What mechanism supports the remnant core of a Sun-like star after it forms a white dwarf?

Answer

Electron degeneracy pressure

The white dwarf remnant is no longer supported by thermal pressure from fusion but is held up by electron degeneracy pressure, a quantum mechanical effect resisting the squeezing of electrons into the same quantum state.

What mechanism supports the remnant core of a Sun-like star after it forms a white dwarf?
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