The probability distribution function of the Lyman α transmitted flux from a sample of Sloan Digital Sky Survey quasars

We present a measurement of the probability distribution function (PDF) of the transmitted flux in the Lyman alpha (Ly alpha) forest from a sample of 3492 quasars included in the Sloan Digital Sky Survey data release 3 (SDSS DR3). Our intention is to investigate the sensitivity of the Ly alpha flux PDF as measured from low-resolution and low signal-to-noise ratio data to a number of systematic errors such as uncertainties in the mean flux, continuum and noise estimate. The quasar continuum is described by the superposition of a power law and emission lines. We perform a power-law continuum fitting on a spectrum-by-spectrum basis, and obtain an average continuum slope of alpha(nu) = 0.59 +/- 0.36 in the redshift range 2.5 < z < 3.5. We take into account that the variation in the continuum indices increases the mean flux by 3 and 7 per cent at z = 3 and 2.4, respectively, as compared to the values inferred with a single (mean) continuum slope. We compare our measurements to the PDF obtained with mock lognormal spectra, whose statistical properties have been constrained to match the observed Ly alpha flux PDF and power spectrum of high-resolution data. Using our power-law continuum fitting and the SDSS pipeline noise estimate yields a poor agreement between the observed and mock PDFs. Allowing for a break in the continuum slope and, more importantly, for residual scatter in the continuum level substantially improves the agreement. A decrease of similar to 10-15 per cent in the mean quasar continuum with a typical rms variance at the 20 per cent level can account for the data, provided that the noise excess correction is no larger than less than or similar to 10 per cent.