Observations of the Lyman-α (Lyα) forest in spectra of distant quasars enable us to probe the matter power spectrum at relatively small scales. With several upcoming surveys, it is expected that there will be a many-fold increase in the quantity and quality of data, and hence it is important to develop efficient simulations to forward model these data sets. One such semi-numerical method is based on the assumption that the baryonic densities in the intergalactic medium (IGM) follow a lognormal distribution. In this work, we test the robustness of the lognormal model of the Lyα forest in recovering a set of IGM parameters by comparing with high-resolution Sherwood SPH simulations. We study the recovery of the parameters T0 (temperature of the mean-density IGM), γ (slope of the temperature-density relation) and Γ12 (hydrogen photoionization rate) at z ∼ 2.5 using a Markov Chain Monte Carlo (MCMC) technique for parameter estimation. Using three flux statistics, the probability distribution, the mean flux and the power spectrum, values of all three parameters, T0, γ and Γ12 implied in the SPH simulations are recovered within 1 − σ (∼ 9, 4 and 1% respectively) of the median (best-fit) values. We verify the validity of our results at different baryon smoothing filter, SNR, box size & resolution, and data seed and confirm that the lognormal model can be used as an efficient tool for modelling the Lyα transmitted flux at z ∼ 2.5.

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We investigate the evolution of axis ratios of triaxial haloes using the phase space description of triaxial collapse. In this formulation, the evolution of the triaxial ellipsoid is described in terms of the dynamics of eigenvalues of three important tensors: the Hessian of the gravitational potential, the tensor of velocity derivatives and the deformation tensor. The eigenvalues of the deformation tensor are directly related to the parameters that describe triaxiality, namely, the minor to major and intermediate to major axes ratios (s and q) and the triaxiality parameter T . Using the phase space equations, we evolve the eigenvalues and examine the evolution of the PDF (probability distribution function) of the axes ratios as a function of mass scale and redshift for Gaussian initial conditions. We find that the ellipticity and prolateness increase with decreasing mass scale and decreasing redshift. These trends agree with previous analytic studies but differ from numerical simulations. However, the PDF of the scaled parameterq = (q − s)/(1 − s) follows a universal distribution over two decades in mass range and redshifts which is in qualitative agreement with the universality for conditional PDF reported in simulations. We further show using the phase space dynamics that, in fact,q is a phase space invariant and is conserved individually for each halo. These results, demonstrate that the phase space analysis is a useful tool that provides a different perspective on the evolution of perturbations and can be applied to more sophisticated models in the future.