Differential Interferometric Signatures of Close Binaries of Supermassive Black Holes in Active Galactic Nuclei: II. Merged Broad Line Regions

Pairs of supermassive black holes (SMBHs) at different stages are natural results of galaxy mergers in the hierarchical framework of galaxy formation and evolution. However, identifications of close binaries of SMBHs (CB-SMBHs) with sub-parsec separations in observations are still elusive. Recently, unprecedented spatial resolutions achieved by GRAVITY/GRAVITY+ onboard The Very Large Telescope Interferometer through spectroastrometry (SA) provide new opportunities to resolve CB-SMBHs. Differential phase curves of CB-SMBHs with two independent broad-line regions (BLRs) are found to have distinguished characteristic structures from a single BLR \citep{songsheng2019}. Once the CB-SMBH evolves to the stage where BLRs merge to form a circumbinary BLR, it will hopefully be resolved by the pulsar timing array (PTA) in the near future as sources of nano-hertz gravitational waves. In this work, we use a parameterized model for circumbinary BLRs to calculate line profiles and differential phase curves for SA observations. We show that both profiles and phase curves exhibit asymmetries caused by the Doppler boosting effect of accretion disks around individual black holes, depending on the orbital parameters of the binary and geometries of the BLR. We also generate mock SA data using the model and then recover orbital parameters by fitting the mock data. Degeneracies between parameters contribute greatly to uncertainties of parameters but can be eased through joint analysis of multiple-epoch SA observations and reverberation mappings.Comment: 21 pages, 17 figures, accepted by Ap

Final stage of merging binaries of supermassive black holes: observational signatures

There are increasing interests in binary supermassive black holes (SMBHs), but merging binaries with separations smaller than ~1 light days (~10^2 gravitational radii for 10^8 Msun), which are rapidly evolving under control of gravitational waves, are elusive in observations. In this paper, we discuss fates of mini-disks around component SMBHs for three regimes: 1) low rates (advection-dominated accretion flows: ADAFs); 2) intermediate rates; 3) super-Eddington accretion rates. Mini-disks with intermediate rates are undergoing evaporation through thermal conduction of hot corona forming a hybrid radial structure. When the binary orbital periods are shorter than sound propagation timescales of the evaporated mini-disks, a new instability, denoted as sound instability, arises because the disks will be highly twisted so that they are destroyed. We demonstrate a critical separation of A_{crit}~10^2 Rg from the sound instability of the mini-disks and the cavity is full of hot gas. For those binaries, component SMBHs are accreting with Bondi mode in the ADAF regime, showing periodic variations resulting from Doppler boosting effects in radio from the ADAFs due to orbital motion. In the mean while, the circumbinary disks (CBDs) are still not hot enough (ultraviolet deficit) to generate photons to ionize gas for broad emission lines. For slightly super-Eddington accretion of the CBDs, MgII line appears with decreases of UV deficit, and for intermediate super-Eddington Balmer lines appear, but CIV line never unless CBD accretion rates are extremely high. Moreover, if the CBDs are misaligned with the binary plane, it is then expected to have optical periodical variations with about ten times radio periods.Comment: 10 pages, 3 figures; accepted to MNRA

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.Comment: accepted for publication in the journal Astronomy & Astrophysic

Search for Continuous Gravitational-wave Signals in Pulsar Timing Residuals: A New Scalable Approach with Diffusive Nested Sampling

Detecting continuous nanohertz gravitational waves (GWs) generated by individual close binaries of supermassive black holes (CB-SMBHs) is one of the primary objectives of pulsar timing arrays (PTAs). The detection sensitivity is slated to increase significantly as the number of well-timed millisecond pulsars will increase by more than an order of magnitude with the advent of next-generation radio telescopes. Currently, the Bayesian analysis pipeline using parallel tempering Markov Chain Monte Carlo has been applied in multiple studies for CB-SMBH searches, but it may be challenged by the high dimensionality of the parameter space for future large-scale PTAs. One solution is to reduce the dimensionality by maximizing or marginalizing over uninformative parameters semianalytically, but it is not clear whether this approach can be extended to more complex signal models without making overly simplified assumptions. Recently, the method of diffusive nested (DNest) sampling has shown capability in coping with high dimensionality and multimodality effectively in Bayesian analysis. In this paper, we apply DNest to search for continuous GWs in simulated pulsar timing residuals and find that it performs well in terms of accuracy, robustness, and efficiency for a PTA including pulsars. DNest also allows a simultaneous search of multiple sources elegantly, which demonstrates its scalability and general applicability. Our results show that it is convenient and also highly beneficial to include DNest in current toolboxes of PTA analysis