A concordance model of the Lyman a forest at z= 1.95

We present 40 fully hydrodynamical numerical simulations of the intergalactic gas that gives rise to the Lyα forest. The simulation code, input and output files are available at. http://www.cosmos.ucsd.edu/∼gso/index.html. For each simulation we predict the observable properties of the H i absorption in quasar or quasi-stellar object (QSO) spectra. We then find the sets of cosmological and astrophysical parameters which result in spectra whose properties match that of the QSO spectra. We present our results as scaling relationships between input and output parameters. The input parameters include the main cosmological parameters Δb, Δm, ΔΛ, H0 and σ8; and two astrophysical parameters γ912 and X228. The parameter γ912 controls the rate of ionization of H i, He i and He ii and is equivalent to the intensity of the ultraviolet background (UVB). The second parameter X228 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 σ8, γ912 and X228, affect the output parameters that we measure in simulated spectra. These parameters are the mean flux , a measure of the most common (as defined more precisely in Section 5.1) Lyα linewidth (b-value) bσ, and the one-dimensional power spectrum of the flux on scales from 0.01 to 0.1 s km−1. We compare the simulation output with data from Kim et al. and Tytler et al., and we give a new measurement of the flux power from HIRES and UVES spectra for the low-density intergalactic medium (IGM) alone at z= 1.95. We find that simulations with a wide variety of σ8-values, from at least 0.8 to 1.1, can fit the small-scale flux power and b-values when we adjust X228 to compensate for the σ8 change. We can also use γ912 to adjust the H i ionization rate to match the mean flux simultaneously. When we examine only the mean flux, b-values and small-scale flux power we cannot readily break the strong degeneracy between σ8 and X228. We can break the degeneracy using large-scale flux power or other data to fix σ8. When we pick a specific σ8-value the simulations give the value of X228 that we need to match the observed small-scale flux power and b-values. We can then also find the γ912 required to match the mean flux for that combination of σ8 and X228. We derive scaling relations that give the output parameter values expected for a variety of input parameters. We predict the linewidth parameter bσ with an error of 1.4 per cent and