White dwarfs are fascinating remnants of low-mass stars. These dense objects are supported by electron degeneracy pressure, preventing gravitational collapse. Their unique properties and evolution offer insights into stellar lifecycles and the ultimate fate of stars like our Sun.

As white dwarfs cool over billions of years, they undergo observable changes in luminosity, temperature, and color. Understanding their progenitors and formation process helps us piece together the complex story of stellar evolution and the diverse objects populating our universe.

The Death of Low-Mass Stars

Degenerate matter in white dwarfs

• Matter in a state where pressure depends only on density, not temperature occurs when electrons or neutrons are packed closely together (neutron stars)
• Electron degeneracy pressure supports the white dwarf against gravitational collapse
  • Electrons are compressed, providing pressure to support the star (Pauli exclusion principle)
• Neutron degeneracy pressure occurs when neutrons are compressed, providing even greater pressure than electron degeneracy
• As mass increases, the white dwarf becomes smaller and denser due to increased gravitational force
• The Chandrasekhar limit $\approx 1.4$ solar masses represents the maximum mass a white dwarf can have before electron degeneracy pressure is insufficient to prevent collapse into a neutron star or black hole

Long-term evolution of white dwarfs

• White dwarfs gradually cool and fade over billions of years since they have no fusion energy source
  • Cooling rate depends on mass and composition, with more massive white dwarfs cooling faster
• As a white dwarf cools, its core begins to crystallize, releasing latent heat and slowing the cooling process
• Observable changes in white dwarfs over time:
  1. Luminosity and temperature decrease
  2. Color shifts from white to red ($\approx 5000$ K)
  3. Spectral features change as the atmosphere cools and composition changes (hydrogen and helium absorption lines)

Progenitors of white dwarfs

• Low to medium-mass stars with initial masses $< 8-10$ solar masses evolve into white dwarfs
  • Sufficient mass to fuse hydrogen into helium in their cores during main sequence
  • Evolve into red giants and shed outer layers to form planetary nebulae (Cat's Eye Nebula)
• Main-sequence lifetime depends on initial mass, with more massive stars having shorter lifetimes
  • Example: Sun will become a white dwarf in $\approx 5$ billion years
• Composition of white dwarfs:
  • Primarily carbon and oxygen for stars with initial masses $< 8-10$ solar masses
  • Oxygen-neon-magnesium white dwarfs form from stars with initial masses $\approx 8-10$ solar masses near the upper limit for white dwarf progenitors

Late stages of low-mass stellar evolution

• Helium flash occurs when helium fusion suddenly ignites in the degenerate core of a red giant
• Horizontal branch phase follows the helium flash, characterized by stable helium fusion in the core
• Asymptotic giant branch (AGB) represents the final stage of nuclear burning for low and intermediate-mass stars
• Mass loss becomes significant during the AGB phase, driven by strong stellar winds
• Stellar winds play a crucial role in shaping the star's final evolution and the formation of planetary nebulae