Comparing estimators of the galaxy correlation function

Details Comparing estimators of the galaxy correlation function Comparing estimators of the galaxy correlation function

1999-06-22

arxiv.org/abs/astro-ph/9906344v1

Astronomy and Astrophysics

Astrophysics

28 pages, 12 figures, LateX, uses aaspp4.sty, ApJ, in press, October 1, 1999 issue, Vol. 523 #2

Scientific paper

10.1086/307754

We present a systematic comparison of some usual estimators of the 2--point correlation function, some of them currently used in Cosmology, others extensively employed in the field of the statistical analysis of point processes. At small scales, it is known that the correlation function follows reasonably well a power--law expression $\xi(r) \propto r^{-\gamma}$. The accurate determination of the exponent $\gamma$ (the order of the pole) depends on the estimator used for $\xi(r)$; on the other hand, its behavior at large scale gives information on a possible trend to homogeneity. We study the concept, the possible bias, the dependence on random samples and the errors of each estimator. Errors are computed by means of artificial catalogues of Cox processes for which the analytical expression of the correlation function is known. We also introduce a new method for extracting simulated galaxy samples from cosmological simulations.

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