Light cone effect on the reionization 21-cm signal II: Evolution, anisotropies and observational implications

Measurements of the HI 21-cm power spectra from the reionization epoch will be influenced by the evolution of the signal along the line-of-sight direction of any observed volume. We use numerical as well as semi-numerical simulations of reionization in a cubic volume of 607 Mpc across to study this so-called light cone effect on the HI 21-cm power spectrum. We find that the light cone effect has the largest impact at two different stages of reionization: one when reionization is $\sim 20\%$ and other when it is $\sim 80\%$ completed. We find a factor of $\sim 4$ amplification of the power spectrum at the largest scale available in our simulations. We do not find any significant anisotropy in the 21-cm power spectrum due to the light cone effect. We argue that for the power spectrum to become anisotropic, the light cone effect would have to make the ionized bubbles significantly elongated or compressed along the line-of-sight, which would require extreme reionization scenarios. We also calculate the two-point correlation functions parallel and perpendicular to the line-of-sight and find them to differ. Finally, we calculate an optimum frequency bandwidth below which the light cone effect can be neglected when extracting power spectra from observations. We find that if one is willing to accept a $10 \%$ error due to the light cone effect, the optimum frequency bandwidth for $k= 0.056 \, \rm{Mpc}^{-1}$ is $\sim 7.5$ MHz. For $k = 0.15$ and $0.41 \, \rm{Mpc}^{-1}$ the optimum bandwidth is $\sim 11$ and $\sim 16$ MHz respectively.