The HDO/H2O ratio in interstellar gas is often used to draw conclusions on the origin of water in star-forming regions and on Earth. In cold cores and in the outer regions of protoplanetary disks, gas-phase water comes from photodesorption of water ice. We present fitting formulae for implementation in astrochemical models using photodesorption efficiencies for all water ice isotopologues obtained using classical molecular dynamics simulations. We investigate if the gas-phase HDO/H2O ratio reflects that present in the ice or whether fractionation can occur during photodesorption. Probabilities for the top four monolayers are presented for photodesorption of X (X=H,D) atoms, OX radicals, and X2O and HDO molecules following photodissociation of H2O, D2O, and HDO in H2O amorphous ice at temperatures from 10-100 K. Isotope effects are found for all products: (1) H atom photodesorption probabilities from H2O ice are larger than those for D atom photodesorption from D2O ice by a factor of 1.1; the ratio of H and D photodesorbed upon HDO photodissociation is a factor of 2. This process will enrich the ice in deuterium atoms over time; (2) the OD/OH photodesorption ratio upon D2O and H2O photodissociation is on average a factor of 2, but the ratio upon HDO photodissociation is almost constant at unity for all temperatures; (3) D atoms are more effective in kicking out neighbouring water molecules than H atoms. However, the ratio of the photodesorbed HDO and H2O molecules is equal to the HDO/H2O ratio in the ice, therefore, there is no isotope fractionation upon HDO and H2O photodesorption. Nevertheless, the enrichment of the ice in D atoms due to photodesorption can over time lead to an enhanced HDO/H2O ratio in the ice, and, when photodesorbed, also in the gas. The extent to which the ortho/para ratio of H2O can be modified by the photodesorption process is also discussed. (Abridged)
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