**Energy transport** inside a star takes place in three ways:

**Radiation**: dependent on*opacity*,*flux, density,*and*temperature.*Larger opacity and flux involve steeper decrease in*T*with increasing*r*.

**Convection**: cool masses move “down” (in the direction of gravitational pull) and hot masses move “up” (against gravitational pull). If the*T*gradient is too steep, convection can play an important role.**Conduction**: generally negligible.

We look more closely at **convection**.

- Its treatment is very complex, and the theory is not yet fully developed.
- It relies on
*Navier-Strokes**equations*in 3-D. - For the study of stellar structure, usually we use 1-D approximations (only spatial variable is
*r*, i.e. we impose spherical symmetry). - The
**pressure scale height**(a characteristic length scale for convection) is in the same order as the size of the star, thus convection is coupled to star’s behavior.

The **model** that we use is that of a **hot bubble** which (1) **rises and expands adiabatically**, and then after travelling some distance, (2) it **thermalizes** with the medium.

This is a thermodynamic model based on state functions (changes in thermodynamic state functions depend only on the starting and final states of the system, and not in the way followed).

The following equation describes how the temperature of the gas inside the bubble changes as the bubble rises and expands adiabatically:

*C _{P}* and

*C*are the specific heat capacities at constant pressure and constant volume respectively.

_{V}**Superadiabaticity**: Case that the star’s actual temperature gradient is steeper than the adiabatic temperature gradient (i.e. inside the bubble). It represents a condition for convection domination:

If “act” is larger than “ad”, all luminosity is carried by convection.

It can be alternatively written as (assuming that the *µ* -mean molecular weight- does not vary):

So, either radiation or convection dominate in different circumstances. When is convection favored?

- Conditions of
**large stellar opacity** **Ionization**taking place, which means large specific heat, and low adiabatic*T*gradient.**Low local gravitational acceleration****Large**of nuclear reactions (e.g. CNO cycle and triple alpha)*T*dependence