H$_2$ ortho-to-para conversion on grains: A route to fast deuterium
  fractionation in dense cloud cores?
  Deuterium fractionation, i.e. the enhancement of deuterated species with
respect to the non-deuterated ones, is considered to be a reliable chemical
clock of star-forming regions. This process is strongly affected by the
ortho-to-para (o-p) H$_2$ ratio. In this letter we explore the effect of the
o-p H$_2$ conversion on grains on the deuteration timescale in fully depleted
dense cores, including the most relevant uncertainties that affect this complex
process. We show that (i) the o-p H$_2$ conversion on grains is not strongly
influenced by the uncertainties on the conversion time and the sticking
coefficient and (ii) that the process is controlled by the temperature and the
residence time of ortho-H$_2$ on the surface, i.e. by the binding energy. We
find that for binding energies in between 330-550 K, depending on the
temperature, the o-p H$_2$ conversion on grains can shorten the deuterium
fractionation timescale by orders of magnitude, opening a new route to explain
the large observed deuteration fraction $D_\mathrm{frac}$ in dense molecular
cloud cores. Our results suggest that the star formation timescale, when
estimated through the timescale to reach the observed deuteration fractions,
might be shorter than previously proposed. However, more accurate measurements
of the binding energy are needed to better assess the overall role of this
process.
