Stars orbiting the compact radio source Sgr A* in the Galactic Center serve as precision probes of the gravitational field around the closest massive black hole. In addition to adaptive ...optics-assisted astrometry (with NACO/VLT) and spectroscopy (with SINFONI/VLT, NIRC2/Keck and GNIRS/Gemini) over three decades, we have obtained 30–100 μas astrometry since 2017 with the four-telescope interferometric beam combiner GRAVITY/VLTI, capable of reaching a sensitivity of
m
K
= 20 when combining data from one night. We present the simultaneous detection of several stars within the diffraction limit of a single telescope, illustrating the power of interferometry in the field. The new data for the stars S2, S29, S38, and S55 yield significant accelerations between March and July 2021, as these stars pass the pericenters of their orbits between 2018 and 2023. This allows for a high-precision determination of the gravitational potential around Sgr A*. Our data are in excellent agreement with general relativity orbits around a single central point mass,
M
•
= 4.30 × 10
6
M
⊙
, with a precision of about ±0.25%. We improve the significance of our detection of the Schwarzschild precession in the S2 orbit to 7
σ
. Assuming plausible density profiles, the extended mass component inside the S2 apocenter (≈0.23″ or 2.4 × 10
4
R
S
) must be ≲3000
M
⊙
(1
σ
), or ≲0.1% of
M
•
. Adding the enclosed mass determinations from 13 stars orbiting Sgr A* at larger radii, the innermost radius at which the excess mass beyond Sgr A* is tentatively seen is
r
≈ 2.5″ ≥ 10× the apocenter of S2. This is in full harmony with the stellar mass distribution (including stellar-mass black holes) obtained from the spatially resolved luminosity function.
The GRAVITY instrument on the ESO VLTI pioneers the field of high-precision near-infrared interferometry by providing astrometry at the 10−100
μ
as level. Measurements at this high precision ...crucially depend on the control of systematic effects. We investigate how aberrations introduced by small optical imperfections along the path from the telescope to the detector affect the astrometry. We develop an analytical model that describes the effect of these aberrations on the measurement of complex visibilities. Our formalism accounts for pupil-plane and focal-plane aberrations, as well as for the interplay between static and turbulent aberrations, and it successfully reproduces calibration measurements of a binary star. The Galactic Center observations with GRAVITY in 2017 and 2018, when both Sgr A* and the star S2 were targeted in a single fiber pointing, are affected by these aberrations at a level lower than 0.5 mas. Removal of these effects brings the measurement in harmony with the dual-beam observations of 2019 and 2020, which are not affected by these aberrations. This also resolves the small systematic discrepancies between the derived distance
R
0
to the Galactic Center that were reported previously.
The star S2 orbiting the compact radio source Sgr A* is a precision probe of the gravitational field around the closest massive black hole (candidate). Over the last 2.7 decades we have monitored the ...star’s radial velocity and motion on the sky, mainly with the SINFONI and NACO adaptive optics (AO) instruments on the ESO VLT, and since 2017, with the four-telescope interferometric beam combiner instrument GRAVITY. In this Letter we report the first detection of the General Relativity (GR) Schwarzschild Precession (SP) in S2’s orbit. Owing to its highly elliptical orbit (
e
= 0.88), S2’s SP is mainly a kink between the pre-and post-pericentre directions of motion ≈±1 year around pericentre passage, relative to the corresponding
Kepler
orbit. The superb 2017−2019 astrometry of GRAVITY defines the pericentre passage and outgoing direction. The incoming direction is anchored by 118 NACO-AO measurements of S2’s position in the infrared reference frame, with an additional 75 direct measurements of the S2-Sgr A* separation during bright states (“flares”) of Sgr A*. Our 14-parameter model fits for the distance, central mass, the position and motion of the reference frame of the AO astrometry relative to the mass, the six parameters of the orbit, as well as a dimensionless parameter
f
SP
for the SP (
f
SP
= 0 for Newton and 1 for GR). From data up to the end of 2019 we robustly detect the SP of S2,
δ
ϕ
≈ 12′ per orbital period. From posterior fitting and MCMC Bayesian analysis with different weighting schemes and bootstrapping we find
f
SP
= 1.10 ± 0.19. The S2 data are fully consistent with GR. Any extended mass inside S2’s orbit cannot exceed ≈0.1% of the central mass. Any compact third mass inside the central arcsecond must be less than about 1000
M
⊙
.
