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

We present 40 fully hydrodynamical numerical simulations of the intergalactic gas that gives rise to the Ly alpha forest. The simulation code, input and output files are available at http://www.cosmos.ucsd.edu/similar to gso/index.html. For each simulation we predict the observable properties of the HI 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 Omega(b), Omega(m), Omega(Lambda), H-0 and sigma(8); and two astrophysical parameters gamma(912) and X-228. The parameter. 912 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 X-228 controls the rate of heating from the photoionization of He II and can be related to the shape of the UVB at lambda < 228 angstrom. We show how these input parameters, especially s8,. 912 and X-228, affect the output parameters that we measure in simulated spectra. These parameters are the mean flux (F) over bar F, a measure of the most common ( as defined more precisely in Section 5.1) Ly alpha linewidth (b-value) b(sigma), 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 sigma(8)-values, from at least 0.8 to 1.1, can fit the small-scale flux power and b-values when we adjust X-228 to compensate for the s 8 change. We can also use. 912 to adjust the HI 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 s 8 and X-228. We can break the degeneracy using large-scale flux power or other data to fix s8. When we pick a specific sigma(8)-value the simulations give the value of X-228 that we need to match the observed small-scale flux power and b-values. We can then also find the gamma(912) required to match the mean flux for that combination of s 8 and X-228. We derive scaling relations that give the output parameter values expected for a variety of input parameters. We predict the linewidth parameter b(sigma) with an error of 1.4 per cent and the mean amount of HI absorption to 2 per cent, equivalent to a 0.27 per cent error on (F) over bar at z = 1.95. These errors are four times smaller than those on the best current measurement. We can readily calculate the sets of input parameters that give outputs that match the data. For sigma(8) = 0.9, with Omega(b) = 0.044, Omega(m) = 0.27, Omega(Lambda) = 0.73, h = 0.71 and n = 1.0, we find X-228 = 1.26 and gamma(912) = 1.00, equivalent to Gamma(912) = 1.33 x 10(-12) ionizations per H I atom per second. If we run an optically thin simulation with these parameters in a box size of 76.8 Mpc comoving and with a cell size of 18.75 kpc comoving, we expect that the simulated spectra will match Lya forest data at z = 1.95. The rates predicted by Madau, Haardt & Rees correspond to gamma(912) = 1 and X-228 = 1. Our results for gamma(912) match while the larger X-228 is reasonable to correct for the opacity that is missing from the optically thin simulations. For a smaller value of sigma(8) the structures are generally more extended and we need a smaller X-228 corresponding to a cooler IGM, as found by Bryan & Machacek ( their fig. 7). We also need a larger gamma(912) to stop the neutral fraction from increasing at the lower temperatures.