The observed probability distribution function, power spectrum, and correlation function of the transmitted flux in the Ly alpha forest

A sample of eight quasars observed at high resolution and signal-to-noise r atio is used to determine the transmitted flux probability distribution fun ction (TFPDF), and the power spectrum and correlation function of the trans mitted flux in the Ly alpha forest, in three redshift bins centered at z = 2.41, 3.00, and 3.89. All the results are presented in tabular form, with f ull error covariance matrices, to allow for comparisons with any numerical simulations and with other data sets. The observations are compared with a numerical simulation of the Lya forest of a ACDM model with Omega = 0.4, kn own to agree with other large-scale structure observational constraints. Th ere is excellent agreement for the TFPDF if the mean transmitted flux is ad justed to match the observations. A small difference between the observed a nd predicted TFPDF is found at high fluxes and low redshift, which may be d ue to the uncertain effects of fitting the spectral continuum. Using the nu merical simulation, we show how the flux power spectrum can be used to reco ver the initial power spectrum of density fluctuations. From our sample of eight quasars, we measure the amplitude of the mass power spectrum to corre spond to a linear variance per unit Ink of Delta (2)(rho)(k)= 0.72 +/- 0.09 at k = 0.04(km s(-1))(-1) and z = 3, and the slope of the power spectrum n ear the same k to be n(p) = -2.55 +/- 0.10 (statistical error bars). The re sults are statistically consistent with those of Croft et al., although our value for the rms fluctuation is lower by a factor of 0.75. For the ACDM m odel we use, the implied primordial slope is n = 0.93 +/- 0.10, and the nor malization is sigma (8) = 0.68 + 1.16(0.95 - n) +/- 0.04.