Recently, it has been found that the field traced by QSO's Lyα forests is intermittent on small scales. Intermittent behavior is essential for understanding the statistics and dynamics of cosmic gravitational clustering in the nonlinear regime. The most effective method of describing intermittency uses the structure functions and the intermittent exponent, which measure the scale-and order-dependencies of the ratio between the higher order to second order moments of the field. These properties can be used not only to confirm the non-gaussianity of fields, but also to detect the type of non-gaussianity.In this paper, we calculate the structure function and intermittent exponent of 1.) Keck data, which consists of 28 high resolution, high signal to noise ratio (S/N) QSO Lyα absorption spectra, and 2.) Lyα forest simulation samples produced via the pseudo hydro scheme for the low density cold dark matter (LCDM) model and warm dark matter (WDM) model with particle mass m W = 300, 600, 800 and 1000 eV. Aside from the WDM model with m W = 300 eV, the simulation samples are in agreement with observations in the context of the power spectrum. We find, however, that the intermittent behavior of all the simulation samples is substantially inconsistent, both quantitatively and qualitatively, with the Keck data. Specifically, 1.) the structure functions of the simulation samples are significantly larger than that of Keck data on scales k ≥ 0.1 km −1 s, 2.) the intermittent exponent of the simulation samples is more negative than that of Keck data on all redshifts considered, 3.) the order-dependence of the structure functions of simulation samples are closer to the intermittency of hierarchical clustering on all scales, while the Keck data are closer to a lognormal field on small scales. These differences are independent of noise and show that the intermittent evolution modeled by the pseudo-hydro simulation is substantially different from observations, even though they are in good agreement with each other in terms of second and lower order statistics. This result also shows that "weakly" clustered samples, like high resolution Lyα absorption spectrum, are effective in testing dynamical models of structure formation if their intermittent features are considered.Subject headings: cosmology: theory -large-scale structure of the universe

Using a set of 28 high‐resolution, high signal‐to‐noise ratio quasi‐stellar object 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−1 is highly spiky or intermittent. The probability distribution functions 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 owing 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 does not require any extra parameter such as 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 for CLT convergence.

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Using cosmological hydrodynamic simulations of the ÃCDM model, we present a comparison between the simulation sample and real data sample of H i and He ii Ly transmitted flux in the absorption spectra of the QSO HE 2347À4342. The ÃCDM model is successful in simultaneously explaining the statistical features of both H i and He ii Ly transmitted flux. It includes the following features: (1) The power spectra of the transmitted flux of H i and He ii can be well fitted on all scales !0.28 h À1 Mpc for H and !1.1 h À1 Mpc for He. (2) The Doppler parameters of absorption features of He ii and H i are found to be turbulent broadening. (3) The ratio of He ii to H i optical depths are substantially scattered, due to the significant effect of noise. A large part of the scatter is due to the noise in the He ii flux. However, the real data contain more low-events than the simulation sample. This discrepancy may indicate that the mechanism leading extra fluctuations on the simulation data, such as a fluctuating UV radiation background, is needed. Yet models of these extra fluctuations should satisfy the following constraints: (1) If the fluctuations are Gaussian, they should be limited by the power spectra of observed H i and He ii flux. (2) If the fluctuations are nonGaussian, they should be limited by the observed non-Gaussian features of the H i and He ii flux. Subject headingg s: cosmology: theory -large-scale structure of universe

The calculation of the transmission power spectrum of QSO's Lyα absorption requires two parameters for the normalization: the continuum F c and mean transmission e −τ . Traditionally, the continuum is obtained by a polynomial fitting truncating it at a lower order, and the mean transmission is calculated over the entire wavelength range considered. The flux F is then normalized by F c e −τ . However, the fluctuations in the transmitted flux are significantly correlated with the local background flux on scales for which the field is intermittent. As a consequence, the normalization of the entire power spectrum by an over-all mean transmission e −τ will overlook the effect of the fluctuation-background correlation upon the powers. In this paper, we develop a self-normalization algorithm of the transmission power spectrum based on a multiresolution analysis. This self-normalized power spectrum estimator needs neither a continuum fitting, nor pre-determining the mean transmission. With simulated samples, we show that the self-normalization algorithm can perfectly recover the transmission power spectrum from the flux regardless of how the continuum varies with wavelength. We also show that the self-normalized power spectrum is also properly normalized by the mean transmission. Moreover, this power spectrum estimator is sensitive to the non-linear behavior of the field. That is, the self-normalized power spectrum estimator can distinguish 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 Lyα forest, we demonstrate that the proposed power spectrum estimator can perform correct normalization, and effectively reveal the correlation between the fluctuations and background of the transmitted flux on small scales. Therefore, the self-normalized power spectrum would be useful for the discrimination among models without the uncertainties caused by free (or fitting) parameters.