Sensitivity for 21cm Bispectrum from Epoch of Reionization

The 21cm line brightness temperature brings rich information about Epoch of Reionizaton (EoR) and high-$z$ universe (Cosmic Dawn and Dark Age). While the power spectrum is a useful tool to investigate the EoR signal statistically, higher-order statistics such as bispectrum are also valuable because the EoR signal is expected to be highly non-Gaussian. In this paper, we develop a formalism to calculate the bispectrum contributed from the thermal noise taking array configularion of telescopes into account, by extending a formalism for the power spectrum \cite{2006ApJ...653..815M}. We apply our formalism to the ongoing and future telescopes such as expanded Murchison Widefield Array (MWA), LOw Frequency ARray (LOFAR) and Square Kilometre Array (SKA). We find that expanded MWA does not have enough sensitivity to detect the bispectrum signal. On the other hand, LOFAR has better sensitivity and will be able to detect the peaks of the bispectrum as a function of redshift at large scales with comoving wavenumber $k \lesssim 0.03 {\rm Mpc}^{-1}$. The SKA has enough sensitivity to detect the bispectrum for much smaller scales $k \lesssim 0.3 {\rm Mpc}^{-1}$ and redshift $z \lesssim 20$