Distinguishing gravitational and emission physics in black hole imaging: spherical symmetry

Imaging a supermassive black hole and extracting physical information requires good knowledge of both the gravitational and the astrophysical conditions near the black hole. When the geometrical properties of the black hole are well understood, extracting information on the emission properties is possible. Similarly, when the emission properties are well understood, extracting information on the black hole geometry is possible. At present however, uncertainties are present both in the geometry and in the emission, and this inevitably leads to degeneracies in the interpretation of the observations. We explore here the impact of varying geometry and emission coefficient when modelling the imaging of a spherically accreting black hole. Adopting the Rezzolla-Zhidenko parametric metric to model arbitrary static black holes, we first demonstrate how shadow-size measurements leave degeneracies in the multidimensional space of metric-deviation parameters, even in the limit of infinite-precision measurements. Then, at finite precision, we show that these degenerate regions can be constrained when multiple pieces of information, such as the shadow-size and the peak image intensity contrast, are combined. Such degeneracies can potentially be eliminated with measurements at increased angular resolution and flux sensitivity. While our approach is restricted to spherical symmetry and hence idealized, we expect our results to hold also when more complex geometries and emission processes are considered.