In this paper we calculate the escape fraction ($f_{\rm esc}$) of ionizingphotons from starburst galaxies. Using 2-D axisymmetric hydrodynamicsimulations, we study superbubbles created by overlapping supernovae in OBassociations. We calculate the escape fraction of ionizing photons from thecenter of the disk along different angles through the superbubble and the gasdisk. After convolving with the luminosity function of OB associations, we showthat the ionizing photons escape within a cone of $\sim 40 ^\circ$, consistentwith observations of nearby galaxies. The evolution of the escape fraction withtime 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 fractionthrough the polar regions rises again. The angle-averaged escape fractioncannot exceed $\sim [1- \cos (1 \, {\rm radian})] = 0.5$ from geometricalconsiderations (using the emission cone opening angle). We calculate thedependence of the time- and angle-averaged escape fraction on the mid-planedisk gas density (in the range $n_0=0.15-50$ cm $^{-3}$) and the disk scaleheight (between $z_0=10-600$ pc). We find that the escape fraction is relatedto the disk parameters (the mid-plane disk density and scale height) roughly sothat $f_{\rm esc}^\alpha n_0^2 z_0^3$ (with $\alpha\approx 2.2$) is a constant.For disks with a given WNM temperature, massive disks have lower escapefraction than low mass galaxies. For Milky Way ISM parameters, we find $f_{\rmesc}\sim 5\%$, and it increases to $\approx 10\%$ for a galaxy ten times lessmassive. We discuss the possible effects of clumpiness of the ISM on theestimate of the escape fraction and the implications of our results for thereionization of the universe.
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