Where intermediate-mass black holes could hide in the Galactic Centre

A full parameter study with the S2 orbit

¹ Max Planck Institute for Extraterrestrial Physics, Giessenbachstraße 1, 85748 Garching, Germany
² ORIGINS Excellence Cluster, Boltzmannstraße 2, 85748 Garching, Germany
³ Department of Physics, University of Illinois, 1110 West Green Street, Urbana, IL 61801, USA
⁴ European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching, Germany
⁵ LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, 92195 Meudon, France
⁶ Universidade de Lisboa – Faculdade de Ciências, Campo Grande, 1749-016 Lisboa, Portugal
⁷ CENTRA – Centro de Astrofísica e Gravitação, IST, Universidade de Lisboa, 1049-001 Lisboa, Portugal
⁸ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
⁹ Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
¹⁰ Universidade do Porto, Faculdade de Engenharia, Rua Dr. Roberto, Frias, 4200-465 Porto, Portugal
¹¹ Department of Astrophysical & Planetary Sciences, JILA, University of Colorado, Duane Physics Bldg., 2000 Colorado Ave, Boulder, CO 80309, USA
¹² Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
¹³ Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
¹⁴ Departments of Physics and Astronomy, Le Conte Hall, University of California, Berkeley, CA 94720, USA
¹⁵ European Southern Observatory, Casilla, 19001 Santiago 19, Chile
¹⁶ Max Planck Institute for Astrophysics, Karl-Schwarzschild-Straße 1, 85748 Garching, Germany
¹⁷ Institute of Physics, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany
¹⁸ Max Planck Institute for Radio Astronomy, Auf dem Hügel 69, 53121 Bonn, Germany
¹⁹ Institute of Multidisciplinary Mathematics, UPV, Camino de Vera, s/n 46022 Valencia, Spain
²⁰ Kavli Institute for Astronomy and Astrophysics, Peking University, 5 Yiheyuan Rd, Haidian, Beijing 100871, PR China
²¹ Advanced Concepts Team, European Space Agency, TEC-SF, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
²² Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark

Received: 4 October 2022
Accepted: 16 February 2023

Abstract

Context. In the Milky Way the central massive black hole, Sgr A^*, coexists with a compact nuclear star cluster that contains a sub-parsec concentration of fast-moving young stars called S-stars. Their location and age are not easily explained by current star formation models, and in several scenarios the presence of an intermediate-mass black hole (IMBH) has been invoked.

Aims. We use GRAVITY astrometric and SINFONI, KECK, and GNIRS spectroscopic data of S2, the best known S-star, to investigate whether a second massive object could be present deep in the Galactic Centre (GC) in the form of an IMBH binary companion to Sgr A^*.

Methods. To solve the three-body problem, we used a post-Newtonian framework and consider two types of settings: (i) a hierarchical set-up where the star S2 orbits the Sgr A^*–IMBH binary and (ii) a non-hierarchical set-up where the IMBH trajectory lies outside the S2 orbit. In both cases we explore the full 20-dimensional parameter space by employing a Bayesian dynamic nested sampling method.

Results. For the hierarchical case we find the strongest constraints: IMBH masses > 2000 M_⊙ on orbits with smaller semi-major axes than S2 are largely excluded. For the non-hierarchical case, the chaotic nature of the problem becomes significant: the parameter space contains several pockets of valid IMBH solutions. However, a closer analysis of their impact on the resident stars reveals that IMBHs on semi-major axes larger than S2 tend to disrupt the S-star cluster in less than a million years. This makes the existence of an IMBH among the S-stars highly unlikely.

Conclusions. The current S2 data do not formally require the presence of an IMBH. If an IMBH hides in the GC, it has to be either a low-mass IMBH inside the S2 orbit that moves on a short and significantly inclined trajectory or an IMBH with a semi-major axis > 1″. We provide the parameter maps of valid IMBH solutions in the GC and discuss the general structure of our results and how future observations can help to put even stronger constraints on the properties of IMBHs in the GC.