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Fundamental radiation processes

Although astronomy is the discipline dealing with objects at the largest distances that we can measure, and thus the very largest spatial scales imaginable, the creation of light received (and investigated) by us occurs on microscopic scales, at the level of molecules, atoms or elementary particles therein. Therefore, in order to gain a basic understanding of what kind of light reaches us from the depth of space, we need to have a very brief look at some basic physics first (not to worry - I won't go into detail).

Line emission

According to the laws of quantumphysics some types of particles are only allowed to have certain, fixed levels of energy (but not in between these). One can compare this with climbing stairs or a ladder - one has a stable footing only at fixed levels, but not in between).

Once we accept that this is the case, it has the natural consequence that such an elementary particle can also absorb or emit only very specific amounts of energy when making a transition from one allowed energy state to another (in our example of scaling a ladder this means that each time we climb one rung we must invest an exactly defined amount of energy, the exact amount of which is released again when we descend).

An elementary particle has two principle ways of absorbing or emitting energy. One of them is to either emit or absorb a photon. The photon will carry exactly the amount of energy corresponding to the difference in allowed values between which the transition takes place (meaning: if we don't push hard enough, we won't climb a rung; but pushing a bit harder won't give us a stable footing in between two rungs). So the energies must match! The particle will absorb a photon only when its energy will bring it exactly to the next higher allowed state; and it will emit only a photon that releases exactly the amount of energy set free by relaxing to the next lower allowed energy state.

Imagine a large number of tiny particles, say electrons, that have in the past been heated up (or "excited") by a nearby energy source, such as a star. But now they have moved away and their surroundings become a bit cooler and suddenly the energy they carry is no longer in equilibrium with their environment. Physical laws rule that such particles will sooner or later release that surplus energy to the environment in order to reach equilibrium again. Statistically, this will often happen over long times. But in outer space, although it might appear to be almost empty, there are in fact an enormous number of such particles. When they release their surplus energy, one can pick up the light (photons) emitted by them if only enough emit light at the same time. Since all emit their photon at the same energy when undergoing the same transition (under the same circumstances), one will see lots of photons coming our way, all with (almost...) the same energy. Now what does that look like in a plot? If we draw a sketch, this means that over a range of energies we see no light coming our way, only at the energy of the transition the particles are undergoing, there will be lots (see figure below). That peak is what is called an "emission line". The process of emitting such light is accordingly called "line emission". It is as easy as that! Now if you have lots of particles moving around at different speeds, you will not measure just one narrow spike, but the emission line will have substructure reflecting the various particle motions. This is what astronomers use to tell how celestial objects are moving. In the image below, all the HI line emission of a rotating spiral galaxy is captured.

Spectrum of the total HI emission of an external galaxy. The width and shape of the emission line are caused by the rotation of the galaxy disk and the distribution of gas in it.

There are, of course, many types of atoms and molecules in the interstellar gas of galaxies. So many more emission lines exist outside the displayed range of energies (wavelengths). Our observing bandwidth being limited, they cannot be investigated all at the same time. However, many (actually most) of them are weaker than the HI line and a good many emission lines cannot be studied in detail, because the signals we receive are too weak.

Note that in the process of being heated up (our starting point in the example above) particles absorb energy/photons and thus one will find, when looking at the particles, photons with the energy they absorb to be "missing". This is what one calls an "absorption line". In the plot above, the line would then not stand up, but show up as a trough.

The technical process employed to measure astronomical line emission is called "spectroscopy".

Continuum radiation processes

There are physical quantities that are not "quantized" as the ones leading to line emission. For example, when two particles collide they can do so under all kinds of circumstances (different speeds, angles, different masses of the particles involved). Therefore, the energy that might be transferred in the process from one particle to the other is in no way pre-determined, or quantized. Any value (up to a certain maximum - no particle can have infinite energy!) is allowed. This means that there are no disallowed energy values; photons emitted by such particles may thus have a "continuous" energy distribution - therefore the term "continuum emission". An example is shown below. An emission line, as presented above, is depicted superimposed on continuum emission (which, actually, consists of two types, as we will see further below).

Sketch describing the superposition of continuum and line emission and their separation for measuring line properties.

Let us consider an analogue from our daily life, in which particles exchange energy by bouncing off each other ("collisional excitation"). Question: How does water at the surface of a pot know that the bottom of the pot is hot? Answer: The particles (water molecules) at the bottom are excited (heated up) by the boiler plate and start erratic motions. (Don't we all start moving erratically when getting excited?) This way, they collide with neighbouring water molecules, which in turn collide with others, and so on, until the whole lot of them knows: There's heat coming from below. Water at high temperatures evaporates in the form of steam; other particles produce light when hitting each other - light that we can observe with very sensitive instruments. An astronomical example of continuum emission, in this case continuum radiation from dust in the spiral galaxy NGC 4565, is displayed below.

Image of millimetre wavelength continuum emission from NGC 4565 by Neininger et al. (1996), Astron. & Astrophys.

