Extracting Bias Using the Cross-bispectrum: An EoR and 21 cm–[C ii]–[C ii] Case Study

Abstract

The amplitude of redshifted 21 cm fluctuations during the Epoch of Reionization (EoR) is expected to show a distinctive “rise and fall” behavior with decreasing redshift as reionization proceeds. On large scales ( k  ≲ 0.1 Mpc −1 ) this can mostly be characterized by evolution in the product of the mean 21 cm brightness temperature and a bias factor, . This quantity evolves in a distinctive way that can help in determining the average ionization history of the intergalactic medium from upcoming 21 cm fluctuation data sets. Here we consider extracting using a combination of future redshifted 21 cm and [C ii ] line-intensity mapping data sets. Our method exploits the dependence of the 21 cm–[C ii ]–[C ii ] cross-bispectrum on the shape of triangle configurations in Fourier space. This allows one to determine yet, importantly, is less sensitive to foreground contamination than the 21 cm auto-spectrum and so can provide a valuable cross-check. We compare the results of simulated bispectra with second-order perturbation theory: on the largest scales well probed by our simulations ( k ∼ 0.05 Mpc −1 ), the perturbative estimate of matches the true value to within 10% for . The perturbative formula is most accurate early in the EoR. We consider the 21 cm auto-bispectrum and show that this statistic may also be used to extract the 21 cm bias factor. Finally, we discuss the survey requirements for measuring the cross-bispectrum. Although we focus on the 21 cm–[C ii ]–[C ii ] bispectrum during reionization, our method may be of broader interest and can be applied to any two fields throughout cosmic history.