  The community agrees that Type Ia supernovae arise from Carbon/Oxygen white
dwarfs undergoing thermonuclear runaway. However, the full progenitor system
and the process that prompts the white dwarf to explode remain unknown. Most
current models suggest that the white dwarf explodes because of interaction
with a binary companion which may survive the process and remain within the
resulting remnant of the exploded star. Furthermore, both the pre-supernova
interaction process and the explosion of the primary are expected to imprint a
significant departure from ordinary stellar radii and temperatures onto the
secondary, making the star identifiable against the unrelated stellar
population. Identification of a surviving companion inside an SN Ia remnant
might confirm a specific corresponding SN Ia progenitor channel based on the
identity of the companion. We conducted a surviving companion search of the
Type Ia remnant SNR 0509-67.5 based in the Large Magellanic Cloud. The
well-constrained distance to and foreground extinction of the Large Magellanic
Cloud allow for Bayesian inference of stellar parameters with low correlation
and uncertainties. We present a deep catalog of fully characterized stars
interior to SNR 0509-67.5 with radii, effective temperatures, and metallicities
inferred using combined Hubble Space Telescope photometric observations across
multiple visits. We then compile a list of surviving companion models
appropriate for the age of the remnant (roughly 400 years after the explosion).
We compare these predictions with the inferred stellar parameters and conclude
that none of the stars are consistent with the predicted signatures of a
surviving companion.
