Three-Dimensional Distribution of the ISM in the Milky Way Galaxy: IV.
  3D Molecular Fraction and Galactic-Scale HI-to-H$_2$ Transition
  Three dimensional (3D) distribution of the volume-density molecular fraction,
defined by fmol_rho=rho_H2/(rho_HI + rho_H2), is studied in the Milky Way
Galaxy. The molecular front appears at galacto-centric distance of R \sim 8
kpc, where the phase transition from atomic to molecular hydrogen occurs
suddenly with fmol_rho dropping from \sim 0.8 to 0.2 within a radial interval
as narrow as \sim 0.5 kpc. The front in fmol_rho is much sharper than that for
surface density molecular fraction. The front also appears in the vertical
direction with a full width of the high-fmol_rho disk to be \sim 100 pc. The
radial and vertical fmol_rho profiles, particularly the front behaviors, are
fitted by theoretical curves calculated using the observed density profile and
assumed radiation field and metallicity with exponential gradients. The
molecular fraction was found to be enhanced along the Perseus and some other
spiral arms. The fmol_rho arms imply that the molecular clouds are produced
from HI gas in the spiral arms and are dissociated in the interarm region. We
also show that there is a threshold HI density over which the gas is
transformed into molecules.
