Bounds on the fine structure constant variability from Fe II absorption lines in QSO spectra

The Single Ion Differential a Measurement (SIDAM) method for measuring Delta alpha/alpha and its figures of merit are illustrated together with the results produced by means of Fe II absorption lines of QSO intervening systems. The method provides Delta alpha/alpha = -0.12 +/- 1.79 ppm (parts-per-million) at z(abs) = 1.15 towards HE 0515-4414 and Delta alpha/alpha = 5.66 +/- 2.67 ppm at z(abs) = 1.84 towards Q 1101-264, which are so far the most accurate measurements for single systems. SIDAM analysis for 3 systems from the Chand et al. [1] sample provides inconsistent results which we interpret as due to calibration errors of the Chand et al. data at the level approximate to 10 ppm. In one system evidence for photo-ionization Doppler shift between Mg II and Fe II lines is found. This evidence has important bearings on the Many Multiplet method where the signal for Delta alpha/alpha variability is carried mainly by systems involving Mg II absorbers. Some correlations are also found in the Murphy et al. [10] sample which suggest larger errors than previously reported. Thus, we consider unlikely that both the Chand et al. and Murphy et al. datasets could provide an estimate of Delta alpha/alpha with an accuracy at the level of 1 ppm. A new spectrograph like the ESPRESSO project will be crucial to make progress in the astronomical determination of Delta alpha/alpha