  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.
