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.

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More About the Sun

The Sun

The Sun: Basics

  • Radius: 696,000 km (109 times Earth’s radius)
  • Mass: 2×10³º kg (332,946 times Earth’s mass)
  • Temperature: 15,000,000 K – center; 5,780 K – photosphere; 2-5 million K – corona
  • Luminosity: 3.8×1026 watts
  • Rotation Period at Equator: 25.4 days
  • Photospheric Composition (by number of atoms): 92.1% hydrogen, 7.8% helium, 0.1% other elements
  • Photospheric Composition (by mass %): 73.5% hydrogen, 24.9% helium, 1.6% other elements

Energy Transport Mechanisms

  • Conduction: most important in solids (e.g. pot over open flame or stove)
  • Radiation: transport of energy by motion of photons; efficiency depends on how opaqueness of the matter (e.g. heater in a cold room)
  • Convection: bulk transport of packets of matter in a liquid or gas (e.g. boiling water — hot water rises, cold water sinks)

Layers of the Sun

  • Radiative Zone: the sun’s center is opaque, so energy takes hundreds of thousands of years to escape
  • Convective Zone: hot gases rise, cold gases sink

Solar Atmosphere (photosphere, corona, chromosphere)

  • Photosphere: 5,800 K; 500 km thick; granulation in solar atmosphere
  • Chromosphere: 10,000 K; 1,000 km thick; red color, Balmer series emission line of hydrogen
  • Corona: 2 million K; large region of high-density plasma

Solar Magnetic Activity

  • Sunspots: magnetic field prevents convective bubbles; lower temperature than rest of Sun’s surface; has magnetic storms; maximum number of sunspots at 11 years, which is half of a 22-year cycle; every 11 years, sunspots’ magnetic fields change
  • Solar Flares: powerful, energetic eruptions that releases magnetic energy, and up to 20 million K
  • Corona Mass Ejections: huge flows of hot gas at 1,500 km/sec

Detecting Solar Neutrinos

  • Neutrinos: matter that interact very weakly with normal matter; the interior of the Sun is transparent to neutrinos (discovered in 1956 by Clyde Cowan and Frederick Reines)
  • First neutrino “telescope” at Homestead gold mine, South Dakota: used 400,000 liters of dry-cleaning fluid (perchloroethylene -C2Cl4) because a neutrino can interact with a chlorine nucleus to form an argon nucleus
  • Only 1 out of 10²² passing neutrinos reacted, once every two days
  • 1/3 of expected neutrinos detected based on understanding of the proton-proton chain
  • Other experiments: Sudbury Neutrino Observatory (1,000 tons of heavy water) and Super-Kamiokande experiment in Japan (50,000 tons of water)

Light and Black Body Radiation

Light is composed of mass-less infinitesimal particles called photons that travel at the speed of light (300,000,000 m/s).

Electromagnetic Spectrum

THE ELECTROMAGNETIC SPECTRUM: depicts the different wavelengths and energies of light

Radio Waves –> Microwaves –> Infrared Light –> Visible Light (ROYGBIV) –> Ultraviolet Radiation –> X-Rays –> Gamma Rays (longest –> shortest wavelengths, lowest –> highest energies)

  • The Electromagnetic Spectrum and Stellar Spectra = continuous spectrum (energy emission over a  broad range of wavelengths – curve)
  • Laser = line spectrum (energy emission at a narrow range of wavelength – peak)

Black-bodies at Different Temperatures

A “black-body” is an object which absorbs all light incident on it and doesn’t reflect or transmit any light. Black bodies are perfect emitters of light. Their classification depends only on temperature, and not other properties such as chemical composition; hence, black-body radiation is also “thermal” radiation. In 1900, Max Planck discovered that a black body emits an energy spectrum of light. Black body radiation includes lava flow (800 K), incandescent light bulbs – tungsten wire heated (2,800 K). Comparing two black bodies of different temperatures, the hotter black-body will: 1) emit more radiation (more luminous); 2) emit more photons; 3) peaks at shorter wavelengths; 4) have a bluer color. Measuring the shape of a star’s spectrum can reveal the star’s temperature.

Wien’s Lawγ peak = 2,900 μm K/ T; using the wavelength of the black-body’s spectrum’s peak to determining the star’s surface temperature

Luminosity: amount of energy radiated by an object per second, in Watts

Brightness: how bright an object appears as seen by an observer; also known as flux received from the star

Stefan- Boltzmann LawL = σT4 x surface area, where L = luminosity, T = temperature, and σ = 5.67 x 10-8 W/ (m²•K4), Stefan-Boltzmann constant; to determine a star’s luminosity

 Apparent Brightness: how bright stars appear to the observer; depends on luminosity and distance

  • considering a set of photons that emerge at the same moment from the star’s surface, the spherical shell of photons is 4∏r², where r = distance from the star
  • L/4∏r² (L = luminosity) = energy per second per surface area of photons
  • apparent brightness or flux: b = L/4∏r²

Absolute Brightness: considering temperature and mass and disregarding distance, how bright the stars actually are

PHOTONS AND THE ATOM

The Atom

The Atom and Its Subatomic Particles

  • Subatomic particles: Electrons (-), Protons (+), and Neutrons (neutral)
  • The mass of a proton is 1830 times the mass of an electron; the mass of a proton is approximately equal to the mass of a neutron
  • While protons and neutrons form the atom’s nucleus, electrons have discrete energy levels in atom
  • The electron can only be on energy levels, not in between
  • Outer orbits have higher energy than inner orbits
  • Most of the space within an atom is empty!

Absorption/ Emission: Photons

Photons: Emission and Absorption

  • Photons are emitted in random fashion (cascade from level to level or all at once – from current level to the ground state, or the lowest energy level, the closest to the nucleus)
  • Absorption of a photon causes the electron to a higher energy level
  • A photon can only be absorbed if its energy is equal to the difference in energy between two energy levels
  • An electron can only stay in a higher energy level for a very short time
  • Ionization: If a photon is large enough, it can kick the electron out of the atom
  • Recombination: When a free electron becomes bound to an atom
  • Electrons give up energy by emitting a photon

Emission Lines from Gas Clouds

Emission Line Spectrum

  • A dilute (non-opaque) gas cloud is not a back-body emitter
  • Atoms in a hot, dilute cloud of ionized gas will emit a characteristic pattern of spectra lines (Emission Line Spectrum)

Absorption Line Spectra

Absorption Spectrum

  • Normal stars have absorption lines
  • Black-body radiation originates from the star’s interior