ENERGY TRANSPORT MECHANISM IN THE SUN

ALLAN GUEMO ALAURIN

BTTE-1

• Energy generated in the star’s center must be transported to the surface

• Inner layers of the Sun:

• Radiation

• Energy carried by photons

• Outer layers of the Sun:

• Convection

• Energy carried by convective motion of large masses

Energy Transport

• There are three possible mechanisms for energy transport from one location to another: conduction, radiation, and convection.

• Conduction is the transfer of energy within a substance by collisions between atoms and/or molecules. This is not a significant factor in transporting energy within the Sun.

Radiation• The energy produced by the Sun is carried out by

photons emitted at one spot and absorbed at another (radiative diffusion).

• The speed at which photons get out from the Sun depends heavily on its opacity – the ability of a substance to stop photons (the opposite of transparency).

• In the Sun’s core, the photons typically travel 10-6 m before being reabsorbed.

• About 1025 absorptions and reemissions are needed before the energy reaches the Sun’s surface

Convection• Radiative diffusion carries solar energy out to

70% of the Sun’s radius.• At this distance, the temperature has dropped to

1.5 million K and hydrogen atoms start to from, increasing the opacity.

• As a result, the rate of temperature decline becomes steep and convection takes over the energy transport in the outer 30% of the Sun’s radius

• Typically, the diffusion of energy from core to surface takes on average 170,000 years.

• Radiative zone – This region is comparatively transparent to EM

radiation.– energy is carried away from core as electromagnetic

radiation (photons) by the radiative diffusion mechanism.

– However light has a tough time traveling through this region since the solar material in this region is very dense.

– Therefore, it takes light 170,000 years for the energy created at the core to travel through the radiativezone (696,000 km) at a rate of 50cm per hour (20 times slower than a snails pace)

• Convective zone –– In this region the temperature is low enough for

nuclei to join with electrons and form hydrogen atoms, and these absorb light very efficiently.

– Gases are opaque to light, thus convection is the transportation mechanism.

– Therefore, radiative diffusion is not an efficient method of energy transport in this region.

– material(gas) convects energy (heat) to surface.

– Hot gas goes up & cooler gas comes down.

• Conduction –molecule to molecule within a substance

• Convection (and advection) –mass movement of a fluid

• Radiation –absorption of electromagnetic waves

Energy transport in solar interior

• How is energy transported outwards through the Sun?

• Three possible mechanisms:

1. Conduction

2. Radiation

3. Convection

• Role of conduction: gas pressure >> radiation pressure in the Sun,

• so, since the thermal energy of the electrons is greater than that

• of the photons, we might expect thermal conduction to be important.

• But the mean free path of the electrons is tiny compared with the

• dimensions of the solar interior. Thus, thermal conduction is

• negligible in the Sun – at most it makes a very small contribution at the solar core (inner 0.2 Rʘ where Rʘ = solar radius).

Radiation and convection transport in the solar interior

Of the 2 remaining transport processes, energy is transported by radiation in the inner part of the solar interior (0.25Rʘ < r < 0.71 Rʘ) and convection in the outer part (r > 0.71 Rʘ).

We now calculate how the temperature drops off –the temperature gradient dT/dr – with distance rfrom the Sun’s centre assuming first radiativeenergy transport then derive conditions for when convection takes over as the energy transport mechanism.

Role of Radiation energy transfer:Photon transport in the solar interior

• The time for a photon to travel from the solarcore to the solar photosphere can beestimated from a random walk formula. Thephotons are continually stopped by scatteringoff free electrons in the solar interior –Thomson scattering.

• Random walk process:

• Core

– Where the energy is created.

– Nuclear reactions burn every second about 700 million tons of hydrogen into helium.

• Radiation Zone

– Where energy is transported by radiation.

– Although the photons travel at the speed of light, they bounce so many times through the dense material that they use about a million years to escape the Sun.

• Convection Zone

– Energy transported by convection (just like boiling soup) where heat is transported to the photosphere.