On Estimating the Qso Transmission Power Spectrum

The Lyman-alpha forest has become an important tool for measuring the mass power spectrum at high redshifts (z = 2−4). A crucial intermediate step is the measurement of the transmission power spectrum. We present new methods to minimize the systematic and random errors for such a measurement, and discuss their implications for observing strategies. 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 continuumfitting. Moreover, 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. We further show that a measurement of the continuum power spectrum (plus a related quantity) using trend-removal, from either low redshift quasar spectra or the red-side of Lyman-alpha, can be used to constrain the amount of spurious large scale power introduced by the uncertain continuum, and in principle allows the removal of such contamination 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 instruments, 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 (SDSS), which has the potential to measure the power spectrum accurate to better than 1% per mode (∆k ∼ 10−4 s/km) – the techniques presented here will be useful for tackling the anticipated issues of shot-noise and continuum contamination.