The radiation does not leak out quickly because it is connected with the matter through the processes of absorption and emission. In¬deed, as noted above, the typical mean free path of a photon is about 1 cm. A measure of the resistance to radiation is the opacity of the material: this quantity indicates how difficult the radiation finds it to get through the material. Any process which causes a photon to deviate from its path will contribute to the opacity. In simple terms we can see that the main sources of opacity are scattering and absorption. Scattering takes place when the photon is hindered in its chosen path by an interaction with a particle, usually an electron, but sometimes an atomic nucleus. In the scattering processes the photon maintains its identity; it is not destroyed, but its direction is altered. In an absorption process the photon is absorbed; it is destroyed and it gives its energy to an electron, which consequently changes its relationship with an atom. When an electron is orbiting an atom we call it a BOUND ELECTRON. If the electron is initially bound to the atom and, after absorption of the photon, it remains bound, but in a higher energy state, the process is called BOUND-BOUND ABSORPTION. Sometimes after absorption the previously-bound electron may be given enough energy by the absorbing photon to ionize the atom, that is, the electron frees itself from being tied to the parent atom; such a process is called BOUND-FREE ABSORPTION. The last main process is FREE-FREE ABSORPTION in which an electron not bound to an atom absorbs a photon and in¬creases its energy still further while remaining free of an atom. All of these absorption processes may be followed by analogous emission processes which may return photons of the same or different energies to the energy transport pool. Scattering and absorption give opacity to the stellar material. Atomic physics and quantum mechanics enable us to estimate the total opacity.

Having outlined the physical processes that tend to slow the flow of energy from a star, it is interesting to ask ourselves how long it takes energy to move from the deep interior of a star, where it is created, to the surface, where it will journey through the Universe. We will therefore work out the transport time for solar energy. A rough estimate can be made of the time it takes radiation to leak out from the centre to the surface of the Sun, by remembering that the mean free path of a photon is typically 1 cm. The leaking process is similar to what mathematicians term a RANDOM WALK. In a random (or drunkard’s) walk successive steps are taken in an arbitrary direction. The average effect is that after N steps of unit length the object is \/N distance units from the place where the walk commenced (figure 3.6). In a random walk of 100 paces of 1 metre each, the average drunkard would end up only 10 metres from the place where he gets drunk; after 10,000 paces he will have managed 100 metres! A step of 1 cm for a photon and a solar radius of about 109 m (10ucm) means that VN = 1011, or N = 1022. Therefore 1022 steps of 1 cm each must be made by a photon in random walking its way out from the centre to surface of the Sun.

The total distance travelled is 1020m (10aacm). After the 1022 steps, or interactions, the average photon reaches the surface. note that in random walk we cannot predict where on the surface a given packet of energy created in the star centre will finally emerge ; this is the essence of the natural randomness of the the process now that we have estimated statistically the distance that a photon has to travel aimlessly ,we can work out correspondingly the length of time it dallies on its journey. Since the speed of photons is that of light. (c — 3x 108 ms- l) we find a time of 104 years. This estimate is very approximate and only gives an idea of the order of magnitude of the quantity involved. However. it does imply that a long time elapses before the outside of a star is aware of any thermal changes in its deep interior. A more rigorous calculation would give a time of 107 years: the discrepancy is due to the assumption that the mean free path of the photon is always 1 cm.

Whatever the mode of heat transport in a star there is a mathematical equation that relates the flux of energy transported to the physical quantifies (pressure, temperature, etc.) at every point of a star. This is called the ENERGY or HEAT TRANSPORT EQUATION .

There is one extra aspect which is important when energy trans¬port is by convection, namely mixing. In convection, material is moving in order to carry the energy, so that layers of a star that are convective are mixed up. Within a short time the chemical structure becomes uniform throughout the stirred-up layer of a star.By contrast, in the radiative and conductive layers of a star the material is not moving significantly: therefore each layer retains its own chemical composition, which may be influenced by any nuclear transmutations taking place there.

We can summarize as follows the way in which a star works: the mass of the star supplies the strong self-gravitational force which in equilibrium must be checked by an opposing pressure force. The thermal structure of the star, which is related to the heat How and the pressure structure,, requires a temperature gradient. Energy flows from the interior and through the stellar surface and the star shines. Several disciplines of physics, including dynamics, thermodynamics, quantum mechanics and atomic physics, have been used to deduce this basic structure.

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