Constraining large scale HI bias using redshifted 21-cm signal from the post-reionization epoch

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In the absence of complex astrophysical processes that characterize the reionization era, the 21-cm emission from neutral hydrogen (HI) in the post-reionization epoch is believed to be an excellent tracer of the underlying dark matter distribution. Assuming a background cosmology, it is modelled through (i) a bias function b(k,z), which relates HI to the dark matter distribution and (ii) a mean neutral fraction (xHI) which sets its amplitude. In this paper, we investigate the nature of large scale HI bias. The post-reionization HI is modelled using gravity only N-Body simulations and a suitable prescription for assigning gas to the dark matter halos. Using the simulated bias as the fiducial model for HI distribution at z≤ 4, we have generated a hypothetical data set for the 21-cm angular power spectrum (Cₗ) using a noise model based on parameters of an extended version of the GMRT. The binned Cₗ is assumed to be measured with SNR 4 in the range 400 ≤ l ≤ 8000 at a fiducial redshift z=2.5. We explore the possibility of constraining b(k) using the Principal Component Analysis (PCA) on this simulated data. Our analysis shows that in the range 0.2 < k < 2 Mpc⁻¹, the simulated data set cannot distinguish between models exhibiting different k dependences, provided 1 b(k) 2 which sets the 2-sigma limits. This justifies the use of linear bias model on large scales. The largely uncertain xHI is treated as a free parameter resulting in degradation of the bias reconstruction. The given simulated data is found to constrain the fiducial xHI with an accuracy of 4% (2-sigma error). The method outlined here, could be successfully implemented on future observational data sets to constrain b(k,z) and xHI and thereby enhance our understanding of the low redshift Universe.