On the normalization of the QSO Ly alpha forest power spectrum

The calculation of the transmission power spectrum of QSO Ly alpha absorpti on requires two parameters for the normalization: the continuum F-c and mea n transmission (e) over bar (-tau). Traditionally, the continuum is obtaine d by a polynomial fitting truncating it at a lower order, and the mean tran smission is calculated over the entire wavelength range considered. The flu x F is then normalized by Fc (e) over tilde (-tau). However, the fluctuatio ns in the transmitted flux are significantly correlated with the local back ground flux on scales for which the field is intermittent. As a consequence , the normalization of the entire power spectrum by an overall mean transmi ssion (e) over bar (-tau) will overlook the effect of the fluctuation-backg round correlation upon the powers. In this paper we develop a self-normaliz ation algorithm of the transmission power spectrum based on a multiresoluti on analysis. This self-normalized power spectrum estimator needs neither a continuum fitting nor a predetermining of the mean transmission. With simul ated samples, we show that the self-normalization algorithm can perfectly r ecover the transmission power spectrum from the flux regardless of how the continuum varies with wavelength. We also show that the self-normalized pow er spectrum is also properly normalized by the mean transmission. Moreover, this power spectrum estimator is sensitive to the nonlinear behavior of th e field. That is, the self-normalized power spectrum estimator can distingu ish between fields with or without the fluctuation-background correlation. This cannot be accomplished by the power spectrum with the normalization by an overall mean transmission. Applying this analysis to a real data set of Q1700+642 Ly alpha forest, we demonstrate that the proposed power spectrum estimator can perform correct normalization and effectively reveal the cor relation between the fluctuations and background of the transmitted flux on small scales. Therefore, the self-normalized power spectrum would be usefu l for the discrimination among models without the uncertainties caused by f ree (or fitting) parameters.