Direct Measurement of Black Hole Spin: Theory of Infalling Gas Clouds and VLBI Observational Approaches

The observational measurement of the black hole spacetime is one of the most important topics for proving the general relativity. The black hole spacetime is described by two quantities: the black hole mass and spin. The mass can be relatively accurately estimated from astrometric observations of orbiting stars around the central black hole as long as they are in the sphere of its gravitational influence. Measuring the black hole spin requires information from the vicinity of the event horizon, which is spatially resolved for the Galactic center Sagittarius A* (Sgr A*) and nearby radio galaxy M 87 by means of very long baseline interferometry (VLBI) observations with the Event Horizon Telescope (EHT). However, it is not easy to extract the spin information from the horizon-scale emission, which depends on the complexity of accretion flow properties and spacetime effects. The construction of the method which is less affected by accretion models is essential to constrain the spin of the blackhole with EHT observations.

In this presentation, 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. We investigate the signature of spin dependency of relativistic flux variation by calculating the motion of an infalling gas cloud and photon trajectories in the Kerr spacetime by the general relativistic ray-tracing method. 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.

To optimize our new method for the spin measurement, we perform synthetic EHT observations for Sgr A* under a more realistic situation by performing three dimensional general relativistic magnetohydrodynamics (3D-GRMHD) simulations. Even for the more realistic situation, the signature of the black hole spin dependency 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* since April 2017-2021.