Context. Deuterated molecules are good tracers of the evolutionary stage of star-forming cores. During the star formation process, deuterated molecules are expected to be enhanced in cold, dense pre-stellar cores and to deplete after protostellar birth. Aims. In this paper, we study the deuteration fraction of formaldehyde in high-mass star-forming cores at different evolutionary stages to investigate whether the deuteration fraction of formaldehyde can be used as an evolutionary tracer. Methods. Using the APEX SEPIA Band 5 receiver, we extended our pilot study of the J = 3 →2 rotational lines of HDCO and D2CO to eleven high-mass star-forming regions that host objects at different evolutionary stages. High-resolution follow-up observations of eight objects in ALMA Band 6 were performed to reveal the size of the H2CO emission and to give an estimate of the deuteration fractions HDCO/H2CO and D2CO/HDCO at scales of ~6″ (0.04–0.15 pc at the distance of our targets). Results. Our observations show that singly and doubly deuterated H2CO are detected towards high-mass protostellar objects (HMPOs) and ultracompact H II regions (UC H II regions), and the deuteration fraction of H2CO is also found to decrease by an order of magnitude from the earlier HMPO phases to the latest evolutionary stage (UC H II), from ~0.13 to ~0.01. We have not detected HDCO and D2CO emission from the youngest sources (i.e. high-mass starless cores or HMSCs). Conclusions. Our extended study supports the results of the previous pilot study: the deuteration fraction of formaldehyde decreases with the evolutionary stage, but higher sensitivity observations are needed to provide more stringent constraints on the D/H ratio during the HMSC phase. The calculated upper limits for the HMSC sources are high, so the trend between HMSC and HMPO phases cannot be constrained.
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