We investigate the origin of the FIR continuum of SDSS J1148+5251, using it as a prototype for the more general class of high-luminosity high-redshift QSOs. 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. The model is based on the output of the semi-analytical merger tree code, GAMETE/QSOdust, which enables to 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. We find that the radiation emitted by the central source 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]micron. 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 Msun/yr at z=6.4. This points to a co-evolution scenario where, during their hierarchical assembly, the first SMBHs and their host galaxies first grow at the same pace until the black hole reaches a mass of ~ 2 10^8 Msun and 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 QSOs, and imply that current dynamical mass measurements may have missed an important fraction of the host galaxy stellar mass. We conclude that the FIR luminosity of high-z quasars is a sensitive tracer of the rapidly changing physical conditions in the host galaxy.
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