Tuan Do

IMPROVING GALACTIC CENTER ASTROMETRY BY REDUCING THE EFFECTS OF GEOMETRIC DISTORTION

We present significantly improved proper motion measurements of the Milky Way’s central stellar cluster. These nimprovements are made possible by refining our astrometric reference frame with a new geometric optical distortion nmodel for the W. M. Keck II 10 m telescope’s adaptive optics camera (NIRC2) in its narrow field mode. For the nfirst time, this distortion model is constructed from on-sky measurements and is made available to the public in the nform of FITS files.When applied to widely dithered images, it produces residuals in the separations of stars that are na factor of ~3 smaller compared with the outcome using previous models. By applying this new model, along with ncorrections for differential atmospheric refraction, to widely dithered images of SiO masers at the Galactic center n(GC), we improve our ability to tie into the precisely measured radio Sgr A*-rest frame. The resulting infrared nreference frame is ~2–3 times more accurate and stable than earlier published efforts. In this reference frame, nSgr A* is localized to within a position of 0.6 mas and a velocity of 0.09 mas yr^(−1), or ~3.4 km s^(−1) at 8 kpc (1σ). nAlso, proper motions for members of the central stellar cluster are more accurate, although less precise, due to the nlimited number of these wide field measurements. These proper motion measurements show that, with respect to nSgr A*, the central stellar cluster has no rotation in the plane of the sky to within 0.3 mas yr^(−1) arcsec^(−1), has no nnet translational motion with respect to Sgr A* to within 0.1 mas yr^(−1), and has net rotation perpendicular to the nplane of the sky along the Galactic plane, as has previously been observed. While earlier proper motion studies ndefined a reference frame by assuming no net motion of the stellar cluster, this approach is fundamentally limited nby the cluster’s intrinsic dispersion and therefore will not improve with time.We define a reference frame with SiO nmasers and this reference frame’s stability should improve steadily with future measurements of the SiO masers in nthis region (∝t^(−3/2)). This is essential for achieving the necessary reference frame stability required to detect the neffects of general relativity and extended mass on short-period stars at the GC.

The Shortest-Known–Period Star Orbiting Our Galaxy’s Supermassive Black Hole

Close to a Black Hole At the center of our Galaxy, there is a black hole that is 4 million times as massive as the Sun. Using data from the Keck Observatory, Meyer et al. (p. 84) detected a star orbiting this black hole with a period of 11.5 years, the shortest period among the stars orbiting it. The star is the second well-sampled star with an orbital period under 20 years. Having detailed knowledge about two stars with short periods and full orbit coverage will be crucial in testing Einsteins theory of general relativity in the gravitational field close to a massive black hole. A star can help probe Einstein’s general relativity theory close to a black hole that is 4 million times as massive as the Sun. Stars with short orbital periods at the center of our Galaxy offer a powerful probe of a supermassive black hole. Over the past 17 years, the W. M. Keck Observatory has been used to image the galactic center at the highest angular resolution possible today. By adding to this data set and advancing methodologies, we have detected S0-102, a star orbiting our Galaxy’s supermassive black hole with a period of just 11.5 years. S0-102 doubles the number of known stars with full phase coverage and periods of less than 20 years. It thereby provides the opportunity, with future measurements, to resolve degeneracies in the parameters describing the central gravitational potential and to test Einstein’s theory of general relativity in an unexplored regime.

STELLAR POPULATIONS IN THE CENTRAL 0.5 pc OF THE GALAXY. II. THE INITIAL MASS FUNCTION

The supermassive black hole at the center of the Milky Way plays host to a massive, young cluster that may have formed in one of the most inhospitable environments in the Galaxy. We present new measurements of the global properties of this cluster, including the initial mass function (IMF), age, and cluster mass. These results are based on Keck laser-guide-star adaptive optics observations used to identify the young stars and measure their Kp-band luminosity function as presented in Do et al. 2013. A Bayesian inference methodology is developed to simultaneously fit the global properties of the cluster utilizing the observations and extensive simulations of synthetic star clusters. We find that the slope of the mass function for this cluster is alpha = 1.7 +/- 0.2, which is steeper than previously reported, but still flatter than the traditional Salpeter slope of 2.35. The age of the cluster is between 2.5-5.8 Myr with 95% confidence, which is a younger age than typically adopted but consistent within the uncertainties of past measurements. The exact age of the cluster is difficult to determine since our results show two distinct age solutions (3.9 Myr and 2.8 Myr) due to model degeneracies in the relative number of Wolf-Rayet and OB stars. The total cluster mass is between 14,000 - 37,000 msun above 1 msun and it is necessary to include multiple star systems in order to fit the observed luminosity function and the number of observed Wolf-Rayet stars. The new IMF slope measurement is now consistent with X-ray observations indicating a factor of 10 fewer X-ray emitting pre-main-sequence stars than expected when compared with a Salpeter IMF. The young cluster at the Galactic center is one of the few definitive examples of an IMF that deviates significantly from the near-universal IMFs found in the solar neighborhood.

