  Microlensing observations indicate that quasar accretion discs have
half-light radii larger than expected from standard theoretical predictions
based on quasar fluxes or black hole masses. Blackburne and colleagues have
also found a very weak wavelength dependence of these half-light radii. We
consider disc temperature profile models that might match these observations.
Nixon and colleagues have suggested that misaligned accretion discs around
spinning black holes will be disrupted at radii small enough for the
Lense-Thirring torque to overcome the disc's viscous torque. Gas in precessing
annuli torn off a disc will spread radially and intersect with the remaining
disc, heating the disc at potentially large radii. However, if the intersection
occurs at an angle of more than a degree or so, highly supersonic collisions
will shock-heat the gas to a Compton temperature of T~10^7 K, and the spectral
energy distributions (SEDs) of discs with such shock-heated regions are poor
fits to observations of quasar SEDs. Torn discs where heating occurs in
intermittent weak shocks that occur whenever the intersection angle reaches a
tenth of a degree pose less of a conflict with observations, but do not have
significantly larger half-light radii than standard discs. We also study two
phenomenological disc temperature profile models. We find that discs with a
temperature spike at relatively large radii and lowered temperatures at radii
inside the spike yield improved and acceptable fits to microlensing sizes in
most cases. Such temperature profiles could in principle occur in sub-Keplerian
discs partially supported by magnetic pressure. However, such discs overpredict
the fluxes from quasars studied with microlensing except in the limit of
negligible continuum emission from radii inside the temperature spike.
