The Observed Probability Distribution Function, Power Spectrum, and Correlation Function of the Transmitted Flux in the Lyα Forest

Abstract

A sample of eight quasars observed at high resolution and signal-to-noise is used to determine the probability distribution function (PDF), the power spectrum, and the correlation function of the transmitted flux in the Lyα forest, in three redshift bins centered at z = 2.41, 3.00, and 3.89. All the results are presented in tabular form, with full 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 Lyα forest of a ΛCDM model with Ω = 0.4, known to agree with other large-scale structure observational constraints. There is excellent agreement for the PDF, if the mean transmitted flux is adjusted to match the observations. A small difference between the observed and predicted PDF is found at high fluxes and low redshift, which may be due to the uncertain effects of fitting the spectral continuum. Using the numerical simulation, we show how the flux power spectrum can be used to recover the initial power spectrum of density fluctuations. From our sample of eight quasars, we measure the amplitude of the mass power spectrum to correspond to a linear variance per unit ln k of ∆ 2 ρ (k) = 0.72 ± 0.09 at k = 0.04( km s −1 ) −1 and z = 3, and the slope of the power spectrum near the same k to be n p = −2.55 ± 0.10 (statistical error bars). The results are statistically consistent with Croft et al. , although our value for the rms fluctuation is lower by a factor 0.75. For the ΛCDM model we use, the implied primordial slope is n = 0.93 ± 0.10, and the normalization is σ 8 = 0.68 + 1.16(0.95 − n) ± 0.04.

Constraints on Cosmological Parameters from the Lyα Forest Power Spectrum andCOBEDMR

“…However, assuming gravitational instability and a CDM power spectrum shape, they extrapolate from their result to derive values of l and *2 that can be directly compared to CWPHKÏs measurement at z \ 2.5, k p \ 0.008 (km s~1)~1, obtaining l \ [2.24^0.10 and Despite the entirely independent data *2(k p ) \ 0.32^0.07. sets and very di †erent modeling procedures, the CWPHK and McDonald et al (2000) measurements agree almost perfectly in slope and are consistent in amplitude at the D1 p level. We plot the McDonald et al (2000) measurement as error crosses in Figures 2 and 3.…”

“…Conveniently, the McDonald et al (2000) point lies almost exactly on our [1 p error contour, so to a good approximation one can obtain the parameter constraint equations (7) and (8) Table 2 by k [ v.…”

“…A factor of 2 improvement in the precision of the Lya P(k) measurement could greatly restrict the range of models compatible with all three constraints, especially if the Lya P(k) amplitude is somewhat lower, as McDonald et al (2000) Ðnd.…”

“…However, this equation cannot describe the results of Figure 3 as accurately as equation (7) describes the results of Figure 2. Recently, McDonald et al (2000) measured the Lya forest Ñux power spectrum in a sample of eight Keck HIRES spectra and used it to infer the amplitude and shape of the mass power spectrum. Their mean absorption redshift is z B 3 rather than z \ 2.5, and their data best constrain the P(k) amplitude at k \ 0.04 (km s~1)~1 rather than at 0.008 (km s~1)~1.…”

Simulations of Damped Lyα and Lyman Limit Absorbers in Different Cosmologies: Implications for Structure Formation at High Redshift

“…A model with somewhat less small-scale power, such as the lower amplitude LCDM model favored by recent Lya forest studies (McDonald et al 2000 ;Croft et al 2001), might fare better in this regard, perhaps matching the observed DLA abundance with a closer to the v c,min expected photoionization value. We are unable to make predictions for total absorption in the TCDM model with our current simulations because the paucity of structure above our resolution threshold makes our extrapolation procedure unreliable.…”