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Rotational and rovibrational spectroscopy of CD$_3$OH with an account of CD$_3$OH toward IRAS 16293$-$2422

Solar-type protostars harbor highly deuterated complex organics. While this degree of deuteration may provide important clues in studying the formation of these species, spectroscopic information on multiply deuterated isotopologs is often insufficient. In particular, searches for triply deuterated methanol, CD$_3$OH, are hampered by the lack of intensity information from a spectroscopic model. The aim of the present study is to develop such a model of CD$_3$OH in low-lying torsional states that is sufficiently accurate to facilitate further searches for CD$_3$OH in space. We performed a new measurement campaign for CD$_3$OH involving three spectroscopic laboratories that covers the 34 GHz-1.1 THz and the 20-900 cm$^{-1}$ ranges. The analysis was performed using the torsion-rotation Hamiltonian model based on the rho-axis method. We determined a model that describes the ground and first excited torsional states of CD$_3$OH, up to quantum numbers $J \leqslant 55$ and $K_a \leqslant 23$, and we derived a line list for radio-astronomical observations. This list is accurate up to at least 1.1 THz and should be sufficient for all types of radio-astronomical searches for this methanol isotopolog. It was used to search for CD$_3$OH in data from the Protostellar Interferometric Line Survey of IRAS 16293-2422 using ALMA. CD$_3$OH is securely detected in the data, with a large number of clearly separated and well-reproduced lines. We detected lines belonging to the ground and the first excited torsional states. The derived abundance of CD$_3$OH relative to non-deuterated isotopolog confirm the significant enhancement of this multiply deuterated variant. This finding is in line with other observations of multiply deuterated complex organic molecules and may serve as an important constraint on their formation models.