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Energy Transport

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There are five methods of energy transport, and they all work together: radiation, opacity, convection, mixing, and rotation.


The photon released by nuclear fusion begins its trip to the surface by way of the random walk. The photon must pass through existing molecules, so it goes into a process of re-absorption and re-emission - mostly because of the very high energy of the photon (Wien's Law). In order to determine the distance traveled by every interaction, we measure the "mean free path" of the photon. The distance between interactions is equal to the energy of the photon and the square root of its interactions.

This means the overall displacement (d) will only be high if there are a very large number of interactions. This can take a long time - somewhere along the lines of 10,000,000 years and 2 x 1022 collisions for one photon. The final result of this radiation is a few high energy photons will turn into a larger group of lower energy photons.

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We all know what opacity is, but what this means for stellar physics is the resistive properties of opacity.

This looks worse than it is. What we are trying to determine is with a given intensity, how does opacity affect the final result. An analogy:

We have an open ended tube filled with a density (p) or a material (D) that has a certain mass with an opacity (k) that is called an "absorption coefficient" - which is a known number depending on the material. A photon with a level of intensity (I initial) enters the tube and is resisted by the material in the tube and exists with an altered (less) intensity (I final).

The mechanism of opacity varies, but is based on one of four parameters:

bound-bound absorption an atom with a free orbit of a particular energy level absorbs a photon of equal energy to occupy the gap
bound-free absorption an atom with a populated orbit of a particular energy level is met with a photon with a higher energy level and bumps the electron out of orbit by transferring the energy difference
free-free absorption an electron absorbs the energy of a nearby photon and moves up in energy level
scattering high energy photons can knock an electron out of orbit and does not occupy the gap - both are free

The "mean-free" path when opacity is part of the equation:

A more complicated version is called the Rosseland mean opacity - this is an average of all wavelengths to determine the sum of all the opacity for a given opacity (based on temperature, density, and composition)

There is much more detail in regards to opacity, but what all of this shows is that increased opacity generally decreased temperature and reduces the energy level of photons.

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This is a pretty simple idea because we witness the effects of this on Earth. Hot, less dense air rises while cold, more dense air falls. This is called convection. So can astrophysicists confuse this simple idea? Yes:

Kidding aside, this is actually an easy equation to understand. This is called the condition of convection, and shows what is required: temperature (T), pressure (P), radius (r), and specific heat of the object in question (γ). The value 'd' is just some number - i.e. 'dP' is the value assigned to P.

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The idea of mixing is still new to stellar astrophysics, but basically it is the result of pressure and movement of heavier material outside the realm of radiation or convection. This of adding sugar to tea - you are not altering the composition (or even the temperature) of the tea, you are only mixing the sugar with the tea. However, it is this end result that can be applied to the opacity dynamics.

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Mixing and rotation provide the same interactions of material within the convective layers, but rotation also provides the engine needed for sunspot formation. This is a process of energy transport as the sunspot magnetic field reconnection allows for the liberation of some excess material near the surface of the Sun.

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The Solar Nebula



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