Robust limit on a varying proton-to-electron mass ratio from a single H2 system

Context. The variation of the dimensionless fundamental physical constant mu = m(p)/m(e) can be checked through observation of Lyman and Werner lines of molecular hydrogen in the spectra of distant QSOs. Only few, at present four, systems have been used for the purpose providing different results between the different authors. Aims. Our intention is to asses the accuracy of the investigation concerning a possible variation of the fundamental physical constant mu = m(p)/m(e) and to provide more robust results. The goal in mind is to resolve the current controversy on variation of mu and devise explanations for the different findings. Methods. The demand for precision requires a deep understanding of the errors involved. Self-consistency in data analysis and effective techniques to handle unknown systematic errors are essential. An analysis based on independent data sets of QSO 0347-383 is put forward and new approaches for some of the steps involved in the data analysis are introduced. In this work we analyse two independent sets of observations of the same absorption system and for the first time we apply corrections for the observed offsets between discrete spectra mainly caused by slit illumination effects. Results. Drawing on two independent observations of a single absorption system in QSO 0347-383 our detailed analysis yields Delta mu/mu = (15 +/- (9(stat) + 6(sys))) x 10(-6) at z(abs) = 3.025. Based on the scatter of the measured redshifts and the corresponding low significance of the redshift-sensitivity correlation we estimate the limit of accuracy of Delta mu measurements to similar to 300 ms(-1), consisting of roughly 180 ms(-1) due to the uncertainty of the absorption line fit and about 120 ms(-1) allocated to systematics. Conclusions. Current analyses tend to underestimate the impact of systematic errors. This work presents alternative approaches to handle systematics and introduces methods required for precision analysis of QSO spectra available in the near future.