STELLAR POPULATIONS IN THE CENTRAL 0.5 pc OF THE GALAXY. I. A NEW METHOD FOR CONSTRUCTING LUMINOSITY FUNCTIONS AND SURFACE-DENSITY PROFILES

We present new high angular resolution near-infrared spectroscopic observations of the nuclear star cluster surrounding the Milky Ways central supermassive black hole. Using the integral-field spectrograph OSIRIS on Keck II behind the laser-guide-star adaptive optics system, this spectroscopic survey enables us to separate early-type (young, 4-6 Myr) and late-type (old, >1 Gyr) stars with a completeness of 50% down to K = 15.5 mag, which corresponds to ~10 M_☉ for the early-type stars. This work increases the radial extent of reported OSIRIS/Keck measurements by more than a factor of three from 4 to 14 (0.16 to 0.56 pc), along the projected disk of young stars. For our analysis, we implement a new method of completeness correction using a combination of star-planting simulations and Bayesian inference. We assign probabilities for the spectral type of every source detected in deep imaging down to K = 15.5 mag using information from spectra, simulations, number counts, and the distribution of stars. The inferred radial surface-density profiles, Σ(R)∝ R^(-Γ), for the young stars and late-type giants are consistent with earlier results (Γ_(early) = 0.93 ± 0.09, Γ_(late) = 0.16 ± 0.07). The late-type surface-density profile is approximately flat out to the edge of the survey. While the late-type stellar luminosity function is consistent with the Galactic bulge, the completeness-corrected luminosity function of the early-type stars has significantly more young stars at faint magnitudes compared with previous surveys with similar depth. This luminosity function indicates that the corresponding mass function of the young stars is likely less top-heavy than that inferred from previous surveys.

PROPER MOTIONS OF THE ARCHES CLUSTER WITH KECK LASER GUIDE STAR ADAPTIVE OPTICS: THE FIRST KINEMATIC MASS MEASUREMENT OF THE ARCHES

We report the first detection of the intrinsic velocity dispersion of the Arches cluster—a young (~2 Myr), massive (10^4 M_☉) starburst cluster located only 26 pc in projection from the Galactic center. This was accomplished using proper motion measurements within the central 10 × 10 of the cluster, obtained with the laser guide star adaptive optics system at Keck Observatory over a three-year time baseline (2006-2009). This uniform data set results in proper motion measurements that are improved by a factor ~5 over previous measurements from heterogeneous instruments. By careful, simultaneous accounting of the cluster and field contaminant distributions as well as the possible sources of measurement uncertainties, we estimate the internal velocity dispersion to be 0.15 ± 0.01 mas yr^(–1), which corresponds to 5.4 ± 0.4 km s^(–1) at a distance of 8.4 kpc. Projecting a simple model for the cluster onto the sky to compare with our proper motion data set, in conjunction with surface density data, we estimate the total present-day mass of the cluster to be M(r < 1.0 pc) = 1.5^(+0.74)_(–0.60) × 10^4 M_☉. The mass in stars observed within a cylinder of radius R (for comparison to photometric estimates) is found to be M(R < 0.4 pc) = 0.90^(+0.40)_(–0.35) × 10^4 M_☉ at formal 3σ confidence. This mass measurement is free from assumptions about the mass function of the cluster, and thus may be used to check mass estimates from photometry and simulation. Photometric mass estimates assuming an initially Salpeter mass function (Γ_0 = 1.35, or Γ ~ 1.0 at present, where dN/d(log M)∝ M^Γ) suggest a total cluster mass M_cl ~ (4-6) × 10^4 M_☉ and projected mass (~2 ≤ M(R < 0.4 pc) ≤ 3) × 10^4 M_☉. Photometric mass estimates assuming a globally top-heavy or strongly truncated present-day mass function (PDMF; with Γ ~ 0.6) yield mass estimates closer to M(R < 0.4 pc) ~ 1-1.2 × 10^4 M_☉. Consequently, our results support a PDMF that is either top-heavy or truncated at low mass, or both. Collateral benefits of our data and analysis include: (1) cluster membership probabilities, which may be used to extract a clean-cluster sample for future photometric work; (2) a refined estimate of the bulk motion of the Arches cluster with respect to the field, which we find to be 172 ± 15 km s^(–1), which is slightly slower than suggested by previous measurements using one epoch each with the Very Large Telescope and the Keck telescope; and (3) a velocity dispersion estimate for the field itself, which is likely dominated by the inner Galactic bulge and the nuclear disk.

THREE-DIMENSIONAL STELLAR KINEMATICS AT THE GALACTIC CENTER: MEASURING THE NUCLEAR STAR CLUSTER SPATIAL DENSITY PROFILE, BLACK HOLE MASS, AND DISTANCE

We present 3D kinematic observations of stars within the central 0.5 pc of the Milky Way nuclear star cluster using adaptive optics imaging and spectroscopy from the Keck telescopes. Recent observations have shown that the cluster has a shallower surface density profile than expected for a dynamically relaxed cusp, leading to important implications for its formation and evolution. However, the true three dimensional profile of the cluster is unknown due to the difficulty in de-projecting the stellar number counts. Here, we use spherical Jeans modeling of individual proper motions and radial velocities to constrain for the first time, the de-projected spatial density profile, cluster velocity anisotropy, black hole mass (

Testing General Relativity with Stellar Orbits around the Supermassive Black Hole in Our Galactic Center

M_mathrm{BH}

Modeling anisoplanatism in the Keck II laser guide star AO system

), and distance to the Galactic center (

Measuring the stellar luminosity function and spatial density profile of the inner 0.5 pc of the Milky Way nuclear star cluster

R_0

Off-axis PSF reconstruction for integral field spectrograph: instrumental aberrations and application to Keck/OSIRIS data

) simultaneously. We find that the inner stellar density profile of the late-type stars,