The Sun Notes

The Sun

Physical Properties of the Sun

• The Sun is the closest star, approximately 8 light minutes away from Earth.
• Radius: $700,000 \text{ km}$ or $1 R_{\odot}$ (109 times the Earth's radius).
• Mass: $2.0 \times 10^{30} \text{ kg}$ or $1 M_{\odot}$.
• Density: $1410 \text{ kg/m}^3$.
• Surface temperature (T): $5780 \text{ K}$.
• Luminosity (L): Total energy radiated per second (power). Based on the Stefan-Boltzmann law, where $4\pi R^2$ is the surface area of a sphere.
• $L = 3.84 \times 10^{26} \text{ W}$, which is equivalent to 10 billion 1-megaton nuclear bombs per second.
• Axial tilt: $7.25^\circ$ relative to the ecliptic.
• Rotation: Differential; the equator rotates in 25 days, while the poles take 36 days (average is about a month). The interior rotates differently, similar to Earth’s core, taking 27 days.
• Composition: Mostly Hydrogen (H) and Helium (He).
• Angular diameter from Earth: $32.5' = 0.5^\circ$ (same as the Moon).

The Solar Interior

• The Sun is in hydrostatic equilibrium, where the inward gravitational force is balanced by outward heat pressure.
• Interior Structure (zones):
  • Core: 200,000 km - where nuclear fusion takes place (hottest part of the Sun).
  • Radiation zone: 300,000 km - moves heat by electromagnetic (EM) waves.
  • Convection zone: 200,000 km - moves heat by currents.
• Energy Transport:
  • The radiation zone is relatively transparent, while the convection zone is opaque.
  • Radiation from the interior.
• The visible top layer of the convection zone is granulated, with areas of upwelling material surrounded by areas of sinking material due to currents. These are called granules and are comparable in size to Earth’s continents.

The Sun’s Atmosphere

• Three zones make up the atmosphere:
  • Photosphere: 5800 K (where the surface temperature of the Sun is measured).
  • Chromosphere: 4500 K.
  • Transition zone: 8000 K.
• Corona: Highest temperature (of outer layers) and lowest density.
• Solar wind: Ionized particles that flow outward from the Sun into space.
• The temperature increases in the transition zone. The corona is much hotter than the layers below it, indicating a heat source (still being studied).
• Spectral analysis can identify elements present, but only in the chromosphere and photosphere.
• The most abundant elements in the Sun are Hydrogen and Helium.

Solar Magnetism

• Sunspots: First studied by Galileo in 1613.
• Appear dark because they are slightly cooler than their surroundings.
• Sunspots can be used to determine the Sun's rotation.
• Two parts of Sunspots:
  • Umbra: dark center - 4500 K.
  • Penumbra: lighter surround - 5500 K.
• Can change in size and shape.
• May form in groups over several days.
• Last about 50 days (group). Individual spots can last 1-100 days.
• Sunspots are linked by pairs of magnetic field lines.
• Sunspots originate when magnetic field lines are distorted by the Sun's differential rotation.

The Active Sun

• Areas around sunspots are active regions, which are sites of energetic events in the atmosphere.
• Three types of active regions (in order of least to most energetic):
  • Prominences
  • Flares
  • Coronal mass ejections
• Solar prominence: a loop or sheet of ejected gas due to instability in the magnetic field of sunspots. Can last for days or weeks and can extend 10 times the diameter of the Earth out from the Sun.
• Solar flare: a larger explosion and more violent event that emits a similar amount of energy to a prominence but in seconds or minutes. Less understood.
• Coronal mass ejection: a large “bubble” of ionized gas escapes into space.
  • During solar minimum: once per week.
  • During solar maximum: three per day.
• Coronal mass ejections have the most energy and, if oriented correctly, can merge with Earth's magnetic field, causing disruption in communications and power outages by overloading satellites.
• The Sun has an 11-year sunspot cycle, during which sunspot numbers rise, fall, and then rise again.
• Maunder minimum: a period between 1645-1715 with few, if any, sunspots. This corresponds to the “Little Ice Age,” indicating that changes in solar activity can cause changes in climate on Earth.

