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

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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. (2016) have simulated the real space HI 21-cm signal, and have modelled the HI power spectrum as P HI(k)=b² P(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 predict the expected redshift space HI 21-cm power spectrum Pˢ HI(k⊥,k∥) using two different prescriptions for the HI distributions and peculiar velocities. We model Pˢ HI(k⊥,k∥) assuming that it is the product of P HI(k)=b² P(k) with a Kaiser enhancement term and a Finger of God (FoG) damping which has σₚ 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 Pˢ HI(k⊥,k∥) over the entire range 1 ≤ z ≤ 6. The best fit value of σₚ 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 < 0.3 Mpc⁻¹ over the entire z range for the monopole Pˢ₀(k), and at z ≤ 3 for the quadrupole Pˢ₂(k). At z ≥ 4 the models underpredict Pˢ₂(k) at large k, and the fit is restricted to k < 0.15 Mpc⁻¹.