2D k-th nearest neighbor statistics: a highly informative probe of galaxy clustering

Kavli Affiliate: Tom Abel

| First 5 Authors: Sihan Yuan, Alvaro Zamora, Tom Abel, ,

| Summary:

Beyond standard summary statistics are necessary to summarize the rich
information on non-linear scales in the era of precision galaxy clustering
measurements. For the first time, we introduce the 2D k-th nearest neighbor
(kNN) statistics as a summary statistic for discrete galaxy fields. This is a
direct generalization of the standard 1D kNN by disentangling the projected
galaxy distribution from the redshift-space distortion signature along the
line-of-sight. We further introduce two different flavors of 2D $k$NNs that
trace different aspects of the galaxy field: the standard flavor which
tabulates the distances between galaxies and random query points, and a ”DD”
flavor that tabulates the distances between galaxies and galaxies. We showcase
the 2D kNNs’ strong constraining power both through theoretical arguments and
by testing on realistic galaxy mocks. Theoretically, we show that 2D kNNs are
computationally efficient and directly generate other statistics such as the
popular 2-point correlation function, voids probability function, and
counts-in-cell statistics. In a more practical test, we apply the 2D kNN
statistics to simulated galaxy mocks that fold in a large range of
observational realism and recover parameters of the underlying extended halo
occupation distribution (HOD) model that includes velocity bias and galaxy
assembly bias. We find unbiased and significantly tighter constraints on all
aspects of the HOD model with the 2D kNNs, both compared to the standard 1D
kNN, and the classical redshift-space 2-point correlation functions.

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