Efficient Simulations of Early Structure Formation and Reionization

We present a method to construct semi-numerical ``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. We test our halo-finding and HII bubble-finding algorithms independently 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. 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, though 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 x10^8 M_sun. We show that accurately modeling the late stages of reionization requires such large scales. The speed and dynamic range provided by our semi-numerical approach will be extremely useful in the modeling of early structure formation and reionization.