A Concordance Model of the Lyman-alpha Forest at z = 1.95

We present 40 fully hydrodynamical numerical simulations of the intergalactic gas that gives rise to the Ly-alpha forest. We make artificial spectra from each and measure three output parameters: the mean flux, a measure of the most common Ly-alpha line width (b-value), and the 1D power spectrum of the flux on scales from 0.01 - 0.1 s/km. We investigate how these output parameters are correlated with the input parameters that describe the simulations. These input parameters include the main cosmological parameters; and two astrophysical parameters gammah and gammahe. The parameter gammah controls the rate of ionization of H I, He I and He II while gammahe controls the rate of heating. We compare the output from the simulations to data from HIRES and UVES spectra and we give a new measurement of the flux power from these spectra at z=1.95. We find that simulations with a wide variety of sigma_8 values, from at least 0.8 - 1.1, can fit the small scale flux power and b-values when we adjust gammahe to compensate for the sigma_8 change. We can also use gammah to adjust the H I ionization rate to simultaneously match the mean flux. We derive scaling relations that give the output parameter values expected for a variety of input parameters with errors of 2% for optical depth and 1.4% for b-balues. We can break the degeneracy between gammahe and sigma_8 using large scale power or other data to fix sigma_8.