The Relation between the Two‐Point and Three‐Point Correlation Functions in the Nonlinear Gravitational Clustering Regime | Zendy

Hiroko Koyama | Zendy; Taihei Yano | Zendy

Open Access

The Relation between the Two‐Point and Three‐Point Correlation Functions in the Nonlinear Gravitational Clustering Regime

Author(s) -

Hiroko Koyama,

Taihei Yano

Publication year - 2005

Publication title -

the astrophysical journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.376

H-Index - 489

eISSN - 1538-4357

pISSN - 0004-637X

DOI - 10.1086/423262

Subject(s) - correlation function (quantum field theory) , scaling , physics , mathematical physics , power function , nonlinear system , connection (principal bundle) , statistical physics , point (geometry) , riemann zeta function , mathematics , mathematical analysis , spectral density , quantum mechanics , statistics , geometry

The connection between the two-point and the three-point correlationfunctions in the non-linear gravitational clustering regime is studied. Under ascaling hypothesis, we find that the three-point correlation function, $\zeta$,obeys the scaling law $\zeta\propto \xi^{\frac{3m+4w-2\epsilon}{2m+2w}}$ in thenonlinear regime, where $\xi$, $m$, $w$, and $\epsilon$ are the two-pointcorrelation function, the power index of the power spectrum in the nonlinearregime, the number of spatial dimensions, and the power index of the phasecorrelations, respectively. The new formula reveals the origin of the powerindex of the three-point correlation function. We also obtain the theoreticalcondition for which the ``hierarchical form'' $\zeta\propto\xi^2$ isreproduced.Comment: 16 pages, 4 figures. Accepted for publication in APJ. Some sentences and figures are revise

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