On estimating the QSO transmission power spectrum

The Ly alpha forest has become an important tool for measuring the mass pow er 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 discus s their implications for observing strategies. Sources of systematic errors explored include metal line contamination and continuum fitting. We advoca te 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 introduce d by continuum fitting. Moreover, trend removal can be easily applied to sp ectra where continuum fitting is difficult, such as when the resolution or signal-to-noise ratio (S/N) is low, or for spectra at high redshifts. We fu rther show that a measurement of the continuum power spectrum (plus a relat ed quantity) using trend removal, from either low-redshift quasar spectra o r the red side of Ly alpha, can be used to constrain the amount of spurious large-scale power introduced by the uncertain continuum and in principle a llows the removal of such contamination and thereby expanding scales probed to larger ones. We also derive expressions for the shot noise bias and var iance of the power spectrum estimate, taking into account the non-Poissonia n nature of the shot noise and the non-Gaussianity of the cosmic fluctuatio ns. An appropriate minimum variance weighting of the data is given. Finally , we give practical suggestions on observing strategy: the desired resoluti on and S/N for different purposes and instruments, as well as how to distri bute one's finite observing time among quasar targets. Also discussed is th e 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 (Deltak similar to 10(-4) s km(-1)). The techniques presented here will be useful for tackling the anticipated issues of shot noise and conti nuum contamination.