post-AGB star

The term post-AGB star (pAGB) is a general term for a post-main-sequence star for which fusion has ceased (ending its AGB phase), lasting until it is a white dwarf (WD). The term is often used more explicitly for an observed star within this phase but which has not yet developed a planetary nebula (PN, which makes it very different, observationally). The term protoplanetary nebula (PPN) is also used for such astronomical objects, PPN suggesting the object shows signs that a PN is imminent. The term pre-white dwarf is used for such stars approaching the white dwarf stage. Some Wolf-Rayet stars, in particular, some WC stars, are within the pAGB stage.

The pAGB phase (taken as everything after AGB but before it is a white dwarf) generally lasts 1,000 to 100,000 years, shortest for the most massive stars. The luminosity remains roughly constant: the lack of fusion energy from the center allows it to shrink, and the more-concentrated heat along with the KH mechanism raises the surface temperature from that of a cool red giant, roughly balancing so as to maintain the luminosity. When the star reaches roughly 30,000 K, it produces enough ionizing radiation to ionize the circumstellar envelope (CSE, produced by the substantial stellar wind during the AGB phase), producing a larger glowing object, the PN.

During the pAGB phase, a brief episode of fusion can occur, termed a TPC (VLTP). Also, the star crosses the instability strip on the H-R diagram, during which it can be a pulsating star such as a RV Tauri Variable.

Regarding the more-massive stars that undergo the rapid core collapse that potentially produces a core collapse supernova, I'm not sure how much time passes between fusion ceasing and the rapid collapse: what I've found seems like it could be days, hours, minutes, seconds, or even less than a second. In any of these, the term pAGB might be used, but I'm guessing it is more likely to be termed a "pre-supernova" stage. Being so short (and not predictable with much precision), any observation of this brief period is likely to be the result of chance and to lack much detail, such as that which would be provided by spectrography.