Power spectrum and Intermittency of the Transmitted Flux of QSOs’ Lyα Absorption Spectra

Using a set of 28 high resolution, high signal to noise ratio (S/N) QSO Lyα absorption spectra, we investigate the non-Gaussian features of the transmitted flux fluctuations, and their effect upon the power spectrum of this field. We find that the spatial distribution of the local power of the transmitted flux on scales k ≥ 0.05 s/km is highly spiky or intermittent. The probability distribution functions (PDFs) of the local power are long-tailed. The power on small scales is dominated by small probability events, and consequently, the uncertainty in the power spectrum of the transmitted flux field is generally large. This uncertainty arises due to the slow convergence of an intermittent field to a Gaussian limit required by the central limit theorem (CLT). To reduce this uncertainty, it is common to estimate the error of the power spectrum by selecting subsamples with an “optimal” size. We show that this conventional method actually does not calculate the variance of the original intermittent field but of a Gaussian field. Based on the analysis of intermittency, we propose an algorithm to calculate the error. It is based on a bootstrap resampling among all independent local power modes. This estimation doesn’t require any extra parameter like the size of the subsamples, and is sensitive to the intermittency of the fields. This method effectively reduces the uncertainty in the power spectrum when the number of independent modes matches the condition of the CLT convergence.