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

Hydraulic economy and logographic writing in ancient China: factor of topography

Chinese civilisation is characterised by two distinctive features – a strong centralised administration and the system of logographic writing. This paper investigates nature’s powerful impacts on human development, in terms of organisation and communication in ancient China. It argues that ancient China’s topography played a crucial role in the formation of ancient Chinese civilisation and its hydraulic economy pushed the state stronger than society, hence a strong centralised government emerged

Lyα\alpha Leaks in the Absorption Spectra of High Redshift QSOs

Spectra of high redshift QSOs show deep Gunn-Peterson absorptions on the blue sides of the \Lya emissions lines. They can be decomposed into components called \Lya leaks, defined to be emissive regions in complementary to otherwise zero-fluxed absorption gaps. Just like \Lya absorption forests at low redshifts, \Lya leaks are both easy to find in observations and containing rich sets of statistical properties that can be used to study the early evolution of the IGM. Among all properties of a leak profile, we investigate its equivalent width in this paper, since it is weakly affected by instrumental resolution and noise. Using 10 Keck QSO spectra at $z\sim6$, we have measured the number density distribution function $n(W,z)$, defined to be the number of leaks per equivalent width $W$ and per redshift $z$, in the redshift range $5.4 - 6.0$. These new observational statistics, in both the differential and cumulative forms, fit well to hydro numerical simulations of uniform ionizing background in the $\Lambda$CDM cosmology. In this model, Ly $\alpha$ leaks are mainly due to low density voids. It supports the early studies that the IGM at $z\simeq6$ would still be in a highly ionized state with neutral hydrogen fraction $\simeq 10^{-4}$. Measurements of $n(W,z)$ at $z>6$ would be effective to probe the reionization of the IGM.Comment: 3 figs, accepted by ApJ

Abundance and Clustering of C IV Absorption Systems in the SCDM, LCDM and CHDM Models

We have developed a method for calculating the two-point correlation function of nonlinearly evolved mass and collapsed halos in the Press-Schechter formalism. The nonlinear gravitational interaction is treated as the sum of various individual spherical top-hat clustering. Because no collapsed halo of mass M can exist in initial regions (or top-hat spheres) of mass less than M, the bias that massive halos have stronger correlation than the background mass can be naturally introduced. We apply this method to derive constraints on popular dark-matter models from the spatial number density and the correlation function of C IV absorption systems in QSO spectra. Considering C IV systems should behosted by collapsed halos, one can obtain an upper limit to the threshold mass of the collapsed halos by requiring their number density to be larger than that of observed C IV systems. On the other hand, in order to explain the observed clustering of C IV systems, a lower limit to the threshold mass will be set for the hosting halos. The cold dark matter model, the Lamda CDM model and the cold-plus-hot dark matter model are tested using the C IV observations.Comment: 23 pages, LaTeX, plus 11 figures in the PS format to be published in Ap