The Big Bang Theory

The Big Bang Theory

About 14 billion years ago, the Universe was much smaller and hotter. In the 1960s, Robert Dicke predicted a remnant “glow” from the Big Bang. In 1965, radio astronomers Penzias and Wilson discovered that glow, named the cosmic microwave background radiation. The CBR was seen in all directions in empty space, with a black body curve (temperature ~3K). About 1 second after the Big Bang, the Universe was very hot, at ~1 billion K. At 3 minutes, protons and neutrons combine to form the nuclei of atoms. The hydrogen/ helium ratio (3:1) found today is about the same as what’s expected after the Big Bang. Atoms were “ionized” with electrons roaming free without being bound. At 300,000 years after the Big Bang, the Universe becomes transparent with a temperature of 3,000K. Light red-shifted by a factor of 1000.

Big Bang: Timeline

*Recent measurements show the Big Bang at 13.75 billion years ago. Scientists recently discovered dark energy; the Universe is not only expanding, but accelerating in expansion. So, earlier estimates of the age of the Universe at 15 billion years have been reduced to 13.75 billion years.

The Universe: Main Points

  1. Expansion of the Universe
  2. Cosmic Microwave Background
  3. Primordial Nucleosynthesis
  4. Evolution of Galaxies and Large Scale Structure Over 14 Billion Years

The Universe: Composition

  • 0.03% heavy elements
  • 0.3% neutrinos
  • 4% stars and gas
  • 25% dark matter
  • 70% dark energy
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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.

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)