Modelling the post-reionization neutral hydrogen (H i ) 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_ H\, I(k,z)| across the redshift range 1 ≤ z ≤ 6. We have modelled the H i bias as a complex quantity |b̃(k,z)| whose modulus squared b2(k, z) relates |P_ H\, I(k,z)| to the matter power spectrum P(k, z), and whose real part br(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 = br/b which is important for cross-correlation studies.