Self-Similar Bumps and Wiggles: Isolating the Evolution of the BAO Peak with Power-law Initial Conditions

TL;DR

This study uses N-body simulations with power-law initial conditions to analyze the non-linear evolution of the BAO feature in galaxy clustering, revealing how the BAO bump broadens and shifts under different conditions.

Contribution

It introduces a detailed analysis of BAO evolution using self-similar models with various power spectra, extending understanding beyond previous studies and testing analytic descriptions.

Findings

BAO bump broadens and flattens while preserving area.

No significant shift in BAO peak for n=-0.5 and -1.

Peak shifts to smaller scales for n=-1.5, following a specific relation.

Abstract

Motivated by cosmological surveys that demand accurate theoretical modeling of the baryon acoustic oscillation (BAO) feature in galaxy clustering, we analyze N-body simulations in which a BAO-like gaussian bump modulates the linear theory correlation function \xi_L(r)=(r_0/r)^{n+3} of an underlying self-similar model with initial power spectrum P(k)=A k^n. These simulations test physical and analytic descriptions of BAO evolution far beyond the range of most studies, since we consider a range of underlying power spectra (n=-0.5, -1, -1.5) and evolve simulations to large effective correlation amplitudes (equivalent to \sigma_8=4-12 for r_bao = 100 Mpc/h). In all cases, non-linear evolution flattens and broadens the BAO bump in \xi(r) while approximately preserving its area. This evolution resembles a "diffusion" process in which the bump width \sigma_bao is the quadrature sum of the linear theory width and a length proportional to the rms relative displacement \Sigma_pair(r_bao}) of particle pairs separated by r_bao. For n=-0.5 and n=-1, we find no detectable shift of the location of the BAO peak, but the peak in the n=-1.5 model shifts steadily to smaller scales, following r_peak}/r_bao = 1-1.08(r_0/r_bao)^{1.5}. The "SimpleRG" perturbation theory scheme and, to a lesser extent, standard 1-loop perturbation theory are fairly successful at explaining the non-linear evolution of the fourier power spectrum of our models. Analytic models also explain why the \xi(r) peak shifts much more for n=-1.5 than for n >= -1, though no ab initio model we have examined reproduces all of our numerical results. Simulations with L_box = 10 r_bao} and L_box = 20 r_bao yield consistent results for \xi(r) at the BAO scale, provided one corrects for the integral constraint imposed by the uniform density box.