Can the Lyman Continuum leaked out of H II regions explain Diffuse Ionized Gas?

We present an attempt to explain the diffuse H_alpha emission of a face-on galaxy M 51 with the ``standard'' photoionization model, in which the Lyman continuum (Lyc) escaping from H II regions propagates large distances into the diffuse interstellar medium (ISM). The diffuse H_alpha emission of M 51 is analyzed using thin slab models and exponential disk models in the context of the ``on-the-spot'' approximation. The scale height of the ionized gas needed to explain the diffuse H_alpha emission with the scenario is found to be of the order of ~ 1-2 kpc, consistent with those of our Galaxy and edge-on galaxies. The model also provides a vertical profile, when the galaxy is viewed edge-on, consisting of two-exponential components. However, it is found that an incredibly low absorption coefficient of kappa_0 ~ 0.4-0.8 kpc^{-1} at the galactic plane, or, equivalently, an effective cross-section as low as sigma_eff ~ 10^{-5} of the photoionization cross-section at 912A is required to allow the stellar Lyc photons to travel through the H I disk. Such a low absorption coefficient is out of accord with the properties of the ISM. Furthermore, we found that even the model that has the DIG phase only and no H I gas phase shows highly concentrated H_alpha emissions around H II regions, and can account for only < 26% of the H_alpha luminosity of the DIG. This result places a strong constraint on the ionizing source of the DIG. We also report that the H_alpha intensity distribution functions not only of the DIG, but also of H II regions in M 51, appear to be lognormal.