Question and Answer from an OU 2nd level astronomy course.
Q. Describe how photons are generated in the core of the Sun, the order of magnitude of the time it takes them to reach the photosphere, the changes in the spectrum of the photons as they travel from the core to the photosphere and why there are no great changes in the photon spectrum as they travel from the photosphere to Earth.
A. Photons are produced in the core of the Sun by the process of nuclear fusion. In the Sun, this is the process, whereby relatively low mass nuclei of hydrogen collide and fuse to form comparatively heavy nuclei of helium. Energy is released in the form of high frequency Gamma rays that are photons of electromagnetic radiation. The ppI chain is the nuclear reaction responsible for most of the Sun's radiant energy. The result of this nuclear fusion reaction, is that four hydrogen nuclei are converted into one helium nucleus, with the release of electromagnetic waves of gamma rays.
The time taken by the photons to reach the photosphere is about one million years, which in seconds is:- (106 × 365 × 24 × 60 × 60)s = 3.15 × 1013s which, when expressed as an order of magnitude is 1013s.
If the Sun were transparent it would take photons released at the core and travelling at the speed of light, 2.32s to reach the photosphere.
This is calculated by the formula R/c where R is the radius of the Sun (6.96 × 108m) and c is the speed of light in a vacuum (3.0 × 108ms-1).
R/c = 6.96 × 108m/ 3.00 × 108ms-1 = 2.32s.
The main method of energy transport in the central 70% of the Sun's radius is by radiation. The photons emitted in the core collide with other particles every few centimetres and are either scattered, or absorbed and emitted. After emerging from these encounters they have a fifty/fifty chance of travelling in any direction, therefore their progress to the surface is entirely random. This is known as a random walk and the energy generated in the core spreads outwards in a gradual 'diffusive' process. The temperature gradient for the remaining 25% - 30% of the Sun's radius up to the photosphere, is such that the method of energy transport is by convection. Conventionally, these regions are called the radiative zone and the convective zone.
As the photons travel outwards from the core, the temperature decreases. The energy of the photons is gradually reduced as they are influenced by the particles that scatter and absorb them. The energy is not lost, but shared and redistributed by ever increasing numbers of photons. The radiation is said to be in local thermodynamic equilibrium with the material it is passing through. Where the temperature is T, the spectrum is about that of a black-body source at temperature T. The end result is that the gamma ray photons produced in the core at 1.5 × 107K, emerge at the photosphere predominantly identical to the spectrum of visible light at 6 × 103K.
The solar spectrum is approximately that of a black body at 6000K and the Earth's lower atmosphere is at a temperature of approximately 300K. The reason for this is that because the Earth's atmosphere is mainly transparent to sunlight, there are very few reactions between sunlight and the air in the Earth's lower atmosphere so there is little chance of creating local thermodynamic equilibrium. Therefore the photon spectrum from the photosphere reaches the Earth with very little change.