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.
Download