Narrow escape: how ionizing photons escape from disc galaxies
  In this paper we calculate the escape fraction ($f_{\rm esc}$) of ionizing
photons from starburst galaxies. Using 2-D axisymmetric hydrodynamic
simulations, we study superbubbles created by overlapping supernovae in OB
associations. We calculate the escape fraction of ionizing photons from the
center of the disk along different angles through the superbubble and the gas
disk. After convolving with the luminosity function of OB associations, we show
that the ionizing photons escape within a cone of $\sim 40 ^\circ$, consistent
with observations of nearby galaxies. The evolution of the escape fraction with
time shows that it falls initially as cold gas is accumulated in a dense shell.
After the shell crosses a few scale heights and fragments, the escape fraction
through the polar regions rises again. The angle-averaged escape fraction
cannot exceed $\sim [1- \cos (1 \, {\rm radian})] = 0.5$ from geometrical
considerations (using the emission cone opening angle). We calculate the
dependence of the time- and angle-averaged escape fraction on the mid-plane
disk gas density (in the range $n_0=0.15-50$ cm $^{-3}$) and the disk scale
height (between $z_0=10-600$ pc). We find that the escape fraction is related
to the disk parameters (the mid-plane disk density and scale height) roughly so
that $f_{\rm esc}^\alpha n_0^2 z_0^3$ (with $\alpha\approx 2.2$) is a constant.
For disks with a given WNM temperature, massive disks have lower escape
fraction than low mass galaxies. For Milky Way ISM parameters, we find $f_{\rm
esc}\sim 5\%$, and it increases to $\approx 10\%$ for a galaxy ten times less
massive. We discuss the possible effects of clumpiness of the ISM on the
estimate of the escape fraction and the implications of our results for the
reionization of the universe.
