Near-Infrared Microlensing of Stars by the Supermassive Black Hole in the Galactic Center

摘要

We investigate microlensing amplification of faint stars in the dense stellar cluster in the Galactic center by the supermassive black hole, which is thought to coincide with the radio source Sgr A*. Such amplification events would appear very close to the position of Sgr A* and could be observed, in principle, during the monitoring of stellar proper motions in the Galactic center. We use observations of the near-infrared K-band (2.2 μm) luminosity function in the Galactic center and in Baade's window, as well as stellar population synthesis computations, to construct empirical and theoretical K luminosity function models for the inner 300 pc of the Galaxy. These, together with the observed dynamical properties of the central cluster and inner bulge, are used to compute the rates of microlensing events that amplify stars with different intrinsic luminosities above specified detection thresholds. We present computations of the lensing rates as functions of the event durations, which range from several weeks to a few years, for detection thresholds ranging from K0 = 16 to 19 mag. We find that events with durations shorter than a few months dominate the lensing rate because of the very high stellar densities and velocities very near the black hole, where the effective lens size is small. For the current detection limit of K0 = 17 mag, the total microlensing rate is 3 × 10-3 yr-1. The rate of events with durations ≥1 yr is 1 × 10-3 yr-1. The median value of the peak amplification for short events is ΔK ~ 0.75 mag above the detection threshold and is only weakly dependent on K0. Long events are rarer and are associated with more distant stars, stars at the low-velocity tail of the velocity distribution or stars that cross closer to the line of sight to Sgr A*. Therefore, the median peak amplifications of long events are larger and attain values ΔK ~ 1.5 mag above the threshold. Recent proper-motion studies of stars in the Galactic center have revealed the possible presence of one or two variable K-band sources very close to, or coincident with, the position of Sgr A*. These sources may have attained peak brightnesses of K ≈ 15 mag, about 1.5-2 mag above the observational detection limits, and appear to have varied on a timescale of ~1 yr. This behavior is consistent with long-duration microlensing amplification of faint stars by the central black hole. However, we estimate that the probability that a single such event could have been detected during the course of the recent proper-motion monitoring campaigns is ~0.5%. A 10-fold improvement in the detection limit and 10 yr of monthly monitoring could increase the total detection probability to ~20%.