The highly elliptical, 16-year-period orbit of the star S2 around the massive black hole candidate Sgr A✻ is a sensitive probe of the gravitational field in the Galactic centre. Near pericentre at ...120 AU ≈ 1400 Schwarzschild radii, the star has an orbital speed of ≈7650 km s−1, such that the first-order effects of Special and General Relativity have now become detectable with current capabilities. Over the past 26 years, we have monitored the radial velocity and motion on the sky of S2, mainly with the SINFONI and NACO adaptive optics instruments on the ESO Very Large Telescope, and since 2016 and leading up to the pericentre approach in May 2018, with the four-telescope interferometric beam-combiner instrument GRAVITY. From data up to and including pericentre, we robustly detect the combined gravitational redshift and relativistic transverse Doppler effect for S2 of z = Δλ / λ ≈ 200 km s−1/c with different statistical analysis methods. When parameterising the post-Newtonian contribution from these effects by a factor f , with f = 0 and f = 1 corresponding to the Newtonian and general relativistic limits, respectively, we find from posterior fitting with different weighting schemes f = 0.90 ± 0.09|stat ± 0.15|sys. The S2 data are inconsistent with pure Newtonian dynamics.
We report the detection of continuous positional and polarization changes of the compact source SgrA* in high states (“flares”) of its variable near-infrared emission with the near-infrared ...GRAVITY-Very Large Telescope Interferometer (VLTI) beam-combining instrument. In three prominent bright flares, the position centroids exhibit clockwise looped motion on the sky, on scales of typically 150 μas over a few tens of minutes, corresponding to about 30% the speed of light. At the same time, the flares exhibit continuous rotation of the polarization angle, with about the same 45(±15) min period as that of the centroid motions. Modelling with relativistic ray tracing shows that these findings are all consistent with a near face-on, circular orbit of a compact polarized “hot spot” of infrared synchrotron emission at approximately six to ten times the gravitational radius of a black hole of 4 million solar masses. This corresponds to the region just outside the innermost, stable, prograde circular orbit (ISCO) of a Schwarzschild–Kerr black hole, or near the retrograde ISCO of a highly spun-up Kerr hole. The polarization signature is consistent with orbital motion in a strong poloidal magnetic field.
We study the time-variable linear polarisation of Sgr A* during a bright near-infrared flare observed with the GRAVITY instrument on July 28, 2018. Motivated by the time evolution of both the ...observed astrometric and polarimetric signatures, we interpret the data in terms of the polarised emission of a compact region (“hotspot”) orbiting a black hole in a fixed, background magnetic field geometry. We calculated a grid of general relativistic ray-tracing models, created mock observations by simulating the instrumental response, and compared predicted polarimetric quantities directly to the measurements. We take into account an improved instrument calibration that now includes the instrument’s response as a function of time, and we explore a variety of idealised magnetic field configurations. We find that the linear polarisation angle rotates during the flare, which is consistent with previous results. The hotspot model can explain the observed evolution of the linear polarisation. In order to match the astrometric period of this flare, the near horizon magnetic field is required to have a significant poloidal component, which is associated with strong and dynamically important fields. The observed linear polarisation fraction of ≃30% is smaller than the one predicted by our model (≃50%). The emission is likely beam depolarised, indicating that the flaring emission region resolves the magnetic field structure close to the black hole.
GRAVITY is a new instrument to coherently combine the light of the European Southern Observatory Very Large Telescope Interferometer to form a telescope with an equivalent 130 m diameter angular ...resolution and a collecting area of 200 m2. The instrument comprises fiber fed integrated optics beam combination, high resolution spectroscopy, built-in beam analysis and control, near-infrared wavefront sensing, phase-tracking, dual-beam operation, and laser metrology. GRAVITY opens up to optical/infrared interferometry the techniques of phase referenced imaging and narrow angle astrometry, in many aspects following the concepts of radio interferometry. This article gives an overview of GRAVITY and reports on the performance and the first astronomical observations during commissioning in 2015/16. We demonstrate phase-tracking on stars as faint as mK ≈ 10 mag, phase-referenced interferometry of objects fainter than mK ≈ 15 mag with a limiting magnitude of mK ≈ 17 mag, minute long coherent integrations, a visibility accuracy of better than 0.25%, and spectro-differential phase and closure phase accuracy better than 0.5°, corresponding to a differential astrometric precision of better than ten microarcseconds (μas). The dual-beam astrometry, measuring the phase difference of two objects with laser metrology, is still under commissioning. First observations show residuals as low as 50 μas when following objects over several months. We illustrate the instrument performance with the observations of archetypical objects for the different instrument modes. Examples include the Galactic center supermassive black hole and its fast orbiting star S2 for phase referenced dual-beam observations and infrared wavefront sensing, the high mass X-ray binary BP Cru and the active galactic nucleus of PDS 456 for a few μas spectro-differential astrometry, the T Tauri star S CrA for a spectro-differential visibility analysis, ξ Tel and 24 Cap for high accuracy visibility observations, and η Car for interferometric imaging with GRAVITY.
