Robustness of direct measurements of the mean free path of ionizing photons in the epoch of reionization

Measurements of the mean free path of Lyman-continuum photons in the intergalactic medium during the epoch of reionization can help constrain the nature of the sources as well as sinks of hydrogen-ionizing radiation. A recent approach to this measurement has been to utilize composite spectra of multiple quasars at $z\sim 6$, and infer the mean free path after correcting the spectra for the presence of quasar proximity zones. This has revealed not only a steep drop in the mean free path from $z=5$ to $z=6$, but also potentially a mild tension with reionization simulations. We critically examine such direct measurements of the mean free path for biases due to quasar environment, incomplete reionization, and quasar proximity zones. Using cosmological radiative transfer simulations of reionization combined with one-dimensional radiative transfer calculations of quasar proximity zones, we find that the bias in the mean free path due to overdensities around quasars is minimal at $z\sim 6$. Patchiness of reionization at this redshift also does not affect the measurements significantly. Fitting our model to the data results in a mean free path of $\lambda_{\mathrm{mfp}}=0.90^{+0.66}_{-0.40}$ pMpc at $z=6$, which is consistent with the recent measurements in the literature, indicating robustness with respect to the modelling of quasar proximity zones. We also compare various ways in which the mean free path has been defined in simulations before the end of reionization. Overall, our finding is that recent measurements of the mean free path appear to be robust relative to several sources of potential bias.Comment: 10 pages, 9 figures, submitted to MNRA

The need for obscured supermassive black hole growth to explain quasar proximity zones in the epoch of reionization

Proximity zones of quasars with redshifts $z \gtrsim 6$ are unique probes of the growth of supermassive black holes. But simultaneously explaining proximity zone sizes and black hole masses at this redshift has proved to be challenging because of the very short quasar lifetimes implied by the proximity zones. We study the robustness of some of the assumptions that are usually made to infer quasar lifetimes from proximity zone sizes. We show that thanks to the short equilibration time of gas inside the proximity zones, small proximity zones can be readily explained by quasars that vary in brightness with a short duty cycle of $f_\mathrm{duty}\sim 0.1$ and short bright periods of $t_\mathrm{on}\sim 10^4$ yr, even for long lifetimes. We further show that reconciling this with black hole mass estimates requires the black hole to continue to grow and accrete during its obscured phase. The consequent obscured fractions of $\gtrsim$ 0.7 or higher are consistent with low-redshift measurements and models of black hole accretion. Further, the large dynamic range of our simulation, and its calibration to the Lyman-$\alpha$ forest, allows us to investigate the influence of the large-scale topology of reionization and the quasar's host halo mass on proximity zones. We find that incomplete reionization can impede the growth of proximity zones and make them smaller up to 30%, but the quasar host halo mass only affects proximity zones weakly and indirectly. Our work suggests that high-redshift proximity zones can be an effective tool to study quasar variability and black hole growth.Comment: 19 pages, 17 figures, submitted to MNRAS, comments welcom

New quasar proximity zone size measurements at z∼6z\sim 6 using the enlarged XQR-30 sample

Proximity zones of high-redshift quasars are unique probes of their central supermassive black holes as well as the intergalactic medium in the last stages of reionization. We present 22 new measurements of proximity zones of quasars with redshifts between 5.8 and 6.6, using the enlarged XQR-30 sample of high-resolution, high-SNR quasar spectra. The quasars in our sample have UV magnitudes of $M_{1450}\sim -27$ and black hole masses of $10^9$\unicode{x2013}$10^{10}$ M$_\odot$. Our inferred proximity zone sizes are 2\unicode{x2013}7 physical Mpc, with a typical uncertainty of less than 0.5 physical Mpc, which, for the first time, also includes uncertainty in the quasar continuum. We find that the correlation between proximity zone sizes and the quasar redshift, luminosity, or black hole mass, indicates a large diversity of quasar lifetimes. Two of our proximity zone sizes are exceptionally small. The spectrum of one of these quasars, with $z=6.02$, displays, unusually for this redshift, damping wing absorption without any detectable metal lines, which could potentially originate from the IGM. The other quasar has a high-ionization absorber $\sim$0.5 pMpc from the edge of the proximity zone. This work increases the number of proximity zone measurements available in the last stages of cosmic reionization to 87. This data will lead to better constraints on quasar lifetimes and obscuration fractions at high redshift, which in turn will help probe the seed mass and formation redshift of supermassive black holes.Comment: 16 pages, 9 figures, Accepted in MNRA

Probing Ultralate Reionization: Direct Measurements of the Mean Free Path over 5 < z < 6

The mean free path of ionizing photons, λ _mfp , is a critical parameter for modeling the intergalactic medium (IGM) both during and after reionization. We present direct measurements of λ _mfp from QSO spectra over the redshift range 5 < z < 6, including the first measurements at z ≃ 5.3 and 5.6. Our sample includes data from the XQR-30 VLT large program, as well as new Keck/ESI observations of QSOs near z ∼ 5.5, for which we also acquire new [C ii ] 158 μ m redshifts with ALMA. By measuring the Lyman continuum transmission profile in stacked QSO spectra, we find ${\lambda }_{\mathrm{mfp}}={9.33}_{-1.80}^{+2.06}$ , ${5.40}_{-1.40}^{+1.47}$ , ${3.31}_{-1.34}^{+2.74}$ , and ${0.81}_{-0.48}^{+0.73}$ pMpc at z = 5.08, 5.31, 5.65, and 5.93, respectively. Our results demonstrate that λ _mfp increases steadily and rapidly with time over 5 < z < 6. Notably, we find that λ _mfp deviates significantly from predictions based on a fully ionized and relaxed IGM as late as z = 5.3. By comparing our results to model predictions and indirect λ _mfp constraints based on IGM Ly α opacity, we find that the evolution of λ _mfp is consistent with scenarios wherein the IGM is still undergoing reionization and/or retains large fluctuations in the ionizing UV background well below redshift 6