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 ...

Nature volume 577, pages337-340 (2020) https://www.nature.com/articles/s41586-019-1883-yThe central 0.1 parsecs of the Milky Way host a supermassive black hole identified with the position of the radio and infrared source Sagittarius A* (refs 1,2 ), a cluster of young, massive stars (the S stars 3 ) and various gaseous features 4,5 . Recently, two unusual objects have been found to be closely orbiting Sagittarius A*: the so-called G sources, G1 and G2. These objects are unresolved (having a size on the order of 100 astronomical units, except at periapse where the tidal interaction with the black hole stretches them along the orbit) and they show both thermal dust emission and line emission from ionized gas 6-10 . G1 and G2 have generated attention because they appear to be tidally interacting with the supermassive Galactic black hole, possibly enhancing its accretion activity. No broad consensus has yet been reached concerning their nature: the G objects show the characteristics of gas and dust clouds but display the dynamical properties of stellar-mass objects. Here we report observations of four additional G objects, all lying within 0.04 parsecs of the black hole, and forming a class that is probably unique to this environment. The widely varying orbits derived for the six G objects demonstrate that they were commonly but separately formed.We used near-infrared (NIR) spectro-imaging data obtained over the past 13 years 11 at the W. M. Keck Observatory with the OSIRIS integral field spectrometer 12 , coupled with laser guide star adaptive optics wave front corrections 13 . OSIRIS data-cubes have two spatial dimensions -about 3 arcsec × 2 arcsec surrounding Sgr A* with a plate-scale of 35 mas-and one wavelength dimension -covering the Kn3 band, 2.121-2.229 µm, with a spectral resolution of R ≈ 3,800. We selected 24 datacubes based on image-quality and signal-to-noise ratio; see Methods section 'Observations'. These cubes were processed through the OSIRIS pipeline 14 . We also removed the stellar continua to isolate emission features associated with interstellar gas (Methods section 'Continuum subtraction'). The reduced data-cubes were analysed with a 3D visualization tool, OsrsVol 15 , that simultaneously displays all dimensions of the data-cube. This helps disentangle the many features of this crowded region, which are often superimposed in the spatial dimension but are separable in the wavelength dimension (Fig. 1).Analysing the data with OsrsVol as well as conventional 2D and 1D tools, we identify four new compact objects in Brackett-γ line emission (Brγ; 2.1661 µm rest wavelength) that consistently appear in the data across the observed timeline. In addition to Brγ, all four objects show two [Fe III] emission lines (at 2.1457 µm and 2.2184 µm; ref. 16 ).

We propose a new approach to Bayesian prior probability distributions (priors) that can improve orbital solutions for low-phase-coverage orbits, where data cover less than ∼40% of an orbit. In instances of low phase coveragesuch as with stellar orbits in the Galactic center or with directly imaged exoplanets-data have low constraining power and thus priors can bias parameter estimates and produce underestimated confidence intervals. Uniform priors, which are commonly assumed in orbit fitting, are notorious for this. We propose a new observable-based prior paradigm that is based on uniformity in observables. We compare performance of this observable-based prior and of commonly assumed uniform priors using Galactic center and directly imaged exoplanet (HR 8799) data. The observable-based prior can reduce biases in model parameters by a factor of two and helps avoid underestimation of confidence intervals for simulations with less than ∼40% phase coverage. Above this threshold, orbital solutions for objects with sufficient phase coverage-such as S0-2, a short-period star at the Galactic center with full phase coverage-are consistent with previously published results. Below this threshold, the observablebased prior limits prior influence in regions of prior dominance and increases data influence. Using the observablebased prior, HR 8799 orbital analyses favor low-eccentricity orbits and provide stronger evidence that the four planets have a consistent inclination of ∼30°to within 1σ. This analysis also allows for the possibility of coplanarity. We present metrics to quantify improvements in orbital estimates with different priors so that observable-based prior frameworks can be tested and implemented for other low-phase-coverage orbits.

We present the results of the first systematic search for spectroscopic binaries within the central 2 × 3 arcsec2 around the supermassive black hole at the center of the Milky Way galaxy. This survey is based primarily on over a decade of adaptive optics-fed integral-field spectroscopy (R ∼ 4000), obtained as part of the Galactic Center Orbits Initiative at Keck Observatory, and it has a limiting K’-band magnitude of 15.8, which is at least 4 mag deeper than previous spectroscopic searches for binaries at larger radii within the central nuclear star cluster. From this primary data set, over 600 new radial velocities are extracted and reported, increasing by a factor of 3 the number of such measurements. We find no significant periodic signals in our sample of 28 stars, of which 16 are massive, young (main-sequence B) stars and 12 are low-mass, old (M and K giant) stars. Using Monte Carlo simulations, we derive upper limits on the intrinsic binary star fraction for the young star population at 47% (at 95% confidence) located ∼20 mpc from the black hole. The young star binary fraction is significantly lower than that observed in the field (70%). This result is consistent with a scenario in which the central supermassive black hole drives nearby stellar binaries to merge or be disrupted, and it may have important implications for the production of gravitational waves and hypervelocity stars.