Higher order contributions to the 21 cm power spectrum

We consider the contribution of third- and fourth-order terms to the 21 cm power spectrum during the epoch of reionization, which arise because the 21 cm brightness temperature involves a product of the hydrogenic neutral fraction and the gas density. The third-order terms vanish for Gaussian random fields and have been previously neglected or ignored. We measure these terms from radiative transfer simulations and estimate them using cosmological perturbation theory. In our simulated models, the higher order terms are significant, and neglecting them leads to inaccurate 21 cm power spectrum estimates. On small scales the higher order terms are produced by gravitational mode coupling. Small-scale structure grows more readily in large-scale overdense regions, but the same regions tend to be ionized and hence do not contribute to the 21 cm signal. This modifies an earlier intuition that the 21 cm power spectrum simply traces the density power spectrum on scales smaller than that of a typical bubble and implies that small-scale measurements contain more information about the ionizing sources than previously believed. On large scales, higher order moments are not directly related to gravity. They are nonzero because overdense regions tend to ionize first and are important in magnitude at late times, due to large fluctuations in the neutral fraction. Finally, we show that second-order Lagrangian perturbation theory approximately reproduces the statistics of the density field from full numerical simulations for all redshifts and scales of interest, including the mode-coupling effects mentioned above. It can, therefore, be used in conjunction with semianalytic models to explore the broad regions of parameter space relevant for future 21 cm surveys.