Methanol deuteration in high-mass protostars

The deuteration of molecules forming in the ices such as methanol (CH$_3$OH) is sensitive to the physical conditions during their formation in dense cold clouds and can be probed through observations of deuterated methanol in hot cores. Observations with ALMA containing transitions of CH$_3$OH, CH$_2$DOH, CHD$_2$OH, $^{13}$CH$_3$OH, and CH$_3^{18}$OH are investigated. The column densities of CH$_2$DOH, CHD$_2$OH, and CH$_3$OH are determined for all sources, where the column density of CH$_3$OH is derived from optically thin $^{13}$C and $^{18}$O isotopologues. Consequently, the D/H ratio of methanol is derived taking statistical effects into account. Singly deuterated methanol (CH$_2$DOH) is detected toward 25 of the 99 sources in our sample of the high-mass protostars. Including upper limits, the $\rm (D/H)_{CH_3OH}$ ratio inferred from $N_\mathrm{CH_2DOH}/N_\mathrm{CH_3OH}$ was derived for 38 of the 99 sources and varies between $\sim10^{-3}-10^{-2}$. Including other high-mass hot cores from the literature, the mean methanol D/H ratio is $1.1\pm0.7\times10^{-3}$. This is more than one order of magnitude lower than what is seen for low-mass protostellar systems ($2.2\pm1.2\times10^{-2}$). Doubly deuterated methanol (CHD$_2$OH) is detected toward 11 of the 99 sources. Including upper limits for 15 sources, the $\rm (D/H)_{CH_2DOH}$ ratios derived from $N_\mathrm{CHD_2OH}/N_\mathrm{CH_2DOH}$ are more than two orders of magnitude higher than $\rm (D/H)_{CH_3OH}$ with an average of $2.0\pm0.8\times10^{-1}$ which is similar to what is found for low-mass sources. Comparison with literature GRAINOBLE models suggests that the high-mass prestellar phases are either warm ($>20$ K) or live shorter than the free-fall timescale. In contrast, for low-mass protostars, both a low temperature of $<15$ K and a prestellar phase timescale longer than the free-fall timescale are necessary.