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One of the major challenges in observational cosmology is related to theredshift evolution of the average hydrogen ionization in the Universe. In orderto probe the ionization level of the IGM and the ionization capabilities ofbright 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-framespectra of the whole QSO sample, we estimate the escape fraction and free pathindividually for each of them. We calculate the Lyman Continuum (LyC) escapefraction as the flux ratio blue-ward (~900 A rest-frame) and red-ward (~930 Arest-frame) of the Lyman limit. We then obtain the probability distributionfunction (PDF) of the individual free paths of the QSOs in the sample and studyits evolution in luminosity and redshift, comparing our results with the onesfound in literature so far. We find a lower limit to the mean LyC escapefraction of 0.49, in agreement with the values obtained for both brighter andfainter sources at the same redshift. We show that the free paths of ionizingphotons are characterized by a skewed distribution function peaked at lowvalues, with an average of ~49-59 proper Mpc at z~4, after excluding possibleassociated absorbers. This value is larger than the one obtained at the sameredshift by many authors in the literature using different techniques. Finally,we also find that the redshift evolution of this parameter results to bepossibly milder than previously thought. Our new determination of the mean freepath at z~4 implies that previous estimates of the HI photo-ionization rateGamma_HI available in the literature should be corrected by a factor of1.2-1.7. These results have important implications if extrapolated at the epochof reionization.

The Lyman continuum escape fraction and the Mean Free Path of hydrogen ionizing photons for bright z~4 QSOs from SDSS DR14