Solar–Terrestrial Relations

• The Maunder minimum corresponds to the “little ice age” in the late 1600s and early 1700s in Northern Europe and North America.
• There is a correlation between the Sun’s activity and Earth’s weather, but it is complex and not well understood, posing a problem in terrestrial climatology.
• More is known about the correlation between solar activity and Earth’s geomagnetic disturbance.
• Flares and coronal mass ejections ionize the atmosphere, disrupt electronics, and endanger astronauts.

Fundamental Forces

• Physicists recognize four fundamental forces in nature:
  1. Strong nuclear force: Keeps the nucleus together; short range; very strong.
  2. Weak nuclear force: Responsible for beta decay; short range (1-2 proton diameters); weak.
  3. Electromagnetic: Much stronger than gravity but either attractive or repulsive; infinite in range.
  4. Gravity: Very weak, always attractive, and infinite in range.

The Heart of the Sun

• Heat in the Sun comes from nuclear fusion: the combination of two light nuclei into heavier ones.
• In the Sun, two hydrogen nuclei (protons) fuse into helium.
• Since like charges repel, there must be enough mass so that gravity increases the temperature enough (10 million K) for the protons to reach a high enough speed so that the strong nuclear force will bind them together.
• Nuclear fusion is the energy source for the Sun.
• In general, nuclear fusion works like this: $\text{nucleus 1} + \text{nucleus 2} \rightarrow \text{nucleus 3} + \text{energy}$
• The energy comes from the mass difference.
• Einstein’s famous equation relates mass and energy: $E = mc^2$, where $c$ is the speed of light, a very large number.
• This equation tells us that a small amount of mass is equivalent to a large amount of energy.
• The ultimate result of the process: $4(^1\text{H}) \rightarrow ^4\text{He} + \text{energy} + 2 \text{neutrinos}$
• The helium stays in the core. All hydrogen-burning stars use this to create their energy. The neutrinos escape without interacting.
• The Sun converts 4.3 million tons of matter into energy every second.
• Our Sun has enough fuel for a 10-billion-year lifetime and is halfway through it (5 billion years).
• The Sun has enough hydrogen left to continue fusion for about another 5 billion years.

Observations of Solar Neutrinos

• Most particles take too long to escape the core (a million years).
• Neutrinos emitted directly from the core interact with virtually nothing, with 100 trillion passing through you every second.
• Observing these neutrinos would give us a direct picture of what is happening in the core.
• The only way to capture them is to have a huge detector volume and to be able to observe single interaction events.
• Only see one in $10^{16}$.
• Experiments from the 1960s to the 1990s captured about two neutrinos per week, which is one-third of the expected value.
• The discrepancy between predicted (theoretical) and observed (experimental) neutrino counts is called the Solar Neutrino Problem.
• The solution is that neutrinos can change into other types in the 8 light minutes it takes to travel between the Sun and the Earth. We were only detecting one type.
• If they have mass, then they can oscillate and change types. In 1998, a Japanese group discovered that neutrinos have mass. By 2001 and 2002, other neutrino types were found, and now the observations match (there are now known to be 3 types).

Summary

• Absorption lines in the spectrum tell composition and temperature.
• Sunspots are associated with intense magnetism.
• The number of sunspots varies in an 11-year cycle.
• Large solar ejection events: prominences, flares, and coronal ejections.
• Observations of solar neutrinos show a deficit due to peculiar neutrino behavior.
• Main interior regions of Sun: core, radiation zone, convection zone, photosphere, chromosphere, transition region, corona, solar wind.
• Energy comes from nuclear fusion, which produces neutrinos along with energy.
• The standard solar model is based on the hydrostatic equilibrium of the Sun.