Using HCO$^+$ isotopologues as tracers of gas depletion in
  protoplanetary disk gaps
  The widespread rings and gaps seen in the dust continuum in protoplanetary
disks are sometimes accompanied by similar substructures seen in molecular line
emission. One example is the outer gap at 100 au in AS 209, which shows that
the H$_{13}$CO$^+$ and C$_{18}$O emission intensities decrease along with the
continuum in the gap, while the DCO$^+$ emission increases inside the gap.
  We aim to study the behavior of DCO$^+$/H$_{13}$CO$^+$ and DCO$^+$/HCO$^+$
ratios in protoplanetary disk gaps assuming the two scenarios: the gas
depletion follows the dust depletion and only the dust is depleted.
  We first modeled the physical disk structure using the thermo-chemical model
ANDES. This 1+1D steady-state disk model calculates the thermal balance of gas
and dust and includes the FUV, X-rays, cosmic rays, and other ionization
sources together with the reduced chemical network for molecular coolants.
Afterward, this physical structure was adopted for calculations of molecular
abundances with the extended gas-grain chemical network with deuterium
fractionation. Ideal synthetic spectra and 0th-moment maps were produced with
LIME.
  We are able to qualitatively reproduce the increase in the DCO$^+$ intensity
and the decrease in the H$_{13}$CO$^+$ and C$_{18}$O intensities inside the
disk gap, which is qualitatively similar to what is observed in the outer AS
209 gap. The corresponding disk model assumes that both the gas and dust are
depleted in the gap. The model with the gas-rich gap, where only the dust is
depleted, produces emission that is too bright in all HCO$^+$ isotopologues and
C$_{18}$O.
  The DCO$^+$/H$_{13}$CO$^+$ line ratio can be used to probe gas depletion in
dust continuum gaps outside of the CO snow line. The DCO$^+$/C$_{18}$O line
ratio shows a similar, albeit weaker, effect; however, these species can be
observed simultaneously with a single ALMA or NOEMA setup.
