Systematic Effects of Foreground Removal in 21cm Surveys of Reionization

It is well-known that foreground subtraction in 21cm surveys removes large scale power. We investigate associated systematic biases. We show that removing line-of-sight fluctuations on large scales aliases into suppression of the 3D power spectrum across a broad range of scales. This bias can be eliminated by marginalizing over small k in the 1D power spectrum; however, the unbiased estimator will have unavoidably larger variance. We also show that Gaussian realizations of the power spectrum permit accurate and extremely rapid Monte-Carlo simulations for error analysis; repeated realizations of the fully non-Gaussian field are unnecessary. We perform Monte-Carlo maximum-likelihood simulations of foreground removal which yield unbiased, minimum variance estimates of the power spectrum in agreement with Fisher matrix estimates. Foreground removal also distorts the 21cm PDF, reducing the contrast between neutral and ionized regions. We show that it is the subtraction of large-scales modes which is responsible for this distortion, and that it is less severe in the earlier stages of reionization. It can be reduced by using larger bandwidths for foreground removal. In the late stages of reionization, the largest ionized regions (which consist of foreground emission only) provides calibration points which potentially allow recovery of large-scale modes. Finally, we also show that: (i) the broad frequency response of synchrotron and free-free emission will smear out any features in the electron momentum distribution and ensure spectrally smooth foregrounds; (ii) extragalactic radio recombination lines should be negligible foregrounds.