How are AGB stars formed?
AGB stars are stars approaching the end of their life.
On the Hertzprung-Russell diagram, asymptotic Giant Branch stars are a track that represents the evolution of old stars rather than newly formed stars.
The AGB phase begins when the star's helium supply runs out and it once again turns into a red giant.
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As stars with initial masses ranging from 0.8 to 8 solar masses exhaust their core hydrogen, they expand and turn into red giants. The star then becomes an asymptotic giant branch (AGB) star when the helium core contracts and heats up, causing hydrogen shell burning and expanding outer envelope.
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AGB (Asymptotic Giant Branch) stars are formed through a series of stages in the life cycle of intermediate-mass stars (stars with masses between 0.6 and 10 times that of the Sun). The formation process of AGB stars can be summarized as follows:
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Main Sequence Phase: AGB stars begin their lives as main sequence stars, where nuclear fusion reactions in their cores convert hydrogen into helium. During this phase, the star is in a stable equilibrium between inward gravitational force and outward radiation pressure.
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Red Giant Phase: As the star exhausts its hydrogen fuel in the core, it begins to evolve into a red giant. The core contracts and heats up, while the outer envelope expands and cools, causing the star to become larger and redder.
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Helium Shell Burning: In the core of the red giant, helium fusion reactions start when the temperature becomes high enough to fuse helium into carbon and oxygen. This process occurs in a shell surrounding the inert helium core.
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Thermal Pulses: As helium burning continues in the shell, the star undergoes periodic helium shell flashes or thermal pulses. These pulses are caused by instabilities in the fusion process and lead to dramatic expansions of the star's outer layers.
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AGB Phase: The star enters the AGB phase when it is experiencing helium shell burning and thermal pulses. During this phase, the star becomes highly luminous and develops an extended atmosphere of expelled material.
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Mass Loss and Envelope Expansion: AGB stars undergo significant mass loss through stellar winds, which are driven by radiation pressure and the pulsations of the star. This mass loss leads to the expansion of the star's envelope and the formation of a circumstellar shell of gas and dust.
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Formation of Planetary Nebulae: Towards the end of the AGB phase, the star sheds its outer layers more rapidly, forming a planetary nebula around the hot core of the star. The ejected material enriches the surrounding interstellar medium with heavy elements synthesized during the star's lifetime.
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Remnant Stage: After the ejection of its outer layers, the remaining core of the AGB star becomes a white dwarf, a dense stellar remnant composed mainly of carbon and oxygen. The white dwarf gradually cools over billions of years.
In summary, AGB stars are formed from intermediate-mass stars that have evolved off the main sequence, gone through helium burning in their cores, experienced thermal pulses, and undergone significant mass loss, ultimately leading to the formation of a planetary nebula and a white dwarf remnant.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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