The imprint of Baryonic Acoustic Oscillations (BAO) on the matter power spectrum can be constrained using the neutral hydrogen density in the intergalactic medium as a tracer of the matter density. One of the goals of the Baryon Oscillation Spectrosc
opic Survey (BOSS) of the Sloan Digital Sky Survey (SDSS-III) is to derive the Hubble expansion rate and the angular scale from the BAO signal in the IGM. To this aim, the Lyman-alpha forest of 10^5 quasars will be observed in the redshift range 2.2<z<3.5 and over 10,000 deg^2. We simulated the BOSS QSO survey to estimate the statistical accuracy on the BAO scale determination provided by such a large scale survey. In particular, we discuss the effect of the poorly constrained estimate of the unabsorbed intrinsic quasar spectrum. The volume of current N-body simulations being too small for such studies, we resorted to Gaussian random field (GRF) simulations. We validated the use of GRFs by comparing the output of GRF simulations with that of the Horizon N-body simulation with the same initial conditions. Realistic mock samples of QSO Lyman-alpha forest were generated; their power spectrum was computed and fitted to obtain the BAO scale. The rms of the results for 100 different simulations provides an estimate of the statistical error expected from the BOSS survey. We confirm the results from Fisher matrix estimate. In the absence of error on the unabsorbed quasar spectrum, the BOSS quasar survey should measure the BAO scale with an error of the order of 2.3%, or the transverse and radial BAO scales separately with errors of the order of 6.8% and 3.9%, respectively. The significance of the BAO detection is assessed by an average Deltachi^2=17 but for individual realizations Deltachi^2 ranges from 2 t o 35. The error on the unabsorbed quasar spectrum increases the error on the BAO scale by 10 to 20% and results in a sub percent bias.
From a Principal Component Analysis (PCA) of 78 z~3 high quality quasar spectra in the SDSS-DR7, we derive the principal components characterizing the QSO continuum over the full wavelength range available. The shape of the mean continuum, is similar
to that measured at low-z (z~1), but the equivalent width of the emission lines are larger at low redshift. We calculate the correlation between fluxes at different wavelengths and find that the emission line fluxes in the red part of the spectrum are correlated with that in the blue part. We construct a projection matrix to predict the continuum in the Lyman-$alpha$ forest from the red part of the spectrum. We apply this matrix to quasars in the SDSS-DR7 to derive the evolution with redshift of the mean flux in the Lyman-$alpha$ forest due to the absorption by the intergalactic neutral hydrogen. A change in the evolution of the mean flux is apparent around z~3 in the sense of a steeper decrease of the mean flux at higher redshifts. The same evolution is found when the continuum is estimated from the extrapolation of a power-law continuum fitted in the red part of the quasar spectrum if a correction, derived from simple simulations, is applied. Our findings are consistent with previous determinations using high spectral resolution data. We provide the PCA eigenvectors over the wavelength range 1020-2000 AA and the distribution of their weights that can be used to simulate QSO mock spectra.
