| Abstract
| - The primordial abundance of deuterium (D/H) yields a measure of the density of baryons in the Universe and is an important complement to determinations from cosmic microwave background (CMB) experiments. Indeed, the current small samples of high-redshift D/H measurements from quasar absorption line studies are in excellent agreement with CMB-derived values. Conversely, absorption line measurements of the Galactic D/H ratio in almost 50 stellar sightlines show a puzzlingly large scatter outside the local bubble which is difficult to explain simply by astration from the primordial value. The currently favoured explanation for these large variations is that D is differentially depleted relative to H in some parts of the local interstellar medium (ISM). Here, we test this scenario by studying the correlation between D/H and the abundance of titanium, one of the most refractory elements readily observed in the ISM. Previous work by Prochaska, Tripp & Howk found tentative evidence for a correlation between Ti/H and D/H based on seven sightlines. Here we almost triple the number of previous Ti measurements and include several sightlines with very high or low D/H that are critical for quantifying any correlations with D/H. With our larger sample, we confirm a correlation between Ti/H and D/H at the 97 per cent confidence level. However, the magnitude of this dependence is difficult to reconcile with a simple model of dust depletion for two reasons. First, contrary to what is expected from local depletion rates, the gradient of the highly refractory Ti is much shallower than that observed for Fe and Si. Secondly, we do not observe the established tight, steep correlation between [Ti/H] and the mean volume density of hydrogen. Therefore, whilst dust remains a plausible explanation for the local D/H variations, the abundances of at least some of the refractory elements do not provide unanimous support for this scenario. We also argue that the correlations of [Si/H], [Fe/H] and [Ti/H] with D/H are inconsistent with a simple infall model of low-metallicity gas with approximately solar abundances as the dominant cause for D variations.
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