Observational constraints of stellar collapse: Diagnostic probes of nature's extreme matter experiment

Supernovae are Nature's high-energy, high density laboratory experiments, reaching densities in excess of nuclear densities and temperatures above 10 MeV. Astronomers have built up a suite of diagnostics to study these supernovae. If we can utilize these diagnostics, and tie them together with a theoretical understanding of supernova physics, we can use these cosmic explosions to study the nature of matter at these extreme densities and temperatures. Capitalizing on these diagnostics will require understanding a wide range of additional physics. Here we review the diagnostics and the physics needed to use them to learn about the supernova engine, and ultimate nuclear physics.