The temperature of thermal X-ray and gamma-ray sources

The temperature of a source can be accurately measured, assuming that it is optically thin and exhibits a bremsstrahlung, on the basis of the shape of its spectral distribution. An explicit relation is derived for the temperature in terms of this slope, and as a sum of correction terms to the limiting form of the bremsstrahlung formula. The corrections can be evaluated easily in terms of simple, accurate asymptotic formulae. For the case where there is a distribution of temperatures in the plasma, an additional correction is derived in terms of the rms variation in the plasma temperature. Corrections due to a modified Bessel function, the Born approximation, plasma electron energy distribution and electron-electron bremsstrahlung are discussed