Modeling Nonlinear Evolution of Baryon Acoustic Oscillations: Convergence Regime of $N$ -body Simulations and Analytic Models

We used a series of cosmological $N$ -body simulations and various analytic models to study the evolution of the matter power spectrum in real space in a $\Lambda$ cold dark matter universe. We compared the results of $N$ -body simulations against three analytical model predictions; standard perturbation theory, renormalized perturbation theory, and a closure approximation. We included the effects from a finite simulation box size under comparison. We determined the values of the maximum wavenumbers, $k^{\rm lim}_{1\%}$ and $k^{\rm lim}_{3\%}$ , below which the analytic models and the simulation results agree with accuracy to within 1 and 3 percent. We then provided a simple empirical function that describes the convergence regime determined by comparisons between our simulations and the analytical models. We found that if we use the Fourier modes within the convergence regime alone, the characteristic scale of baryon acoustic oscillations can be determined with an accuracy of 1% from future surveys with a volume of a few $h^{-3}$ Gpc $^3$ at z $\sim$ 1 or z $\sim$ 3 in the absence of any systematic distortion of the power spectrum.