Fine-structure constant constraints on Bekenstein-type models

Astrophysical tests of the stability of dimensionless fundamental couplings, such as the fine-structure constant $\alpha$, are an area of much increased recent activity, following some indications of possible spacetime variations at the few parts per million level. Here we obtain updated constraints on the Bekenstein-Sandvik-Barrow-Magueijo model, which is arguably the simplest model allowing for $\alpha$ variations. Recent accurate spectroscopic measurements allow us to improve previous constraints by about an order of magnitude. We briefly comment on the dependence of the results on the data sample, as well as on the improvements expected from future facilities.