Constraints on the Progenitor of SN 2010jl and Pre-Existing Hot Dust in
  its Surrounding Medium
  A search for the progenitor of SN~2010jl, an unusually luminous core-collapse
supernova of Type~IIn, using pre-explosion {\it Hubble}/WFPC2 and {\it
Spitzer}/IRAC images of the region, yielded upper limits on the UV and
near-infrared (IR) fluxes from any candidate star. These upper limits constrain
the luminosity and effective temperature of the progenitor, the mass of any
preexisting dust in its surrounding circumstellar medium (CSM), and dust
proximity to the star. A {\it lower} limit on the CSM dust mass is required to
hide a luminous progenitor from detection by {\it Hubble}. {\it Upper} limits
on the CSM dust mass and constraints on its proximity to the star are set by
requiring that the absorbed and reradiated IR emission not exceed the IRAC
upper limits. Using the combined extinction-IR emission constraints we present
viable $M_d-R_1$ combinations, where $M_d$ and $R_1$ are the CSM dust mass and
its inner radius. These depend on the CSM outer radius, dust composition and
grain size, and the properties of the progenitor. The results constrain the
pre-supernova evolution of the progenitor, and the nature and origin of the
observed post-explosion IR emission from SN~2010jl. In particular, an
$\eta$~Car-type progenitor will require at least 4~mag of visual extinction to
avoid detection by the {\it Hubble}. This can be achieved with dust masses
$\gtrsim 10^{-3}$~\msun\ (less than the estimated 0.2-0.5~\msun\ around
$\eta$~Car) which must be located at distances of $\gtrsim 10^{16}$~cm from the
star to avoid detection by {\it Spitzer}.
