We present measurements of the properties of the central radio source in M87 using Event Horizon Telescope data obtained during the 2017 campaign. We develop and fit geometric crescent models (asymmetric rings with interior brightness depressions) using two independent sampling algorithms that consider distinct representations of the visibility data. We show that the crescent family of models is statistically preferred over other comparably complex geometric models that we explore. We calibrate the geometric model parameters using general relativistic magnetohydrodynamic (GRMHD) models of the emission region and estimate physical properties of the source. We further fit images generated from GRMHD models directly to the data. We compare the derived emission region and black hole parameters from these analyses with those recovered from reconstructed images. There is a remarkable consistency among all methods and data sets. We find that >50% of the total flux at arcsecond scales comes from near the horizon, and that the emission is dramatically suppressed interior to this region by a factor >10, providing direct evidence of the predicted shadow of a black hole. Across all methods, we measure a crescent diameter of 42 ± 3 μas and constrain its fractional width to be <0.5. Associating the crescent feature with the emission surrounding the black hole shadow, we infer an angular gravitational radius of GM/Dc2 = 3.8 ± 0.4 μas. Folding in a distance measurement of ${16.8}_{-0.7}^{+0.8}\,\mathrm{Mpc}$ gives a black hole mass of $M=6.5\pm 0.2{| }_{\mathrm{stat}}\pm 0.7{| }_{\mathrm{sys}}\times {10}^{9}\hspace{2pt}{M}_{\odot }$. This measurement from lensed emission near the event horizon is consistent with the presence of a central Kerr black hole, as predicted by the general theory of relativity.

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First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole

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.Key words: Galaxy: center / gravitation / black hole physics⋆ This paper is dedicated to Tal Alexander, who passed away about a week before the pericentre approach of S2.⋆⋆ GRAVITY is developed in a collaboration by the Max Planck Institute for extraterrestrial Physics, LESIA of Paris Observatory/CNRS/Sorbonne Universite/Univ. Paris Diderot and IPAG of Universite Grenoble Alpes/CNRS, the Max Planck Institute for Astronomy, the University of Cologne, the CENTRA – Centro de Astrofisica e Gravitacao, and the European Southern Observatory.⋆⋆⋆ Corresponding author: F. Eisenhauer e-mail: eisenhau@mpe.mpg.de

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Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole

Very compact objects probe extreme gravitational fields and may be the key to understand outstanding puzzles in fundamental physics. These include the nature of dark matter, the fate of spacetime singularities, or the loss of unitarity in Hawking evaporation. The standard astrophysical description of collapsing objects tells us that massive, dark and compact objects are black holes. Any observation suggesting otherwise would be an indication of beyond-the-standard-model physics. Null results strengthen and quantify the Kerr black hole paradigm. The advent of gravitational-wave astronomy and precise measurements with very long baseline interferometry allow one to finally probe into such foundational issues. We overview the physics of exotic dark compact objects and their observational status, including the observational evidence for black holes with current and future experiments.

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Testing the nature of dark compact objects: a status report

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 ⊙ .

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Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole

Astrophysical black hole candidates are thought to be the Kerr black holes of general relativity, but there is not yet direct observational evidence that the spacetime geometry around these objects is described by the Kerr solution. The study of the properties of the electromagnetic radiation emitted by gas or stars orbiting these objects can potentially test the Kerr black hole hypothesis. This paper reviews the state of the art of this research field, describing the possible approaches to test the Kerr metric with current and future observational facilities and discussing current constraints.

Testing black hole candidates with electromagnetic radiation

The center of our Galaxy hosts the best constrained supermassive black hole in the universe, Sagittarius A* (Sgr A*). Its mass and distance have been accurately determined from stellar orbits and proper motion studies, respectively, and its high-frequency radio, and highly variable near-infrared and x-ray emission originate from within a few Schwarzschild radii of the event horizon. The theory of general relativity (GR) predicts the appearance of a black hole shadow, which is a lensed image of the event horizon. This shadow can be resolved by very long baseline radio interferometry and test basic predictions of GR and alternatives thereof. In this paper we review our current understanding of the physical properties of Sgr A*, with a particular emphasis on the radio properties, the black hole shadow, and models for the emission and appearance of the source. We argue that the Galactic Center holds enormous potential for experimental tests of black hole accretion and theories of gravitation in their strong limits.

https://iopscience.iop.org/article/10.1088/0264-9381/30/24/244003/pdf

S.B. Markoff

Papers

Toward the event horizon—the supermassive black hole in the galactic center