The Contribution of Host Galaxies to the Infrared Energy Output of
  $z\gtrsim5.0$ QUASARS
  The infrared spectral energy distributions (SEDs) of $z\gtrsim 5$ quasars can
be reproduced by combining a low-metallicity galaxy template with a standard
AGN template. The host galaxy is represented by Haro 11, a compact, moderately
low metallicity, star-bursting galaxy that shares typical features of high-$z$
galaxies. For the vast majority of $z\gtrsim 5$ quasars, the AGN contribution
is well modeled by a standard empirical template with the contamination of star
formation in the infrared subtracted. Together, these two templates can
separate the contributions from the host galaxy and the AGN even in the case of
limited data points, given that this model has only two free parameters. Using
this method, we re-analyze 69 $z\gtrsim 5$ quasars with extensive Herschel
observations, and derive their AGN luminosities $L_{\rm AGN}$ in a range $\sim
(0.78-27.4) \times10^{13}\, L_{\odot}$, the infrared luminosities from star
formation $L_{\rm SF,IR} \sim (<1.5-25.7)\times10^{12}\, L_{\odot}$, and the
corresponding star formation rates ${\rm SFR}\sim (<290-2650)\, M_\odot/{\rm
yr}$. The average infrared luminosity from star formation and the average total
AGN luminosity of the $z\gtrsim5$ quasar sample follows the correlation defined
by quasars at $z < 2.6$. We assume these quasar host galaxies maintain a
constant average SFR ($\sim620\, M_\odot/{\rm yr}$) during their mass assembly
and estimate the stellar mass that could form till $z\sim5-6$ to be $\langle
M_* \rangle \sim(3-5)\times10^{11} M_\odot$. Combining with the black hole (BH)
mass measurements, this stellar mass is adequate to establish a BH-galaxy mass
ratio $M_{\rm BH}/M_{*}$ at 0.1-1%, consistent with the local relation.
