Reconstruction of Static Black Hole Images Using Simple Geometric Forms

General Relativity predicts that the emission close to a black hole must be lensed by its strong gravitational field, illuminating the last photon orbit. This results in a dark circular area known as the black hole 'shadow'. The Event Horizon Telescope (EHT) is a (sub)mm VLBI network capable of Schwarzschild-radius resolution on Sagittarius A* (or Sgr A*), the 4 million solar mass black hole at the Galactic Center. The goals of the Sgr A* observations include resolving and measuring the details of its morphology. However, EHT data are sparse in the visibility domain, complicating reliable detailed image reconstruction. Therefore, direct pixel imaging should be complemented by other approaches. Using simulated EHT data from a black hole emission model we consider an approach to Sgr A* image reconstruction based on a simple and computationally efficient analytical model that produces images similar to the synthetic ones. The model consists of an eccentric ring with a brightness gradient and a two-dimensional Gaussian. These elemental forms have closed functional representations in the visibility domain, which lowers the computational overhead of fitting the model to the EHT observations. For model fitting we use a version of the Markov chain Monte-Carlo (MCMC) algorithm based on the Metropolis-Hastings sampler with replica exchange. Over a series of simulations we demonstrate that our model can be used for determining geometric measures of a black hole, thus providing information on the shadow size, linking General Relativity with accretion theory.