Interstellar radiation as a Maxwell field: improved numerical scheme and application to the spectral energy density

The existing models of the interstellar radiation field (ISRF) do not produce a Maxwell field. Here, the recent model of the ISRF as a Maxwell field is improved by considering separately the different frequencies at the stage of the fitting. Using this improved procedure: (i) It is checked in detail that the model does predict extremely high values of the spectral energy density (SED) on the axis of a galaxy, that however decrease very rapidly when $\rho$, the distance to the axis, is increased from zero. (ii) The difference between the SED values (with $\rho =1\,$kpc or $8\,$kpc), as predicted either by this model or by a recent radiation transfer model, is reduced significantly. (iii) The slower decrease of the SED with increasing altitude $z$, as compared with the radiation transfer model, is confirmed. We also calculate the evolutions of the SED at large $\rho$. We interpret these evolutions by determining asymptotic expansions of the SED at large $z$, and also ones at large $\rho$.