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 \sim 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 } \approx 0.4 - 0.8 kpc ^ { -1 } at the galactic plane , or , equivalently , an effective cross-section as low as \sigma _ { { eff } } \sim 10 ^ { -5 } of the photoionization cross-section at 912Å 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 \lesssim 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 .