Empirical determination of Einstein A-coefficient ratios of bright [Fe II] lines

The Einstein spontaneous rates (A-coefficients) of Fe+ lines have been computed by several authors with results that differ from each other by up to 40%. Consequently, models for line emissivities suffer from uncertainties that in turn affect the determination of the physical conditions at the base of line excitation. We provide an empirical determination of the A-coefficient ratios of bright [Fe ii] lines that would represent both a valid benchmark for theoretical computations and a reference for the physical interpretation of the observed lines. With the ESO-Very Large Telescope X-shooter instrument between 3000A˚ and 24700 A˚, we obtained a spectrum of the bright Herbig-Haro object HH 1. We detect around 100 [Fe ii] lines, some of which with a signal-to-noise ratios ≥100. Among these latter lines, we selected those emitted by the same level, whose dereddened intensity ratios are direct functions of the Einstein A-coefficient ratios. From the same X-shooter spectrum, we got an accurate estimate of the extinction toward HH 1 through intensity ratios of atomic species, H I recombination lines and H2 ro-vibrational transitions. We provide seven reliable A-coefficient ratios between bright [Fe ii] lines, which are compared with the literature determinations. In particular, the A-coefficient ratios involving the brightest near-infrared lines (λ12570/λ16440 and λ13209/λ16440) are in better agreement with the predictions by the Quinet et al. relativistic Hartree-Fock model. However, none of the theoretical models predict A-coefficient ratios in agreement with all of our determinations. We also show that literature data of near-infrared intensity ratios better agree with our determinations than with theoretical expectations.