4 A Concordance Model of The Lyman - Alpha Forest at z = 1 . 95

We present 40 fully hydrodynamical numerical simulations of the intergalac-tic gas that gives rise to the Lyα forest. For each simulation we predict the observable properties of the H I absorption in QSO spectra. We then find the sets of cosmological and astrophysical parameters that match the QSO spectra. We present our results as scaling relationships between input and output parameters. The input parameters include the main cosmological parameters Ω b , Ω m , Ω Λ , H 0 and σ 8 ; and two astrophysical parameters γ 912 and X 228. The parameter γ 912 controls the rate of ionization of H I, He I and He II and is equivalent to the intensity of the UV background. The second parameter X 228 controls the rate of heating from the photoionization of He II and can be related to the shape of the UVB at λ < 228Å. We show how these input parameters; especially σ 8 , γ 912 and X 228 ; effect the output parameters that we measure in simulated spectra. These parameters are the mean flux ¯ F , a measure of the most common Lyα line width (b-value) b σ , and the 1D power spectrum of the flux on scales from 0.01 – 0.1 s/km. We compare the simulation output to data from Kim et al. (2004) and Tytler et al. (2004) and we give a new measurement of the flux power from HIRES and UVES spectra for the low density IGM alone at z = 1.95. We find that simulations with a wide variety of σ 8 values, from at least 0.8 – 1.1, can fit the small scale flux power and b-values when we adjust X 228 to compensate for the σ 8 change. We can also use γ 912 to adjust the H I ionization rate to simultaneously match the mean flux. When we examine only the mean flux, b-values and small scale power we can not readily break the strong degeneracy between σ 8 and X 228. We can break the degeneracy using large scale power or other data to fix σ 8. When we pick a specific σ 8 value the simulations give X 228 and hence the – 2 – IGM temperature that we need to match the observed small scale flux power and b-values. We can then also find the γ 912 required to match …