  Recent studies have found that obscured quasars cluster more strongly and are
thus hosted by dark matter haloes of larger mass than their unobscured
counterparts. These results pose a challenge for the simplest unification
models, in which obscured objects are intrinsically the same as unobscured
sources but seen through a dusty line of sight. There is general consensus that
a structure like a "dusty torus" exists, meaning that this intrinsic similarity
is likely the case for at least some subset of obscured quasars. However, the
larger host halo masses of obscured quasars implies that there is a second
obscured population that has an even higher clustering amplitude and typical
halo mass. Here, we use simple assumptions about the host halo mass
distributions of quasars, along with analytical methods and cosmological
$N$-body simulations to isolate the signal from this population. We provide
values for the bias and halo mass as a function of the fraction of the
"non-torus obscured" population. Adopting a reasonable value for this fraction
of $\sim$25% implies a non-torus obscured quasar bias that is much higher than
the observed obscured quasar bias, because a large fraction of the obscured
population shares the same clustering strength as the unobscured objects. For
this non-torus obscured population, we derive a bias of $\sim$3, and typical
halo masses of $\sim3\times10^{13}$ M$_{\odot}/h$ at $z=1$. These massive
haloes are likely the descendants of high-mass unobscured quasars at high
redshift, and will evolve into members of galaxy groups at $z=0$.
