| Abstract
| - Context. Understanding the history of formation of z> 6 quasars is a major challenge to theoretical models. Physical insights on the connection between the central black hole and its host galaxy can be gained by means of the quasar infrared properties. Aims. Here we investigate the origin of the far-infrared continuum of SDSS J1148+5251, using it as a prototype for the more general class of high-luminosity high-redshift quasars. Methods. We run the radiative transfer code TRADING to follow the transfer of radiation from the central source and from stellar sources through the dusty environment of the host galaxy. We adopt simple models for the central source, including all the radiation that can travel beyond the dusty torus. The radiation from stellar sources is modelled using the code PÉGASE. The model is based on the output of the semi-analytical merger tree code, GAMETE/QSO dust, which lets us predict the evolution of the host galaxy and of its nuclear black hole, following the star formation history and chemical evolution - including dust - in all the progenitor galaxies of SDSS J1148+5251. Results. We find that the radiation emitted by the central source, which dominates the observed spectral energy distribution from UV/optical to near- and mid-infrared wavelengths, can also provide an important source of heating for the dust distributed in the host galaxy, powering at least 30% and up to 70% of the observed far-infrared emission at rest-frame wavelengths [20−1000] μm. The remaining fraction is contributed by stellar sources and can only be achieved if the host galaxy is able to sustain a star formation rate of ≈900 M⊙/yr at z = 6.4 . This points to a co-evolution scenario where, during their hierarchical assembly, the first super-massive black holes and their host galaxies grow at the same pace until the black hole reaches a mass of ~2 × 10 8M⊙; it then starts growing faster than its host, reaching the bright quasar phase when the black hole and stellar mass fall within the scatter of the scaling relation observed in local galaxies. This same evolutionary scenario has been recently shown to explain the properties of a larger sample of 5 < z< 6.4 quasars, with the implication that current dynamical mass measurements may have missed an important fraction of the host galaxy stellar mass. Conclusions. We conclude that the far-infrared luminosity of high- z quasars is a sensitive tracer of the rapidly changing physical conditions in the host galaxy. Quasars appear far-infrared bright when the host galaxy can still sustain strong starbursts, with star formation rates 100 M⊙/yr <SFR< 1000 M⊙/yr, and progressively dim as large quasar-driven outflows deplete the host galaxy of its gas content, damping star formation and leaving the central source as the only source of dust heating.
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