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.