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The amplitude of redshifted 21 cm fluctuations during the Epoch ofReionization (EoR) is expected to show a distinctive "rise and fall" behaviorwith decreasing redshift as reionization proceeds. On large scales (k <~ 0.1Mpc^{-1}) this can mostly be characterized by evolution in the product of themean 21 cm brightness temperature and a bias factor, b_21(z). This quantityevolves in a distinctive way that can help in determining the averageionization history of the intergalactic medium (IGM) from upcoming 21 cmfluctuation data sets. Here we consider extracting <T_21> b_21(z) using acombination of future redshifted 21 cm and [CII] line-intensity mapping datasets. Our method exploits the dependence of the 21 cm-[CII]-[CII]cross-bispectrum on the shape of triangle configurations in Fourier space. Thisallows one to determine <T_21> b_21(z) yet, importantly, is less sensitive toforeground contamination than the 21 cm auto-spectrum, and so can provide avaluable cross-check. We compare the results of simulated bispectra withsecond-order perturbation theory: on large scales the perturbative estimate of<T_21> b_21(z) matches the true value to within 10% for <x_i> <~ 0.8. Weconsider the 21 cm auto-bispectrum and show that this statistic may also beused to extract the 21 cm bias factor. Finally, we discuss the surveyrequirements for measuring the cross-bispectrum. Although we focus on the 21cm-[CII]-[CII] bispectrum during reionization, our method may be of broaderinterest and can be applied to any two fields throughout cosmic history.

Extracting bias using the cross-bispectrum: An EoR and 21 cm-[CII]-[CII] case study