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

Recent studies have proposed that GRAVITY+ instrument is able to trace the circular orbit of the subparsec close-binary supermassive black holes (CB-SMBHs) by measuring the photocentre 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. We investigate the problem of detecting the CB-SMBH with hot dust emission and high eccentricity (eCBSMBH, e=0.5) when the observed time baselines of their astrometric data and radial velocities are considerably shorter than the orbital period. The parameter space of the Keplerian model of the eCBSMBH is large for exploratory purposes. We therefore applied the Bayesian method to fit orbital elements of the eCBSMBH to combined radial velocity and astrometric data covering a small fraction of the orbital period. We estimate that a number of potential eCBSMBH systems within reach of GRAVITY + will be similar to the number of the 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 eCBSMBH. When the observational time baseline becomes too short (~ 5%), the quality of the retrieved eCBSMBH parameters degrades. We also illustrate how interferometry may be used to estimate the photo-centre at the eCBSMBH emission line, which could be relevant for GRAVITY+ successors. Even if the astrometric signal for eCBSMBH systems is reduced by a factor of sqrt{1-e^{2}} compared to circular ones, we find that the hot dust emission of eCBSMBHs can be traced by GRAVITY+ at the elementary level.