On Estimating the QSO Transmission Power Spectrum

We present new methods to minimize the systematic and random errors for measuring the transmission power spectrum from the Lyman-alpha forest. Sources of systematic errors explored include metal line contamination and continuum-fitting. We advocate the technique of trend-removal in place of traditional continuum-fitting -- here, a spectrum is normalized by its (smoothly varying) mean rather than its continuum -- this method is easily automated and removes biases introduced by continuum-fitting. Trend- removal can be easily applied to spectra where continuum-fitting is difficult, such as when the resolution or signal-to-noise is low, or for spectra at high redshifts. Furthermore, a measurement of the continuum power spectrum using trend-removal, from either low redshift quasar spectra or the red-side of Lyman-alpha, allows in principle the removal of spurious power introduced by the continuum and thereby expanding scales probed to larger ones. We also derive expressions for the shot-noise bias and variance of the power spectrum estimate, taking into account the non-Poissonian nature of the shot-noise and the non-Gaussianity of the cosmic fluctuations. An appropriate minimum variance weighting of the data is given. Finally, we give practical suggestions on observing strategy: the desired resolution and S/N for different purposes, and how to distribute one's finite observing time among quasar targets. Also discussed is the quasar spectroscopic study of the Sloan Digital Sky Survey, which has the potential to measure the power spectrum at z ~ 2-4 accurate to better than 1 % per mode -- the techniques presented here will be useful for tackling the anticipated issues of shot-noise and continuum contamination.