There are three ways in which energy can be transported in stars:
- Convection - energy transport by mass motions of
elements of the gas.
- Conduction - energy transport by exchange of energy
during collisions of gas particles (usually electrons).
- Radiation - energy transport by the emission
and reabsorption of photons generated in the gas.
Let us first consider conduction and radiation (we will consider
convection later).
Conduction and radiation are similar processes because
they both involve the transfer of energy by direct interaction,
either between particles in the case
of conduction or between particles and photons in the case
of radiation.
Which of the two energy transport mechanisms - conduction and
radiation - is dominant in stars?
The energy carried by a typical particle, 3kT/2, is
comparable to that carried by a typical photon,
hc/
, but the number density
of particles in a star is much greater than that of photons. This means that
the energy density in the form of particles is much greater than that
in the form of photons, so it might be expected that
conduction is a more important mechanism of energy transport
in stars than radiation. However, the smaller number of photons
is far outweighed by their much larger mean free path between
collisions: a photon at a typical point inside a star travels
about 10-2 m before being absorbed or scattered, whereas
a particle only travels around 10-10 m. This means that
photons can get more easily from a point where the temperature is
high to one where it is significantly lower before colliding and
transferring energy, resulting in a larger transport of energy.
Conduction is therefore negligible in nearly all
main sequence stars and radiation is the dominant energy transport
mechanism in most stars.
It should be noted that although the mean free path of photons
is much larger than the mean free path of particles, it is still
very small. This means it takes a long time for a photon to diffuse
from the centre of the Sun to its surface, even though the light
travel time is only ~2 seconds. In fact, it can be shown that
a photon generated near the centre of the Sun will be absorbed
and re-emitted ~1022 times before it escapes
at the surface and the time it takes to do this is approximately
equal to the thermal timescale of
the Sun, which is 3 × 107 years. This means
that when we observe
energy radiated at the solar surface we are usually seeing the results
of nuclear reactions which occurred tens of millions of years ago.
We will now turn to the third form of energy transport -
convection.
©Vik Dhillon, 11th October 2011
