The Astrophysics Spectator
The Astrophysics Spectator
We are fortunate that most sources are out of thermal equilibrium. Among electromagnetic spectra, the thermal spectrum contains the least information. With a black-body spectrum we can determine the temperature, and therefore the energy density, at the source, but nothing more. We cannot even determine a velocity from a Doppler shift, because a Doppler shifted thermal spectrum simply looks like a thermal spectrum of a different temperature.
To derive more information from a spectrum, we need to observe features that are created through well-known processes. This occurs when light from a source is created either by a non-thermal plasma or by a plasma that is locally thermal but has a range of temperatures. Radiation created under such conditions will deviate in telltale ways from a thermal radiation field, which gives us a more information about conditions at the source. As you see, the study of astronomy is the study of the universe out of equilibrium.
An atmosphere is said to be in local thermal equilibrium, often abbreviated as LTE in the astronomy literature, when at each point the electrons and ions are described by a thermal energy distribution, but the temperature of that distribution varies from point to point. Atmospheres of stars and planets are generally in local thermal equilibrium. In a star, the temperature falls as one moves out, until the chromosphere is reached, and the temperature begins to rise again.
Radiation that passes through such an atmosphere attempts to come into thermal equilibrium with the plasma as it flows through the photosphere into space. But by the definition of what the photosphere is?the point where the probability of a photon interacting with the plasma is roughly equal to the probability of a photon escaping into space?the radiation does not have time to come fully into equilibrium with its surounds. Instead, the radiation is a distorted black-body spectrum. The nature of the distortion depends on the form of the interactions between the plasma and the photons and on the precise temperature structure.
The plasma in a stellar atmosphere is partially ionized. This means that some of the electrons in the gas are free, and the remainder are bound to atomic nuclei to form ions. The ions interact strongly with electromagnetic radiation, which is a consequence of quantum mechanics. The electrons that are bound to a nucleus are restricted by quantum mechanics in the energy that they carry. There is a finite separation in energy between each of the possible energy states. In every atom, there is one level with the lowest possible energy, which is called the ground state, and then an infinite number of higher levels, with the amount of energy between a level and the next higher level being of finite value. The energy separation between states goes to zero as the energy level increases. The energy separation between the ground state and the uppermost levels goes to a finite value as the upper levels go to infinity. Above this finite energy separation between the ground state and the infinity of upper level, an electron becomes unbound from the ion; there are a continuum of such energy levels, rather than an infinite number of finite energy separation.
If an electron in one energy is to transition into another energy state, it must receive or give up the finite amount of energy that separate the two states. This energy can be transferred through a collision with an electron or an ion in the plasma, which keeps the distribution of levels in the ions at their thermal value, or it can be transferred through an interaction involving a photon, which acts to bring the radiation field into thermal equilibrium with the bound electrons.
Only photons that can change an electron's energy can interact with the plasma. If, for instance, a photon has enough energy to move an electron from the ground state to the first energy state, it can be absorbed by a ground-state electron. On the other hand, a photon with half more than this energy, but less than the energy separating the ground state from the second energy level cannot interact with a bound electron, and the medium of ions appears transparent to this photon.
The energy separation between lines and the position of the ground state varied depending on the atomic nucleus of the ion and the number of electrons bound to the ion.
So we have the two pieces of physics that explain why the spectra of stars have lines. Lines in a radiation field are produced when a radiative field characterized by one temperature interacts with ions of another temperature. The photons with energies that cannot cause an atomic transition are unaffected, and enter space with the energy density expected for a thermal radiation field. These photons form the continuum spectrum of a source. The photons that can cause transitions between atomic energy levels, however, interact and thermalize with the ions, being driven to an energy density that is characteristic of a thermal radiation field with the temperature of the ions. For a hot radiation field passing through a cooler atmosphere, which characterizes most of the emission through the atmosphere of a star, this interaction produces absorption lines, which are dips in the continuum spectrum. A cool radiation field passing through a hot region, on the other hand, acquires emission lines, where the energy density of photons is higher than in the surrounding continuum.
These lines, because their positions are fixed by fundamental physics, provide the means of calculating a redshift for a moving object. They also contain information about the temperature structure and composition of the atmosphere. Evidence of the amount of ionization in the plasma also gives us a measure of the density, because density determines the rate at which ions capture electrons.
