White dwarfs are fascinating stellar remnants that mark the end of most stars' lives. These dense objects, supported by electron degeneracy pressure, have an inverse mass-radius relationship and come in various compositions.

The Chandrasekhar limit, a crucial concept in white dwarf physics, sets the maximum mass for these stars at about 1.44 solar masses. This limit plays a key role in understanding stellar evolution, supernovae, and cosmic distance measurements.

White Dwarf Structure

Electron Degeneracy Pressure and Mass-Radius Relationship

• Electron degeneracy pressure supports white dwarfs against gravitational collapse
• Quantum mechanical effect prevents electrons from occupying same energy states
• Results in an inverse mass-radius relationship for white dwarfs
• More massive white dwarfs have smaller radii due to increased gravitational compression
• Typical white dwarf mass ranges from 0.6 to 1.4 solar masses
• Radii of white dwarfs generally fall between 0.008 and 0.02 solar radii (comparable to Earth's size)

Composition and Types of White Dwarfs

• Carbon-oxygen white dwarfs comprise the majority of observed white dwarfs
  • Form from low to intermediate-mass stars (up to about 8 solar masses)
  • Carbon and oxygen produced through helium fusion in the star's core
• Helium white dwarfs exist but are less common
  • Result from binary star evolution or very low-mass stars
  • Consist primarily of helium with a thin hydrogen envelope
• Oxygen-neon-magnesium white dwarfs form from more massive progenitor stars
  • Rare type of white dwarf with masses approaching the Chandrasekhar limit

White Dwarf Evolution

Cooling Sequence and Spectral Changes

• White dwarfs gradually cool over billions of years
• Initial surface temperatures can exceed 100,000 K
• Cooling follows a predictable sequence used to estimate white dwarf ages
• Spectral classification changes as the white dwarf cools
  • Hot white dwarfs show strong helium lines (DB spectral type)
  • Cooler white dwarfs display prominent hydrogen lines (DA spectral type)
• Cooling rate slows significantly at lower temperatures due to decreased thermal energy loss
• Oldest white dwarfs in our galaxy have cooled to temperatures around 4,000 K

Accretion Processes and Binary Systems

• White dwarfs in binary systems can accrete matter from companion stars
• Accretion increases the white dwarf's mass and can lead to various phenomena
  • Classical novae occur when accreted hydrogen undergoes thermonuclear fusion
  • Type Ia supernovae result from white dwarfs approaching the Chandrasekhar limit
• Accretion disks form around white dwarfs in close binary systems
  • Disks emit X-rays and ultraviolet radiation due to high temperatures
• Magnetic white dwarfs can channel accreted material along magnetic field lines
  • Creates hot spots on the white dwarf's surface (AM Herculis stars)

White Dwarf Limits

The Chandrasekhar Limit and Its Implications

• Chandrasekhar limit defines the maximum mass of a stable white dwarf
• Theoretical upper limit calculated to be approximately 1.44 solar masses
• Derived from the balance between electron degeneracy pressure and gravity
• White dwarfs approaching this limit become unstable
  • Electron capture by protons reduces electron degeneracy pressure
  • Can lead to collapse into a neutron star or trigger a Type Ia supernova
• Chandrasekhar limit plays a crucial role in understanding stellar evolution and supernovae
• Provides a standard candle for measuring cosmic distances (Type Ia supernovae)
• Recent observations suggest some white dwarfs may slightly exceed the limit
  • Rotation or strong magnetic fields might provide additional support