Tutorial on sun

Sun:

The Sun is a self-luminous ball of gas held together by its own gravity and powered by thermonuclear fusion in its core. Our Sun is a typical star among the various stars in the Galaxy, average in mass, size and temperature. It is a ``dwarf'' star (compared to supergiant stars, see AST122 next term) with a radius of 109 Earth radii and a mass of 3.3x10⁵ Earth masses.

The Sun's lifetime is about 10 billion years, meaning that after this time the hydrogen in its core will be depleted. The Sun will then evolve into a red giant, consuming Mercury, Venus and the Earth in its expanded envelope. The Sun is currently 5 billion years old.

The most outstanding characteristic of the Sun is the fact that it emits huge quantities of electro-magnetic radiation of all wavelengths. The total output of the Sun is 3.99x10³³ ergs/sec. Only 1.8x10²⁴ ergs/sec strikes the Earth (since it is small in angular size), which is called the solar constant, but the amount of energy reaching the Earth in 30 mins is more than the power generated by all of human civilization. This energy is what powers the atmosphere and our oceans (storms, wind, currents, rainfall, etc.).

The energy emitted by the Sun is divided into 40% visible light, 50% IR, 9% UV and 1% x-ray, radio, etc. The light we see is emitted from the ``surface'' of the Sun, the photosphere. The Sun below the photosphere is opaque and hidden.

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Solar Structure:

The Sun is divided into six regions based on the physical characteristics of these regions. The boundaries are not sharp.

• fusion core - region of energy generation
• radiation shell - the region where energy transport is by radiation flow
• convection shell - the region where energy transport is by convection cells
• photosphere - the surface where photons are emitted
• chromosphere - the atmosphere of the Sun
• corona - the superhot region where the solar wind originates

The radii and temperatures of these regions are the following:

region                  radius        temperature
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fusion core         0.3 solar radii     15x10^6 K
radiation shell   0.3-0.6 solar radii    6x10^6 K
convection shell  0.6-1.0 solar radii    1x10^6 K
photosphere             100 km             6000 K
chromosphere           2000 km           30,000 K
corona                 10^6 km           1x10^6 K

The Sun rotates differentially since it is not a solid. The solar equator completes one rotation in 25 days. The poles complete one rotation in 36 days.

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Sun's Interior:

Stars form from clouds of gas and collapse under self-gravity. The collapse is stopped by internal pressure in the core of the star. During the collapse, the potential energy of infalling hydrogen atoms is converted to kinetic energy, heating the core. As the temperature goes up, the pressure goes up to stop the collapse. The heat from the collapse is sufficient for the Sun to shine, but only for a timescale of 15 million years (called the Kelvin-Helmholtz time). Since the Sun is 5 billion years old, then it must be producing its own energy rather than shining on leftover energy from formation (like Jupiter).

The structure of the Sun is determined by 5 relations or physical concepts:

1. hydrostatic equilibrium - the fact that pressure balances the self-gravity
   
2. thermal equilibrium - the amount of energy generated equals the amount radiated away
   
3. opacity - the resistance of the solar envelope to the flow of photons (how fast the energy is released)
   
4. energy transport - how energy is transported from the core to the photosphere (convection or radiation)
   There are three ways to transfer energy; conduction, convection and radiation. Conduction, the collisional transfer of energy between atoms, only occurs between solids (such as a hot pan and your hand), so is not found in the Sun. Convection is the motion of heated material, such as bubbles in boiling water. Radiation is the transfer of energy by electromagnetic waves (light). Only convection and radiation transfer are important in the Sun and the opacity determines which method is used. When the temperature is high and all the atoms are stripped of their electrons, the opacity is low and radiation transfer is dominant.
   When the temperature drops, such as in the outer layers of the solar interior, the protons and electrons recombine to form atoms and the opacity goes up. High opacity slows the transfer of energy by radiation, so bubbles form. These bubbles are hot and low in density, thus starting a convective flow.
   
5. energy production - in the case of stars, energy is produced by thermonuclear fusion (see below)

These 5 relationships, described as mathematical formula, show how energy is generated, how that energy effects the structure of the Sun and how that energy is transported to the surface to make the Sun shine.

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Thermonuclear Fusion:

Energy generation is the heart of the solar process. Normally, particles with like charges (positive-positive or negative-negative) repel each other, this is called electrostatic repulsion. But at temperatures above 15x10⁶ K, the motions of protons are high enough to overcome the electrostatic forces and the nuclei can ``fuse''. Nuclear reactions involve many elementary particles that make up all of matter (this is called the Standard Model). The primary output from nuclear reactions are photons in the form of gamma-rays, but a large number of other particles are important as well.

This fusion reaction in the Sun is called the proton-proton chain (the same process that powers H-bombs). It has the following four stages:

All the gamma-rays in the core are scattered many, many times. Each scattering exchanges energy so that the photons convert into visible, UV, IR and radio photons, as well as high energy ones, producing a thermal spectrum.

There are several tests to a solar model produced from the about relationships:

1. Solar oscillations - the Sun is not in perfect balance (hydrostatic equilibrium) but oscillates with periods from 5 to 160 minutes. The details are similar to seismic waves and are used to investigate the density changes in the core.
2. Solar neutrinos - since the interact weakly with matter, solar neutrinos created during the proton-proton chain reactions are a direct look into the current reaction rates. Large underground neutrino detectors, such as the Super Kamiokande in Japan, are currently detecting less than a 1/3 of the number of neutrinos then what is predicted by the equations.