Lyα emission-line reconstruction for high- z QSOs

We introduce an intrinsic Lya emission-line profile reconstruction method for high-z quasars (QSOs). This approach utilises a covariance matrix of emission-line properties obtained from a large, moderate-z (2 = z = 2.5), high signal to noise (S/N > 15) sample of BOSS QSOs. For each QSO, we complete a Monte Carlo Markov Chain fitting of the continuum and emission-line properties and perform a visual quality assessment to construct a large data base of robustly fit spectra. With this data set, we construct a covariance matrix to describe the correlations between the high-ionization emission lines Lya, Civ, Siiv +Oiv] and Ciii], and find it to be well approximated by an N-dimensional Gaussian distribution. This covariance matrix characterizes the correlations between the linewidth, peak height and velocity offset from systemic while also allowing for the existence of broad- and narrow-line components for Lya and Civ. We illustrate how this covariance matrix allows us to statistically characterize the intrinsic Lya line solely from the observed spectrum redward of 1275 A. This procedure can be used to reconstruct the intrinsic Lya line emission profile in cases where Lya may otherwise be obscured. Applying this reconstruction method to our sample of QSOs, we recovered the Lya line flux to within 15 per cent of the measured flux at 1205 A (1220 A) ~85 (90) per cent of the time.