Comparison of the ion-to-electron temperature ratio prescription: GRMHD simulations with electron thermodynamics

The Event Horizon Telescope (EHT) collaboration, an Earth-size sub-millimetre radio interferometer, recently captured the first images of the central supermassive black hole in M87. These images were interpreted as gravitationally-lensed synchrotron emission from hot plasma orbiting around the black hole. In the accretion flows around low-luminosity active galactic nuclei such as M87, electrons and ions are not in thermal equilibrium. Therefore, the electron temperature, which is important for the thermal synchrotron radiation at EHT frequencies of 230 GHz, is not independently determined. In this work, we investigate the commonly used parameterised ion-to-electron temperature ratio prescription, the so-called R-$\beta$ model, considering images at 230 GHz by comparing with electron-heating prescriptions obtained from general-relativistic magnetohydrodynamical (GRMHD) simulations of magnetised accretion flows in a Magnetically Arrested Disc (MAD) regime with different recipes for the electron thermodynamics. When comparing images at 230 GHz, we find a very good match between images produced with the R-$\beta$ prescription and those produced with the turbulent- and magnetic reconnection- heating prescriptions. Indeed, this match is on average even better than that obtained when comparing the set of images built with the R-$\beta$ prescription with either a randomly chosen image or with a time-averaged one. From this comparative study of different physical aspects, which include the image, visibilities, broadband spectra, and light curves, we conclude that, within the context of images at 230 GHz relative to MAD accretion flows around supermassive black holes, the commonly-used and simple R-$\beta$ model is able to reproduce well the various and more complex electron-heating prescriptions considered here.