  An analysis of the CH molecule in non-local thermodynamic equilibrium (NLTE)
is performed for the physical conditions of cool stellar atmospheres typical of
red giants (log g = 2.0, Teff = 4500 K) and the Sun. The aim of the present
work is to explore whether the G-band of the CH molecule, which is commonly
used in abundance diagnostics of Carbon-Enhanced Metal-Poor (CEMP) stars, is
sensitive to NLTE effects. LTE and NLTE theoretical spectra are computed with
the MULTI code. We use one-dimensional (1D) LTE hydrostatic MARCS model
atmospheres with parameters representing eleven red giant stars with
metallicities ranging from [Fe/H] = -4.0 to [Fe/H] = 0.0 and carbon-to-iron
ratios [C/Fe] = 0.0, +0.7, +1.5, and +3.0. The CH molecule model is represented
by 1981 energy levels, 18377 radiative bound-bound transitions, and 932
photo-dissociation reactions. The rates due to transitions caused by collisions
with free electrons and hydrogen atoms are computed using classical recipes.
Our calculations suggest that NLTE effects in the statistical equilibrium of
the CH molecule are significant and cannot be neglected for precision
spectroscopic analysis of C abundances. The NLTE effects in the G-band increase
with decreasing metallicity. We show that the C abundances are always
under-estimated if LTE is assumed. The NLTE corrections to C abundance inferred
from the CH feature range from +0.04 dex for the Sun to +0.21 dex for a red
giant with metallicity [Fe/H] = -4.0. Departures from the LTE assumption in the
CH molecule are non-negligible and NLTE effects have to be taken into account
in the diagnostic spectroscopy based on the CH lines. We show here that the
NLTE effects in the optical CH lines are non-negligible for the Sun and red
giant stars, but further calculations are warranted to investigate the effects
in other regimes of stellar parameters.
