The impact of non-thermal electrons on event horizon scale images and spectra of Sgr A*

Decomposing an arbitrary electron energy distribution into sums of Maxwellian and power law components is an efficient method to calculate synchrotron emission and absorption. We use this method to study the effect of non-thermal electrons on submm images and spectra of the Galactic center black hole, Sgr A*. We assume a spatially uniform functional form for the electron distribution function and use a semi-analytic radiatively inefficient accretion flow and a 2D general relativistic MHD snapshot as example models of the underlying accretion flow structure. We develop simple analytic models which allow us to generalize from the numerical examples. A high energy electron component containing a small fraction (few per cent) of the total internal energy (e.g. a "power law tail") can produce a diffuse halo of emission, which modifies the observed image size and structure. A population of hot electrons with a larger energy fraction (e.g. resulting from a diffusion in electron energy space) can dominate the emission, so that the observed images and spectra are well approximated by considering only a single thermal component for a suitable choice of the electron temperature. We discuss the implications of these results for estimating accretion flow or black hole parameters from images and spectra, and for the identification of the black hole "shadow" in future mm-VLBI data. In particular, the location of the first minimum in visibility profiles does not necessarily correspond to the shadow size as sometimes assumed.