The far-infrared-submillimetre spectral energy distribution of high-redshift quasars

We combine photometric observations of high-redshift (z > 4) quasars, obtained at submillimetre to millimetre wavelengths, to obtain a mean far-infrared (rest-frame) spectral energy distribution (SED) of the thermal emission from dust, parametrized by a single temperature (T) and power-law emissivity index (beta). The best-fitting values are T = 41 +/- 5 K and beta = 1.95 +/- 0.3. Our method exploits the redshift spread of this set of quasars, which allows us to sample the SED at a larger number of rest wavelengths than is possible for a single object: the wavelength range extends down to similar to 60 mum, and therefore samples the turnover in the greybody curve for these temperatures. This parametrization is of use to any studies that extrapolate from a flux at a single wavelength, for example to infer dust masses and far-infrared luminosities. We interpret the cool, submillimetre component as arising from dust heated by star formation in the host galaxy of the quasar, although we do not exclude the presence of dust heated directly by the active galactic nucleus (AGN). Applying the mean SED to the data, we derive consistent star formation rates similar to 1000 M. yr(-1) and dust masses similar to 10(9) M., and investigate a simple scheme of AGN and host galaxy co-evolution to account for these quantities. The time-scale for formation of the host galaxy is 0.5-1 Gyr, and the luminous quasar phase occurs towards the end of this period, just before the reservoir of cold gas is depleted. Given the youth of the Universe at z = 4 (1.6 Gyr), the coexistence of a massive black hole and a luminous starburst at high redshifts is a powerful constraint on models of quasar host galaxy formation.