Radio spectrum of M31. The data points (from Battistelli et al. 2019) denote the whole-galaxy radio flux reduced to the estimated flux expected from within the R_⋆ radial region as described in the text. Also shown are: (top) Battistelli et al. (2019) fit (single electron population synchrotron: dotted curve; thermal free–free emission: dot-dashed curve), and (bottom) our LH emission model. The latter includes primary and secondary synchrotron radiation (dotted curves of increasing flux at their peaks) and a thermal free–free component (dot-dashed curve).