Infrared observations of Sgr A* probe the region close to the event horizon of the black hole at the Galactic center. These observations can constrain the properties of low-luminosity accretion as ...well as that of the black hole itself. The GRAVITY instrument at the ESO VLTI has recently detected continuous circular relativistic motion during infrared flares which has been interpreted as orbital motion near the event horizon. Here we analyze the astrometric data from these flares, taking into account the effects of out-of-plane motion and orbital shear of material near the event horizon of the black hole. We have developed a new code to predict astrometric motion and flux variability from compact emission regions following particle orbits. Our code combines semi-analytic calculations of timelike geodesics that allow for out-of-plane or elliptical motions with ray tracing of photon trajectories to compute time-dependent images and light curves. We apply our code to the three flares observed with GRAVITY in 2018. We show that all flares are consistent with a hotspot orbiting at
R
∼ 9 gravitational radii with an inclination of
i
∼ 140°. The emitting region must be compact and less than ∼5 gravitational radii in diameter. We place a further limit on the out-of-plane motion during the flare.
We report the definite spectroscopic identification of 40 OB supergiants, giants, and main-sequence stars in the central parsec of the Galaxy. Detection of their absorption lines has become possible ...with the high spatial and spectral resolution and sensitivity of the adaptive optics integral field spectrometer SPIFFI/SINFONI on the ESO VLT. Several of these OB stars appear to be helium- and nitrogen-rich. Almost all of the 80 massive stars now known in the central parsec (central arcsecond excluded) reside in one of two somewhat thick (<|h|/R> 0.14) rotating disks. These stellar disks have fairly sharp inner edges (R 1) and surface density profiles that scale as R super(-2). We do not detect any OB stars outside the central 0.5 pc. The majority of the stars in the clockwise system appear to be on almost circular orbits, whereas most of those in the "counterclockwise" disk appear to be on eccentric orbits. Based on its stellar surface density distribution and dynamics, we propose that IRS 13E is an extremely dense cluster (r sub(core) > 3 x 10 super(8) M sub(z) pc super(-3)) that has formed in the counterclockwise disk. The stellar contents of both systems are remarkably similar, indicating a common age of 6 c 2 Myr. The K-band luminosity function of the massive stars suggests a top-heavy mass function and limits the total stellar mass contained in both disks to 1.5 x 10 super(4) M sub(z). Our data strongly favor in situ star formation from dense gas accretion disks for the two stellar disks. This conclusion is very clear for the clockwise disk and highly plausible for the counterclockwise system.
Abstract
We present
K
-band interferometric observations of the PDS 70 protoplanets along with their host star using VLTI/GRAVITY. We obtained
K
-band spectra and 100
μ
as precision astrometry of ...both PDS 70 b and c in two epochs, as well as spatially resolving the hot inner disk around the star. Rejecting unstable orbits, we found a nonzero eccentricity for PDS 70 b of 0.17 ± 0.06, a near-circular orbit for PDS 70 c, and an orbital configuration that is consistent with the planets migrating into a 2:1 mean motion resonance. Enforcing dynamical stability, we obtained a 95% upper limit on the mass of PDS 70 b of 10
M
Jup
, while the mass of PDS 70 c was unconstrained. The GRAVITY
K
-band spectra rules out pure blackbody models for the photospheres of both planets. Instead, the models with the most support from the data are planetary atmospheres that are dusty, but the nature of the dust is unclear. Any circumplanetary dust around these planets is not well constrained by the planets’ 1–5
μ
m spectral energy distributions (SEDs) and requires longer wavelength data to probe with SED analysis. However with VLTI/GRAVITY, we made the first observations of a circumplanetary environment with sub-astronomical-unit spatial resolution, placing an upper limit of 0.3 au on the size of a bright disk around PDS 70 b.
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