Impact of Cosmic-Ray Feedback on Accretion and Chemistry in
  Circumstellar Disks
  We use the gas-grain chemistry code UCLCHEM to explore the impact of
cosmic-ray feedback on the chemistry of circumstellar disks. We model the
attenuation and energy losses of the cosmic-rays as they propagate outwards
from the star and also consider ionization due to stellar radiation and
radionuclides. For accretion rates typical of young stars, $\dot M_* \sim
10^{-9}-10^{-6}$ M_\odot yr$^{-1}$, we show that cosmic rays accelerated by the
stellar accretion shock produce a cosmic-ray ionization rate at the disk
surface $\zeta \gtrsim 10^{-15}$ s$^{-1}$, at least an order of magnitude
higher than the ionization rate associated with the Galactic cosmic-ray
background. The incident cosmic-ray flux enhances the disk ionization at
intermediate to high surface densities ($\Sigma > 10$ g cm$^{-2}$) particularly
within 10 au of the star. We find the dominant ions are C$^+$, S$^+$ and Mg$^+$
in the disk surface layers, while the H$_3^+$ ion dominates at surface
densities above 1.0 g cm$^{-2}$. We predict the radii and column densities at
which the magneto-rotational instability (MRI) is active in T Tauri disks and
show that ionization by cosmic-ray feedback extends the MRI-active region
towards the disk mid-plane. However, the MRI is only active at the mid-plane of
a minimum mass solar nebula disk if cosmic-rays propagate diffusively ($\zeta
\propto r^{-1}$) away from the star. The relationship between accretion, which
accelerates cosmic rays, the dense accretion columns, which attenuate cosmic
rays, and the MRI, which facilitates accretion, create a cosmic-ray feedback
loop that mediates accretion and may produce luminosity variability.
