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An argument could be made that the entire lifetime of a star is a stellar explosion, but in later stages, even the normal brightness of stellar burning pales in comparison to these common types of stellar explosions listed in order of increasing violence:

late stage stellar wind
a star late in life ejects the outer layers into a shell; further winds and ultraviolet radiation often ionize this shell resulting in a planetary nebula; the remaining core or stellar corpse shrinks but remains hot, now a white dwarf
nova
1. literally, “new star”, coined by Tycho Brahe in 1572; the observed “nova” later became classified as a supernova
2. nuclear fusion of a Hydrogen layer collected on the surface or accretion disk of a white dwarf by stripping a companion star in a binary star system and sparked by the energy of the impact of material on the surface of the white dwarf
supernova
explosion of a star's core that exceeds the Chandrasekhar limit in mass; this leaves behind either a neutron star, a quark star, or a black hole as a stellar corpse; most fit into either the type Ia supernova or type II supernova classifications

Of cosmological importance, these explosions release the heavier elements created in the star out to enrich the host galaxy. Note that “heavy elements” include everything except the two lightest elements hydrogen and helium. Nucleosynthesis inside the stars along with the violent final explosion create nearly all the other elements.

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