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 $sim3times10^{13}$ 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 $z=0$.
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