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

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 ${\ensuremath{\xi}}_{L}(r)=({r}_{0}/r{)}^{n+3}$ 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 ($n=\ensuremath{-}0.5$, $\ensuremath{-}1$, $\ensuremath{-}1.5$) and evolve simulations to large effective correlation amplitudes (equivalent to ${\ensuremath{\sigma}}_{8}=4--12$ for ${r}_{\mathrm{bao}}=100{h}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Mpc}$). In all cases, nonlinear evolution flattens and broadens the BAO bump in $\ensuremath{\xi}(r)$ while approximately preserving its area. This evolution resembles a diffusion process in which the bump width ${\ensuremath{\sigma}}_{\mathrm{bao}}$ is the quadrature sum of the linear theory width and a length proportional to the rms relative displacement ${\ensuremath{\Sigma}}_{\mathrm{pair}}({r}_{\mathrm{bao}})$ of particle pairs separated by ${r}_{\mathrm{bao}}$. For $n=\ensuremath{-}0.5$ and $n=\ensuremath{-}1$, we find no detectable shift of the location of the BAO peak, but the peak in the $n=\ensuremath{-}1.5$ model shifts steadily to smaller scales, following ${r}_{\mathrm{peak}}/{r}_{\mathrm{bao}}=1--1.08({r}_{0}/{r}_{\mathrm{bao}}{)}^{1.5}$. 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 $\ensuremath{\xi}(r)$ peak shifts much more for $n=\ensuremath{-}1.5$ than for $n\ensuremath{\ge}\ensuremath{-}1$, though no ab initio model we have examined reproduces all of our numerical results. Simulations with ${L}_{\mathrm{box}}=10{r}_{\mathrm{bao}}$ and ${L}_{\mathrm{box}}=20{r}_{\mathrm{bao}}$ yield consistent results for $\ensuremath{\xi}(r)$ at the BAO scale, provided one corrects for the integral constraint imposed by the uniform density box.