Publication : t16/167

Beyond Kaiser bias: mildly non-linear two-point statistics of densities in distant spheres

Uhlemann C. (Institute for Theoretical Physics, Utrecht University, 3508 TD Utrecht, The Netherlands)
Codis S. (Canadian Institute for Theoretical Astrophysics (CITA), University of Toronto, 60 St. George Street, Toronto, M5S 3H8 Ontario, CANADA)
Pichon C. (Institut d\'Astrophysique de Paris (IAP-CNRS), 98 bis Bld Arago, F-75014 Paris, FRANCE)
Bernardeau F. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Pogosyan D. (Institut d’Astrophysique de Paris, UMR7095 CNRS, Universit´e Pierre & Marie Curie - Paris, 98 bis bd Arago, 75014 Paris, France)
Park C. (Korea Institute for Advanced Study (KIAS), Hoegiro 87(207-43 Cheongnyangni 2-dong), Dongdaemun-gu, Seoul 130-772, KOREA)
L’Huillier B. (Korea Institute for Advanced Study (KIAS), Hoegiro 87(207-43 Cheongnyangni 2-dong), Dongdaemun-gu, Seoul 130-772, KOREA)
Simple parameter-free analytic bias functions for the two-point correlation of densities in spheres at large separation are presented. These bias functions generalize the so-called Kaiser bias to the mildly non-linear regime for arbitrary density contrasts as b(ρ) − b(1) ∝ (1 − ρ−13/21)ρ1+n/3 with b(1) = −4/21 − n/3 for a power-law initial spectrum with in- dex n . The derivation is carried out in the context of large deviation statistics while relying on the spherical collapse model. A logarithmic transformation provides a saddle approxima- tion which is valid for the whole range of densities and shown to be accurate against the 30 Gpc cube state-of-the-art Horizon Run 4 simulation. Special configurations of two concentric spheres that allow to identify peaks are employed to obtain the conditional bias and a proxy to BBKS extrema correlation functions. These analytic bias functions should be used jointly with extended perturbation theory to predict two-point clustering statistics as they capture the non-linear regime of structure formation at the percent level down to scales of about 10 Mpc/h at redshift 0. Conversely, the joint statistics also provide us with optimal dark matter two-point correlation estimates which can be applied either universally to all spheres or to a restricted set of biased (over- or underdense) pairs. Based on a simple fiducial survey, this estimator is shown to perform five times better than usual two-point function estimators. Extracting more information from correlations of different types of objects should prove essential in the context of upcoming surveys like Euclid, DESI, PFS or LSST.
Année de publication : 2017
Preprint : arXiv:1607.01026
Langue : Anglais

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