Digging into the Interior of Hot Cores with ALMA (DIHCA). V. Deuterium Fractionation of Methanol

We have observed the $^{13}$CH$_3$OH $5_1-4_1$ A$^+$, $^{13}$CH$_3$OH $14_1-13_2$ A$^-$, and CH$_2$DOH $8_{2,6}-8_{1,7}$ $e_0$ lines toward 24 high-mass star-forming regions by using Atacama Large Millimeter/submillimeter Array (ALMA) with an angular resolution of about 0$^{\prime\prime}$.3. This resolution corresponds to a linear scale of 400-1600 au, allowing us to resolve individual cores properly. We detected the $^{13}$CH$_3$OH and CH$_2$DOH emission near the continuum peaks in many of these regions. From the two $^{13}$CH$_3$OH lines, we calculated the temperature toward the $^{13}$CH$_3$OH peaks, and confirm that the emission traces hot ($>$100 K) regions. The $N$(CH$_2$DOH)/$N$($^{12}$CH$_3$OH) ratio in the observed high-mass star-forming regions is found to be lower than that in low-mass star-forming regions. We have found no correlation between the $N$(CH$_2$DOH)/$N$($^{13}$CH$_3$OH) or $N$(CH$_2$DOH)/$N$($^{12}$CH$_3$OH) ratios and either temperatures or distance to the sources, and have also found a source-to-source variation in these ratios. Our model calculations predict that the $N$(CH$_2$DOH)/$N$($^{12}$CH$_3$OH) ratio in hot cores depends on the duration of the cold phase; the shorter the cold phase, the lower the deuterium fractionation in the hot cores. We have suggested that the lower $N$(CH$_2$DOH)/$N$($^{12}$CH$_3$OH) ratio in high-mass star-forming regions compared to that in low-mass star-forming regions is due to the shorter duration of the cold phase and that the diversity in the $N$(CH$_2$DOH)/$N$($^{12}$CH$_3$OH) ratio in high-mass star-forming regions is due to the diversity in the length of the cold prestellar phase, and not the time that the objects have been in the hot core phase.