Protostars and the Hertzsprung-Russell (HR) Diagram

• Protostar Development:
  • More massive protostars become main-sequence stars faster than less massive ones.
  • Paths in the HR diagram represent tracks of protostars with different initial masses.
  • Stars become visible when they cross the birth line, initiating visible nuclear fusion.
  • Sun-like stars take about 30 million years to form.
  • Larger stars have higher fusion rates and shorter lifespans.
• Brown Dwarfs:
  • Objects <0.08 solar masses cannot ignite hydrogen fusion.
  • Brown dwarfs are not planets; they are sub-stellar objects.

Star Mass Categories

• Lowest Mass Stars (0.08-0.5 Msun):
  • Red dwarfs, with entirely convective interiors, use all their hydrogen, living very long lives.
• Medium Mass Stars (0.5-8 Msun):
  • Less massive use proton-proton chains, while more massive rely on the CNO cycle.
  • End as white dwarfs.
• High Mass Stars (>8 Msun):
  • Use the CNO cycle for energy.
  • Convective interiors and radiative shells.
  • End as supernovae, leaving behind neutron stars or black holes.

Main Sequence and Hydrostatic Equilibrium

• Hydrostatic Equilibrium:
  • Balance between gravity and internal pressure.
  • Stars increase in luminosity and size as they age.
• Main Sequence Band:
  • Zero-age main sequence (ZAMS) marks the beginning.
  • Stars slowly move across the HR diagram as they age.

Life Cycle of a Star

1. Main Sequence:
   • Hydrogen fusion in core.
2. Giant Formation:
   • Core hydrogen depletion leads to helium fusion.
3. Red Giant Phase:
   • Outer layers expand and cool.
4. Helium Fusion:
   • Core reaches sufficient temperature for helium burning.
5. Post-Helium Fusion:
   • Expansion and contraction cycles.
6. End Stages:
   • Low mass stars do not fuse carbon; high mass stars end in supernovae.

Stellar Measurements

• Measuring Masses and Radii:
  • Use Newton's laws, binary star systems.
  • Radii from luminosity and temperature.
• Measuring Ages:
  • Star clusters provide relative ages.
  • HR diagrams show main sequence turnoff points.

White Dwarfs, Neutron Stars, and Black Holes

• White Dwarfs (<8 MSun):
  • Core runs out of fuel.
  • Planetary nebula formation.
  • Electron degeneracy pressure supports white dwarfs.
• Type Ia Supernovae:
  • Occur when white dwarf reaches Chandrasekhar limit.
  • Standard candles for distance measurement.
• High-Mass Stars (>8 MSun):
  • Supernovae produce heavier elements.
  • Remnants are neutron stars or black holes.

Neutron Stars

• Characteristics:
  • Made entirely of neutrons, extremely dense.
  • Formed from collapsing iron cores.
• Pulsars:
  • Rotating neutron stars emitting beams of radiation.

Black Holes

• Formation and Detection:
  • Form from massive stellar remnants.
  • Detected via gravitational influence and accretion disks.
• Gravitational Effects:
  • Gravitational redshift and time dilation near event horizons.

Star-Gas-Star Cycle

• Interstellar medium provides material for new stars.
• Heavy elements recycled through stellar processes.
• Star formation rates in the universe have declined from their peak.

MISC/Summary

• Element Creation:
  • Elements lighter than iron release energy when fused.
  • Iron fusion requires energy input, marking the end in high-mass stars.
• Star Remnants:
  • White dwarfs, neutron stars, and black holes are remnants of stellar evolution.
• Astrophysical Events:
  • Supernovae and neutron star mergers emit significant energy, observable across the universe.