The C$^{18}$O core mass function toward Orion A: Single-dish
  observations
  We have performed an unbiased dense core survey toward the Orion A Giant
Molecular Cloud in the C$^{18}$O ($J$=1--0) emission line taken with the
Nobeyama Radio Observatory (NRO) 45-m telescope. The effective angular
resolution of the map is 26", which corresponds to $\sim$ 0.05 pc at a distance
of 414 pc. By using the Herschel-Planck H$_2$ column density map, we calculate
the C$^{18}$O fractional abundance and find that it is roughly constant over
the column density range of $\lesssim$ 5 $\times$ 10$^{22}$ cm$^{-3}$, although
a trend of C$^{18}$O depletion is determined toward higher column density.
Therefore, C$^{18}$O intensity can follow the cloud structure reasonably well.
The mean C$^{18}$O abundance in Orion A is estimated to be
5.7$\times$10$^{-7}$, which is about 3 times larger than the fiducial value. We
identified 746 C$^{18}$O cores with astrodendro and classified 709 cores as
starless cores. We compute the core masses by decomposing the Herschel-Planck
dust column density using the relative proportions of the C$^{18}$O integrated
intensities of line-of-sight components. Applying this procedure, we attempt to
remove the contribution of the background emission, i.e., the ambient gas
outside the cores. Then, we derived mass function for starless cores and found
that it resembles the stellar initial mass function (IMF). The CMF for starless
cores, $dN/dM$, is fitted with a power-law relation of $M^\alpha$ with a power
index of $\alpha = -$2.25$\pm$ 0.16 at the high-mass slope ($\gtrsim$ 0.44
$M_\odot$). We also found that the ratio of each core mass to the total mass
integrated along the line of sight is significantly large. Therefore, in the
previous studies, the core masses derived from the dust image are likely to be
overestimated at least by a factor of a few. Accordingly, such previous studies
may underestimate the star formation efficiency of individual cores.
