Recovery of the Power Spectrum of Mass Fluctuations from Observations of the Lyα Forest

We present a method to recover the shape and amplitude of the power spectrum of mass uctuations, P(k), from observations of the high-redshift Lya forest. The method is motivated by the physical picture that has emerged from hydrodynamic cosmological simulations and related semianalytic models, in which typical Lya forest lines arise in a di use, continuous, uctuating intergalactic medium. The thermal state of this low-density gas is governed by simple physical processes, which lead to (do/o [ 10) a tight correlation between the Lya 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 eld with arbitrary normalization, (2) measure the power spectrum of this continuous density eld and convert it to the equivalent three-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 ux. Imposing the observed mean Lya 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 Lya forest. We test the full recovery procedure on smoothed particle hydrodynamics (SPH) simulations of three di erent cosmological models and show that it recovers the true mass power spectrum of the models on comoving scales D110 h~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 D 10), moderate-resolution (D40 km s~1 pixels) spectra. We present an illustrative application to Songaila the recovered P(k) is consistent with that of an ) \ 1, h \ 0.5, cold dark matter model. The statistical uncer-p 8 (z \ 0) B 0.5 tainty in this result is large because it is based on a single QSO, but the method can be applied to large samples of existing QSO spectra and should thereby yield the power spectrum of mass uctuations on small and intermediate scales at redshifts z D 24.