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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 mK = 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 × 106 M⊙, with a precision of about ±0.25%. We improve the significance of our detection of the Schwarzschild precession in the S2 orbit to 7σ. Assuming plausible density profiles, the extended mass component inside the S2 apocenter (≈0.23″ or 2.4 × 104 RS) must be ≲3000 M⊙ (1σ), 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.Key words: black hole physics / instrumentation: interferometers / Galaxy: center⋆ GRAVITY is developed in a collaboration by MPE, LESIA of Paris Observatory/CNRS/Sorbonne Université/Univ. Paris Diderot and IPAG of Université Grenoble Alpes/CNRS, MPIA, Univ. of Cologne, CENTRA – Centro de Astrofisica e Gravitação, and ESO.⋆⋆ Corresponding authors: S. Gillessen (e-mail: ste@mpe.mpg.de), F. Widmann (e-mail: fwidmann@mpe.mpg.de), and G. Heißel (e-mail: gernot.heissel@obspm.fr). The stars orbiting the compact radio source Sgr A* in the Galactic Centre are 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, since 2016/2017 we have obtained 30-100 mu-as astrometry with the four-telescope interferometric beam combiner GRAVITY / VLTI reaching a sensitivity of mK = 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. 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 x 10^6 M_sun with a precision of about +-0.25%. We improve the significance of our detection of the Schwarzschild precession in the S2 orbit to 7 sigma. Assuming plausible density profiles, an extended mass component inside S2's apocentre (= 0.23" or 2.4 x 10^4 R_S) must be 3000 M_sun (1 sigma), 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* tentatively is seen is r = 2.5" >= 10x the apocentre of S2. This is in full harmony with the stellar mass distribution (including stellar-mass black holes) obtained from the spatially resolved luminosity function.

Stellar orbits at the Galactic Center provide a very clean probe of the gravitational potential of the supermassive black hole. They can be studied with unique precision, beyond the confusion limit of a single telescope, with the near-infrared interferometer GRAVITY. Imaging is essential to search the field for faint, unknown stars on short orbits which potentially could constrain the black hole spin. Furthermore, it provides the starting point for astrometric fitting to derive highly accurate stellar positions. Here, we present $\mathrm{G^R}$, a new imaging tool specifically designed for Galactic Center observations with GRAVITY. The algorithm is based on a Bayesian interpretation of the imaging problem, formulated in the framework of information field theory and building upon existing works in radio-interferometric imaging. Its application to GRAVITY observations from 2021 yields the deepest images to date of the Galactic Center on scales of a few milliarcseconds. The images reveal the complicated source structure within the central $100\,\mathrm{mas}$ around Sgr A*, where we detected the stars S29 and S55 and confirm S62 on its trajectory, slowly approaching Sgr A*. Furthermore, we were able to detect S38, S42, S60, and S63 in a series of exposures for which we offset the fiber from Sgr A*. We provide an update on the orbits of all aforementioned stars. In addition to these known sources, the images also reveal a faint star moving to the west at a high angular velocity. We cannot find any coincidence with any known source and, thus, we refer to the new star as S300. From the flux ratio with S29, we estimate its K-band magnitude as $m_\mathrm{K}\left(\mathrm{S300}\right)\simeq 19.0 - 19.3$. Images obtained with CLEAN confirm the detection., 24 pages, 14 figures

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$\sim$9 gravitational radii with an inclination of $i\sim140^\circ$. The emitting region must be compact and less than $\sim5$ gravitational radii in diameter. We place a further limit on the out-of-plane motion during the flare., Comment: Accepted in A&A

