Clusters of galaxies is the largest gravitational bound system in the universe and the brightest X-ray emitter. From the velocity dispersion of member galaxies in clusters, it has been clear that clusters contain the large amount invisible mass, so called 'dark matter', which is about ten times larger than the visible mass. Since the intracluster medium is dissipative, contrary to galaxies in the cluster, the observation of the intracluster medium by X-ray is useful tool to investigate the gravitational mass and dark matter distribution and hence to understand the large scale structure of the universe.
The observation of clusters of galaxies has another importance for the cosmology. This is the observational and traditional approach for cosmology, 'the Hubble constant measurement'. The Hubble constant determines both the expansion timescale and the size of the universe. However, in spite of the fundamental parameter of the cosmology, the measured values are dispersed within factor 2; 50 km sec-1 Mpc-1 ~100 km sec-1 Mpc -1. This dispersion has been caused by the various uncertainty; peculiar motion, absolute magnitude of standard candles, the calibration of 'distance ladder' method, underlying physical process and so on.
The derivation from the X-ray and radio cluster observation using the Sunyaev-Zel'dovich effect has advantages; small uncertainty of peculiar motion, clear underlying physical process. Furthermore, the distance to the cluster at the cosmological distance is available.
We analyzed 6 distant clusters of galaxies observed with ASCA and obtained accurate averaged temperatures and luminosities. Furthermore, we developed the method of the image analysis using the β model fitting in 2 energy bands including the effect of the XRT PSF, and obtained the structural parameters (θc, β) for each cluster.
Using the complete radio data of the Sunyaev-Zel'dovich effect obtained with OVRO 40m single-dish radiometer and X-ray data obtained with only ASCA we obtained the 'global' value of the Hubble constant in the universe to be 68±22 km sec-1 Mpc-1 from the distance of the clusters of galaxies, A2218, A665 and C10016+16 in the redshift range from 0.17 to 0.54 (597 Mpc -1.3 Gpc assuming H0=68 km sec-1 Mpc-1).
It is the first time that the temperature, X-ray flux and the spatially distribution of temperature and density obtained with single mission are used for the Hubble constant determination.