Geometry of irradiated stars

The physical conditions in a variety of objects (e.g. hot exoplanets and close binaries) are fundamentally influenced by external irradiation. In static cases this leads to the development of zones of different temperatures on the ‘day‐side’. In order to combine spectra from all zones to a full visible circular disk and to obtain a 1.5D spectrum we need to calculate the weight of each patch. In the following we present the geometrical considerations and calculate the observed projected area of constant temperature in an irradiated object for specific re‐radiation angles. This allows non‐isotropic models to be used. We supply an IDL code to calculate the observed projected area for any patch given the phase and angle between surface and line of sight as well as a proper weighting for each by numerical integration. We end up with a simple approach to upgrade a 1D irradiation model to a quasi 1.5D one. This method can be applied e.g. to irradiated secondaries in close binaries.