Quantifying Distributions of Lyman Continuum Escape Fraction
  Simulations have indicated that most of the escaped Lyman continuum photons
escape through a minority of solid angles with near complete transparency, with
the remaining majority of the solid angles largely opaque, resulting in a very
broad and skewed probability distribution function (PDF) of the escape fraction
when viewed at different angles. Thus, the escape fraction of Lyman continuum
photons of a galaxy observed along a line of sight merely represents the
properties of the interstellar medium along that line of sight, which may be an
ill-representation of true escape fraction of the galaxy averaged over its full
sky. Here we study how Lyman continuum photons escape from galaxies at $z=4-6$,
utilizing high-resolution large-scale cosmological radiation-hydrodynamic
simulations. We compute the PDF of the mean escape fraction ($\left<f_{\rm
esc,1D}\right>$) averaged over mock observational samples, as a function of the
sample size, compared to the true mean (had you an infinite sample size). We
find that, when the sample size is small, the apparent mean skews to the low
end. For example, for a true mean of 6.7%, an observational sample of (2,10,50)
galaxies at $z=4$ would have have 2.5% probability of obtaining the sample mean
lower than $\left<f_{\rm esc,1D}\right>=$(0.007%, 1.8%, 4.1%) and 2.5%
probability of obtaining the sample mean being greater than (43%, 18%, 11%).
Our simulations suggest that at least $\sim$ 100 galaxies should be stacked in
order to constrain the true escape fraction within 20% uncertainty.
