We revisit the proximity effect produced by QSOs at redshifts 2.1 - 3.3 applying the FLO approach ( 56 ) to a sample of \sim 6300 Ly \alpha lines fitted in 21 high resolution , high signal-to-noise spectra .
This new technique allows to recover the hydrogen density field from the H i column densities of the lines in the Ly \alpha forest , on the basis of simple assumptions on the physical state of the gas .
To minimize the systematic uncertainties that could affect the density recovering in the QSO vicinity , we carefully determined the redshifts of the QSOs in our sample and modelled in detail their spectra to compute the corresponding ionising fluxes .
The mean density field obtained from the observed spectra shows a significant over-density in the region within 4 proper Mpc from the QSO position , confirming that QSOs are hosted in high density peaks .
The absolute value of \rho / \langle \rho \rangle for the peak is uncertain by a factor of \sim 3 , depending on the assumed QSO spectral slope and the minimum H i column density detectable in the spectra .
We do not confirm the presence of a significant over-density extending to separations of \sim 15 proper Mpc from the QSO , claimed in previous works at redshifts \langle z \rangle \simeq 2.5 and 3.8 .
Our best guess for the UV background ionisation rate based on the IGM mean density recovered by FLO is \Gamma _ { UVB } \simeq 10 ^ { -12 } s ^ { -1 } .
However , values of \Gamma _ { UVB } \simeq 3 \times 10 ^ { -12 } s ^ { -1 } could be viable if an inverted temperature-density relation with index \alpha \simeq - 0.5 is adopted .