Cosmological Parameters σ8, the Baryon Density Ωb, the Vacuum Energy Density ΩΛ, the Hubble Constant and the UV Background Intensity from a Calibrated Measurement of H I Lyα Absorption at z = 1.9

We identify a concordant model for the intergalactic medium (IGM) at redshift z = 1.9 that uses popular values for cosmological and astrophysical parameters and accounts for all baryons with an uncertainty of 5%. The amount of absorption by H I in the IGM provides the best evidence on the physical conditions in the IGM, especially the combination of the mean gas density, the density fluctuations, the intensity of the ionizing flux, and the level of ionization. We have measured the amount of absorption, known as the flux decrement (DA), in the Lyα forest at redshift 1.9. We used spectra of 77 QSOs that we obtained with 250 km s-1 resolution from the Kast spectrograph on the Lick observatory 3 m telescope. We fitted unabsorbed continua to these spectra using b-splines. We also fitted equivalent continua to 77 artificial spectra that we made to match the real spectra in most obvious ways: redshift, resolution, signal-to-noise ratio (S/N), emission lines and absorption lines. The typical relative error in our continuum fits to the artificial spectra is 3.5%. Averaged over all 77 QSOs, the mean level is within 1%-2% of the correct value, except at S/N < 6, where we systematically placed the continuum too high. We then adjusted the continua on the real spectra to remove this bias as a function of S/N and a second smaller bias. Absorption from all lines in the Lyα forest at z = 1.9 removes DA(z = 1.9) = 15.1% ± 0.7% of the flux at rest-frame wavelengths 1070 < λr < 1170 Å. This is the first measurement using many QSOs at this z, and the first calibrated measurement at any redshift. Using similar methods on 1225 < λr < 1500 Å, we find metal lines absorb an average 1.6% the flux, increasing slightly as the rest-frame wavelength λr decreases because more types of spectral lines contribute and there is more C IV at lower redshifts. We estimate that the metal lines absorb 2.3% ± 0.5% of the flux in the Lyα forest at z = 1.9. The absorption from Lyα alone then has DA = 12.8% ± 0.9%. The Lyα lines of Lyman limit systems with H I column densities log N > 17.2 cm-2 are responsible for a DA = 1.0% ± 0.4% at z = 1.9. These lines arise in higher density regions than the bulk of the IGM Lyα absorption, and hence they are harder to simulate in the huge boxes required to represent the large-scale variations in the IGM. If we subtract these lines, for comparison with simulations of the lower density bulk of the IGM, we are left with DA = 11.8% ± 1.0%. The mean DA in segments of individual spectra with Δz = 0.1, or 153 Mpc comoving at z = 1.9, has a large dispersion, σ = 6.1% ± 0.3% including Lyman limit systems (LLSs) and metal lines, and σ(Δz = 0.1) = 3.9% for the Lyα from the lower density IGM alone, excluding LLSs and metal lines. This is consistent with the usual description of large-scale structure and accounts for the large variations from QSO to QSO. Although the absorption at z = 1.9 is mostly from the lower density IGM, the Lyα of LLSs and the metal lines are both major contributors to the variation in the mean flux on 153 Mpc scales at z = 1.9, and they make the flux field significantly different from a random Gaussian field with an enhanced probability of a large amount of absorption. We find that a hydrodynamic simulation on a 10243 grid in a 75.7 Mpc box reproduces the observed DA from the low-density IGM alone when we use popular parameters values H0 = 71 km s-1 Mpc-1, Ωb = 0.044, Ωm = 0.27, ΩΛ = 0.73, σ8 = 0.9, and an ultraviolet background (UVB) that has an ionization rate per H I atom of Γ912 = (1.44 ± 0.11) × 10-12 s-1. This is 1.08 ± 0.08 times the prediction by Madau et al. with 61% from QSOs and 39% from stars. Our measurement of the DA gives a new joint constraint on these parameters, and the DA is very sensitive to each parameter. Given fixed values for all other parameters, and assuming the simulation has insignificant errors, the error of our DA measurement gives an error on H0 of 10%, ΩΛ of 6%, Ωb of 5%, and σ8 of 4%, comparable to the best measurements by other methods.