We present results of joint modeling of the probability distribution function ( PDF ) and the one-dimensional power spectrum ( PS ) of the Ly \alpha 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 \Lambda CDM cosmology .
In the first model , the linear power spectrum has a scale-invariant spectral index n _ { s } = 1 , whereas in the second , it has a negative running index ( RSI ) , { d } n / { d } { ln } k < 0 .
We generate mock catalogs of QSO spectra , and compare their statistical properties to those of the observations at z = 3 .
We perform a joint fit of the power spectrum and the PDF .
A scale-invariant model with \sigma _ { 8 } = 0.9 matches well the data if the mean IGM temperature is T~ { } \hbox to 0.0 pt { $ < $ } { \lower 4.3 pt \hbox { $ \sim$ } } 1.5 \times 10 ^ { 4 } { K } .
For higher temperature , it tends to overestimate the flux power spectrum over scales k~ { } \hbox to 0.0 pt { $ < $ } { \lower 4.3 pt \hbox { $ \sim$ } } 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~ { } \hbox to 0.0 pt { $ > $ } { \lower 4.3 pt \hbox { $ \sim$ } } 2 \times 10 ^ { 4 } { K } .
The best fit models reproduce the slope and normalisation of the column density distribution , irrespective of the shape and amplitude of the linear power spectrum .
They are also consistent with the observed line-width distribution given the large uncertainties .
Our joint analysis suggests that \sigma _ { 8 } is likely to be in the range 0.7-0.9 for a temperature 1 ~ { } \hbox to 0.0 pt { $ < $ } { \lower 4.3 pt \hbox { $ \sim$ } } T~ { } \hbox to 0.0 pt { $ < $ } { % \lower 4.3 pt \hbox { $ \sim$ } } 2 \times 10 ^ { 4 } { K } and a reasonable reionization history .