Standard Solar Model - Energy Transport in The Sun

Energy Transport in The Sun

As described in the Sun article, the Sun has a radiative core and a convective outer envelope. In the core, the luminosity due to nuclear reactions is transmitted to outer layers principally by radiation. However, in the outer layers the temperature gradient is so great that radiation cannot transport enough energy. As a result, thermal convection occurs as thermal columns carry hot material to the surface (photosphere) of the Sun. Once the material cools off at the surface, it plunges back downward to the base of the convection zone, to receive more heat from the top of the radiative zone.

In a solar model, as described in stellar structure, one considers the density, temperature T(r), total pressure (matter plus radiation) P(r), luminosity l(r) and energy generation rate per unit mass ε(r) in a spherical shell of a thickness dr at a distance r from the center of the star.

Radiative transport of energy is described by the radiative temperature gradient equation:

where κ is the opacity of the matter, σ is the Stefan-Boltzmann constant, and the Boltzmann constant is set to one.

Convection is described using mixing length theory and the corresponding temperature gradient equation (for adiabatic convection) is:

where γ = c_p / c_v is the adiabatic index, the ratio of specific heats in the gas. (For a fully ionized ideal gas, γ = 5/3.)

Near the base of the Sun's convection zone, the convection is adiabatic, but near the surface of the Sun, convection is not adiabatic.