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 \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.
