We report new precision measurements of the properties of our Galaxy's supermassive black hole. Based on astrometric (1995Y2007) and radial velocity (RV; 2000Y2007) measurements from the W. M. Keck 10 m telescopes, a fully unconstrained Keplerian orbit for the short-period star S0-2 provides values for the distance (R 0 ) of 8:0 AE 0:6 kpc, the enclosed mass (M bh ) of 4:1 AE 0:6 ; 10 6 M , and the black hole's RV, which is consistent with zero with 30 km s À1 uncertainty. If the black hole is assumed to be at rest with respect to the Galaxy (e.g., has no massive companion to induce motion), we can further constrain the fit, obtaining R 0 ¼ 8:4 AE 0:4 kpc and M bh ¼ 4:5 AE 0:4 ; 10 6 M . More complex models constrain the extended dark mass distribution to be less than 3Y4 ; 10 5 M within 0.01 pc, $100 times higher than predictions from stellar and stellar remnant models. For all models, we identify transient astrometric shifts from source confusion (up to 5 times the astrometric error) and the assumptions regarding the black hole's radial motion as previously unrecognized limitations on orbital accuracy and the usefulness of fainter stars. Future astrometric and RV observations will remedy these effects. Our estimates of R 0 and the Galaxy's local rotation speed, which it is derived from combining R 0 with the apparent proper motion of Sgr A Ã , ( 0 ¼ 229 AE 18 km s À1 ), are compatible with measurements made using other methods. The increased black hole mass found in this study, compared to that determined using projected mass estimators, implies a longer period for the innermost stable orbit, longer resonant relaxation timescales for stars in the vicinity of the black hole and a better agreement with the M bh -relation.

2General Relativity predicts that a star passing close to a supermassive black hole should exhibit a relativistic redshift. We test this using observations of the Galactic center star S0-2. We combine existing spectroscopic and astrometric measurements from 1995-2017, which cover S0-2's 16-year orbit, with measurements in 2018 March to September which cover three events during its closest approach to the black hole. We detect the combination of special relativistic-and gravitational-redshift, quantified using a redshift parameter, Υ. Our result, Υ = 0.88 ± 0.17, is consistent with General Relativity (Υ = 1) and excludes a Newtonian model (Υ = 0 ) with a statistical significance of 5 σ.General Relativity (GR) has been thoroughly tested in weak gravitational fields in the Solar System (1), with binary pulsars (2) and with measurements of gravitational waves from stellarmass black-hole binaries (3,4). Observations of short-period stars in our Galactic center (GC) (5-8) allow GR to be tested in a different regime (9): the strong field near a supermassive black hole (SMBH) (10,11). The star S0-2 (also known as S2) has a 16 year orbit around Sagittarius A* (Sgr A*), the SMBH at the center of the Milky Way. In 2018 May, it reached its point of closest approach, at a distance of 120 astronomical units (au) with a velocity reaching 2.7% of the speed of light. Within a 6 months interval of that date, the star also passed through its maximum (March) and minimum velocity (September) along the line-of-sight, spanning a range of 6000 km s −1 in radial velocity (RV - Fig. 1). We present observations of all three events and combine them with data from 1995-2017 ( Fig. 2).During 2018, the close proximity of S0-2 to the SMBH causes the relativistic redshift, which is the combination of the transverse Doppler shift from special relativity and the gravitational redshift from GR. This deviation from a Keplerian orbit was predicted to reach 200 km s −1 (Fig. 3) and is detectable with current telescopes. The GRAVITY collaboration (9) previously reported a similar measurement. Our measurements are complementary: i) we present a 3 complete set of independent measurements with 3 additional months of data, doubling the time baseline for the year of closest approach, and including the third turning point (RV minimum) in September 2018, ii) we use three different spectroscopic instruments in 2018, which allows us to probe the presence of instrumental biases, iii) we perform an analysis of the systematic errors that may arise from an experiment spanning over 20 years to test for bias in the result, and iv) we publicly release the stellar measurements and the posterior probability distributions.We use a total of 45 astrometric positional measurements (spanning 24 years) and 115 RVs (18 years) to fit the orbit of S0-2. Of these, 11 are new astrometric measurements of S0-2 from 2016 to 2018 and 28 are new RV measurements from 2017 and 2018 ( Fig 1). Astrometric measurements were obtained at the W. M. Keck Observatory using speckle imaging (a ...

We present new, more precise measurements of the mass and distance of our Galaxy's central supermassive black hole, Sgr A * . These results stem from a new analysis that more than doubles the time baseline for astrometry of faint stars orbiting Sgr A * , combining 2decades of speckle imaging and adaptive optics data. Specifically, we improve our analysis of the speckle images by using information about a star's orbit from the deep adaptive optics data (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013) to inform the search for the star in the speckle years (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005). When this new analysis technique is combined with the first complete re-reduction of Keck Galactic Center speckle images using speckle holography, we are able to track the short-period star S0-38 (K-band magnitude=17, orbital period=19 yr) through the speckle years. We use the kinematic measurements from speckle holography and adaptive optics to estimate the orbits of S0-38 and S0-2 and thereby improve our constraints of the mass (M bh ) and distance (R o ) of Sgr A * : M bh = (4.02±0.16±0.04) ×10 6 M e and 7.86±0.14±0.04 kpc. The uncertainties in M bh and R o as determined by the combined orbital fit of S0-2 and S0-38 are improved by a factor of 2 and 2.5, respectively, compared to an orbital fit of S0-2 alone and a factor of ∼2.5 compared to previous results from stellar orbits. This analysis also limits the extended dark mass within 0.01 pc to less than 0.13×10 6 M e at 99.7% confidence, a factor of 3 lower compared to prior work.

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. (2012). 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 α = 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 M ⊙ above 1 M ⊙ 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.

We present significantly improved proper motion measurements of the Milky Way's central stellar cluster. These improvements are made possible by refining our astrometric reference frame with a new geometric optical distortion model for the W. M. Keck II 10 m telescope's Adaptive Optics camera (NIRC2) in its narrow field mode. For the first time, this distortion model is constructed from on-sky measurements, and is made available to the public in the form of FITS files. When applied to widely dithered images, it produces residuals in the separations of stars that are a factor of ∼3 smaller compared to the outcome using previous models. By applying this new model, along with corrections for differential atmospheric refraction, to widely dithered images of SiO masers at the Galactic center, we improve our ability to tie into the precisely measured radio Sgr A*-rest frame. The resulting infrared reference frame is ∼2-3 times more accurate and stable than earlier published efforts. In this reference frame, Sgr 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). Also, proper motions for members of the central stellar cluster are more accurate, although less precise, due to the limited number of these wide field measurements. These proper motion measurements show that, with respect to Sgr 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 net translational motion with respect to Sgr A* to within 0.1 mas yr −1 , and has net rotation perpendicular to the plane of the sky along the Galactic plane, as has previously been observed. While earlier proper motion studies defined a reference frame by assuming no net motion of the stellar cluster, this approach is fundamentally limited by the cluster's intrinsic dispersion and therefore will not improve with time. We define a reference frame with SiO masers and this reference frame's stability should improve steadily with future measurements of the SiO masers in this region (∝ t 3/2 ). This is essential for achieving the necessary reference frame stability required to detect the effects of general relativity and extended mass on short-period stars at the Galactic center.