We present a series of high-resolution (20-2000 Msun, 0.1-4 pc) cosmological zoom-in simulations at z~6 from the Feedback In Realistic Environment (FIRE) project. These simulations cover halo masses 10^9-10^11 Msun and rest-frame ultraviolet magnitude Muv = -9 to -19. These simulations include explicit models of the multi-phase ISM, star formation, and stellar feedback, which produce reasonable galaxy properties at z = 0-6. We post-process the snapshots with a radiative transfer code to evaluate the escape fraction (fesc) of hydrogen ionizing photons. We find that the instantaneous fesc has large time variability (0.01%-20%), while the time-averaged fesc over long time-scales generally remains ~5%, considerably lower than the estimate in many reionization models. We find no strong dependence of fesc on galaxy mass or redshift. In our simulations, the intrinsic ionizing photon budgets are dominated by stellar populations younger than 3 Myr, which tend to be buried in dense birth clouds. The escaping photons mostly come from populations between 3-10 Myr, whose birth clouds have been largely cleared by stellar feedback. However, these populations only contribute a small fraction of intrinsic ionizing photon budgets according to standard stellar population models. We show that fesc can be boosted to high values, if stellar populations older than 3 Myr produce more ionizing photons than standard stellar population models (as motivated by, e.g., models including binaries). By contrast, runaway stars with velocities suggested by observations can enhance fesc by only a small fraction. We show that sub-grid star formation models, which do not explicitly resolve star formation in dense clouds with n >> 1 cm^-3, will dramatically over-predict fesc.
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