Relativistic Corrections in the Determination of [ITAL]H[/ITAL][TINF]0[/TINF] from X-Ray and Sunyaev-Zeldovich Measurements

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Abstract
Interpretations of measurements of the Sunyaev-Zeldovich (S-Z) effect and thermal X-ray emission in clusters of galaxies are usually based on nonrelativistic treatments of these processes. The higher sensitivity currently achievable in these measurements has to be matched with the results of more exact calculations of the S-Z effect and bremsstrahlung emissivity. The relativistically correct formulae are summarized and discussed; use of these expressions is particularly necessary in the determination of the Hubble constant, H0, from S-Z and X-ray measurements. These corrections lead to values of H0 lower by 11%-29% than those obtained using the nonrelativistic formulae.