The simulated 21 cm signal during the epoch of reionization: full modeling of the Ly-alpha pumping

The 21 cm emission of neutral hydrogen is the most promising probe of the epoch of reionization (EoR). In the next few years, the SKA pathfinders will provide statistical measurements of this signal, such as its power spectrum. Within one decade, SKA should produce a full tomography of the signal. Numerical simulations predicting these observations are necessary to optimize the design of the instruments and help in the interpretation of the data. Simulations are reaching a reasonable level in terms of scale range, but still often rely on simplifications to compute the strength of the signal. The main difficulty is the computation of the spin temperature of neutral hydrogen which depends on the gas kinetic temperature and on the level of the local Lyman-alpha flux (The Wouthuysen-Field effect). A T-S >> T-CMB assumption is usual. However, this assumption does not apply early in the reionization history, or even later in the history as long as the sources of X-rays are too weak to heat the intergalactic medium significantly. This work presents the first EoR numerical simulations including, beside dynamics and ionizing continuum radiative transfer, a self-consistent treatment of the Ly-alpha radiative transfer. This allows us to compute the spin temperature more accurately. We use two different box sizes, 20 h(-1) Mpc and 100 h(-1) Mpc, and a star source model. Using the redshift dependence of average quantities, maps, and power spectra, we quantify the effect of using different assumptions to compute the spin temperature and the influence of the box size. The first effect comes from allowing for a signal in absorption (i.e. not making the T-S >> T-CMB approximation). The magnitude of this effect depends on the amount of heating by hydrodynamic shocks and X-rays in the intergalactic medium (IGM). With our source model we have little heating so regions seen in absorption survive almost until the end of reionization. The second effects comes from using the real, local, Lyman-alpha flux. This effect is important for an average ionization fraction of less than similar to 10%: it changes the overall amplitude of the 21 cm signal, and adds its own fluctuations to the power spectrum.