Convolution Lagrangian perturbation theory for biased tracers

TL;DR

The paper develops convolution Lagrangian perturbation theory (CLPT), a non-perturbative resummation of Lagrangian perturbation theory, to predict real- and redshift-space two-point correlations for both matter and biased tracers. By exponentiating the large-scale, constant-limit contributions and leveraging a Zel'dovich-based starting point, CLPT naturally incorporates non-linear bias and redshift-space distortions, and reduces to the Zel'dovich result in the appropriate limit. The authors demonstrate improved agreement with N-body simulations for real-space clustering and the monopole of redshift-space clustering, while higher multipoles for halos remain challenging due to bias-model limitations. They discuss avenues for extension, including non-local/tidal bias and integration with velocity-statistics models, to broaden the applicability to galaxy surveys and the bispectrum.

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 halos. 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 (2008a,b) 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.

Figures (5)

• Figure 1: (Top) The real-space, matter correlation function, $\xi(r)$, from linear theory (solid), LRT (dotted) and CLPT (dashed) compared to N-body simulations (squares) at $z=0.55$. In order to plot the results with a linear $y$-axis we have multiplied $\xi$ by $r^2$, which removes much of the trend from $r\simeq 0-100$Mpc. LRT and CLPT agree very well on large scales (the lines can barely be distinguished) and agree well with the N-body results. LRT overshoots the N-body results below $r\simeq 20\,h^{-1}$Mpc while CLPT tracks the N-body results to much smaller scales. Linear theory overshoots at $r\simeq 20\,h^{-1}$Mpc and at $r\simeq 100\,h^{-1}$Mpc. (Bottom) The redshift-space, monopole, matter correlation function, $\xi_0(s)$, from linear theory (solid), LRT (dotted) and CLPT (dashed) compared to N-body simulations (squares). The qualitative behavior is as for $\xi(r)$.
• Figure 2: The redshift-space, quadrupole and hexadecapole, matter correlation functions, $\xi_2(s)$ and $\xi_4(s)$, from linear theory (solid), LRT (dotted) and CLPT (dashed) compared to N-body simulations (squares) at $z=0.55$. For the quadrupole LRT and CLPT agree very well on large scales (and agree well with the N-body results) but LRT departs from the N-body results at much larger scales. For the hexadecapole the disagreement between N-body, CLPT, LRT and linear theory breaks down at larger scales than for the quadrupole.
• Figure 3: The real-space, correlation function for halos with $12.8<{\rm lg}M_h<13.1$ computed in linear theory (solid), LRT (dotted) and CLPT (dashed) compared to N-body simulations (squares) at $z=0.55$. In this plot we allowed $\left\langle F' \right\rangle$ and $\left\langle F" \right\rangle$ to vary independently to obtain the best agreement with the N-body results.
• Figure 4: The real-space, correlation function for halos in three mass bins computed in linear theory (solid), LRT (dotted) and CLPT (dashed) compared to N-body simulations (squares) at $z=0.55$ for three different mass ranges each a factor of two in width: from bottom to top $12.2<{\rm lg}M_h<12.5$, $12.8<{\rm lg}M_h<13.1$ and $13.1<{\rm lg}M_h<13.4$ with masses in $h^{-1}M_\odot$. In this plot we enforced the peak-background split relation to determine $\left\langle F" \right\rangle$ in terms of the best fit $\left\langle F' \right\rangle$, i.e. the theory has only one free parameter.
• Figure 5: The redshift-space, monopole and quadrupole, correlation functions for halos computed in linear theory (solid), LRT (dotted) and CLPT (dashed) compared to N-body simulations (squares) at $z=0.55$.