  We present a novel technique to study Type Ia supernovae by constraining
surviving companions of historical extragalactic SN by combining archival
photographic plates and Hubble Space Telescope imaging. We demonstrate this
technique for Supernova 1972E, the nearest known SN Ia in over 125 years. Some
models of Type Ia supernovae describe a white dwarf with a non-degenerate
companion that donates enough mass to trigger thermonuclear detonation.
Hydrodynamic simulations and stellar evolution models show that these donor
stars survive the explosion, and show increased luminosity for at least a
thousand years. Thus, late-time observations of the exact location of a
supernova after its ejecta have faded can constrain the presence of a surviving
donor star and progenitor models. We find the explosion site of SN 1972E by
analyzing 17 digitized photographic plates taken with the European Southern
Observatory 1m Schmidt and 1 plate taken with the Cerro Tololo Inter-American
Observatory 1.5m telescope from 1972-1974. Using the \textit{Gaia} eDR3 catalog
to determine Supernova 1972E's equatorial coordinates yields: $\alpha$ = 13$^h$
39$^m$ 52.708$^s$ $\pm$ 0.004$^s$ and $\delta$ = $-$31\degree 40' 8\farcs97
$\pm$ 0\farcs04 (ICRS). In 2005, HST/ACS imaged NGC 5253, the host galaxy of SN
1972E, with the $F435W$, $F555W$, and $F814W$ filters covering the explosion
site. The nearest source detected is offset by 3.0 times our positional
precision, and is inconsistent with the colors expected of a surviving donor
star. Thus, the 2005 HST observation rules out all Helium-star companion
models, and the most luminous main-sequence companion model currently in the
literature. The remaining main-sequence companion models could be tested with
deeper HST imaging.
