Plots showing the modeling of the variation of Lyα forest flux power spectrum with astrophysical parameters, T₀ and γ at z = 3. The top panels show the plots of the Lyα forest flux power spectrum corresponding to fiducial and varied T₀ and γ. We added Gaussian noise to the sightlines with an S/N distribution ranging from 20 to 100 (S/N distribution is uniform in the log scale, making the distribution have more low S/N sightlines). We plot the power spectrum corresponding to the fiducial simulation (red) and the varied parameters (blue and green) corresponding to mock Lyα with this S/N distribution. The error bars correspond to bootstrapping errors computed over 5000 sightlines for a sample size of 50 sightlines with 10 000 bootstrap realizations. The power spectra corresponding to the simulation runs (with similar S/N distribution) with fiducial parameters but different initial seed density fields are plotted with colored hollow points in the middle panels. We modeled the power spectrum based on the curves in the top panels. We then used the posterior distribution by running an MCMC with flat priors (see Eq. 4) to estimate the parameter values (see Sect. 3). In the middle panels, hollow blue, green, and red points correspond to the fiducial simulations with different seeds, and the posterior estimates of the parameters (and the posterior standard deviation) are given in the plots. In the bottom panels, we show the sensitivity of the parameter estimates based on power spectrum to noise levels when we lower the S/N distribution (0.85 × S/N_Fid) of the sightlines and use the same power spectrum modeling to estimate the parameters.