Outflowing OH$^+$ in Markarian 231: the ionization rate of the molecular
  gas
  The oxygen-bearing molecular ions OH+, H2O+, and H3O+ are key species that
probe the ionization rate of (partially) molecular gas that is ionized by
X-rays and cosmic rays permeating the interstellar medium. We report Herschel
far-infrared and submillimeter spectroscopic observations of OH+ in Mrk 231,
showing both ground-state P-Cygni profiles, and excited line profiles with
blueshifted absorption wings extending up to ~1000 km s^{-1}. In addition, OH+
probes an excited component peaking at central velocities, likely arising from
the torus probed by the OH centimeter-wave megamaser. Four lines of H2O+ are
also detected at systemic velocities, but H3O+ is undetected. Based on our
earlier OH studies, we estimate an abundance ratio of OH/OH+~5-10 for the
outflowing components and ~20 for the torus, and an OH+ abundance relative to H
nuclei of ~>10^{-7}. We also find high OH+/H2O+ and OH+/H3O+ ratios, both are
~>4 in the torus and ~>10-20 in the outflowing gas components. Chemical models
indicate that these high OH+ abundances relative to OH, H2O+, and H3O+ are
characteristic of gas with a high ionization rate per unit density,
\zeta/n_H~(1-5)x10^{-17} cm^3 s^{-1} and ~(1-2)x10^{-16} cm^3 s^{-1} for the
above components, respectively, and an ionization rate of
\zeta~(0.5-2)x10^{-12} s^{-1}. X-rays appear to be unable to explain the
inferred ionization rate, and thus we suggest that low-energy (10-400 MeV)
cosmic-rays are primarily responsible for the ionization with \dot{M}_{CR}~0.01
M_{sun} yr^{-1} and \dot{E}_{CR}~10^{44} erg s^{-1}, the latter corresponding
to 1% of the AGN luminosity and similar to the energetics of the molecular
outflow. We suggest that cosmic-rays accelerated in the forward shock
associated with the molecular outflow are responsible for the ionization, as
they diffuse through the outflowing molecular phase downstream.
