# Stellar Astrophysics/Energy Transport

*
This section is unfinished.
*

Within a star there are two main methods of energy transport: **radiation** and **convection**. Both of these take place within our Sun, but occur in different regions of the star. Modelling this transfer is important understand how stars function and evolve over time.

## Radiative Transfer

[edit | edit source]Radiative transfer is the transfer of energy via photons, and is the dominant method of transport within the core of the Sun and in the solar atmosphere. Photons passing through a region of gas can be absorbed while other photons may be emitted from the same region, so to model radiative transfer one must consider both the **absorption** and **emission** of radiation.

### Parallel ray equation

[edit | edit source]In this section, we assume that the light is emitted in parallel rays to the observer. The more general non-parallel case will be considered later.

#### Absorption

[edit | edit source]Imagine there is a column of gas with a side area of and length . Assume that the gas has a number density of absorbing particles per unit volume, with each particle having an effective cross-sectional area when interacting with light of a particular wavelength.

From this, the proportion of area A that blocks the light is:This dimensionless value is called **optical depth**, and is proportional to the amount of light absorbed. The number density can be rewritten in terms of the mass density and average molecular mass as: , which allows the above expression to be written as . is also known as the **mass absorption coefficient**, or the **opacity per unit mass**.

From the definition of optical depth, it can be implied that the reduction in light intensity caused by absorption is:

Therefore, if only absorbtion is taking place, the intensity of the light leaving the column can be determined by integrating over the length of the column: