1mas. In total, we have determined orbits for 40 stars so far, a sample which consists of 32 stars with randomly oriented orbits and a thermal eccentricity distribution, plus eight stars for which we can explicitly show that they are members of the clockwise disk of young stars, and which have lower eccentricity orbits.
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.
The gravitational potentials of realistic galaxy models are in general non-integrable, in the sense that they admit orbits that do not have three independent isolating integrals of motion and are therefore chaotic. However, if chaotic orbits are a small minority in a stellar system, it is expected that they have negligible impact on the main dynamical properties of the system. In this paper we address the question of quantifying the importance of chaotic orbits in a stellar system, focusing, for simplicity, on axisymmetric systems. Chaotic orbits have been found in essentially all (non-Stackel) axisymmetric gravitational potentials in which they have been looked for. Based on the analysis of the surfaces of section, we add new examples to those in the literature, finding chaotic orbits, as well as resonantly trapped orbits among regular orbits, in Miyamoto-Nagai, flattened logarithmic and shifted Plummer axisymmetric potentials. We define the fractional contributions in mass of chaotic ($xi_{rm c}$) and resonantly trapped ($xi_{rm t}$) orbits to a stellar system of given distribution function, which are very useful quantities, for instance in the study of the dispersal of stellar streams of galaxy satellites. As a case study, we measure $xi_{rm c}$ and $xi_{rm t}$ in two axisymmetric stellar systems obtained by populating flattened logarithmic potentials with the Evans ergodic distribution function, finding $xi_{rm c}sim 10^{-4}-10^{-3}$ and $xi_{rm t}sim 10^{-2}-10^{-1}$.
We show that with a Next Generation Large Telescope one can detect the accelerated motions of ~100 stars orbiting the massive black hole at the Galactic center. The positions and velocities of these stars will be measured to astrometric and spectroscopic precision several times better than currently attainable enabling detailed measurements of the gravitational potential in the neighborhood of the massive black hole. We show that the monitoring of stellar motions with such a telescopes enables: (1) a measurement of the Galactic center distance R_0 to better than 0.1% accuracy, (2) a measurement of the extended matter distribution near the black hole, including that of the exotic dark matter, (3) a detection of general relativistic effects due to the black hole including the prograde precession of stars and possibly the black hole spin, and (4) a detection of gravitational encounters between monitored stars and stellar remnants that accumulate near the Galactic center. Such encounters probe the mass function of the remnants.
Using the astrometry from the ESAs Gaia mission, previous works have shown that the Milky Way stellar halo is dominated by metal-rich stars on highly eccentric orbits. To shed light on the nature of this prominent halo component, we have analysed 28 Galaxy analogues in the Auriga suite of cosmological hydrodynamics zoom-in simulations. Some three quarters of the Auriga galaxies contain significant components with high radial velocity anisotropy, beta > 0.6. However, only in one third of the hosts do the high-beta stars contribute significantly to the accreted stellar halo overall, similar to what is observed in the Milky Way. For this particular subset we reveal the origin of the dominant stellar halo component with high metallicity, [Fe/H]~-1, and high orbital anisotropy, beta>0.8, by tracing their stars back to the epoch of accretion. It appears that, typically, these stars come from a single dwarf galaxy with a stellar mass of order of 10^9-10^10 Msol that merged around 6-10 Gyr ago, causing a sharp increase in the halo mass. Our study therefore establishes a firm link between the excess of radially anisotropic stellar debris in the Milky Way halo and an ancient head-on collision between the young Milky Way and a massive dwarf galaxy
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