Context. η Car is one of the most intriguing luminous blue variables in the Galaxy. Observations and models of the X-ray, ultraviolet, optical, and infrared emission suggest a central binary in a highly eccentric orbit with a 5.54 yr period residing in its core. 2D and 3D radiative transfer and hydrodynamic simulations predict a primary with a dense and slow stellar wind that interacts with the faster and lower density wind of the secondary. The wind-wind collision scenario suggests that the secondary’s wind penetrates the primary’s wind creating a low-density cavity in it, with dense walls where the two winds interact. However, the morphology of the cavity and its physical properties are not yet fully constrained.\ud \ud Aims. We aim to trace the inner ∼5–50 au structure of η Car’s wind-wind interaction, as seen through Brγ and, for the first time, through the He I 2s-2p line.\ud \ud Methods. We have used spectro-interferometric observations with the K-band beam-combiner GRAVITY at the VLTI. The analyses of the data include (i) parametrical model-fitting to the interferometric observables, (ii) a CMFGEN model of the source’s spectrum, and (iii) interferometric image reconstruction.\ud \ud Results. Our geometrical modeling of the continuum data allows us to estimate its FWHM angular size close to 2 mas and an elongation ratio ϵ = 1.06 ± 0.05 over a PA = 130° ± 20°. Our CMFGEN modeling of the spectrum helped us to confirm that the role of the secondary should be taken into account to properly reproduce the observed Brγ and He I lines. Chromatic images across the Brγ line reveal a southeast arc-like feature, possibly associated to the hot post-shocked winds flowing along the cavity wall. The images of the He I 2s-2p line served to constrain the 20 mas (∼50 au) structure of the line-emitting region. The observed morphology of He I suggests that the secondary is responsible for the ionized material that produces the line profile. Both the Brγ and the He I 2s-2p maps are consistent with previous hydrodynamical models of the colliding wind scenario. Future dedicated simulations together with an extensive interferometric campaign are necessary to refine our constraints on the wind and stellar parameters of the binary, which finally will help us predict the evolutionary path of η Car.

Context. Realistic synthetic observations of theoretical source models are essential for our understanding of real observational data. In using synthetic data, one can verify the extent to which source parameters can be recovered and evaluate how various data corruption effects can be calibrated. These studies are the most important when proposing observations of new sources, in the characterization of the capabilities of new or upgraded instruments, and when verifying model-based theoretical predictions in a direct comparison with observational data. Aims. We present the SYnthetic Measurement creator for long Baseline Arrays (SYMBA), a novel synthetic data generation pipeline for Very Long Baseline Interferometry (VLBI) observations. SYMBA takes into account several realistic atmospheric, instrumental, and calibration effects. Methods. We used SYMBA to create synthetic observations for the Event Horizon Telescope (EHT), a millimetre VLBI array, which has recently captured the first image of a black hole shadow. After testing SYMBA with simple source and corruption models, we study the importance of including all corruption and calibration effects, compared to the addition of thermal noise only. Using synthetic data based on two example general relativistic magnetohydrodynamics (GRMHD) model images of M 87, we performed case studies to assess the image quality that can be obtained with the current and future EHT array for different weather conditions. Results. Our synthetic observations show that the effects of atmospheric and instrumental corruptions on the measured visibilities are significant. Despite these effects, we demonstrate how the overall structure of our GRMHD source models can be recovered robustly with the EHT2017 array after performing calibration steps, which include fringe fitting, a priori amplitude and network calibration, and self-calibration. With the planned addition of new stations to the EHT array in the coming years, images could be reconstructed with higher angular resolution and dynamic range. In our case study, these improvements allowed for a distinction between a thermal and a non-thermal GRMHD model based on salient features in reconstructed images. © 2020 ESO., This work is supported by the ERC Synergy Grant "BlackHoleCam: Imaging the Event Horizon of Black Holes" (Grant 610058). I. Natarajan and R. Deane are grateful for the support from the New Scientific Frontiers with Precision Radio Interferometry Fellowship awarded by the South African Radio Astronomy Observatory (SARAO), which is a facility of the National Research Foundation (NRF), an agency of the Department of Science and Technology (DST) of South Africa. The authors of the present paper further thank the following organizations and programmes: the Academy of Finland (projects 274477, 284495, 312496); the Advanced European Network of E-infrastructures for Astronomy with the SKA (AENEAS) project, supported