On the Normalization of the QSO's Lyman alpha Forest Power Spectrum

The calculation of the transmission power spectrum of QSO's Lyman alpha absorption requires two parameters for the normalization: the continuum Fc and mean transmission, i.e. average of e^{-tau}. 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 the average of Fc e^{-tau}. However, the fluctuations in the transmitted flux are significantly correlated with the local background flux on scales for which the field is intermittent. 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. Therefore, the self-normalized power spectrum would be useful for the discrimination among models without the uncertainties caused by free (or fitting) parameters.Comment: 24 pages, 8 figures, to appear in ApJ tentatively in the Nov 1 2001 issu

Intermittent behavior of cosmic mass field revealed by QSO's Ly_alpha forests

The intermittent behavior of the space-scale distribution of Ly$\alpha$ transmitted flux of QSO HS1700+64 has been analyzed via a discrete wavelet transform. We found that there are strong indications of intermittency on scales down to about 10 $h^{-1}$ kpc. These are: 1.) the probability distribution function of the local fluctuations of the flux is significantly long-tailed on small scales, and 2.) the local power spectrum of the flux shows prominent spiky structures on small scales. Moreover, the local power spectrum averaged on regions with different sizes shows similar spiky structures. Therefore, the random mass density field traced by the Ly$\alpha$ forests is rougher on smaller scales, consistent with singular clustering.Comment: Accepted for publication in ApJ Letters, 12 pages, 3 figure

A Unified Fitting of HI and HeII Ly\alpha Transmitted Flux of QSO HE2347 with LCDM Hydrodynamic Simulations

Using cosmological hydrodynamic simulations of the LCDM model, we present a comparison between the simulation sample and real data sample of HI and HeII Ly\alpha transmitted flux in the absorption spectra of the QSO HE2347-4342. The LCDM model is successful in simultaneously explaining the statistical features of both HI and HeII Ly\alpha transmitted flux. It includes: 1.) the power spectra of the transmitted flux of HI and HeII can be well fitted on all scales > 0.28h^{-1} Mpc for H, and > 1.1h^{-1} Mpc for He; 2.) the Doppler parameters of absorption features of HeII and HI are found to be turbulent-broadening; 3.) the ratio of HeII to HI optical depths are substantially scattered, due to the significant effect of noise. A large part of the \eta-scatter is due to the noise in the HeII flux. However, the real data contain more low-\eta events than simulation sample. This discrepancy may indicate that the mechanism leading extra fluctuations upon the simulation data, such as a fluctuating UV radiation background, is needed. Yet, models of these extra fluctuations should satisfy the constraints: 1.) if the fluctuations are Gaussian, they should be limited by the power spectra of observed HI and HeII flux; 2.) if the fluctuations are non-Gaussian, they should be limited by the observed non-Gaussian features of the HI and HeII flux.Comment: 21 pages, 7 figs, ApJ in pres

Power spectrum and intermittency of the transmitted flux of QSOs Ly-alpha absorption spectra

Using a set of 28 high resolution, high signal to noise ratio (S/N) QSO Ly-alpha 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 re-sampling 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.Comment: 26 pages (incl. figures). Accepted for publication in MNRA

Non-Gaussian Features of Transmitted Flux of QSO's Lyα\alpha Absorption: Intermittent Exponent

We calculate the structure function and intermittent exponent of the 1.) Keck data, which consists of 29 high resolution, high signal to noise ratio (S/N) QSO Ly$\alpha$ absorption spectra, and 2.)the Ly$\alpha$ 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. These two measures detect not only non-gaussianities, but also the type of non-gaussianty in the the field. We find that, 1.) the structure functions of the simulation samples are significantly larger than that of Keck data on scales less than about 100 h$^{-1}$ kpc, 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 in terms of second and lower order statistics. (Abridged)Comment: 17 pages, 13 figures. Accepted by Ap

Intermittency in large scale structures in the universe

I study the weak nonlinear regime of structure formation using high resolution and high signal-to-noise ratio (S/N) samples of Quasi Stellar Objects' (QSOs) Lyα transmission spectra. Using a space-scale decomposition, the Discrete Wavelet Transform (DWT), I show that the field traced by Lyα transmission flux is intermittent on scales less than 2000 km/s. The distribution of the local power of fluctuations is spiky with almost no power between the spikes. This spike-gap-spike feature gets more pronounced on smaller scales (128-16 km/s). This feature contradicts the predictions of the correlation hierarchy model on small scales ( < 64 km/s). Intermittency renders lower order statistics, like the power spectrum of fluctuations, ineffective in describing an intermittent field and discriminating between various structure formation models. I show that the structure functions and the intermittent exponent are not only able to quantitatively differentiate between different dark matter models but also qualitatively describe the nature of non-Gaussianity. The structure functions and the intermittent exponent are powerful tools for describing an intermittent field. Intermittency opens a new window in the study of the nonlinear evolution of structure in the universe