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How old are the stars in the halo of NGC 5128 (Centaurus A)?

NGC 5128 (Centaurus A) is, at the distance of just 3.8 Mpc, the nearest easily observable giant elliptical galaxy. Therefore it is the best target to investigate the early star formation history of an elliptical galaxy. Our aims are to establish when the oldest stars formed in NGC 5128, and whether this galaxy formed stars over a long period. We compare simulated colour-magnitude diagrams with the deep ACS/HST photometry. We find that that the observed colour-magnitude diagram can be reproduced satisfactorily only by simulations that have the bulk of the stars with ages in excess of ~10 Gyr, and that the alpha-enhanced models fit the data much better than the solar scaled ones. Data are not consistent with extended star formation over more than 3-4 Gyr. Two burst models, with 70-80% of the stars formed 12+/-1 Gyr ago and with 20-30% younger contribution with 2-4 Gyr old stars provide the best agreement with the data. The old component spans the whole metallicity range of the models (Z=0.0001-0.04), while for the young component the best fitting models indicate higher minimum metallicity (~1/10 - 1/4 Z_sun). The bulk of the halo stars in NGC5128 must have formed at redshift z>=2 and the chemical enrichment was very fast, reaching solar or even twice-solar metallicity already for the ~11-12 Gyr old population. The minor young component, adding ~20-30% of the stars to the halo, and contributing less than 10% of the mass, may have resulted from a later star formation event ~2-4 Gyr ago. (abridged)