The origin of dust in high redshift QSOs: the case of SDSS J1148+5251

We present a semi-analytical model for the formation and evolution of a high redshift quasar (QSO). We reconstruct a set of hierarchical merger histories of a 10^13 Msun dark matter halo and model the evolution of the corresponding galaxy and of its central super massive black hole. The code GAMETE/QSODUST consistently follows: the black hole assembly via both coalescence with other black holes and gas accretion; the build up and star formation history of the quasar host galaxy, driven by binary mergers and mass accretion; the evolution of gas, stars, metals in the interstellar medium (ISM), accounting for mass exchanges with the external medium (infall and outflow processes); dust formation in Supernova (SN) ejecta and in the stellar atmosphere of Asymptotic Giant Branch (AGB) stars, dust destruction by interstellar shocks and grain growth in molecular clouds; the AGN feedback which powers a galactic-scale wind, self-regulating the black hole growth and eventually halting star formation.We use this model to study the case of SDSS J1148+5251 observed at redshift 6.4, exploring different star formation histories for the QSO host galaxy.