A New Probe of the Molecular Gas in Galaxies: Application to M101
  Recent studies of nearby spiral galaxies suggest that photodissociation regions (PDRs) are capable of producing much of the observed HI in galaxy disks. In that case, measurements of the HI column density and the far-ultraviolet (FUV) photon flux provide a new probe of the volume density of the local underlying H_2. We develop the method and apply it to the giant Scd spiral M101 (NGC 5457). We find that, after correction for the best-estimate gradient of metallicity in the ISM of M101 and for the extinction of the ultraviolet emission, molecular gas with a narrow range of density from 30-1000 cm^-3 is found near star- forming regions at all radii in the disk of M101 out to a distance of 12' (approximately 26 kpc), close to the photometric limit of R_25 = 13.5'.   In this picture, the ISM is virtually all molecular in the inner parts of M101. The strong decrease of the HI column density in the inner disk of the galaxy at R_G < 10 kpc is a consequence of a strong increase in the dust-to-gas ratio there, resulting in an increase of the H_2 formation rate on grains and a corresponding disappearance of hydrogen in its atomic form. 
Denise A. Smith, Ronald J. Allen, Ralph C. Bohlin (STScI), Natalya   Nicholson (McGill), and Theodore P. Stecher (NASA/GSFC)