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-β 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-β 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-β 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-β model is able
to reproduce well the various and more complex electron-heating prescriptions
considered here.Comment: 18 pages, 22 figures, accepted for publication in MNRA