The Mgb-sigma Relation of Elliptical Galaxies at z=0.37

We derive absorption indices of ellipticals in clusters at z=0.37 from medium-resolution spectroscopy together with kinematical parameters. These galaxies exhibit a relationship between the Mgb linestrength and their internal velocity dispersion similar to local dynamically hot galaxies. But for any given sigma, Mgb of the distant ellipticals is significantly lower than the mean value of the nearby sample. The difference of Mgb between the two samples is small and can be fully attributed to the younger age of the distant stellar populations in accordance with the passive evolution model. The low reduction of Mgb at a look-back time of about 5 Gyrs requires that the bulk of the stars in cluster ellipticals have formed at very high redshifts of z_f>2. For the most massive galaxies, where the reduction is even lower, z_f probably exceeds 4. Unlike most methods to measure the evolution of ellipticals using luminosities, surface brightnesses or colours, the Mgb linestrength does not depend on corrections for extinction and cosmic expansion (K-correction) and only very little on the slope of the initial mass function. The combination of a kinematical parameter with a stellar population indicator allows us to study the evolution of very similar objects. In addition, the good mass estimate provided by sigma means that the selection criteria for the galaxy sample as a whole are well controlled. (abriged)