Joint modelling of the probability distribution function and power spectrum of the Ly  forest: comparison with observations at z= 3

We present results of joint modelling of the probability distribution function (PDF) and the one-dimensional power spectrum (PS) of the Lyα forest flux decrement. The sensitivity of these statistical measures to the shape and amplitude of the linear matter power spectrum is investigated using N-body simulations of two variants of the ΛCDM cosmology. In the first model, the linear power spectrum has a scale-invariant spectral index ns= 1, whereas in the second, it has a negative running spectral index (RSI), dn/d ln k < 0. We generate mock catalogues of quasi-stellar object (QSO) spectra, and compare their statistical properties to those of the observations at z= 3. We perform a joint fit of the PS and the PDF. A scale-invariant model with σ8= 0.9 matches the data well if the mean temperature of the intergalactic medium is T≲ 1.5 × 104 K. For higher temperature, it tends to overestimate the flux PS over scales k≲ 0.01 s km −1. The discrepancy is less severe when the PS alone is fitted. However, models matching the PS alone do not yield a good fit to the PDF. A joint analysis of the flux PS and PDF tightens the constraints on the model parameters and reduces systematic biases. The RSI model is consistent with the observed PDF and PS only if the temperature is T≳ 2 × 104 K. The best-fitting models reproduce the slope and normalization of the column density distribution, irrespective of the shape and amplitude of the linear power spectrum. They are also consistent with the observed linewidth distribution, given the large uncertainties. Our joint analysis suggests that σ8 is likely to be in the range 0.7–0.9 for a temperature 1 × 104≲T≲ 2 × 104 K and a reasonable reionization history.