13CO Cores in Taurus Molecular Cloud
  Young stars form in molecular cores, which are dense condensations within
molecular clouds. We have searched for molecular cores traced by $^{13}$CO
$J=1\to 0$ emission in the Taurus molecular cloud and studied their properties.
Our data set has a spatial dynamic range (the ratio of linear map size to the
pixel size) of about 1000 and spectrally resolved velocity information, which
together allow a systematic examination of the distribution and dynamic state
of $^{13}$CO cores in a large contiguous region. We use empirical fit to the CO
and CO$_2$ ice to correct for depletion of gas-phase CO. The $^{13}$CO core
mass function ($^{13}$CO CMF) can be fitted better with a log-normal function
than with a power law function. We also extract cores and calculate the
$^{13}$CO CMF based on the integrated intensity of $^{13}$CO and the CMF from
2MASS. We demonstrate that there exists core blending, i.e.\ combined
structures that are incoherent in velocity but continuous in column density.
  The core velocity dispersion (CVD), which is the variance of the core
velocity difference $\delta v$, exhibits a power-law behavior as a function of
the apparent separation $L$:\ CVD (km/s) $\propto L ({\rm pc})^{0.7}$. This is
similar to Larson's law for the velocity dispersion of the gas. The peak
velocities of $^{13}$CO cores do not deviate from the centroid velocities of
the ambient $^{12}$CO gas by more than half of the line width. The low velocity
dispersion among cores, the close similarity between CVD and Larson's law, and
the small separation between core centroid velocities and the ambient gas all
suggest that molecular cores condense out of the diffuse gas without additional
energy from star formation or significant impact from converging flows.
