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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 ξ_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 σ_8=4-12 for r_bao = 100 Mpc/h). In all cases, non-linear 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 σ_bao is the quadrature sum of the linear theory width and a length proportional to the rms relative displacement Σ_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 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 L_box = 10 r_bao} and L_box = 20 r_bao yield consistent results for ξ(r) at the BAO scale, provided one corrects for the integral constraint imposed by the uniform density box.