Measuring the Mean Free Path of HI Ionizing Photons at $3.2\le z\le 4.6$ with DESI Y1 Quasars

The mean free path of ionizing photons (${\lambda }_{\mathrm{m}\mathrm{f}\mathrm{p}}^{912}$) in the intergalactic medium (IGM) is a crucial quantity in modelling the ionization state of IGM and the extragalactic ultraviolet background (EUVB), and is widely used in hydrodynamical simulations of galaxies and reionization. We construct the largest quasar spectrum dataset to date – 12,595 $\mathrm{S}\mathrm{/}\mathrm{N}>3$ spectra – using the Y1 observation of Dark Energy Spectroscopic Instrument (DESI) to make the most precise model-independent measurement of the mean free path at $3.2\le z\le 4.6$. By stacking the spectra in 17 redshift bins and modelling the Lyman continuum profile, we get a redshift evolution ${\lambda }_{\mathrm{m}\mathrm{f}\mathrm{p}}^{912}\propto (1+z{)}^{-4.27}$ at $2\le z\le 5$, which is much shallower than previous estimate ${\lambda }_{\mathrm{m}\mathrm{f}\mathrm{p}}^{912}\propto (1+z{)}^{-5.4}$. We then explore the sources of systematic bias, including the choice of intrinsic quasar continuum, the consideration of Lyman series opacity and Lyman limit opacity evolution and the definition of ${\lambda }_{\mathrm{m}\mathrm{f}\mathrm{p}}^{912}$. Combining our results with estimates of ${\lambda }_{\mathrm{m}\mathrm{f}\mathrm{p}}^{912}$ at higher redshifts, we conclude at high confidence that the evolution in ${\lambda }_{\mathrm{m}\mathrm{f}\mathrm{p}}^{912}$ steepens at $z\approx 5$. We interpret this inflection as the transition from the end of HI reionization to a fully ionized plasma which characterizes the intergalactic medium of the past $\sim 10$ billion years.