Differential Interferometric Signatures of Close Binaries of Supermassive Black Holes in Active Galactic Nuclei

In the present paper, we explore opportunities of applying the GRAVITY at the Very Large Telescope Interferometry (VLTI) with unprecedented spatial resolution to identify close binaries of supermassive black holes (CB-SMBHs) in active galactic nuclei (AGNs). Each SMBH is assumed to be separately surrounded by their own broad-line regions (BLRs) composed of clouds with virialized motion. Composition of the binary orbital motion and the virial motion of clouds in each BLR determines the projected velocity fields and hence differential phase curves, which are obviously different from that of a single BLR. We calculate emission line profiles and differential phase curves of CB-SMBHs for the GRAVITY. For the simplest case where angular momentums of two BLRs and orbital motion are parallel, a phase plateau generally appears in the phase curves. For other combinations of the angular momentum, the plateau is replaced by new peaks and valleys variously depending on the situations. Given a combination, phase curves are also sensitive to changes of parameters of CB-SMBHs. All these features are easily distinguished from the well-known $S$-shaped phase curves of a single BLR so that the GRAVITY is expected to reveal signals of CB-SMBH from candidates of AGNs. With joint analysis of observations of reverberation mapping campaigns, we can reliably identify CB-SMBHs, and measure their orbital parameters in the meanwhile. This independent measurement of the orbital parameters also has implications to analysis of Pulsar Timing Array (PTA) observations for properties of low-frequency gravitational waves in future.