We present a spectroscopic analysis based on measurements of two mainly age-dependent spectrophotometric indices in the 4000A rest frame region, i.e. H+K(CaII) and Delta4000, for a sample of 15 early-type galaxies (ETGs) at 0.7 < z_{spec} < 1.1, morphologically selected in the GOODS-South field. Ages derived from the two different indices by means of the comparison with stellar population synthesis models, are not consistent with each other for at least nine galaxies (60 per cent of the sample), while for the remaining six galaxies, the ages derived from their global spectral energy distribution (SED) fitting are not consistent with those derived from the two indices. We then hypothesized that the stellar content of many galaxies is made of two stellar components with different ages. The double-component analysis, performed by taking into account both the index values and the observed SED, fully explains the observational data and improves the results of the standard one-component SED fitting in 9 out of the 15 objects, i.e. those for which the two indices point towards two different ages. In all of them, the bulk of the mass belongs to rather evolved stars, while a small mass fraction is many Gyr younger. In some cases, thanks to the sensitivity of the H+K(CaII) index, we find that the minor younger component reveals signs of recent star formation. The distribution of the ages of the younger stellar components appears uniformly in time and this suggests that small amounts of star formation could be common during the evolution of high-z ETGs. We argue the possibility that these new star formation episodes could be frequently triggered by internal causes due to the presence of small gas reservoir.
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