  The Event Horizon Telescope (EHT) collaboration has produced the first
resolved images of the supermassive black holes at the centre of our galaxy and
at the centre of the elliptical galaxy M87. As both technology and analysis
pipelines improve, it will soon become possible to produce spectral index maps
of black hole accretion flows on event horizon scales. In this work, we predict
spectral index maps of both M87* and Sgr A* by applying the general
relativistic radiative transfer (GRRT) code IPOLE to a suite of general
relativistic magnetohydrodynamic (GRMHD) simulations. We analytically show that
the spectral index increases with increasing magnetic field strength, electron
temperature, and optical depth. Consequently, spectral index maps grow more
negative with increasing radius in almost all models, since all of these
quantities tend to be maximised near the event horizon. Additionally, photon
ring geodesics exhibit more positive spectral indices, since they sample the
innermost regions of the accretion flow with the most extreme plasma
conditions. Spectral index maps are sensitive to highly uncertain plasma
heating prescriptions (the electron temperature and distribution function).
However, if our understanding of these aspects of plasma physics can be
tightened, even the spatially unresolved spectral index around 230 GHz can be
used to discriminate between models. In particular, Standard and Normal
Evolution (SANE) flows tend to exhibit more negative spectral indices than
Magnetically Arrested Disk (MAD) flows due to differences in the characteristic
magnetic field strength and temperature of emitting plasma.
