Core mass function of a single giant molecular cloud complex with ~10^4
  cores
  Similarity in shape between the initial mass function (IMF) and the core mass
functions (CMFs) in star-forming regions prompts the idea that the IMF
originates from the CMF through a self-similar core-to-star mass mapping
process. To accurately determine the shape of the CMF, we create a sample of
8,431 cores with the dust continuum maps of the Cygnus X giant molecular cloud
complex, and design a procedure for deriving the CMF considering the mass
uncertainty, binning uncertainty, sample incompleteness, and the statistical
errors. The resultant CMF coincides well with the IMF for core masses from a
few $M_{\odot}$ to the highest masses of 1300 $M_{\odot}$ with a power-law of
${\rm d}N/{\rm d}M\propto M^{-2.30\pm0.04}$, but does not present an obvious
flattened turnover in the low-mass range as the IMF does. More detailed
inspection reveals that the slope of the CMF steepens with increasing mass.
Given the numerous high-mass star-forming activities of Cygnus X, this is in
stark contrast with the existing top-heavy CMFs found in high-mass star-forming
clumps. We also find that the similarity between the IMF and the mass function
of cloud structures is not unique at core scales, but can be seen for cloud
structures of up to several pc scales. Finally, our SMA observations toward a
subset of the cores do not present evidence for the self-similar mapping. The
latter two results indicate that the shape of the IMF may not be directly
inherited from the CMF.
