Lies, Damned Lies and Statistical Mechanics - 3

Recapitulation

The earlier blogs in this series explained how quantum mechanics determines the matter phases of the hydrogen in the Sun and the inability of densely packed atoms to absorb heat due to the Pauli Exclusion Principle. Re-examining the star formation process in this light reveals how fusion is possible in cold hydrogen if it is sufficiently densely packed and under sufficiently high gravitational pressure. These conditions would be extremely difficult, if not impossible, to replicate in Earth-bound laboratories. (Having said that, any facility that stores very cold, or liquid, hydrogen under pressure needs to beware.) It was concluded that the physical structure of a star consists of the following main shells/zones in sequence from the centre (heavy elements e.g. fusion products at the centre), fusion, solid, liquid, gas and plasma. The granular appearance of the photosphere is owed to the boiling surface of the liquid. Effects similar to the majority of solar prominences can be seen above vigorously boiling water.

We now turn to the matter of how these revelations affect the solar spectrum.

It is widely stated that orbital electrons can only jump quantum levels if photons of exactly the correct energy collide with them. This is not correct. If sufficiently high energy photons are present, Compton scattering can occur in which an exchange of energy occurs. If the electron is boosted by an inexact energy match, the excess energy is re-emitted.

There is no black body here. Radiation emitted by the hydrogen fusion zone occupies four distinct wavelengths in the gamma region. In the hydrogen shell, where the atoms are too tightly packed, no absorption is possible. As the pressure eases slightly, Compton collisions occur semi-productively. Electrons may initially absorb energy and jump to a higher energy level, but the pressure forces them back again, emitting hydrogen Balmer line radiation as they do so. The overall effect on the photon compliment is shown in the diagram:

In the above event diagram, time runs left to right. Vertical bars mark the occurrence of events. The black path shows the progress of the status of an electron with time while the red paths represent those of photons. The first event represents the collision between photon and electron, at which the electron gains energy at the expense of the incoming photon. The second event represents the electron rebounding to its original energy level and in doing so emitting a new photon. Effectively the collision has resulted in splitting the original photon into two, and the original spectrum has been altered so that one high energy line has been dimmed, and two new emission lines have appeared.

The directions of travel of the photons are also changed so that photons are now much more likely to undergo collisions amongst themselves, resulting in a spread of wavelengths either side of their original values, due to energy/momentum swapping amongst the photons. This gives rise to a pronounced bump around most of the Balmer region, in the spectrograph. Looking at Jack Martin’s Book “A Spectroscopic Atlas of Bright Stars” the Hydrogen Balmer bulge is plain to see in many of the spectrographs.

As the atom density decreases further, longer term absorption can occur, and it is at this stage that the earlier hydrogen emissions can be absorbed, giving the characteristic absorption spike in the spectrograph. Further rebounds can still occur at the lower levels. It is not necessary for the incoming photon to exactly match the energy required for an electron quantum jump, as long as it has sufficient energy for a productive collision to occur.

This process repeats progressively throughout the height of the corona, and beyond, until the matter and photons are too sparse to collide. The original photon energies are therefore progressively reduced through several energy levels. Similar effects are experienced by the atoms of any other elements that may be present in the above-surface medium.

Thus, the solar spectrum is constructed. Observed absorption lines at higher energies are, in some cases, due to absence, or lower rates, of emissions, leading potentially to false identification of elements in the corona. Since the Sun will have formed from a cloud of mixed gas and dust there are probably several trace elements, other than hydrogen, in the corona however one should always look at forbidden lines with suspicion.

Given that each successive shell, working outwards, is hotter than its inner neighbour, convection does not occur anywhere in the Sun.

Another source of real elements, other than hydrogen, in the corona may be sunspots, which are discussed in the next blog.

This is one component of my solution to the solar heat transfer problem.