Modeling the orbital motion of Sgr A*’s near-infrared flares

¹ Max Planck Institute for Extraterrestrial Physics (MPE), Giessenbachstr.1, 85748 Garching, Germany
e-mail: bauboeck@mpe.mpg.de
² LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Univ. Paris Diderot, Sorbonne Paris Cité, 5 Place Jules Janssen, 92195 Meudon, France
³ Max-Planck-Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
⁴ 1. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany
⁵ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
⁶ CENTRA and Universidade de Lisboa – Faculdade de Ciências, Campo Grande, 1749-016 Lisboa, Portugal
⁷ CENTRA and Universidade do Porto – Faculdade de Engenharia, 4200-465 Porto, Portugal
⁸ European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany
⁹ European Southern Observatory, Casilla 19001, Santiago 19, Chile
¹⁰ Sterrewacht Leiden, Leiden University, Postbus 9513, 2300 RA Leiden, The Netherlands
¹¹ Departments of Physics and Astronomy, Le Conte Hall, University of California, Berkeley, CA 94720, USA
¹² School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
¹³ Max-Planck-Institute for Radio Astronomy, Auf dem Hügel 69, 53121 Bonn, Germany
¹⁴ Center for Computational Astrophysics, Flatiron Institute, 162 5th Ave., New York, NY 10010, USA
¹⁵ JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA
¹⁶ Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel

Received: 2 December 2019
Accepted: 4 February 2020

Abstract

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.