  Star formation occurs via fragmentation of molecular clouds, which means that
the majority of stars born are a members of binaries. There is growing evidence
that planets might form in circumprimary disks of medium-separation binaries.
The tidal forces caused by the secondary generally act to distort the
originally circular disk to an eccentric one. To infer the disk eccentricity
from high-res NIR spectroscopy, we calculate the fundamental band emission
lines of the CO molecule emerging from the atmosphere of the disk. We model
circumprimary disk evolution under the gravitational perturbation of the
orbiting secondary using a 2D grid-based hydrodynamical code, assuming
alpha-type viscosity. The hydrodynamical results are combined with our spectral
code based on the double-layer disk model to calculate the CO molecular line
profiles. We find that the orbital velocity distribution of the gas parcels
differs significantly from the circular Keplerian fashion, thus the line
profiles are asymmetric in shape. The magnitude of asymmetry is insensitive to
the binary mass ratio, the magnitude of viscosity, and the disk mass. In
contrast, the disk eccentricity, thus the level of the line profile asymmetry,
is influenced significantly by the binary eccentricity and the disk geometrical
thickness. We demonstrate that the disk eccentricity profile in the
planet-forming region can be determined by fitting the high-resolution CO line
profile asymmetry using a simple 2D spectral model that accounts for the
velocity distortions caused by the disk eccentricity. Thus, with our novel
approach the disk eccentricity can be inferred with high-resolution near-IR
spectroscopy prior to the era of high angular resolution optical or radio
direct-imaging. By determining the disk eccentricity in medium-separation young
binaries, we might be able to constrain the planet formation theories.
