Modelling redshift space distortion in the post-reionization HI 21-cm power spectrum

The post-reionization HI 21-cm signal is an excellent candidate for precision cosmology, this however requires accurate modelling of the expected signal. Sarkar et al. have simulated the real space HI 21-cm signal and have modelled the HI power spectrum as P_HI(k) = b²P(k), where P(k) is the dark matter power spectrum and b(k) is a (possibly complex) scale-dependent bias for which fitting formulas have been provided. This paper extends these simulations to incorporate redshift space distortion and predicts the expected redshift space HI 21-cm power spectrum P^s _HI(k, k) using two different prescriptions for the HI distributions and peculiar velocities. We model P^s _HI(k, k), assuming that it is the product of P_HI(k) = b²P(k) with a Kaiser enhancement term and a Finger of God (FoG) damping which has σ_p the pair velocity dispersion as a free parameter. Considering several possibilities for the bias and the damping profile, we find that the models with a scale-dependent bias and a Lorentzian damping profile best fit the simulated P^s _HI(k, k) over the entire range 1 ≤ z ≤ 6. The best-fitting value of σ_p falls approximately as (1 + z)^-m with m = 2 and 1.2, respectively, for the two different prescriptions. The model predictions are consistent with the simulations for k < 0.3Mpc^-1 over the entire z range for the monopole P^s ₀(k), and at z ≤ 3 for the quadrupole P^s ₂(k). At z ≥ 4 the models underpredict P^s ₂(k) at large k, and the fit is restricted to k < 0.15 Mpc^-1.