Semi analytic approach to understanding the distribution of neutral hydrogen in the universe: Comparison of simulations with observations

Following Bi & Davidsen (1997), we perform one dimensional semi analytic simulations along the lines of sight to model the intergalactic medium (IGM). Since this procedure is computationally efficient in probing the parameter space -- and reasonably accurate -- we use it to recover the values of various parameters related to the IGM (for a fixed background cosmology) by comparing the model predictions with different observations. For the currently favoured LCDM model (\Omega_m=0.4, \Omega_{\Lambda}=0.6 and h=0.65), we obtain, using statistics obtained from the transmitted flux, constraints on (i) the combination f=(\Omega_B h^2)^2/J_{-12}, where \Omega_B is the baryonic density parameter and J_{-12} is the total photoionisation rate in units of 10^{-12} s^{-1}, (ii) temperature T_0 corresponding to the mean density and (iii) the slope \gamma of the effective equation of state of the IGM at a mean redshift z \simeq 2.5. We find that 0.8 <(T_0/10^4 K)< 2.5 and 1.3<\gamma<2.3. while the constraint obtained on f is 0.020^2<f<0.032^2. A reliable lower bound on J_{-12} can be used to put a lower bound on \Omega_B h^2, which can be compared with similar constraints obtained from Big Bang Nucleosynthesis (BBN) and CMBR studies. We find that if J_{-12}>1.2, the lower bound on \Omega_B h^2 is in violation of the BBN value.