A direct method for measuring heat conductivity in intracluster medium

The inverse Compton scattering of the cosmic microwave background (CMB) radiation with electrons in the intracluster medium, which has a temperature gradient, is examined using third-order perturbation theory of Compton scattering. A new type of spectrum distortion of the CMB was found and named the gradient-T Sunyaev-Zel'dovich effect (grad-T SZE). The spectrum has a universal shape. The spectrum crosses zero at 326 GHz. The sign of the spectrum depends on the relative direction of the line of sight to the direction of the temperature gradient. This unique spectrum shape can be used to detect the grad-T SZE signal by broadband or multifrequency observations of the SZE. The amplitude of the spectrum distortion does not depend on the electron density and is proportional to the heat conductivity. Therefore, the grad-T SZE provides a unique opportunity to measure the thermally nonequilibrium electron momentum distribution function when the ICM has a temperature gradient and a heat conductivity in the ICM. However, the expected amplitude of the signal is very small. The modifications to the thermal SZE spectrum due to a variety of known effects, such as relativistic correction, can become problematic when using multifrequency separation techniques to detect the grad-T SZE signal.