# Energy Transport in stars

I'm trying to understand why convection is an efficient mode of energy transport in the outer layers of the solar interior.

Could anyone give me a little bit of knowledge?

Heat transfer can be achieved by conduction, convection, and radiation. Conduction is more or less a non-factor with regard to heat transfer in stars, leaving convection and radiation. Which of the two dominates over the other depends on the temperature gradient, gravitational acceleration, heat capacity, and opacity.

A packet of gas warmer than the surrounding gas will temporarily rise due to buoyancy. Such a rising packet of gas cools more or less adiabatically as it rises. A low temperature gradient means that a rising warm packet quickly becomes cooler than the surrounding gas; the packet falls back close to where it started. Convection cannot occur if the temperature gradient is lower than the adiabatic lapse rate. Convection can occur if the temperature gradient is greater than the adiabatic lapse rate, and if convection can occur, it will occur and it will dominate over radiative transfer.

The fusion rate is so low in small stars that even the core is convective. Small stars are mildly convective throughout. The extremely temperature sensitive CNO cycle dominates over the p-p chain in very massive stars. This makes those very large stars have a convective core. The large outer shells of those very large stars results in a low temperature gradient outside the core, thereby disabling convection outside the core. Mid-sized stars, between about 2/3 and 3/2 solar masses, have a low temperature gradient in their cores, making their cores unable to sustain convection. The outer shells of those mid-sized stars have a temperature gradient that is large enough to sustain convection.

• Conduction is a non-factor in non-degenerate stars. It is totally dominant in white dwarfs and neutron stars. – Rob Jeffries Apr 22 '18 at 16:02

convection is efficient in that part of a star because radiation, which one might otherwise expect to be the dominant mode of heat transfer, is inefficient inside a star for the following reason: owing to its temperature, the inside of a star is opaque to most photons. They are efficiently scattered off charged particles and hence have very short mean free paths inside a star. Bulk convection is therefore the primary means of transferring heat out of the star's fusion core.

The only exception to this is energy transfer via neutrinos, to which most stars are almost transparent. But since the earth and all of us are similarly transparent to neutrinos, the solar neutrinos are not a source of heat from the sun.

• You last paragraph got me wondering how much energy main sequence stars lose as neutrinos compared to the EM radiation they emit. A quick googling suggests that it's around 1%, but it'd be nice to have more definite figures. So even if a star (and everything else) weren't almost completely transparent to neutrinos they'd only have a very minor impact on the energy transport within the star. – PM 2Ring Apr 22 '18 at 5:44
• right, but then the supernova happens!!! – niels nielsen Apr 22 '18 at 6:14
• @PM2Ring 2% for the Sun. – Rob Jeffries Apr 22 '18 at 16:03
• Thanks @Rob. I guess that 2% figure would apply to all stars that are primarily performing p-p fusion? – PM 2Ring Apr 23 '18 at 11:52
• "then the supernova happens", Well sure, but that's why I was careful to specify "main sequence star". ;) – PM 2Ring Apr 23 '18 at 11:53

David Hammen’s answer went into the issue of convective instability, but I can add some details.

Radiative transport is an efficient mechanism for heat transport when the opacity is low, but it gives way to convection when the opacity is high. What happens is this: If the opacity is high, a steep negative temperature gradient is (or would be) needed to transport the heat flux out. Now if a blob of plasma is somehow displaced upward, entering a region of lower hydrostatic pressure, it will expand adiabatically and cool, according to the rule $T\sim {{P}^{2/5}}$, given $\gamma =\tfrac{5}{3}$ for plasma. If the blob is now cooler and denser than the ambient temperature, it will sink back, but if warmer and buoyant, it will continue rising. The conclusion: Wherever the conductive or radiative temperature gradient would be steeper than the adiabatic temperature gradient, there will be convective instability.

You now ask: Why is opacity high in the Sun’s outer layers? I’m no expert, but I think it has to do with bound-free transitions in incompletely ionized gas.

Convective instability is also at work in the Earth’s atmosphere. The lower atmosphere has a relatively high opacity to infrared radiation, due mainly to density, and is convectively unstable in daytime, but the instability abates at night, after the ground has cooled and less energy needs to be transported. Convection normally stops at the tropopause, roughly 11 km above the ground, but the buildup of greenhouse gases may change that.

Turbulent convection in the Earth’s outer core is what drives the geomagnetic dynamo. You can thank low thermal conductivity in lieu of high opacity for the instability. The operative power source is thought to be the settling of heavier elements, thereby releasing gravitational potential energy. Pure iron then freezes out under extreme pressure onto the solid inner core, releasing a little more.

Why convection is an efficient mode of energy transport ...

For an overly simple explanation see: "What’s the Difference Between Conduction, Convection, and Radiation?".

• Conduction is molecule to molecule, the rate related to the size.

• Convection involves a huge movement of mass, and it's energy.

• Radiation comes from the surface.

Note that the above explanation leaves out a lot, on purpose. Was a more complicated answer desired?

• The process of heat conduction depends on the following factors: temperature gradient, cross-section of the material, length of the travel path, and physical material properties.

• A space heater is a classic convection example. As the space heater heats the air surrounding it near the floor, the air will increase in temperature, expand, and rise to the top of the room. This forces down the cooler air so that it becomes heated, thus creating a convection current.

• Thermal radiation generates from the emission of electromagnetic waves. These waves carry the energy away from the emitting object. Radiation occurs through a vacuum or any transparent medium (either solid or fluid). Thermal radiation is the direct result of random movements of atoms and molecules in matter.

Emissivity for an ideal radiator has a value of 1. Common materials have lower emissivity values. Anodized aluminum has an emissivity value of 0.9 while copper’s is 0.04.

Emissivity is defined as an object’s effectiveness in emitting energy as thermal radiation. It is the ratio, at a given temperature, of the thermal radiation from a surface to the radiation from an ideal black surface as determined by the Stefan-Boltzmann law.