Higher Order Contributions to the 21 cm Power Spectrum

We consider the contribution of 3rd and 4th order terms to the power spectrumof 21 cm brightness temperature fluctuations during the epoch of reionization,which arise because the 21 cm brightness temperature involves a product of thehydrogenic neutral fraction and the gas density. The 3rd order terms vanish forGaussian random fields, and have been previously neglected or ignored. Wemeasure these higher order terms from radiative transfer simulations andestimate them using cosmological perturbation theory. In our simulated models,the higher order terms are significant: neglecting them leads to a >~100% errorin 21 cm power spectrum predictions on scales of k >~ 1 Mpc^{-1} when theneutral fraction is ~0.5. The higher order terms have a simple physicalinterpretation. On small scales they are produced by gravitational modecoupling. Small scale structure grows more readily in large-scale overdenseregions, but the same regions tend to be ionized and hence do not contribute tothe 21 cm signal. This acts to suppress the influence of non-linear densityfluctuations and the small-scale amplitude of the 21 cm power spectrum. Theseresults modify earlier intuition that the 21 cm power spectrum simply tracesthe density power spectrum on scales smaller than that of a typical bubble, andimply that small scale measurements contain more information about the natureof the ionizing sources than previously believed. On large scales, higher ordermoments are not directly related to gravity. They are non-zero becauseover-dense regions tend to ionize first and are important in magnitude at latetimes owing to the large fluctuations in the neutral fraction. (Abridged)Comment: 12 pages, 10 figures, submitted to Ap