A Principal Component Analysis of quasar UV spectra at z~3

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.