  The outer atmosphere of K giants shows thermally inhomogeneous structures
consisting of the hot chromospheric gas and the cool molecular gas. We present
spectro-interferometric observations of the multicomponent outer atmosphere of
the well-studied K1.5 giant Arcturus (alpha Boo) in the CO first overtone lines
near 2.3 micron. We observed Arcturus with the AMBER instrument at the Very
Large Telescope Interferometer (VLTI) at 2.28--2.31 micron with a spectral
resolution of 12000 and at projected baselines of 7.3, 14.6, and 21.8 m. The
high spectral resolution of the VLTI/AMBER instrument allowed us to spatially
resolve Arcturus in the individual CO lines. Comparison of the observed
interferometric data with the MARCS photospheric model shows that the star
appears to be significantly larger than predicted by the model. It indicates
the presence of an extended component that is not accounted for by the current
photospheric models for this well-studied star. We found out that the observed
AMBER data can be explained by a model with two additional CO layers above the
photosphere. The inner CO layer is located just above the photosphere, at 1.04
+/- 0.02 stellar radii, with a temperature of 1600 +/- 400 K and a CO column
density of 10^{20 +/- 0.3} cm^-2. On the other hand, the outer CO layer is
found to be as extended as to 2.6 +/- 0.2 stellar radii with a temperature of
1800 +/- 100 K and a CO column density of 10^{19 +/- 0.15} cm^-2. The
properties of the inner CO layer are in broad agreement with those previously
inferred from the spatially unresolved spectroscopic analyses. However, our
AMBER observations have revealed that the quasi-static cool molecular component
extends out to 2--3 stellar radii, within which region the chromospheric wind
steeply accelerates.
