Tightening constraints from the Lyα forest with the flux probability distribution function

The analysis of the Ly alpha forest of absorption lines in quasar spectra has emerged as a potentially powerful technique to constrain the linear matter power spectrum. In most previous work, the amplitude of the ionizing background was fixed by calibrating simulations to match the observed mean transmitted flux in the Ly alpha forest. This procedure is undesirable in principle, as it requires the estimation of the unabsorbed quasar continuum level, a difficult undertaking subject to various sources of systematic error and bias. We suggest an alternative approach based on measuring the one-point probability distribution function (pdf) of the fluctuations in the flux about the mean, relative to the mean, i.e., the pdf of delta(f) = ( f - < f >)/< f >. This statistic, while sensitive to the amplitude of the ionizing background, has the virtue that its measurement does not require an estimate of the unabsorbed continuum level. We present a measurement of the pdf of delta(f) from seven Keck HIRES spectra, spanning a redshift range of z = 2.2 - 4.4. To illustrate that our method is useful, we compare our measurements of the pdf of delta(f) and measurements of the flux power spectrum from Croft et al. at z = 2.72, with cosmological simulations. From this comparison, we obtain constraints on the mean transmission in the Ly alpha forest, the slope of the temperature-density relation, as well as the amplitude and slope of the mass power spectrum. Our methodology is useful for obtaining more precise constraints with larger data samples from the Sloan Digital Sky Survey (SDSS).