While this article describes one method to determine if the companion star was a dwarf or a giant, other methods have already been employed finding that the donor star was likely a white dwarf: http://phys.org/n...tar.html

That PO article outlines a (failed) search for a giant star progenitor using pre-supernova images from HST and a fortuitous observation of the supernova just hours after the event had begun. Both observations strongly suggest that the donor star in the binary system was a white dwarf.

The type of observations discussed here do show the usefulness of this technique in constraining progenitor possibilities in Type Ia supernovae.

A white dwarf stealing material from another white dwarf? Get real! It's an extremely slow rotating pulsar. The output slowly grows and fades, reaching the same peak. The outputs occur on a regular basis. Low hydrogen content. No companion found.

So, two WDs rapidly revolve around each other, until the less massive (and larger; WDs are degenerate) is tidally disrupted, by the more massive, denser, smaller companion? Then, the sudden infall, of massive amounts of material, onto the more massive companion, causes a SNIa?

Would the merger of two NSs generate a GRB?