Self-similar bumps and wiggles: Isolating the evolution of the BAO peak with power-law initial conditions

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 ξL(r)=(r₀/r)ⁿ⁺³ of an underlying self-similar model with initial power spectrum P(k)=Akⁿ. 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 σ₈=4--12 for rbao=100h^-1 Mpc). In all cases, nonlinear evolution flattens and broadens the BAO bump in ξ(r) while approximately preserving its area. This evolution resembles a diffusion process in which the bump width σbao is the quadrature sum of the linear theory width and a length proportional to the rms relative displacement Σₚₐᵢᵣ(rbao) of particle pairs separated by rbao. 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 rₚₑₐₖ/rbao=1--1.08(r₀/rbao)1.5. The perturbation theory scheme of McDonald (2007) [P. McDonald, Phys. Rev. D 75, 043514 (2007).] and, to a lesser extent, standard 1-loop perturbation theory are fairly successful at explaining the nonlinear evolution of the Fourier power spectrum of our models. Analytic models also explain why the ξ(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 Lbox=10rbao and Lbox=20rbao yield consistent results for ξ(r) at the BAO scale, provided one corrects for the integral constraint imposed by the uniform density box.