Lyα emission-line reconstruction for high-z QSOs

We introduce an intrinsic Ly\alpha\ emission line profile reconstructionmethod for high-$z$ quasars (QSOs). This approach utilises a covariance matrixof emission line properties obtained from a large, moderate-$z$ ($2 \leq z \leq2.5$), high signal to noise (S/N > 15) sample of BOSS QSOs. For each QSO, wecomplete a Monte Carlo Markov Chain fitting of the continuum and emission lineproperties and perform a visual quality assessment to construct a largedatabase of robustly fit spectra. With this dataset, we construct a covariancematrix to describe the correlations between the high ionisation emission linesLy\alpha, C IV, Si IV + O IV] and C III], and find it to be well approximatedby an $N$-dimensional Gaussian distribution. This covariance matrixcharacterises the correlations between the line width, peak height and velocityoffset from systemic while also allowing for the existence of broad and narrowline components for Ly\alpha\ and C IV. We illustrate how this covariancematrix allows us to statistically characterise the intrinsic Ly\alpha\ linesolely from the observed spectrum redward of 1275\AA. This procedure can beused to reconstruct the intrinsic Ly\alpha\ line emission profile in caseswhere Ly\alpha\ may otherwise be obscured. Applying this reconstruction methodto our sample of QSOs, we recovered the Ly\alpha\ line flux to within 15 percent of the measured flux at 1205\AA\ (1220\AA) ~85 (90) per cent of the time.