The Infrared Emission and Opening Angle of the Torus in Quasars
  According to the unified model of active galactic nuclei (AGNs), a putative
dusty torus plays an important role in determining their external appearance.
However, very limited information is known about the physical properties of the
torus. We perform detailed decomposition of the infrared ($1-500\,\mu$m)
spectral energy distribution of 76 $z < 0.5$ Palomar-Green quasars, combining
photometric data from 2MASS, WISE, and Herschel with Spitzer spectroscopy. Our
fits favor recent torus spectral models that properly treat the different
sublimation temperatures of silicates and graphite and consider a polar wind
component. The AGN-heated dust emission from the torus contributes a
significant fraction ($\sim 70\%$) of the total infrared ($1-1000\, \mu$m)
luminosity. The torus luminosity correlates well with the strength of the
ultraviolet/optical continuum and the broad $\rm{H\beta}$ emission line,
indicating a close link between the central ionization source and re-radiation
by the torus. Consistent with the unified model, most quasars have tori that
are only mildly inclined along the line-of-sight. The half-opening angle of the
torus, a measure of its covering factor, declines with increasing accretion
rate until the Eddington ratio reaches $\sim 0.5$, above which the trend
reverses. This behavior likely results from the change of the geometry of the
accretion flow, from a standard geometrically thin disk at moderate accretion
rates to a slim disk at high accretion rates.
