  The mass-loss mechanism in normal K--M giant stars with small variability
amplitudes is not yet understood, although they are the majority among red
giant stars. We present high-spatial and high-spectral resolution observations
of the 2.3 micron CO lines in the M7 giant BK Vir with a spatial resolution of
9.8 mas and a spectral resolution of 12000, using AMBER at the Very Large
Telescope Interferometer (VLTI). The angular diameters observed in the CO lines
are 12--31% larger than those measured in the continuum. We also detected
asymmetry in the CO line-forming region. The data taken 1.5 months apart show
possible time variation on a spatial scale of 30 mas (corresponding to 3 x
stellar diameter) at the CO band head. Comparison of the observed data with the
MARCS photospheric model shows that whereas the observed CO line spectrum can
be well reproduced by the model, the angular sizes observed in the CO lines are
much larger than predicted by the model. Our model with two additional CO
layers above the MARCS photosphere reproduces the observed spectrum and
interferometric data in the CO lines simultaneously. This model suggests that
the inner CO layer at ~1.2 stellar radii is very dense and warm with a CO
column density of ~10^{22} cm^{-2} and temperatures of 1900--2100K, while the
outer CO layer at 2.5--3.0 stellar radii is characterized by column densities
of 10^{19}--10^{20} cm^{-2} and temperatures of 1500--2100K. Our AMBER
observations of BK Vir have spatially resolved the extended molecular outer
atmosphere of a normal M giant in the individual CO lines for the first time.
The temperatures derived for the CO layers are higher than or equal to the
uppermost layer of the MARCS photospheric model, implying the operation of some
heating mechanism in the outer atmosphere.
