A comprehensive and detailed analysis of hadronic abundances measured in Au-Au collisions at RHIC at sqrt(s)_NN = 130 and 200 GeV is presented. The rapidity densities measured in the central rapidity region have been fitted to the statistical hadronization model and the chemical freeze-out parameters determined as a function of centrality, using data from experiments BRAHMS, PHENIX and STAR. The chemical freeze-out temperature turns out to be independent of centrality to a few percent accuracy, whereas the strangeness under-saturation parameter gamma_S decreases from almost unity in central collisions to a significantly lower value in peripheral collisions. Our results are in essential agreement with previous analyses, with the exception that fit quality at sqrt(s)_NN = 200 GeV is not as good as previously found. From the comparison of the two different energies, we conclude that the difference in fit quality, as described by chi2 values, is owing to the improved resolution of measurements which has probably exceeded the intrinsic accuracy of the simplified theoretical formula used in the fits.
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