  Context. Disks around pre-main-sequence stars evolve over time by turbulent
viscous spreading. The main contender to explain the strength of the turbulence
is the Magneto-Rotational-Instability (MRI) model, whose efficiency depends on
the disk ionization fraction. Aims. We aim at computing self-consistently the
chemistry including PAH charge chemistry, the grain charging and an estimate of
an effective value of the turbulence alpha parameter in order to find
observational signatures of disk turbulence. Methods. We introduced PAH and
grain charging physics and their interplay with other gas-phase reactions in
the physico-chemical code ProDiMo. Non-ideal magnetohydrodynamics effects such
as Ohmic and ambipolar diffusion are parametrized to derive an effective value
for the turbulent parameter alpha_eff . We explored the effects of turbulence
heating and line broadening on CO isotopologue sub-millimeter lines. Results.
The spatial distribution of alpha_eff depends on various unconstrained disk
parameters such as the magnetic parameter beta_mag or the cosmic ray density
distribution inside the protoplanetary disks. The inner disk midplane shows the
presence of the so-called dead-zone where the turbulence is quasi-inexistent.
The disk is heated mostly by thermal accommodation on dust grains in the
dead-zone, by viscous heating outside the dead-zone up to a few hundred
astronomical units, and by chemical heating in the outer disk. The CO
rotational lines probe the warm molecular disk layers where the turbulence is
at its maximum. However, the effect of turbulence on the CO line profiles is
minimal and difficult to distinguish from the thermal broadening. Conclusions.
Viscous heating of the gas in the disk midplane outside the dead-zone is
efficient. The determination of alpha from CO rotational line observations
alone is challenging.
