We present a theoretical study of the deuterated species detectability in various types of extragalactic star-forming regions based on our predictions of chemical abundances. This work is motivated by the past and current attempts at observing deuterated species in external galaxies such as NGC~253, IC~342 and the LMC. Here, we investigate the influence of the density, the temperature, the FUV radiation field, the cosmic ray ionisation, and the metallicity on the fractional abundances and D/H abundance ratios of about 20 deuterated species. Without modelling any particular source, we determined how the deuterium chemistry behaves in different physical environments such as starburst, cosmic-rays enhanced environments, low metallicity and high redshift galaxies. In general, our predicted column densities seem in good agreement with those derived from the current limited dataset of observations in external galaxies. We provide, for the first time, a list of key deuterated species whose abundances are high enough to be possibly detectable by the Atacama Large Millimeter Array (ALMA) and Herschel, as a function of galactic nuclear activity and redshift.
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