Non-uniqueness in quasar absorption models and implications for measurements of the fine structure constant.

High resolution spectra of quasar absorption systems provide the best constraints on temporal or spatial changes of fundamental constants in the early universe. An important systematic that has never before been quantified concerns model non-uniqueness; the absorption component structure is generally complicated, comprising many blended lines. This characteristic means any given system can be fitted equally well by many slightly different models, each having a different value of \alpha, the fine structure constant. We use AI Monte Carlo modelling to quantify non-uniqueness and describe how it accounts for previously unexplained scatter seen in the majority of published measurements. Extensive supercomputer calculations are reported, revealing new systematic effects that guide future analyses: (i) systematic errors significantly increase if line broadening models are turbulent but are minimised if gas temperature is included as a free parameter; modelling quasar absorption systems using turbulent broadening should be avoided and compound broadening is preferable. (ii) The general overfitting tendency of AICc dramatically increases non-uniqueness and hence the overall error budget on estimates of \alpha variations. The newly introduced Spectral Information Criterion (SpIC) statistic is more suitable and substantially decreases non-uniqueness compared to AICc-based models.