A C${}^{18}$O study of the origin of the power-law nature in the IMF

We have performed C${}^{18}$O ($J$=1–0) mapping observations of a ${20}^{\mathrm{\prime }}\times {20}^{\mathrm{\prime }}$ area of the OMC-1 region in the Orion A cloud. We identified 65 C${}^{18}$O cores, which have mean radius, velocity width in FWHM, and LTE mass of 0.18$\pm$0.03 pc, 0.40$\pm$0.15 km s${}^{-1}$, and 7.2$\pm$4.5 $M_{\odot }$, respectively. All the cores are most likely to be gravitationally bound by considering the uncertainty in the C${}^{18}$O abundance. We derived a C${}^{18}$O core mass function, which shows a power-law-like behavior above 5 $M_{\odot }$. The best-fit power-law index of $-2.3\pm 0.3$ is consistent with those of the dense core mass functions and the stellar initial mass function (IMF) previously derived in the OMC-1 region. This agreement strongly suggests that the power-law form of the IMF has been already determined at the density of $\sim {10}^3$ cm${}^{-3}$, traced by the C${}^{18}$O ($J$=1–0) line.