It has been hypothesized that photons from young, massive star clusters are responsible for maintaining the ionization of diffuse warm ionized gas seen in both the Milky Way and other disk galaxies. For a theoretical investigation of the warm ionized medium (WIM), it is crucial to solve radiation transfer equations where the ISM and clusters are modeled self-consistently. To this end, we employ a Solar neighborhood model of TIGRESS, a magnetohydrodynamic simulation of the multiphase, star-forming ISM, and post-process the simulation with an adaptive ray tracing method to transfer UV radiation from star clusters. We find that the WIM volume filling factor is highly variable, and sensitive to the rate of ionizing photon production and ISM structure. The mean WIM volume filling factor rises to ~0.15 at |z|~1 kpc. Approximately half of ionizing photons are absorbed by gas and half by dust; the cumulative ionizing photon escape fraction is 1.1%. Our time-averaged synthetic H$alpha$ line profile matches WHAM observations on the redshifted (outflowing) side, but has insufficient intensity on the blueshifted side. Our simulation matches the Dickey-Lockman neutral density profile well, but only a small fraction of snapshots have high-altitude WIM density consistent with Reynolds Layer estimates. We compute a clumping correction factor C = <n_e>/sqrt<n_e^2>~0.2 that is remarkably constant with distance from the midplane and time; this can be used to improve estimates of ionized gas mass and mean electron density from observed H$alpha$ surface brightness profiles in edge-on galaxies.
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