Corrections to weighted opacities and energy exchange rate in 3-T radiation-hydrodynamics

It is often the case that high energy density systems can be well described and simulated in the 3T approximation, where electrons, ions and the radiation field are defined at unique temperatures given by Te, Ti, Tr. The difference in temperature between the electrons and radiation field is important when calculating weighted opacities and electron-radiation energy exchange rates. Often, it is assumed that Tr Te, meaning the quantities can be calculated as functions of Te only. This paper explores the consequences that arise when one uses this assumption in regions where Tr. Te. Mutliplicative correction factors are derived for the Rosseland and Planckian mean opacities (.R and.P) and for the electron-radiation energy exchange rate. We find that there exists a very small region of parameter space where the corrections are negligible. However, for the majority of parameter space explored, numerical corrections vary from factors of 2 to multiple orders of magnitude.