The Central 300 pc of the Galaxy probed by infrared spectra of H$_3^+$
  and CO: part I. Predominance of warm and diffuse gas and high H$_2$
  ionization rate
  The molecular gas in the Central Molecular Zone (CMZ) of the Galaxy has been
studied using infrared absorption spectra of H$_3^+$ lines at 3.5-4.0 $\mu$m
and CO lines near 2.34 $\mu$m. In addition to the previously reported spectra
of these lines toward 8 stars located within 30 pc of Sgr A$^\ast$, there are
now spectra toward $\sim$30 bright stars located from 140 pc west to 120 pc
east of Sgr A$^\ast$. The spectra show the presence of warm ($T\sim 200$ K) and
diffuse ($n < 100 $cm$^{-3}$) gas with $N$(H$_3^+$) $\sim 3 \times 10^{15}
$cm$^{-2}$ on majority of sightlines. Instead of our previous analysis in which
only electrons from photoionization of carbon atoms were considered, we have
developed a simple model calculation in which the cosmic ray ionization of
H$_2$ and H are also taken into account. We conclude: (1) Warm and diffuse gas
dominates the volume of the CMZ. The volume filling factor of dense gas must be
much less than 0.1 and the CMZ is not as opaque as previously considered. The
X-ray emitting ultra-hot 10$^8 $K plasma, which some thought to dominate the
CMZ, does not exist over extended regions. (2) The cosmic ray ionization rate
is $\zeta \sim 2 \times 10^{-14} $s$^{-1}$, higher than in Galactic dense
clouds and diffuse clouds by factors of $\sim$1000 and $\sim$100, respectively.
If the equipartition law stands, this suggests a pervading magnetic field on
the order of $\sim$100 $\mu$G.
