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Towards an accurate model of redshift-space distortions: a bivariate Gaussian description for the galaxy pairwise velocity distributions

Published online by Cambridge University Press:  12 October 2016

Davide Bianchi
Affiliation:
INAF – Osservatorio Astronomico di Brera, via Emilio Bianchi 46, I-23807 Merate, Italy Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, I-20133 Milano, Italy email: davide.bianchi@brera.inaf.it
Matteo Chiesa
Affiliation:
INAF – Osservatorio Astronomico di Brera, via Emilio Bianchi 46, I-23807 Merate, Italy Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, I-20133 Milano, Italy email: davide.bianchi@brera.inaf.it
Luigi Guzzo
Affiliation:
INAF – Osservatorio Astronomico di Brera, via Emilio Bianchi 46, I-23807 Merate, Italy
Corresponding
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Abstract

As a step towards a more accurate modelling of redshift-space distortions (RSD) in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation , such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean μ and variance σ2. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distorsions on all scales, fully capturing the overall linear and nonlinear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of redshift-space distortions is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. More work is needed, but these results indicate a very promising path to make definitive progress in our program to improve RSD estimators.

Type
Contributed Papers
Copyright
Copyright © International Astronomical Union 2016 

References

Bianchi, D., Chiesa, M., & Guzzo, L. 2014, arXiv:1407.4753Google Scholar
Fisher, K. B., 1995, ApJ, 448, 494 CrossRefGoogle Scholar
Riebe, K. et al. 2013, Astronomische Nachrichten, 334, 691 CrossRefGoogle Scholar
Scoccimarro, R. 2004, Phys. Rev D, 70, 083007 CrossRefGoogle Scholar

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