An application of projected distance cross-correlation for Abell clusters
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A new method is applied for the estimation of the spatial two-point correlation function of Abell clusters. This method is based on the projected distance cross-correlation function W SA between the Struble and Rood catalogue and the Abell catalogue. The σ-correlation function is determined, the best fit is W SA (σ) = σ SA /σ, where σ SA = 2.3Mpc. The spatial cross-correlation function can be derived from W SA (σ) by an integral transformation. In our case, we obtain ζ SA (r) = (r/r SA )-γ, where γ = 1.88 and r SA = 40 Mpc. A further normalization, based on a comparison of angular correlations, is needed to obtain the autocorrelation function since the Struble and Rood catalogue is not a fair subsample of the Abell catalogue. Thus we get ζ AA (r) ≈ (r/r AA )−γ, where γ = 1.88 and r AA = 33 Mpc. We note that the estimation is very sensitive to the estimated distance limits of the Abell catalogue. This result agrees well with ζ AA (r) = (r/30 Mpc)−2 obtained from the Limber equation.
KeywordsAngular Correlation Distance Class Distance Limit Extinction Curve Spatial Correlation Function
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