Astrophys. J., 809, 127 (2015/August-3)
On testing the Kerr metric of the massive black hole in the Galactic Center via stellar orbital motion: full general relativistic treatment.
ZHANG F., LU Y. and YU Q.
Abstract (from CDS):
S-stars, discovered in the vicinity of the massive black hole (MBH) in the Galactic center (GC), are anticipated to provide unique dynamical constraints on the MBH spin and metric, in addition to the mass. In this paper, we develop a fast full general relativistic method to simultaneously constrain the MBH mass, spin, and spin direction by considering both the orbital motion of a star close to the GC MBH and the propagation of photons from the star to a distant observer. Based on the current observations and dynamical model predictions, we assume six example stars with different semimajor axes () and eccentricities () and numerically calculate their projected trajectories in the sky plane and redshift curves. Two of those stars are set to have orbital configurations similar to that of S0-2/S2 and S0-102. We find that the spin-induced effects on the projected trajectory and redshift curve of a given star, including the leading term by the Lense-Thirring precession and the frame dragging, and the high-order precession due to the quadruple moment, depend on both the absolute value and the direction of the spin. The maximum values of the spin-induced position displacement and the redshift differences of the star over a full orbit may differ by a factor of several to more than one order of magnitude for two cases with significantly different spin directions. The dependence patterns of the position displacements and redshift differences on the spin direction are different, and thus the position and the redshift data are complementary for constraining the MBH spin and its direction. Adopting the Markov Chain Monte Carlo fitting technique, we illustrate that the spin of the GC MBH is likely to be well constrained by using the motion of S0-2/S2 over a period of ∼45 years if the spin is close to one and if the astrometric and spectroscopic precisions can be as high as, which is expected to be realized by future facilities like GRAVITY on the Very Large Telescope Interferometer, the thirty meter telescope, and the European extremely large telescope. If and can be further improved by a factor of several, the MBH spin can be well constrained by monitoring S0-2/S2 over a period of ∼15 years. In the mean time, the distance from the sun to the GC and the MBH mass can also be constrained to an unprecedented accuracy (0.01%-0.1%). If there exists a star with a semimajor axis that is a few times smaller, and eccentricity larger, than those of S0-2/S2, the MBH spin and its direction can be constrained with high accuracy over a period of years by future facilities, even if the spin is only moderately large. Our results suggest that long-term monitoring of the motions of stars in the vicinity of the GC MBH by the next generation facilities is likely to provide a dynamical test, for the first time, to the spin and metric of the GC MBH.
black hole physics - Galaxy: center - Galaxy: nucleus - gravitation - relativistic processes - stars: kinematics and dynamics
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