OH$^+$ emission from cometary knots in planetary nebulae
  We model the molecular emission from cometary knots in planetary nebulae
(PNe) using a combination of photoionization and photodissociation region (PDR)
codes, for a range of central star properties and gas densities. Without the
inclusion of ionizing extreme ultraviolet (EUV) radiation, our models require
central star temperatures $T_*$ to be near the upper limit of the range
investigated in order to match observed H$_2$ and OH$^+$ surface brightnesses
consistent with observations - with the addition of EUV flux, our models
reproduce observed OH$^+$ surface brightnesses for $T_* \ge 100 \, {\rm kK}$.
For $T_* < 80 \, {\rm kK}$, the predicted OH$^+$ surface brightness is much
lower, consistent with the non-detection of this molecule in PNe with such
central star temperatures. Our predicted level of H$_2$ emission is somewhat
weaker than commonly observed in PNe, which may be resolved by the inclusion of
shock heating or fluorescence due to UV photons. Some of our models also
predict ArH$^+$ and HeH$^+$ rotational line emission above detection
thresholds, despite neither molecule having been detected in PNe, although the
inclusion of photodissociation by EUV photons, which is neglected by our
models, would be expected to reduce their detectability.
