We present accurate analytic fitting formulae which summarize the results of the recent calculation by Nozawa, Itoh & Kohyama on the relativistic thermal bremsstrahlung Gaunt factor for the intracluster plasma. The fitting is carried out for 1 ≤ Z j ≤ 28, 6.0 ≤ log T ≤ 8.5, −4.0 ≤ log(hω/k B T ) ≤ 1.0 by combining the relativisitic Gaunt factor with the nonrelativistic exact Gaunt factor smoothly, where Z j is the charge number of the ion, T is the temperature in kelvins, and ω is the angular frequency of the emitted photon. We also present an accurate analytic fitting formula for the nonrelativistic exact Gaunt factor. This fitting formula is best suited for relatively low-temperature plasmas in which the relativisitic effect is negligible. The present analytic fitting formulae will be useful for the analysis of the X-ray emission which comes from the intracluster plasma as well as the other X-ray sources.

Abstract. We present useful analytic fitting formulae for the study of the radiative processes which take place in the hot intracluster plasma (the plasma which exists in the clusters of galaxies). The first is for the frequencyintegrated emissivity of the relativistic thermal bremsstrahlung. The Gaunt factor for the relativistic thermal bremsstrahlung as a function of the ionic charge Zj, the electron temperature Te, and the photon frequency ω has been recently calculated by us and its analytic fitting formula has been presented. In this paper we will integrate this Gaunt factor over the photon frequency ω and express the results by accurate analytic fitting formulae. These results will be useful when one wishes to evaluate the total amount of energy emitted by the hot intracluster plasma as well as other hot plasmas that exist in supernova remnants. The present results for the frequencyintegrated emissivity of the thermal bremsstrahlung generally have accuracy of the order of 0.1%, thus making the present results the most accurate to date that calculate the thermal bremsstrahlung due to electron-ion scattering. The present accurate results will be especially useful for the analysis of the precision data taken by the Chandra X-Ray Observatory and XMM-Newton. The second analytic fitting formula that we will present in this paper is for the thermal Sunyaev-Zeldovich effect for clusters of galaxies. The thermal Sunyaev-Zeldovich effect for clusters of galaxies has been recently calculated with high precision by the present authors as well as by other groups. We have, in particular, presented an analytic fitting formula for this effect. In this paper we will present an analytic fitting formula which has still higher accuracy. The present fitting formula will be particularly suited for the forthcoming measurements of the kinematical Sunyaev-Zeldovich effect such as the BOLOCAM project that will be carried out in the crossover frequency region where the thermal Sunyaev-Zeldovich signal changes from negative to positive sign.