Chemistry in disks. XI. Sulfur-bearing species as tracers of
  protoplanetary disk physics and chemistry: the DM Tau case
  Context. Several sulfur-bearing molecules are observed in the interstellar
medium and in comets, in strong contrast to protoplanetary disks where only CS,
H$_2$CS and SO have been detected so far. Aims. We combine observations and
chemical models to constrain the sulfur abundances and their sensitivity to
physical and chemical conditions in the DM Tau protoplanetary disk. Methods. We
obtained $0.5^{"}$ ALMA observations of DM Tau in Bands 4 and 6 in lines of CS,
SO, SO$_2$, OCS, CCS, H$_2$CS and H$_2$S, achieving a $\sim 5$ mJy sensitivity.
Using the non-LTE radiative transfer code RADEX and the forward-modeling tool
DiskFit, disk-averaged CS column densities and upper limits for the other
species were derived. Results. Only CS was detected with a derived column
density of $\sim 2-6 \times 10^{12}$ cm$^{-2}$. We report a first tentative
detection of SO$_2$ in DM Tau. The upper limits range between $\sim 10^{11}$
and $10^{14}$ cm$^{-2}$ for the other S-bearing species. The best-fit chemical
model matching these values requires a gas-phase C/O ratio of > 1 at $r \sim
50-100$ au. With chemical modeling we demonstrate that sulfur-bearing species
could be robust tracers of the gas-phase C/O ratio, surface reaction rates,
grain size and UV intensities. Conclusions. The lack of detections of a variety
of sulfur-bearing molecules in DM Tau other than CS implies a dearth of
reactive sulfur in the gas phase, either through efficient freeze-out or
because most of the elemental sulfur is in other large species, as found in
comets. The inferred high CS/SO and CS/SO$_2$ ratios require a non-solar C/O
gas-phase ratio of > 1, consistent with the recent observations of hydrocarbon
rings in DM Tau. The stronger depletion of oxygen-bearing S-species compared to
CS is likely linked to the low observed abundances of gaseous water in DM Tau
and points to a removal mechanism of oxygen from the gas.