by the European Commission Framework Programme Horizon 2020 Research and Innovation action under grant agreement 731016; the Alexander von Humboldt Stiftung; the Black Hole Initiative at Harvard University, through a grant (60477) from the John Templeton Foundation; the China Scholarship Council; Comision Nacional de Investigacio Cientifica y Tecnologica (CONICYT, Chile, via PIA ACT172033, Fondecyt 1171506, BASAL AFB-170002, ALMAconicyt 31140007); Consejo Nacional de Ciencia y Tecnologia (CONACYT, Mexico, projects 104497, 275201, 279006, 281692); the Delaney Family via the Delaney Family John A. Wheeler Chair at Perimeter Institute; Direccion General de Asuntos del Personal Academico-Universidad Nacional Autonoma de Mexico (DGAPA-UNAM, project IN112417); the Generalitat Valenciana postdoctoral grant APOSTD/2018/177; the Gordon and Betty Moore Foundation (grants GBMF-3561, GBMF-5278); the Istituto Nazionale di Fisica Nucleare (INFN) sezione di Napoli, iniziative specifiche TEONGRAV; the GenT Program (Generalitat Valenciana) under project CIDEGENT/2018/021; the International Max Planck Research School for Astronomy and Astrophysics at the Universities of Bonn and Cologne; the Jansky Fellowship program of the National Radio Astronomy Observatory (NRAO); the Japanese Government (Monbukagakusho: MEXT) Scholarship; the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for JSPS Research Fellowship (JP17J08829); the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (CAS, grants QYZDJ-SSW-SLH057, QYZDJ-SSW-SYS008); the Leverhulme Trust Early Career Research Fellowship; the Max-Planck-Gesellschaft (MPG); the Max Planck Partner Group of the MPG and the CAS; the MEXT/JSPS KAKENHI (grants 18KK0090, JP18K13594, JP18K03656, JP18H03721, 18K03709, 18H01245, 25120007); the MIT International Science and Technology Initiatives (MISTI) Funds; the Ministry of Science and Technology (MOST) of Taiwan (105-2112-M-001-025-MY3, 106-2112-M-001-011, 106-2119-M-001027, 107-2119-M-001-017, 107-2119-M-001-020, and 107-2119-M-110-005); the National Aeronautics and Space Administration (NASA, Fermi Guest Investigator grant 80NSSC17K0649); NASA through the NASA Hubble Fellowship grant #HST-HF2-51431.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. , for NASA, under contract NAS5-26555; the National Institute of Natural Sciences (NINS) of Japan; the National Key Research and Development Program of China (grant 2016YFA0400704, 2016YFA0400702); the National Science Foundation (NSF, grants AST-0096454, AST-0352953, AST-0521233, AST-0705062, AST-0905844, AST-0922984, AST-1126433, AST-1140030, DGE-1144085, AST-1207704, AST-1207730, AST-1207752, MRI-1228509, OPP-1248097, AST-1310896, AST-1312651, AST-1337663, AST-1440254, AST-1555365, AST-1715061, AST-1615796, AST-1716327, OISE-1743747, AST-1816420); the Natural Science Foundation of China (grants 11573051, 11633006, 11650110427, 10625314, 11721303, 11725312, 11933007); the Natural Sciences and Engineering Research Council of Canada (NSERC, including a Discovery Grant and the NSERC Alexander Graham Bell Canada Graduate Scholarships-Doctoral Program); the National Youth Thousand Talents Program of China; the National Research Foundation of Korea (the Global PhD Fellowship Grant: grants NRF-2015H1A2A1033752, 2015-R1D1A1A01056807, the Korea Research Fellowship Program: NRF-2015H1D3A1066561); the Netherlands Organization for Scientific Research (NWO) VICI award (grant 639.043.513) and Spinoza Prize SPI 78-409; the New Scientific Frontiers with Precision Radio Interferometry Fellowship awarded by the South African Radio Astronomy Observatory (SARAO), which is a facility of the National Research Foundation (NRF), an agency of the Department of Science and Technology (DST) of South Africa; the Onsala Space Observatory (OSO) national infrastructure, for the provisioning of its facilities/observational support (OSO receives funding through the Swedish Research Council under grant 2017-00648) the Perimeter Institute for Theoretical Physics (research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research, Innovation and Science); the Princeton/Flatiron Postdoctoral Prize Fellowship; the Russian Science Foundation (grant 17-12-01029); the Spanish Ministerio de Economia y Competitividad (grants AYA2015-63939-C21-P, AYA2016-80889-P); the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award for the Instituto de Astrofisica de Andalucia (SEV-2017-0709); the Toray Science Foundation; the US Department of Energy (USDOE) through the Los Alamos National Laboratory (operated by Triad National Security, LLC, for the National Nuclear Security Administration of the USDOE (Contract 89233218CNA000001)); the Italian Ministero dell'Istruzione Universita e Ricerca through the grant Progetti Premiali 2012-iALMA (CUP C52I13000140001); the European Union's Horizon 2020 research and innovation programme under grant agreement No 730562 RadioNet; ALMA North America Development Fund; the Academia Sinica; Chandra TM6-17006X. