The Death of Low-Mass Stars-Chapter 23

23.1 The Death of Low-Mass Stars

Understand the final mass of stars less than approximately 1.4 times the mass of the Sun (M_{Sun}) and why this mass is critical.
Recognize that low-mass stars constitute the majority in the universe, akin to a few musicians becoming superstars in the music industry.

Most stars have a final mass < 1.4 M_{Sun}.
Mass Loss: Many stars initiating with initial masses > 1.4 M_{Sun} eventually decrease to below this threshold due to mass loss.
- E.g., stars starting with 8.0 M{Sun} may lose mass and end up below 1.4 M{Sun}.

Previous section ended with a Sun-like star in the red-giant region and shedding outer layers, forming a planetary nebula.
The core is in energy crisis:
- Previously stable helium fusion produced carbon and oxygen until helium was exhausted.
- Without pressure from fusion, the core collapses under gravity until it reaches extreme densities (1 million times that of water).

Core Collapse: Continued collapse leads to density nearing 200,000 times Earth's average density.
At this density, a new behavior of matter begins, stabilizing the star into a white dwarf.

White dwarfs exhibit behavior indicative of degenerate matter; very dense and stabilized by electron degeneracy pressure.
Pauli Exclusion Principle: No two electrons may occupy the same place and state at once.
- High density leads to significant resistance against further contraction by electrons.
- This phenomenon allows white dwarfs to maintain their structure without additional heat input.
- Electrons in degenerate gas experience restricted movement due to proximity constraints.
Atomic nuclei are not in a degenerate state unless subjected to higher densities.
Core collapse stops due to electron degeneracy pressure, and thus white dwarfs are compact with electron-degenerate cores.

Subrahmanyan Chandrasekhar's Contributions:
- Calculated that white dwarfs would contract until electrons achieve maximum density, limiting mass to about 1.4 M_{Sun} (the Chandrasekhar Limit).
- Beyond this mass, collapse cannot be prevented by electron degeneracy pressure, leading to different end states for stars.

White dwarf radius decreases as mass increases. A typical white dwarf mass > 1.4 M_{Sun} would compress to a zero radius.

After fusion ceases, white dwarfs cool and eventually become black dwarfs, transitioning through billions of years.
They predominantly consist of carbon, oxygen, and neon.
Carbon crystallization results in a diamond-like structure.

Stars below Chandrasekhar limit become white dwarfs based on how mass is shed during red-giant phase.
- Evidence suggests stars > 8 M_{Sun} can shed enough mass to transition into white dwarfs.
- Example: A star that initially had mass of 6 M{Sun} must shed sufficient mass to fall under 1.4 M{Sun}.
- Main-sequence stars can lose significant mass during evolution to reach this final threshold.

Stars initiating at 8 M{Sun} potentially end as white dwarfs, though stars exceeding 150 M{Sun} undergo explosive deaths.

After helium depletion, core contraction raises temperatures to fuse carbon, generating heavier elements like oxygen and iron.
Rates of fusion reaction increase drastically, with heavy elements forming rapidly in comparison to the longer main-sequence phase.
Core resembles an internal structure similar to an onion with layers of differing element states.

Iron fusion halts energy output leading to catastrophic collapse with core densities approaching nuclear densities.
Neutron Creation: Electrons merge with protons to create neutrons and neutrinos, with resultant core shrinkage and neutron disk formation preventing further collapse.
Below a certain threshold (approximately 3 M_{Sun}), neutron stars are formed.

The collapse leading to supernovae releases immense energy, with neutrino luminosity surpassing light from billion galaxies.
A regular star (mass > 8 M{Sun}) expels > 5 M{Sun} during supernova phenomena.

Explosive core collapse releases energy that ejects outer layers in explosive spectacular events.
Type II Supernovae results from massive star collapses versus Type Ia explosions arising from white dwarfs in binary systems.

Supernova has cyclical implications, enriching interstellar medium with heavy elements crucial for future star formation and life's origin.
Supernova explosions recycle materials necessary for new planetary systems, sustaining the universe's evolutionary cycle.
The creation of elements heavier than iron occurs primarily through supernova processes and neutron star mergers.