Detection of eccentric close-binary supermassive black holes with incomplete interferometric data

¹ Department of astronomy, Faculty of mathematics, University of Belgrade Studentski trg 16, Belgrade 11000 Serbia
e-mail: andjelka@matf.bg.ac.rs
² PIFI Research Fellow, Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049 PR China
³ Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, CAS 19B Yuquan Road, Beijing 100049, PR China
e-mail: wangjm@ihep.ac.cn
⁴ School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
⁵ Astronomical observatory Belgrade Volgina 7, PO Box 74 Belgrade 11060, Serbia

Received: 25 February 2022
Accepted: 16 May 2022

Abstract

Context. Recent studies have proposed that General Relativity Analysis via VLT InTerferometrY upgrade (GRAVITY+) on board the Very Large Telescope Interferometer (VLTI) is able to trace the circular orbit of the subparsec (≲0.1 pc) close-binary supermassive black holes (CB-SMBHs) by measuring the photo-centre variation of the hot dust emission. However, the CB-SMBHs orbit may become highly eccentric throughout the evolution of these objects, and the orbital period may be far longer than the observational time baseline.

Aims. We investigate the problem of detecting the CB-SMBH with hot dust emission and high eccentricity (eCB-SMBH, e = 0.5) when the observed time baselines of their astrometric data and radial velocities are considerably shorter than the orbital period.

Methods. The parameter space of the Keplerian model of the eCB-SMBH is large for exploratory purposes. We therefore applied the Bayesian method to fit orbital elements of the eCB-SMBH to combine radial velocity and astrometric data covering a small fraction of the orbital period.

Results. We estimate that a number of potential eCB-SMBH systems within reach of GRAVITY+ will be similar to the number of planned circular targets. We show that using observational time baselines that cover ≳10% of the orbit increases the possibility of determining the period, eccentricity, and total mass of an eCB-SMBH. When the observational time baseline becomes too short (~5%), the quality of the retrieved eCB-SMBH parameters degrades. We also illustrate how interferometry may be used to estimate the photo-centre at the eCB-SMBH emission line, which could be relevant for GRAVITY+ successors. Even if the astrometric signal for eCB-SMBH systems is reduced by a factor of √(1 - e²) compared to circular ones, we find that the hot dust emission of eCB-SMBHs can be traced by GRAVITY+ at the elementary level.