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The mean free path of ionizing photons, lambda(mfp), is a key factor in the photoionization of the intergalactic medium (IGM). At z greater than or similar to 5, however, lambda(mfp) may be short enough that measurements towards QSOs are biased by the QSO proximity effect. We present new direct measurements of lambda(mfp) that address this bias and extend up to z similar to 6 for the first time. Our measurements at z similar to 5 are based on data from the Giant Gemini GMOS survey and new Keck LRIS observations of low-luminosity QSOs. At z similar to 6 we use QSO spectra from Keck ESI and VLT X-Shooter. We measure lambda(mfp) = 9.09(-1.28)(+1.62) proper Mpc and 0.75(-0.45)(+0.65) proper Mpc (68 percent confidence) at z = 5.1 and 6.0, respectively. The results at z = 5.1 are consistent with existing measurements, suggesting that bias from the proximity effect is minor at this redshift. At z = 6.0, however, we find that neglecting the proximity effect biases the result high by a factor of two or more. Our measurement at z = 6.0 falls well below extrapolations from lower redshifts, indicating rapid evolution in lambda(mfp) over 5 < z < 6. This evolution disfavours models in which reionization ended early enough that the IGM had time to fully relax hydrodynamically by z = 6, but is qualitatively consistent with models wherein reionization completed at z = 6 or even significantly later. Our mean free path results are most consistent with late reionization models wherein the IGM is still 20 percent neutral at z = 6, although our measurement at z = 6.0 is even lower than these models prefer.
Constraints on the time-scales of quasar activity are key to understanding the formation and growth of supermassive black holes (SMBHs), quasar triggering mechanisms, and possible feedback effects on their host galaxies. However, observational estimates of this so-called quasar lifetime are highly uncertain (t(Q) similar to 10(4)-10(9) yr), because most methods are indirect and involve many model-dependent assumptions. Direct evidence of earlier activity is gained from the higher ionization state of the intergalactic medium (IGM) in the quasar environs, observable as enhanced Ly alpha transmission in the so-called proximity zone. Due to the similar to 30 Myr equilibration time-scale of He II in the z similar to 3 IGM, the size of the He II proximity zone depends on the time the quasar had been active before our observation t(on) <= t(Q), enabling up to +/- 0.2 dex precise measurements of individual quasar on-times that are comparable to the e-folding time-scale t(S) <= 44 Myr of SMBH growth. Here we present the first statistical sample of 13 quasars whose accurate and precise systemic redshifts allow for measurements of sufficiently precise He II quasar proximity zone sizes between similar or equal to 2 and similar or equal to 15 proper Mpc from science-grade Hubble Space Telescope (HST) spectra. Comparing these sizes to predictions from cosmological hydrodynamical simulations post-processed with 1D radiative transfer, we infer a broad range of quasar on-times from t(on) less than or similar to 1Myr to t(on) > 30 Myr that does not depend on quasar luminosity, black hole mass, or Eddington ratio. These results point to episodic quasar activity over a long duty cycle, but do not rule out substantial SMBH growth during phases of radiative inefficiency or obscuration.