Physical conditions in the central molecular zone inferred by H3+
  The H3+ molecule has been detected in many lines of sight within the central
molecular zone (CMZ) with exceptionally large column densities and unusual
excitation properties compared to diffuse local clouds. The detection of the
(3,3) metastable level has been suggested to be the signature of warm and
diffuse gas in the CMZ. We use the Meudon PDR code to re-examine the
relationship between the column density of H3+ and the cosmic-ray ionization
rate, $\zeta$, up to large values of $\zeta$. We study the impact of the
various mechanisms that can excite H3+ in its metastable state. We produce
grids of PDR models exploring different parameters ($\zeta$, size of clouds,
metallicity) and infer the physical conditions that best match the observations
toward ten lines of sight in the CMZ. For one of them, Herschel observations of
HF, OH+, H2O+, and H3O+ can be used as additional constraints. We check that
the results found for H3+ also account for the observations of these molecules.
We find that the linear relationship between N(H3+) and $\zeta$ only holds up
to a certain value of the cosmic-ray ionization rate, which depends on the
proton density. A value $\zeta \sim 1 - 11 \times 10^{-14}$ s$^{-1}$ explains
both the large observed H3+ column density and its excitation in the metastable
level (3,3) in the CMZ. It also reproduces N(OH+), N(H2O+) and N(H3O+) detected
toward Sgr B2(N). We confirm that the CMZ probed by H3+ is diffuse, nH
$\lesssim$ 100 cm-3 and warm, T $\sim$ 212-505 K. This warm medium is due to
cosmic-ray heating. We also find that the diffuse component probed by H3+ must
fill a large fraction of the CMZ. Finally, we suggest the warm gas in the CMZ
enables efficient H2 formation via chemisorption sites as in PDRs. This
contributes to enhance the abundance of H3+ in this high cosmic-ray flux
environment.
