What is Newton's black body

Why you can see heat

The connection between temperature and the emission of electromagnetic radiation - and the consequences for stars, disks of matter around black holes, and for cosmology

An article by Markus Pössel

Bodies or physical systems that are connected to one another in such a way that they can exchange energy, come into thermal equilibrium over time and then all have the same temperature. We use this fundamental fact almost constantly in everyday life - when we turn on a heater, we rely on the fact that in the end not only the heater but also the room air is warm. And that we turn on a hotplate is not an end in itself, but we trust that the heat is passed on to a pot and its contents, for example.

Even in everyday life, of course, there is still another system present that we usually do not even perceive as such: the entirety of the electromagnetic fields in the relevant spatial region, from radio waves and infrared rays to visible light to UV light and even more energy-rich radiation variants . This system is also in constant contact with other objects - and naturally also strives for thermal equilibrium.

Thermal radiation

This has characteristic consequences that we also know from everyday life: hot bodies emit clearly perceptible amounts of thermal radiation and light. The following illustration shows the glow of a red-hot stove top:

The background to this phenomenon? Bodies transfer their energy not only to other bodies with which they are in thermal contact, but also to the electromagnetic field - in other words, they emit electromagnetic radiation. The energy transfer - and thus the energy of the emitted radiation - is stronger the higher the temperature of the body in question.

The radiation emitted in this way has a very characteristic spectrum - a characteristic system of how much energy of the radiation is allocated to which radiation frequency, how much energy is emitted, for example, in the form of green light or infrared light. The spectrum only depends on a single parameter: the temperature of the radiating body. Such radiation is called Thermal radiation or thermal radiation designated.

The spectrum of a black body

The simplest case is that of a body that can in principle absorb and re-emit any type of electromagnetic radiation, regardless of the frequency of the radiation. Such an idealized object is called among physicists Black body. The spectrum of radiation emitted by such a body always looks roughly like in the following graphic. The frequency is plotted horizontally, the radiated power vertically at the corresponding frequency (i.e. how much energy is emitted at the corresponding frequency per unit of time):

As can already be seen in the figure: At very low frequencies (left part of the curve), comparatively little energy is emitted. Then a maximum follows at a certain frequency, and at the higher frequencies (to the right of it) significantly less energy is emitted again. The maximum lies at the higher frequencies - the further to the right - the higher the temperature is (so-called Wien's law of displacement). The total amount of radiated heat even increases with the fourth power of the temperature: If the temperature of an object doubles, it then radiates 16 times more energy in the form of heat radiation! (This fact is called the Stefan-Boltzmann law among physicists, or simply “T-to the power of four law”.)

The exact course of the curve was first determined by Max Planck in 1900 and is therefore also called the Planck spectrum. (Incidentally, some unusual assumptions about the properties of electromagnetic radiation, which Planck required when attempting to derive his radiation formula, led to a very special physical revolution - the development of quantum theory.)

Many hot objects in everyday life are not perfect black bodies, but their properties come very close (at least in certain frequency ranges). Accordingly, many readers should know examples of both the shift in the frequency maximum and the increase in the total radiated power. A stove top, see the photo above, initially only glows very weakly and dark red: It emits comparatively little energy in the form of thermal radiation, and this above all at rather lower frequencies (infrared and red light). As the temperature rises, the color of heated iron - such as a poker in the fireplace - changes to reddish-yellow, and more and more energy is emitted. The latter is used for lighting in electric light bulbs - inside a light bulb, a metal wire is heated to very high temperatures with the help of an electric current.

Thermal radiation and star colors

But thermal radiation and more or less black bodies are also of great importance in astrophysics. The color and luminosity of stars, for example, follow the laws of thermal radiation. How much energy a star emits per unit of time results directly from the temperature of the star's surface layer, which is decisive for light emission (this is the “effective temperature” of the star) and from its size. And as already said: the temperature determines the energy distribution, the shape of the spectrum. This means that astronomers can see directly what temperature their surface is on objects such as stars!

As with the glowing hotplate, this temperature also determines the color of the star. Some star colors and temperatures are approximated here:

Sirius (α CMa), effective temperature 10200 Kelvin
Sun, effective temperature 5800 Kelvin
Capella (α Aur), effective temperature 5500 Kelvin
Betelgeuse (α Ori), effective temperature 3100 Kelvin

[Converting the spectrum of thermal radiation into computer-compatible colors (RGB) has some pitfalls. More information can be found on the website What color are the stars? from Mitchell Charity, from which I also took the colors shown here.]

The temperatures are all given in Kelvin. The colors can also be roughly traced in the night sky: There the “red giant star” Betelgeuse (Orion's left shoulder star) actually shimmers much more red than the dog star Sirius.

Black holes and cosmology

Stars are all well and good, but last but not least - this is the motivation for this specialization topic - thermal radiation plays an important role in relativistic astrophysics and cosmology.

When matter falls on a black hole, an extremely hot vortex of matter, the accretion disk, forms in its immediate vicinity. With its extreme temperature, it emits enormous amounts of radiation; the radiation maximum is at very high frequencies, with electromagnetic radiation in the X-ray range. (For more information, see the specialization topic Glowing Disks: How Black Holes Make Their Neighborhood Glow; What the observing astronomers see of them is shown in the specialization topic Active Black Holes: Ultra-Hot Beacons in Space).

In cosmology, cosmic background radiation is an important prediction of the Big Bang models, and observations on it provide important information about the early universe. It is also a thermal radiation, created around 400,000 years after the Big Bang, at a time when the entire universe was still filled with an extremely hot plasma. At the time when their development decoupled from the rest of the cosmos, their radiation temperature was a few thousand degrees. Since then, the background radiation has cooled down with the expansion of space. Today their radiation temperature is only 2.7 degrees above absolute zero. The maximum of the radiation energy is thus in the range of microwaves, and one also speaks of the cosmic microwave background.

additional Information

The properties of thermal radiation presented here are particularly interesting in the context of Einstein Online in connection with black holes and neutron stars, and on the other hand in cosmology. Einstein offers an introduction to these sub-areas of relativistic physics for beginners, especially in the Black Holes & Co. section and in the Cosmology section.