Statistical 21-cm Signal Separation via Gaussian Process Regression
  Analysis
  Detecting and characterizing the Epoch of Reionization and Cosmic Dawn via
the redshifted 21-cm hyperfine line of neutral hydrogen will revolutionize the
study of the formation of the first stars, galaxies, black holes and
intergalactic gas in the infant Universe. The wealth of information encoded in
this signal is, however, buried under foregrounds that are many orders of
magnitude brighter. These must be removed accurately and precisely in order to
reveal the feeble 21-cm signal. This requires not only the modeling of the
Galactic and extra-galactic emission, but also of the often stochastic
residuals due to imperfect calibration of the data caused by ionospheric and
instrumental distortions. To stochastically model these effects, we introduce a
new method based on `Gaussian Process Regression' (GPR) which is able to
statistically separate the 21-cm signal from most of the foregrounds and other
contaminants. Using simulated LOFAR-EoR data that include strong instrumental
mode-mixing, we show that this method is capable of recovering the 21-cm signal
power spectrum across the entire range $k = 0.07 - 0.3 \ \rm{h\, cMpc^{-1}}$.
The GPR method is most optimal, having minimal and controllable impact on the
21-cm signal, when the foregrounds are correlated on frequency scales $\gtrsim
3$\,MHz and the rms of the signal has $\sigma_{\mathrm{21cm}} \gtrsim
0.1\,\sigma_{\mathrm{noise}}$. This signal separation improves the 21-cm
power-spectrum sensitivity by a factor $\gtrsim 3$ compared to foreground
avoidance strategies and enables the sensitivity of current and future 21-cm
instruments such as the {\sl Square Kilometre Array} to be fully exploited.
