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.

International audienceWe present new diffraction-limited images of the Galactic center, obtained with the W. M. Keck I 10 m telescope. Within 0.4" of the Galaxy's central dark mass, 17 proper-motion stars, with K magnitudes ranging from 14.0 to 16.8, are identified, and 10 of these are new detections (six were also independently discovered by others). In this sample, three newly identified (S0-16, S0-19, and S0-20) and four previously known (S0-1, S0-2, S0-4, and S0-5) sources have measured proper motions that reveal orbital solutions. Orbits are derived simultaneously so that they jointly constrain the central dark object's properties: its mass, its position, and, for the first time using orbits, its motion on the plane of the sky. This analysis pinpoints the Galaxy's central dark mass to within 1.3 mas (10 AU) and limits its proper motion to 1.5+/-0.5 mas yr-1 (or equivalently 60+/-20 km s-1) with respect to the central stellar cluster. This localization of the central dark mass is consistent with our derivation of the position of the radio source Sgr A* in the infrared reference frame (+/-10 mas) but with an uncertainty that is a factor of 8 times smaller, which greatly facilitates searches for near-infrared counterparts to the central black hole. Consequently, one previous claim for such a counterpart can now be ascribed to a close stellar passage in 1996. Furthermore, we can place a conservative upper limit of 15.5 mag on any steady state counterpart emission. The estimated central dark mass from orbital motions is 3.7(+/-0.2)×106[R0/(8kpc)]3Msolar this is a more direct measure of mass than those obtained from velocity dispersion measurements, which are as much as a factor of 2 smaller. The Galactic center's distance, which adds an additional 19% uncertainty in the estimated mass, is now the limiting source of uncertainty in the absolute mass. For stars in this sample, the closest approach is achieved by S0-16, which came within a mere 45 AU (=0.0002pc=600Rs) at a velocity of 12,000 km s-1. This increases the inferred dark mass density by 4 orders of magnitude compared to earlier analyses based on velocity and acceleration vectors, making the Milky Way the strongest existing case for a supermassive black hole at the center of a normal-type galaxy. Well-determined orbital parameters for these seven Sgr A* cluster stars also provide new constraints on how these apparently massive, young (<10 Myr) stars formed in a region that seems to be hostile to star formation. Unlike the more distant He I emission line stars-another population of young stars in the Galactic center-that appear to have coplanar orbits, the Sgr A* cluster stars have orbital properties (eccentricities, angular momentum vectors, and apoapse directions) that are consistent with an isotropic distribution. Therefore, many of the mechanisms proposed for the formation of the He I stars, such as formation from a preexisting disk, are unlikely solutions for the Sgr A* cluster stars. Unfortunately, alternative theories for producing young stars, or old...

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We have obtained the first detection of spectral absorption lines in one of the high-velocity stars in the vicinity of the Galaxy's central supermassive black hole. Both Brg (2.1661 mm) and He i (2.1126 mm) are seen in absorption in S0-2 with equivalent widths ( and Å ) and an inferred stellar rotational velocity 2.8 ‫ע‬ 0.3 1.7 ‫ע‬ 0.4 ( k ms Ϫ1 ) that are consistent with that of an O8-B0 dwarf, which suggests that it is a massive 220 ‫ע‬ 40 (∼15 M , ) young (less than 10 Myr) main-sequence star. This presents a major challenge to star formation theories, given the strong tidal forces that prevail over all distances reached by S0-2 in its current orbit (130-1900 AU) and the difficulty in migrating this star inward during its lifetime from farther out where tidal forces should no longer preclude star formation. The radial velocity measurements ( km s Ϫ1 ) and our reported Av S p Ϫ510 ‫ע‬ 40 z proper motions for S0-2 strongly constrain its orbit, providing a direct measure of the black hole mass of . The Keplerian orbit parameters have uncertainties that are reduced by a factorof 2-3 compared to previously reported values and include, for the first time, an independent solution for the dynamical center; this location, while consistent with the nominal infrared position of Sgr A*, is localized to a factor of 5 more precisely ‫2ע(‬ mas). Furthermore, the ambiguity in the inclination of the orbit is resolved with the addition of the radial velocity measurement, indicating that the star is behind the black hole at the time of closest approach and counterrevolving against the Galaxy. With further radial velocity measurements in the next few years, the orbit of S0-2 will provide the most robust estimate of the distance to the Galactic center.

We present new proper motions from the 10 m Keck telescopes for a puzzling population of massive, young stars located within 3. 5 (0.14 pc) of the supermassive black hole at the Galactic center. Our proper motion measurements have uncertainties of only 0.07 mas yr −1 (3 km s −1 ), which is 7 times better than previous proper motion measurements for these stars, and enables us to measure accelerations as low as 0.2 mas yr −2 (7 km s −1 yr −1 ). Using these measurements, line-of-sight velocities from the literature, and three-dimensional velocities for additional young stars in the central parsec, we constrain the true orbit of each individual star and directly test the hypothesis that the massive stars reside in two stellar disks as has been previously proposed. Analysis of the stellar orbits reveals only one of the previously proposed disks of young stars using a method that is capable of detecting disks containing at least seven stars. The detected disk contains 50% of the young stars, is inclined by ∼115 • from the plane of the sky, and is oriented at a position angle of ∼100 • east of north. Additionally, the on-disk and off-disk populations have similar K-band luminosity functions and radial distributions that decrease at larger radii as ∝ r −2 . The disk has an out-of-the-disk velocity dispersion of 28 ± 6 km s −1 , which corresponds to a half-opening angle of 7 • ± 2 • , and several candidate disk members have eccentricities greater than 0.2. Our findings suggest that the young stars may have formed in situ but in a more complex geometry than a simple, thin circular disk.

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.

Recent measurements of the velocities of stars near the centre of the Milky Way have provided the strongest evidence for the presence of a supermassive black hole in a galaxy, but the observational uncertainties poorly constrain many of the black hole's properties. Determining the accelerations of stars in their orbits around the centre provides much more precise information about the position and mass of the black hole. Here we report measurements of the accelerations of three stars located approximately 0.005 pc (projected on the sky) from the central radio source Sagittarius A* (Sgr A*); these accelerations are comparable to those experienced by the Earth as it orbits the Sun. These data increase the inferred minimum mass density in the central region of the Galaxy by an order of magnitude relative to previous results, and localize the dark mass to within 0.05 +/- 0.04 arcsec of the nominal position of Sgr A*. In addition, the orbital period of one of the observed stars could be as short as 15 years, allowing us the opportunity in the near future to observe an entire period.