Convolution Lagrangian perturbation theory for biased tracers

Abstract

We present a new formulation of Lagrangian perturbation theory which allows accurate predictions of the real- and redshift-space correlation functions of the mass field and dark matter haloes. Our formulation involves a non-perturbative resummation of Lagrangian perturbation theory and indeed can be viewed as a partial resummation of the formalism of Matsubara in which we keep exponentiated all of the terms which tend to a constant at large separation. One of the key features of our method is that we naturally recover the Zel'dovich approximation as the lowest order of our expansion for the matter correlation function. We compare our results against a suite of N-body simulations and obtain good agreement for the correlation functions in real space and for the monopole correlation function in redshift space. The agreement becomes worse for higher multipole moments of the redshift-space, halo correlation function. Our formalism naturally includes non-linear bias and explains the strong bias-dependence of the multipole moments of the redshift-space correlation function seen in N-body simulations.