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), supported by NSF grant ACI-1548562, and CyVerse, supported by NSF grants DBI-0735191, DBI-1265383, and DBI1743442. XSEDE Stampede2 resource at TACC was allocated through TGAST170024 and TG-AST080026N. XSEDE JetStream resource at PTI and TACC was allocated through AST170028. The simulations were performed in part on the SuperMUC cluster at the LRZ in Garching, on the LOEWE cluster in CSC in Frankfurt, and on the HazelHen cluster at the HLRS in Stuttgart. This research was enabled in part by support provided by Compute Ontario (http://computeontario.ca), Calcul Quebec (http://www. calculquebec.ca) and Compute Canada (http://www.computecanada.ca).We thank the sta ff at the participating observatories, correlation centers, and institutions for their enthusiastic support. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2017.1.00841.V. ALMA is a partnership of the European Southern Observatory (ESO; Europe, representing its member states), NSF, and National Institutes of Natural Sciences of Japan, together with National Research Council (Canada), Ministry of Science and Technology (MOST; Taiwan), Academia Sinica Institute of Astronomy and Astrophysics (ASIAA; Taiwan), and Korea Astronomy and Space Science Institute (KASI; Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, Associated Universities, Inc. (AUI)/NRAO, and the National Astronomical Observatory of Japan (NAOJ). The NRAO is a facility of the NSF operated under cooperative agreement by AUI. APEX is a collaboration between the Max-Planck-Institut fur Radioastronomie (Germany), ESO, and the Onsala Space Observatory (Sweden). The SMA is a joint project between the SAO and ASIAA and is funded by the Smithsonian Institution and the Academia Sinica. The JCMT is operated by the East Asian Observatory on behalf of the NAOJ, ASIAA, and KASI, as well as the Ministry of Finance of China, Chinese Academy of Sciences, and the National Key R&D Program (No. 2017YFA0402700) of China. Additional funding support for the JCMT is provided by the Science and Technologies Facility Council (UK) and participating universities in the UK and Canada. The LMT is a project operated by the Instituto Nacional de Astrofisica, Optica, y Electronica (Mexico) and the University of Massachusetts at Amherst (USA). The IRAM 30m telescope on Pico Veleta, Spain is operated by IRAM and supported by CNRS (Centre National de la Recherche Scientifique, France), MPG (Max-Planck-Gesellschaft, Germany) and IGN (Instituto Geografico Nacional, Spain). The SMT is operated by the Arizona Radio Observatory, a part of the Steward Observatory of the University of Arizona, with financial support of operations from the State of Arizona and financial support for instrumentation development from the NSF. The SPT is supported by the National Science Foundation through grant PLR-1248097. Partial support is also provided by the NSF Physics Frontier Center grant PHY-1125897 to the Kavli Institute of Cosmological Physics at the University of Chicago, the Kavli Foundation and the Gordon and Betty Moore Foundation grant GBMF 947. The SPT hydrogen maser was provided on loan from the GLT, courtesy of ASIAA. The EHTC has received generous donations of FPGA chips from Xilinx Inc., under the Xilinx University Program. The EHTC has benefited from technology shared under open-source license by the Collaboration for Astronomy Signal Processing and Electronics Research (CASPER). The EHT project is grateful to T4Science and Microsemi for their assistance with Hydrogen Masers. This research has made use of NASA's Astrophysics Data System. We gratefully acknowledge the support provided by the extended staff of the ALMA, both from the inception of the ALMA Phasing Project through the observational campaigns of 2017 and 2018. We would like to thank A. Deller and W. Brisken for EHT-specific support with the use of DiFX. We acknowledge the significance that Maunakea, where the SMA and JCMT EHT stations are located, has for the indigenous Hawaiian people. The software presented in this work makes use of the Numpy (van derWalt et al. 2011), Scipy (Jones et al. 2001), Astropy (Astropy Collaboration 2013, 2018) libraries and the KERN software bundle (Molenaar & Smirnov 2018).