Nonlinear clustering during the cosmic Dark Ages and its effect on the 21-cm background from minihalos

Hydrogen atoms inside virialized minihalos generate a radiation background from redshifted 21-cm line emission whose angular fluctuations reflect clustering during before and during reionization. We have shown elsewhere that this emission may be detectable with the planned Low Frequency Array (LOFAR) and Square Kilometer Array (SKA) in a flat LambdaCDM. This is a direct probe of structure during the Dark Ages'' at redshifts z>6 and down to smaller scales than have previously been constrained. In our original calculation, we used a standard approximation known as the linear bias’’ [e.g. Mo & White (1996)]. Here we improve upon that treatment by considering the effect of nonlinear clustering. To accomplish this, we develop a new analytical method for calculating the nonlinear Eulerian bias of halos, which should be useful for other applications as well. Predictions of this method are compared with the results of LambdaCDM N-body simulations, showing significantly better agreement than the standard linear bias approximation. When applied to the 21-cm background from minihalos, our formalism predicts fluctuations that differ from our original predictions by up to 30% at low frequencies and small scales. However, within the range of frequencies and angular scales at which the signal could be observable by LOFAR and SKA as currently planned, the differences are small and our original predictions prove robust. Our results indicate that while a smaller frequency bandwidth of observation leads to a higher signal that is more sensitive to nonlinear effects, this effect is counteracted by the lowered sensitivity of the radio arrays. We calculate the best frequency bandwidth for these observations to be Delta nu~2 MHz.(abbreviated)