  Hydrogenated amorphous carbon (a-C:H) has been proposed as one of the
carbonaceous solids detected in the interstellar medium. Energetic processing
of the a-C:H particles leads to the dissociation of the C-H bonds and the
formation of hydrogen molecules and small hydrocarbons. Photo-produced H2
molecules in the bulk of the dust particles can diffuse out to the gas phase
and contribute to the total H2 abundance. We have simulated this process in the
laboratory with plasma-produced a-C:H and a-C:D analogs under astrophysically
relevant conditions to investigate the dependence of the diffusion as a
function of temperature. Plasma-produced a-C:H analogs were UV-irradiated using
a microwave-discharged hydrogen flow lamp. Molecules diffusing to the gas-phase
were detected by a quadrupole mass spectrometer, providing a measurement of the
outgoing H2 or D2 flux. By comparing the experimental measurements with the
expected flux from a one-dimensional diffusion model, a diffusion coefficient D
could be derived for experiments carried out at different temperatures.
Dependance on the diffusion coefficient D with the temperature followed an
Arrhenius-type equation. The activation energy for the diffusion process was
estimated (ED(H2)=1660+-110 K, ED(D2)=2090+-90 K), as well as the
pre-exponential factor (D0(H2)=0.0007+0.0013-0.0004 cm2 s-1,
D0(D2)=0.0045+0.005-0.0023 cm2 s-1) The strong decrease of the diffusion
coefficient at low dust particle temperatures exponentially increases the
diffusion times in astrophysical environments. Therefore, transient dust
heating by cosmic rays needs to be invoked for the release of the photo-
produced H2 molecules in cold PDR regions, where destruction of the aliphatic
component in hydrogenated amorphous carbons most probably takes place.
