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

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 − e 2 compared to circular ones, we find that the hot dust emission of eCB-SMBHs can be traced by GRAVITY+ at the elementary level.

Bayesian Synthesis of Astrometric Wobble and Total Light Curves in Close Binary Supermassive Black Holes

“…In this section, we provide an analytical description of the astrometric wobble of CB-SMBH system with nonfixed geometry. Then, we introduce a Bayesian protocol (for further details, see Kovačević et al 2022b) designed to extract both the binary's orbital parameters and the individual emission light curves of its constituent components. Notably, our method can be universally applied to analyze any data set comprising the astrometric wobble and the total emission light curve of a quasar, making it instrumental agnostic.…”

“…We outline a two-tier Bayesian protocol (see also Kovačević et al 2022b). The first tier involves a Simulator that generates observational multi-instrument data encompassing the astrometric wobble and optical light curves, predicated upon specified characteristics of the CB-SMBH.…”

“…However, we also see that, for CB-SMBH systems with mild eccentric orbits (0 < e < 0.3), the offset ratio tends to approach unity, implying that even at pericenter, the observed offset can be relatively nonneglibile. This phasedependent behavior necessitates careful consideration when interpreting observed offsets, especially for systems with varying eccentricities (see related discussions in Kovačević et al 2022b The potential contribution of circumbinary structures, such as circumbinary disks or circumbinary broad-line regions, to the emission from CB-SMBH systems could impact the observed photocenter motion. The extent of this impact and its implications for binary framework studies remain subjects for future exploration (Dexter et al 2020;Popović et al 2021;Guo et al 2022;Kovačević et al 2022b;Simić et al 2022).…”

“…We solve for the radial velocity for both binary components, a prescription given in Kovačević et al (2020aKovačević et al ( , 2022b for binary mass ratio q < 1. Both components are assumed to be Doppler-modulated with corresponding line-of-sight velocities and that emission from both black holes share the same spectral index with a value a ~-…”

“…Further details on the binary components position projection onto the sky plane, can be found inKovačević et al (2022b).…”