Chemical probes of turbulence in the diffuse medium: the TDR model
  Context. Tens of light hydrides and small molecules have now been detected
over several hundreds sight lines sampling the diffuse interstellar medium
(ISM) in both the Solar neighbourhood and the inner Galactic disk. They provide
unprecedented statistics on the first steps of chemistry in the diffuse gas.
Aims. These new data confirm the limitations of the traditional chemical
pathways driven by the UV photons and the cosmic rays (CR) and the need for
additional energy sources, such as turbulent dissipation, to open highly
endoenergetic formation routes. The goal of the present paper is to further
investigate the link between specific species and the properties of the
turbulent cascade in particular its space-time intermittency. Methods. We have
analysed ten different atomic and molecular species in the framework of the
updated model of turbulent dissipation regions (TDR). We study the influence on
the abundances of these species of parameters specific to chemistry (density,
UV field, and CR ionisation rate) and those linked to turbulence (the average
turbulent dissipation rate, the dissipation timescale, and the ion neutral
velocity drift in the regions of dissipation). Results. The most sensitive
tracers of turbulent dissipation are the abundances of CH+ and SH+, and the
column densities of the J = 3, 4, 5 rotational levels of H2 . The abundances of
CO, HCO+, and the intensity of the 158 $\mu$m [CII] emission line are
significantly enhanced by turbulent dissipation. The vast diversity of chemical
pathways allows the independent determinations of free parameters never
estimated before: an upper limit to the average turbulent dissipation rate,
$\overline{\varepsilon}$ < 10$^{-23}$ erg cm$^{-3}$ s$^{-1}$ for $n_H$=20
cm$^{-3}$, from the CH+ abundance; an upper limit to the ion-neutral velocity
drift, $u_{in}$ < 3.5 km s$^{-1}$, from the SH+ to CH+ abundance ratio; and a
range of dissipation timescales, 100 < $\tau_V$ < 1000 yr, from the CO to HCO+
abundance ratio. For the first time, we reproduce the large abundances of CO
observed on diffuse lines of sight, and we show that CO may be abundant even in
regions with UV-shieldings as low as $5 \times 10^{-3}$ mag. The best range of
parameters also reproduces the abundance ratios of OH, C2H, and H2O to HCO+ and
are consistent with the known properties of the turbulent cascade in the
Galactic diffuse ISM. Conclusions. Our results disclose an unexpected link
between the dissipation of turbulence and the emergence of molecular richness
in the diffuse ISM. Some species, such as CH+ or SH+, turn out to be unique
tracers of the energy trail in the ISM. In spite of some degeneracy, the
properties of the turbulent cascade, down to dissipation, can be captured
through specific molecular abundances.
