FOREST unbiased Galactic plane imaging survey with the Nobeyama 45 m
  telescope (FUGIN). VII. molecular fraction of HI clouds
  In this study, we analyze molecular gas formation in neutral atomic hydrogen
(HI) clouds using the latest CO data obtained from the four-beam receiver
system on a 45-m telescope (FOREST) unbiased Galactic plane imaging survey with
the Nobeyama 45-m telescope (FUGIN) and HI data taken from the Very Large Array
(VLA) Galactic plane survey (VGPS). We applied a dendrogram algorithm to the HI
data cube to identify HI clouds, and we calculated the HI mass and molecular
gas mass by summing the CO line intensity within each HI cloud. On the basis of
the results, we created a catalog of 5,737 identified HI clouds with local
standard of rest (LSR) velocity of $V_{\rm LSR}\le -20$ km s$^{-1}$ in Galactic
longitude and latitude ranges of $20^\circ \le l \le 50^\circ$ and $-1^\circ
\le b \le 1^\circ$, respectively. We found that most of the HI clouds are
distributed within a Galactocentric distance of 16 kpc, most of which are in
the Cold Neutral Medium (CNM) phase. In addition, we determined that the
high-mass end of the mass HI function is well fitted with the power-law
function with an index of 2.3. Although two sequences of self-gravitating and
diffuse clouds are expected to appear in the M$_{\rm tot}$-M$_{{\rm H}_2}$
diagram according to previous works based on a plane-parallel model, the
observational data show only a single sequence with large scattering within
these two sequences. This implies that most of the clouds are mixtures of these
two types of clouds. Moreover, we suggest the following scenario of molecular
gas formation: An HI-dominant cloud evolved with increasing H$_2$ mass along a
path of $M_{{\rm H}_2} \propto M_{\rm tot}^2$ by collecting diffuse gas before
reaching and moving along the curves of the two sequences.
