Black Hole Spin Measurement Based on Time-domain VLBI Observations of Infalling Gas Clouds

The black hole spacetime is described by general relativity and characterized by two quantities: the black hole mass and spin. Black hole spin measurement requires information from the vicinity of the event horizon, which is spatially resolved for the Galactic center Sagittarius A∗ (Sgr A∗) and the nearby radio galaxy M87 by means of very long baseline interferometry observations with the Event Horizon Telescope (EHT). In this paper, we simulate EHT observations for a gas cloud intermittently falling onto a black hole and construct a method for spin measurement based on its relativistic flux variation. The light curve of the infalling gas cloud is composed of peaks formed by photons which directly reach a distant observer and by secondary ones reaching the observer after more than one rotation around the black hole. The time interval between the peaks is determined by a period of photon rotation near the photon circular orbit which uniquely depends on the spin. We perform synthetic EHT observations for Sgr A∗ under the more realistic situation where a number of gas clouds intermittently fall toward the black hole with various initial parameters. Even for this case, the black hole spin dependence is detectable in correlated flux densities which are accurately calibrated by baselines between sites with redundant stations. The synthetic observations indicate that our methodology can be applied to EHT observations of Sgr A∗ from 2017 April.