Dust charge distribution in the interstellar medium
  We investigate the equilibrium charge distribution of dust grains in the
interstellar medium (ISM). Our treatment accounts for collisional charging by
electrons and ions, photoelectric charging due to a background interstellar
radiation field, the collection of suprathermal cosmic ray electrons and
photoelectric emission due to a cosmic ray induced ultraviolet radiation field
within dense molecular clouds. We find that the charge equilibrium assumption
is valid throughout the multi-phase ISM conditions investigated here, and
should remain valid for simulations with resolutions down to AU scales. The
charge distribution of dust grains is size, composition, and ISM environment
dependent: local radiation field strength, $G$, temperature, $T$, and electron
number density, $n_{\mathrm{e}}$. The charge distribution is tightly correlated
with the `charging parameter', $G\sqrt{T}/n_{\mathrm{e}}$. In the molecular
medium, both carbonaceous and silicate grains have predominantly negative or
neutral charges with narrow distributions. In the cold neutral medium,
carbonaceous and silicate grains vary from negative and narrow distributions,
to predominantly positive and wide distributions depending on the magnitude of
the charging parameter. In the warm neutral medium, grains of all sizes are
positively charged with wide distributions. We derive revised parametric
expressions that can be used to recover the charge distribution function of
carbonaceous and silicate grains from 3.5 {\AA} to 0.25 $\mu$m as a function of
the size, composition and ambient ISM parameters. Finally, we find that the
parametric equations can be used in environments other than Solar neighborhood
conditions, recovering the charge distribution function of dust grains in
photon dominated regions.
