Extreme lensing induced X-ray correlations: Estimation of black hole parameters

A considerable fraction of photons from an optically thin source near a black hole can be extremely lensed, orbiting the black hole because of its intense gravitational pull. Such photons, when they eventually reach an observer, are expected to give rise to photon rings (yet unresolved) in interferometric images. We develop a method to decipher the signatures of photon rings through their manifestation in spectrotemporal correlations of X-ray light curves of black holes. Using semi-analytical ray tracing, we generate light curves at different energies and numerically compute their two-point correlation function. Our method incorporates the relativistic effects of photon redshift and time delay, and includes both direct and extremely-lensed photons. We will present the results of these light-curve correlations for a simplified source model, of a monochromatic hot spot orbiting the black hole at a random radius. The spectrotemporal correlations we find show a clear dependence on black hole spin, inclination, mass, and hot spot location. Deep learning models based on Convolutional Neural Networks (CNNs) are trained to estimate the black hole source parameters from observed correlation maps. We will discuss future prospects for detecting photon-ring signals using X-ray observations of Active Galactic Nuclei and X-ray binaries with upcoming missions like New Athena.