Probing midplane CO abundance and gas temperature with DCO$^+$ in the
  protoplanetary disk around HD 169142
  This work aims to understand which midplane conditions are probed by the
DCO$^+$ emission in the disk around the Herbig Ae star HD 169142. We explore
the sensitivity of the DCO$^+$ formation pathways to the gas temperature and
the CO abundance. The DCO$^+$ $J$=3-2 transition was observed with ALMA at a
spatial resolution of 0.3". The HD 169142 DCO$^+$ radial intensity profile
reveals a warm, inner component at radii <30 AU and a broad, ring-like
structure from ~50-230 AU with a peak at 100 AU just beyond the millimeter
grain edge. We modeled DCO$^+$ emission in HD 169142 with a physical disk
structure adapted from the literature, and employed a simple deuterium chemical
network to investigate the formation of DCO$^+$ through the cold deuterium
fractionation pathway via H$_2$D$^+$. Contributions from the warm deuterium
fractionation pathway via CH$_2$D$^+$ are approximated using a constant
abundance in the intermediate disk layers. Parameterized models show that
alterations to the midplane gas temperature and CO abundance of the literature
model are both needed to recover the observed DCO$^+$ radial intensity profile.
The best-fit model contains a shadowed, cold midplane in the region z/r < 0.1
with an 8 K decrease in gas temperature and a factor of five CO depletion just
beyond the millimeter grain edge, and a 2 K decrease in gas temperature for r >
120 AU. The warm deuterium fractionation pathway is implemented as a constant
DCO$^+$ abundance of 2.0$\times$10$^{-12}$ between 30-70 K. The DCO$^+$
emission probes a reservoir of cold material in the HD 169142 outer disk that
is not revealed by the millimeter continuum, the SED, nor the emission from the
12CO, 13CO, or C18O $J$=2-1 lines.
