ABSTRACT In this paper we explore the properties of the $z=6.853$ obscured hyperluminous quasar COS-87259, discovered in the Cosmological Evolution Survey (COSMOS) field, with our recently developed Bayesian spectral energy distribution (SED) fitting code SMART (Spectral energy distributions Markov chain Analysis with Radiative Transfer models). SMART fits SEDs exclusively with multicomponent radiative transfer models that constitute four different types of pre-computed libraries for the active galactic nucleus (AGN) torus, the starburst, and the spheroidal or disc host. We explore two smooth radiative transfer models for the AGN torus and two two-phase models, in order to put constraints on the AGN fraction of the galaxy, the black hole mass, and its star formation rate (SFR). We find that either of the smooth tapered disc or the two-phase flared disc models provide a good fit to the SED of COS-87259. The best-fitting models predict an AGN fraction in the range $86-92$ per cent, a bolometric AGN luminosity of $5.8-10.3 \times 10^{13} L_\odot$, a black hole mass of $1.8-3.2 \times 10^{9} M_\odot$ (assuming the quasar is accreting at the Eddington limit), and an SFR in the range $1985-2001~M_\odot \rm yr^{-1}$. The predicted space density of such objects in the redshift range $4-7$ is $\sim 20$ times more than that of co-eval unobscured quasars.
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