Nuclear Fusion: What Fuels Stars

CONTRACTION OF PRE-MAIN SEQUENCE STARS

  • The interior heats due to gravitational contraction and radiates away this energy as black-body radiation
  • At 10K, fusion starts, pressure increases, and the star establishes hydrostatic equilibrium (the balance between gravity and gas pressure)
  • As gravity pulls inwards (fusion releases energy, and maintains the core’s high temperature), gas pressure pushes outwards (high temperature prevents the star from collapsing under its own weight)
  • When a star reaches hydrostatic equilibrium, it enters main sequence

* Energy produced more efficiently at core’s center

Difference Between Fission and Fusion

Nuclear Fission vs. Nuclear Fusion

Fission: splitting heavy nuclei into lighter ones (e.g. atomic bombs and nuclear reactors derive their energy from fission of uranium or plutonium)

Fusion: merging light nuclei into heavy nuclei (e.g. how stars shine, hydrogen bombs, “nuclear burning” – different from ordinary chemical burning processes)

Strong Nuclear Forces: protons in the nucleus repel by electrical forces, but strong nuclear forces, which can only occur at close distances, keep the atom together. As temperature rises, protons move faster. When 2 protons fuse, the output is 1 neutron, 1 positron, and 1 neutrino.

How Fusion Works: Proton-Proton Chain & CNO Cycle

Common Elements (and Their Isotopes) Involved in Fusion: ¹H (hydrogen) [1 proton], ²H (deuterium) [1 proton, 1 neutron], ³H (tritium) [1 proton, 2 neutrons], ³He (helium-3) [2 protons, 1 neutron], 4He (helium-4) [2 protons, 2 neutrons]

Proton-Proton Chain

Proton-Proton Chain

Step 1: 2 hydrogen nuclei –> deuterium nucleus => releases positron + neutrino

  • Positron (e+): antimatter of electron
  • Neutrino (ν): unchanged particle that only interacts very weakly with normal matter

Step 2: deuterium + hydrogen nuclei –> helium-3 => releases gamma ray

-> Repeat first two steps.

Step 3: 2 helium-3 –> helium-4 => releases two protons

Summary

Input: 6 protons

Output: 2 positrons, 2 neutrinos, 2 gamma rays, 1 helium nucleus, 2 protons

Net Output: 4 protons –> 1 helium-4 => releases 2 positrons, 2 neutrinos, 2 gamma rays

0.7% of the total mass of 4 protons is converted into energy, while 99.3% results in 1 helium nucleus. Some of the mass is converted into energy. Since E = mc², a little mass and release tremendous energy. While at rest, however, energy is equal to mass.

CNO Cycle

CNO (Carbon-Nitrogen-Oxygen) Cycle

The CNO Cycle is the main nuclear burning chain in main sequence stars hotter than the Sun. Using carbon as a catalyst to convert hydrogen into helium, the CNO cycle also converts 7% of hydrogen’s mass into energy; hydrogen fuses with carbon to form helium. 10% of the Sun’s nuclear fusion reactions is from the CNO Cycle. In 1967, Hans Bethe theorized on the energy production in stars.

Evolution/ Death of Low-Mass Stars

Evolution of Low-Mass Stars

  • For stars on the main sequence, luminosity is proportional to the star’s mass to the 3.5th power (L α M3.5)
  • For the Sun: original composition about 30% helium in mass –> today – 65% helium –> 5 billion years later: 100% helium
  • The total amount of hydrogen “fuel” in a star is proportional to the star’s mass; the rate of fuel use is proportional to luminosity; lifetime α mass α 1/L
  • The Sun’s main sequence lifetime is 10¹º years; its entire lifetime is 10¹º + 1/M2.5 years, where M = the star’s mass in solar masses

How Lifetime, Luminosity, and Mass Compare Among Various Spectral Types

Spectral Type  Mass (M☉)   Luminosity (L☉)  Lifetime (years)

  • O5                        60                          800,000                        3 million
  • A5                         3                                55                              4 million
  • G2                        1                                  1                             10 billion
  • M0                      0.5                           0.08                             70 billion
  • M5                      0.2                           0.01                           190 billion

Stars with masses below 0.8 M☉ have never left the main sequence and have lifetimes longer than the current age of the Universe.

Post- Main Sequence

  • Core can’t maintain its balance between gravity and pressure; gravity compresses the star to a much smaller size
  • Electron Degeneracy Pressure: halts collapse of the star
  • Core’s radius swells to several thousand km, or about the size of Earth
  • Hydrogen converts to helium at  a very rapid rate; luminosity more than 1000 times greater than before; star swells to enormous size

Red Giant

Red Giants: 50x Sun’s radius, 1000x Sun’s luminosity

  • H –> He in a shell
  • Helium core swells to the size of Earth; no fusion anymore
  • Non-burning hydrogen atmosphere
  • Helium fusion needs higher velocities and energy to overcome repulsion
  • At 100 million K, helium atoms yield carbon atoms, also known as “helium flash”
  • Triple-Alpha Process“: 4He + 4He –> 8Be; 4He + 8Be –> ¹²C
  • In half an hour, half the helium yields carbon in the core
  • Horizontal Branch Star: after the core expands and the star enters a steady phase (50-100 million years) of helium burning and becomes less luminous

    Evolution of Low-Mass Stars: H-R Diagram

  • Core contracts again, He –> C in a shell around the core; hydrogen burning shell around that layer
  • Asymptotic Giant Brand“: star moves upward toward the H-R Diagram “Red Giant” area, exceeds 10,000 L☉

*Blue-Stragglers: stars in a dense environment; when two stars collide, the core could be “rejuvenated,” giving the star extra lifetime

Planetary Nebula

Planetary Nebulae

  • The outer layers, about 20% of the star’s mass, are ejected in a strong wind
  • Gas is ionized by UV protons from hot, exposed stellar core
  • Star shines for 50,000 years before gases disperse and fade
  • About 1,000 in the Milky Way Galaxy
  • Have many shapes and sizes because of binary star systems’ different orbits, temperature, rotation, luminosity, mass

Binary System: Sirius A (brighter, Main Sequence) & Sirius B (dimmer, white dwarf)

White Dwarfs:  (0.6 – 0.7 M☉) bare core of a star often all fusion reactions ended, supported against gravity by electron degeneracy pressure; density at 1 million grams/cm³

  • e.g. Sirius A: Main Sequence, A1, -1.5; Sirius B: white dwarf, 8.5

End States: Initial Mass and White Dwarf Composition

  • >0.45 M☉: helium
  • 0.45-4 M☉: carbon, oxygen –> (Sun)
  • 4-8 M☉: oxygen, neon, magnesium