tokens: mean water abundance is 5 × 10 −5 n H . The accreting D/H ratio is inferred from the observed CH 2 DOH/CH 3 OH ratio (see Table 2 ) as α m = 1.1 × 10 −3 , assuming that the initial (statistical) deuteration of CH 2 DOH in the ice is conserved during the hot core phase. The post-evaporative gas-phase chemistry is also entirely neglected (full details can be found in Faure et al. 2015a ). The results of the model are plotted in Fig. 5 : it is found that the observed CH 2 DOH/CH 3 OD ratio of 3.2 ± 1.5 can be reproduced for a solid s-HDO/s-H 2 O ratio in the range ~8 × 10 −4 −2 × 10 −3 . Therefore, while the CH 2 DOH/CH 3 OD ratio of 3.2 ± 1.5 is consistent with a statistical deuteration, the occurrence of H/D exchanges cannot be excluded. In particular, it should be noted that H/D exchanges can explain the range of values depicted in Fig. 4 , that is CH 2 DOH/CH 3 OD ratios in the range ~0.1−10. To our knowledge, this is currently the only mechanism able to explain the nonstatistical deuteration of methanol in both low- and high-mass protostars. Fig. 5 Gas-phase abundance ratio of the deuterated isotopologs, CH 2 DOH/CH 3 OD, as function of the initial (cold) water ice deuteration. The dotted line corresponds to the analytic solution CH 2 DOH/CH 3 OD = 0.004/(HDO/H 2 O), see Faure et al. (2015a ) for details.The ratio observed toward NGC 7538-IRS1 is represented by the orange hatched zone. 5 Conclusions To summarize, we investigated the deuteration of methanol in the high-mass star-forming regions NGC 7538-IRS1 using IRAM-30m observations. Our study shows that the fractionation degree of deuterated methanol is low in this source. From the numerous (≥10) detected lines, we estimate a CH 2 DOH/CH 3 OD relative abundance ratio of 3.2 ± 1.5. Although our findings are commensurate with statistical deuteration at the icy surface of grain mantles, we cannot exclude H/D exchanges between water and methanol at the present time. Further observations of water and HDO are required to address this point. Appendix A Spectroscopic and observational line parameters Tables A.1 – A.4 list the spectroscopic and observational line parameters for the observed CH 3 OH-A, CH 3 OH-E, 13 CH 3 OH, CH 2 DOH, CH 3 OD-A and CH 3 OD-E transitions. Table A.1 Methanol. Table A.2 Methanol. Table A.3 13 C methanol. Table A.4 Deuterated methanol. Appendix B Partitionfunction of CH<sub>3</sub>OD Table B.1 gives the respective CH 3 OD-A and CH 3 OD-E rotation partition functions we use in the present study. Table B.1 Rotational partition function for CH 3 OD. Appendix C IRAM-30m observations overlaid with our LTE modeling for <sup>13</sup> CH<sub>3</sub>OH, CH<sub>3</sub>OD-A and CH<sub>3</sub>OD-E Figures C.1 – C.3 show a montage of the detected 13 CH 3 OH, CH 2 DOH, CH 3 OD-A and CH 3 OD-E transitions (see Tables A.3 and A.4 for the observational line parameters) along with our LTE modeling. Fig. C.1 Montage of detected transitions associated with the methanol 13 C isotopolog
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