Accurate Fitting Formula for the Two-Point Correlation Function of Dark Matter Halos

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Abstract
An accurate fitting formula is reported for the two-point correlation function ξhh(r;M) of dark matter halos in hierarchical clustering models. It is valid for the linearly clustering regime, and its accuracy is about 10% in ξhh(r;M) for the halos with mass M > (10−2-10−3)M*, where M* is the characteristic nonlinear mass. The result is found on the basis of a careful analysis for a large set of scale-free simulations with 2563 particles. The fitting formula has a weak explicit dependence on the index n of the initial power spectrum but can be equally well applied to the cold dark matter (CDM) cosmological models if the effective index neff of the CDM power spectrum at the scale of the halo mass replaces the index n. The formula agrees with the analytical formula of Mo & White for massive halos with M > M*, but the Mo & White formula significantly underpredicts ξhh(r;M) for the less massive halos. The difference between the fitting and the analytical formulae amounts to a factor 2 in ξhh(r;M) for M=0.01M*. One of the most interesting applications of this fitting formula would be the clustering of galaxies, since the majority of halos hosting galaxies satisfies MM*.

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