Stars that have properties between Asymptotic Giant Branch stars and red supergiants
A super-AGB star is a star with a mass intermediate between those that end their lives as a white dwarf and those that end with a core collapse supernova, and properties intermediate between asymptotic giant branch (AGB) stars and red supergiants. They have initial masses of 7.5–9.25 M☉ in stellar-evolutionary models, but have exhausted their core hydrogen and helium, left the main sequence, and expanded to become large, cool, and luminous.
HR diagram.
Super-AGB stars occupy the top-right of the Hertzsprung–Russell diagram (HR diagram), and have cool temperatures between 3,000 and , which is similar to normal AGB stars and red supergiant stars (RSG stars). These cool temperatures allow molecules to form in their photospheres and atmospheres. Super-AGB stars emit most of their light in the infra-red spectrum because of their extremely cool temperatures.
The Chandrasekhar limit and their life.
A super-AGB star's core may grow to (or past) the Chandrasekhar mass because of continued hydrogen (H) and helium (He) shell burning, ending as core-collapse supernovae. The most massive super-AGB stars (at around 9 M☉) are theorized to end in electron capture supernovae. The error in this determination due to uncertainties in the third dredge-up efficiency and AGB mass-loss rate could lead to about a doubling of the number of electron-capture supernovae, which also supports the theory that these stars make up 66% of the supernovae detected by satellites. 
These stars are at a similar stage in life to red giant stars, such as Aldebaran, Mira, and Chi Cygni, and are at a stage where they start to brighten, and their brightness tends to vary, along with their size and temperature. 
These stars represent a transition to the more massive supergiant stars that undergo full fusion of elements heavier than helium. During the triple-alpha process, some elements heavier than carbon are also produced: mostly oxygen, but also some magnesium, neon, and even heavier elements, gaining an oxygen-neon (ONe) core. Super-AGB stars develop partially degenerate carbon–oxygen cores that are large enough to ignite carbon in a flash analogous to the earlier helium flash. The second dredge-up is very strong in this mass range and that keeps the core size below the level required for burning of neon as occurs in higher-mass supergiants.
References.
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