Modelling the post-reionization neutral hydrogen (HI) bias

Observations of the neutral hydrogen (H I) 21-cm signal hold the potential of allowing us to map out the cosmological large-scale structures (LSS) across the entire post-reionization era (z ≤ 6). Several experiments are planned to map the LSS over a large range of redshifts and angular scales, many of these targeting the Baryon Acoustic Oscillations. It is important to model the H I distribution in order to correctly predict the expected signal, and more so to correctly interpret the results after the signal is detected. In this paper we have carried out semi-numerical simulations to model the H I distribution and study the H I power spectrum P_HI(k,z) across the redshift range 1 ≤ z ≤ 6. We have modelled the H I bias as a complex quantity b~(k,z) whose modulus squared b²(k,z) relates P_HI(k,z) to the matter power spectrum P(k,z), and whose real part b_r(k,z) quantifies the cross-correlation between the H I and the matter distribution. We study the z and k dependence of the bias, and present polynomial fits which can be used to predict the bias across 0 ≤ z ≤ 6 and 0.01 ≤ k ≤ 10 Mpc^-1. We also present results for the stochasticity r = b_r/b which is important for cross-correlation studies.