Bolometric treatment of irradiation effects: general discussion and application to binary stars

A general framework for dealing with irradiation effects in the bolometric sense --- specifically, reflection with heat absorption and the consequent redistribution of the absorbed heat, for systems of astrophysical bodies where the boundaries are used as support for the description of the processes, is presented. Discussed are its mathematical and physical properties, as well as its implementation approximations, with a focus on three plausible redistribution processes (uniform, latitudinal, and local redistribution). These are tested by extending PHOEBE 2.1 ( http://phoebe-project.org ), the open-source package for modeling eclipsing binaries, and applied to a toy model of the known two-body eclipsing systems.