Is the star-formation rate in z similar to 6 quasars overestimated?

The large total infrared (TIR) luminosities (L-TIR; greater than or similar to 10(12) L-circle dot) observed in z similar to 6 quasars are generally converted into high star-formation rates (SFRs; greater than or similar to 10(2) M-circle dot yr(-1)) of their host galaxies. However, these estimates rely on the assumption that dust heating is dominated by stellar radiation, neglecting the contribution from the central active galactic nucleus (AGN). We test the validity of this assumption by combining cosmological hydrodynamic simulations with radiative transfer calculations. We find that, when AGN radiation is included in the simulations, the mass (luminosity)-weighted dust temperature in the host galaxies increases from T approximate to 50 K (T approximate to 70 K) to T approximate to 80 K (T approximate to 200 K), suggesting that AGN effectively heats the bulk of dust in the host galaxy. We compute the AGN-host galaxy SFR from the synthetic spectral energy distribution by using standard SFR - L-TIR relations, and compare the results with the 'true' values in the simulations. We find that the SFR is overestimated by a factor of approximate to 13 (greater than or similar to 10) for AGN bolometric luminosities of L-boi approximate to 10(12) L-circle dot (greater than or similar to 10(13) L-circle dot), implying that the SFRs of z similar to 6 quasars can be overestimated by over an order of magnitude.