The Astrophysics Spectator
The Astrophysics Spectator
We can think of light in two ways: as waves of electric and magnetic fields, and as particles. The first way of looking at electromagnetic radiation is the classical way, and it was fully developed in the 19th century. The second way is dictated by experiments that lead to the development of quantum mechanics in the first half of the 20th century. Which of these points of views one adopts depends on the problem under consideration. Generally, when one studies radio wave, the classical physics of electromagnetic fields is used to study the generation and propagation of electromagnetic waves. When one considers visible light, x-rays, or gamma-rays, one generally employs quantum mechanics.
A particle of light is called a photon. The particle nature of light—or equivalently the quantum nature of light—has an interesting implication: one can apply the concepts of thermodynamics to light. This means that we can treat light as a gas of photons, and like any gases, a photon gas is characterized by its pressure, thermal energy, and entropy. If this photon gas is thermalized, which means that the energy of the gas is distributed among the photons in the most probable fashion, it has a distribution of energies that is characterized by temperature alone.
A photon field, however, have two properties that are not normally seen in a conventional gas: photons do not interact with each other, but only with other particles such as electrons, and photons can be created and destroyed. This first property means that a thermalized photon field is always thermalized with some other gas. Often in astrophysics this gas is of free electrons. Second, because interactions among electrons and ions can create and destroy photons, the temperature of thermalized photons not only gives the distribution of energy among photons, but the number of photons per unit volume. In contrast, two independent variables, the temperature and the density, are required to fully describe a gas of ions and electrons.
This live figure shows the black-body (Planck) spectrum. By double-clicking on a temperature cell in the table with the right-hand mouse button, the temperature for that spectrum can be changed. After editing the value, replot the spectrum by clicking on another part of the table. The two sets of buttons define the units of temperature and the units of photon energy. More information on how to control the applet is given by the Applet Control Guide.
A thermal photon spectrum is called the black-body spectrum, or the Planck spectrum. It is the touchstone for understanding the radiation that reaches us from the stars. All processes in astronomical sources try to drive radiation to a black-body spectrum, because this is the most probable state for the distribution of energy among photons; in thermodynamic terms, this is the state with the highest entropy. The black-body spectrum rises proportionally with the square of the photon energy until the peak of the spectrum is reached at hν = kT, where h is the Planck constant, which relates a photon's frequency to its energy, ν is the photon frequency, k is the Boltzmann constant, which relates temperature in degrees Kelvin to energy, and T is the photon energy. Above the peak, the spectrum falls-off exponentially. The total energy density of a black-body radiation field rises as the temperature to the fourth power, so a small increase in temperature increases dramatically the energy density of the radiation field.
Black body radiation is created when electromagnetic radiation is trapped within a thermal gas. The radiation field deep in a star is black body. The temperatures of the black-body radiation in a star's interior ranges from greater than 10 million Copyright �K (slightly less than 1keV) at the core to around 5,000 Copyright �K (0.43 eV) at the surface. Radiation deep in a planet's atmosphere is also black body, but characterized by much lower temperatures than in a star. At the other extreme, neutron stars often have a black-body spectrum that peaks in the x-ray band (above 1 keV); the surface temperatures of these neutron stars are therefore several tens of millions of degrees.
The radiation that emerges from a star's photosphere is generally close to a black-body spectrum. This means that by observing the overall shape of a star's spectrum, one can derive a temperature for the photosphere. If the distance to the star is known, one can derive a luminosity for the star from its apparent brightness. From this measurement and the inference about the photon energy density based on the measured temperature, one can derive an approximate radius for the star's photosphere.
An important instance of black-body radiation is the 3Copyright � background radiation of the universe. This radiation, which was created when the universe was young, sets a lower limit on how cold objects in space can be. In the absence of star light and other sources of heating, an object would radiatively cool until it was in thermal equilibrium with the background radiation, which means that its temperature would equal the background radiation temperature.
