2024MNRAS.528.6550W

Searches for space-time variations of fundamental constants have entered an era of unprecedented precision. New, high-quality quasar spectra require increasingly refined analytical methods. In this paper, a continuation in a series to establish robust and unbiased methodologies, we explore how convergence criteria in non-linear least-squares optimization impact on quasar absorption system measurements of the fine structure constant α. Given previous claims for high-precision constraints, we critically examine the veracity of a so-called blinding approach, in which α is fixed at the terrestrial value during the model building process, releasing it as a free parameter only after the 'final' absorption system kinematic structure has been obtained. We show that this approach results in such small consecutive parameter steps during minimization that convergence is unlikely to be reached, even after as many as 1000 iterations. The fix is straightforward: α must be treated as a free parameter from the earliest possible stages of absorption system model building. The implication of the results presented here is that all previous measurements that have used initially fixed α should be reworked.