Detectability of deuterated water in prestellar cores

Context Water is an important molecule in the chemical and thermal balance of dense molecular gas, but knowing its history throughout the various stages of the star formation is a fundamental problem. Its molecular deuteration provides us with a crucial clue to its formation history. H2O has recently been detected for the first time towards the prestellar core L1544 with the Herschel Space Observatory with a high spectral resolution (HIFI instrument). Aims. Prestellar cores provide the original reservoir of material from which future planetary systems are built, but few observational constraints exist on the formation of water and none on its deuteration before the collapse starts and a protostar forms at the centre. We report on new APEX observations of the ground state 1(0,1)-0(0,0) HDO transition at 464 GHz towards the prestellar core L1544. The line is undetected, and we present an extensive study of the conditions for its detectability in cold and dense cloud cores. Methods. The water and deuterated water abundances have been estimated using an advanced chemical model simplified for the limited number of reactions or processes that are active in cold regions (< 15 K). In this model, water is removed from the gas phase by freezing onto dust grains and by photodissociation. We use the LIME radiative transfer code to compute the expected intensity and profile of both H2O and HDO lines and compare them with the observations. Results. The predicted H2O line intensity of the LIME model using an abundance and structure profile, coupled with their dust opacity, is over-estimated by a factor of similar to 3.5 compared to the observations. We present several ad hoc profiles that best-fit the observations and compare the profiles with results from an astrochemical modelling, coupling gas phase and grain surface chemistry. The water deuteration weakly depends on the external visual extinction, the external ISRF, and contraction timescale. The [HDO]/[H2O] and [D2O]/[H2O] abundance ratios tend to increase towards the centre of the core up to 25% and similar to 8%, respectively. Conclusions. Our comparison between observations, radiative transfer, and chemical modelling shows the limits of detectability for singly deuterated water, through the ground-state transitions 10,1-00,0 and 11,1-00,0 at 464.9 and 893.6 GHz, respectively, with both single-dish telescope and interferometric observations. This study also highlights the need of a detailed benchmark amongst different radiative transfer codes for this particular problem of water in prestellar cores.