Efficient simulations of early structure formation and reionization

Detailed theoretical studies of the high-redshift universe, and especially reionization, are generally forced to rely on time-consuming N-body codes and/or radiative transfer algorithms. We present a method to construct seminumerical simulations,'' which can efficiently generate realizations of halo distributions and ionization maps at high redshifts. Our procedure combines an excursion-set approach with first-order Lagrangian perturbation theory and operates directly on the linear density and velocity fields. As such, the achievable dynamic range with our algorithm surpasses the current practical limit of N-body codes by orders of magnitude. This is particularly significant in studies of reionization, where the dynamic range is the principal limiting factor, because ionized regions reach scales of tens of comoving Mpc. We test our halo-finding and ionization-mapping algorithms separately against N-body simulations with radiative transfer and obtain excellent agreement. We compute the size distributions of ionized and neutral regions in our maps. We find even larger ionized bubbles than do purely analytic models at the same volume-weighted mean hydrogen neutral fraction, (x) over bar (HI), especially early in reionization. We also generate maps and power spectra of 21 cm brightness temperature fluctuations, which for the first time include corrections due to gas bulk velocities. We find that velocities widen the tails of the temperature distributions and increase small-scale power, although these effects quickly diminish as reionization progresses. We also include some preliminary results from a simulation run with the largest dynamic range to date: a 250 Mpc box that resolves halos with masses M >= 2.2 X 10(8) M-circle dot. We show that accurately modeling the late stages of reionization, (x) over bar (HI) less than or similar to 0.5, requires such large scales. The speed and dynamic range provided by our seminumerical approach will be extremely useful in the modeling of early structure formation and reionization.