Thermal modelling of Advanced LIGO test masses

High-reflectivity fused silica mirrors are at the epicentre of today's advanced gravitational wave detectors. In these detectors, the mirrors interact with high power laser beams. As a result of finite absorption in the high reflectivity coatings the mirrors suffer from a variety of thermal effects that impact on the detectors' performance. We propose a model of the Advanced LIGO mirrors that introduces an empirical term to account for the radiative heat transfer between the mirror and its surroundings. The mechanical mode frequency is used as a probe for the overall temperature of the mirror. The thermal transient after power build-up in the optical cavities is used to refine and test the model. The model provides a coating absorption estimate of 1.5-2.0 ppm and estimates that 0.3 to 1.3 ppm of the circulating light is scattered onto the ring heater.