Constraining the Recent Star Formation History of the Galactic Center with High Precision Astrometry

The proximity of the Galactic center has allowed for the detailed study of the environs of a supermassive black hole (SMBH). While the region is inhabited predominantly by old, late-type giants, there exists a population of ∼200 young (6 ± 2 Myr), massive (10-100 msun) stars within the central parsec. Their presence here is puzzling since the standard mode of star formation cannot proceed in the face of the strong tidal forces from the SMBH. Given their youth, the dynamics of these stars can be used to understand their origin and lend insight into star formation processes in the hostile environment surrounding a supermassive black hole. In this thesis, I use high resolution infrared imaging from the W. M. Keck telescopes in order to determine precise orbital parameter estimates of the young stars and understand the Galactic center's most recent epoch of star formation.First, we present a new optical distortion model for the Keck/NIRC2 narrow camera that is based upon on-sky measurements of a globular cluster. With an improved distortion model, we show that a stable astrometric reference frame for the GC can be established with Sgr A* at rest to within 0.09 mas/yr (∼3.4 km/s at a distance of 8 kpc), thereby improving the stability of the reference frame. Accurate proper motions of the central stellar cluster are presented and the stars are shown to have significant net rotation parallel to Galactic rotation. These stars can be used as astrometric standards for defining a reference frame without requiring the assumption of no net motion of the central stellar cluster, as has been done in earlier proper motion studies.Second, we use high-precision astrometry, measured in the newly constructed reference frame, and radial velocities of ∼115 young stars at projected radii between R = 0.8" - 13.3" in order to estimate their orbital properties. This constitutes the largest sample of stars used for this type of study to date. The median proper motion uncertainty for the stars within R=6", for which we have up to a 16-year baseline of measurements, is 0.03 mas/yr (∼1.2 km/s). Acceleration uncertainties are typically 10 microarcsec/yr/yr (∼0.4 km/s/yr), which has allowed for the detection of six significant accelerations in the plane of the sky outside the central arcsecond. Such measurements provide direct calculations of the line of sight distance and therefore precise orbital parameter estimates. We detect the clockwise stellar disk reported in previous studies, but find that the fraction of young stars within the disk is much smaller than once thought. We do not find evidence for the previously-claimed counter-rotating disk. The clockwise disk has an inclination of ∼130° and an angle to the ascending node of ∼96°, with an opening angle of 15.2°. The orientation of the disk plane does not change with radius, contrary to recent claims of a highly-warped disk. We identify a bias in the orbital solutions of disk stars near the line of nodes that stems from a previously adopted line-of-sight distance prior and show that this bias leads to an apparently-warped disk. The candidate disk members have orbital eccentricities of e ∼ 0.3. This can be explained by dynamical relaxation in an initially circular disk with a moderately top-heavy mass function (Gamma ∼ 1.6), consistent with the latest estimates of the young star population's IMF. This cannot, however, account for the high inclinations of the out-of-disk population, which makes up at least half of the central parsec's young stars. Thus, if all of the young stars formed in a single disk, an additional dynamical mechanism must be invoked to explain their orbits