The Lyman continuum escape fraction and the Mean Free Path of hydrogen
  ionizing photons for bright z~4 QSOs from SDSS DR14
  One of the major challenges in observational cosmology is related to the
redshift evolution of the average hydrogen ionization in the Universe. In order
to probe the ionization level of the IGM and the ionization capabilities of
bright QSOs at z=4, we have selected a sample of 2508 QSOs from the SDSS survey
(DR14) at 3.6<z<4.6 and -29.0<M1450<-26.0. Starting from UV/optical rest-frame
spectra of the whole QSO sample, we estimate the escape fraction and free path
individually for each of them. We calculate the Lyman Continuum (LyC) escape
fraction as the flux ratio blue-ward (~900 A rest-frame) and red-ward (~930 A
rest-frame) of the Lyman limit. We then obtain the probability distribution
function (PDF) of the individual free paths of the QSOs in the sample and study
its evolution in luminosity and redshift, comparing our results with the ones
found in literature so far. We find a lower limit to the mean LyC escape
fraction of 0.49, in agreement with the values obtained for both brighter and
fainter sources at the same redshift. We show that the free paths of ionizing
photons are characterized by a skewed distribution function peaked at low
values, with an average of ~49-59 proper Mpc at z~4, after excluding possible
associated absorbers. This value is larger than the one obtained at the same
redshift by many authors in the literature using different techniques. Finally,
we also find that the redshift evolution of this parameter results to be
possibly milder than previously thought. Our new determination of the mean free
path at z~4 implies that previous estimates of the HI photo-ionization rate
Gamma_HI available in the literature should be corrected by a factor of
1.2-1.7. These results have important implications if extrapolated at the epoch
of reionization.
