Recovery of the Power Spectrum of Mass Fluctuations from Observations of the Lyman-alpha Forest

We present a method to recover the shape and amplitude of the power spectrum of mass fluctuations, P (k), from observations of the high redshift Lyα forest. The method is motivated by the physical picture that has emerged from hydrodynamic cosmological simulations and related semi-analytic models, in which typical Lyα forest lines arise in a diffuse, continuous, fluctuating intergalactic medium. The thermal state of this low density gas (δρ/ρ ∼< 10) is governed by simple physical processes, which lead to a tight correlation between the Lyα optical depth and the underlying matter density. To recover the mass power spectrum, we (1) apply a monotonic Gaussian mapping to convert the QSO spectrum to an approximate line-of-sight density field with arbitrary normalization, (2) measure the power spectrum of this continuous density field and convert it to the equivalent 3-dimensional P (k), and (3) evolve cosmological simulations with this P (k) shape and a range of normalizations and choose the normalization for which the simulations reproduce the observed power spectrum of the transmitted QSO flux. Imposing the observed mean Lyα opacity as a constraint in step (3) makes the derived P (k) normalization insensitive to the choice of cosmological parameters, ionizing background spectrum, or reionization history. Thus, in contrast to estimates of P (k) from galaxy clustering, there are no uncertain “bias parameters” in the recovery of the mass power spectrum from the Lyα forest. We test the full recovery procedure on smoothed-particle hydrodynamics (SPH) simulations of three different cosmological models and show that it recovers the true mass power spectrum of the models on comoving scales ∼ 1− 10h−1 Mpc, the upper scale being set by the size of the simulation boxes. The procedure works well even when it is applied to noisy (S/N∼10), moderate resolution (∼ 40 km s−1 pixels) spectra. We present an Department of Astronomy, The Ohio State University, Columbus, OH 43210 2 Department of Physics and Astronomy, University of Massachusetts, Amherst, MA, 01003 Lick Observatory, University of California, Santa Cruz, CA 95064 Presidential Faculty Fellow [email protected] [email protected] [email protected] [email protected]