Thermal emission

Ha! This is an easy chapter to write. The above example of continuum emission from dust is in fact thermal emission. What that means is that the mean energy of the photons emitted is directly proportional to the temperature of the material the emission comes from. The person to formulate this dependence was Max Planck. In the example displayed below the temperature of the emitter is 2000 degrees Kelvin [K].

Sketch of the Planck spectrum of a 2000 K black body. It indicates that only a small fraction of the emitted light arises in the form of optical emission. Most of the photons are emitted in the near-infrared regime.

Synchrotron processes

What kind of radiation might then not be of thermal origin? Our naive comprehension of such processes is limited, because we do not encounter them in everyday life. So let's be a bit inventive and assume that you are an electron. As such you are a charged particle, which means that you cannot just do as you please, but your motions will be controlled by magnetic fields in your surroundings. Moving towards a magnet you actually start pivoting around the magnetic field line capturing you in crazy spins, entering a helical motion.

Sketch of the helical motion of an electron in a magnetic field and its radiation characteristics, if moving at a velocity close to the speed of light (so-called "relativistic" electron).

Stretching your imagination just a bit further, you might be able to figure out what such motions might do to your stomach.... well, an electron doing the same will emit radiation, because the spiralling motion constitutes a constant change of direction, meaning an accelerated motion, during which the particle loses energy - energy that is set free in the form of low-energy light. The escaping radiation has radio wavelengths and the effect of electrons (i.e. particles at almost the speed of light) in a magnetic field emitting such radiation is called the "synchrotron effect". One measures the same radiation, depending on the setup of the experiment at different wavelengths, in particle accelerators in laboratories on Earth.

An example for such synchrotron emission is the radio image of the edge-on spiral galaxy NGC 891 displayed below. All this emission comes from electrons spiralling in magnetic fields. One can discern a thin galaxy disk, seen on edge, and a more extended component, the "synchrotron halo".

Observed 1.4 GHz radio image of the northern edge-on spiral galaxy NGC 891. All the continuum emission seen in the image comes from relativistic electrons (synchrotron continuum emission).

Continuum emission is usually observed using the technique of imaging. Note that in the specific case of the above image of NGC 891, the image was obtained by an interferometer, which implies special rules for imaging that are different from those of a single telescope. For polarised emission one would perform polarimetry, while time-variable sources would be studied photometrically.

Colours and spectral indices

Compared to line emission processes, continuum emission carries much less diagnostic information on the object studied. There is little, if any, information to be gained of an object's kinematics and dynamics. But still, studying wide ranges in frequencies/wavelengths, some important clues can still be gleaned from continuum observations.

Optical colours

Let us come back to the graph shown above of the Planck spectrum of a fiducial black body.

Sketch of the Planck spectrum of a 2000 K black body.

Such a spectrum is emitted, for example, by a star with a very cool surface temperature. Most of its photons have near-infrared energies, with some emission also in the red visible part of the spectrum (shaded area). Such a star would appear to the human eye to be "red".

A much hotter star, say with a temperature of 10000 K, would have its emission peak in the ultra-violet part of the spectrum, very close to the y-axis in the plot shown above. Most of its photons are thus UV photons, with some optical blue emission as well - and more blue optical photons than red photons. Such a star would then appear to an observer to be "blue".

Therefore, as long as stars with various surface temperatures indeed all emit black-body Planck spectra, we can use their colours to gain a rough estimate of their temperatures. Blue stars are much hotter than red stars. A star like the Sun, with a surface temperature of about 5800 K, appears to be white-yellowish.

Spectral indices

Outside the optical regime the ratio of flux densities observed at different frequencies/wavelengths is not called "colour", but has been given the name "spectral index". Let us have a look at what a spectral index is and what it can tell us about the emitting object; in doing so we use the radio waveband as an example, although the following is equally true in any other waveband. Yet again the graph of a black-body Planck spectrum is of help.

Sketch of the Planck spectrum of a 2000 K black body.

In radio astronomy one observes lots of gases in between stars, rather than predominantly emission from stars. Gas in the vicinity of massive young stars emitting UV photons typically has a temperature in the ballpark of 10000 K. Its emission peak in the graph above would then be far to the left, close to the y-axis, towards the ultraviot part of the electromagnetic spectrum (as was the case for a 10000 K hot star, there is no difference between them in this respect). RADIO waves have wavelengths of centimetres to metres, typically. So while the gas's emission peak would shift to the left for a temperature of 10000 K, we would be studying waves very far to the right of the plotted wavelength range. You can imagine just how flat the slope of the Planck spectrum is in that regime. This is called the "Rayleigh-Jeans" wing of the Planck spectrum. In that part of the continuum spectrum its slope can be approximated by a so-called "power law", where the spectral index is the power of that power law:

S ∝ να

Here S is the measured flux density at frequency ν. A negative value of α indicates that there are less high-energy photons than at lower energies.

For thermal emission of a 10000 K gas, the radio spectral index, α, is -0.1. So by measuring the spectral index in the radio regime, we can tell whether the emission comes from a thermal gas.

Non-thermal emission processes, such as the synchrotron radiation introduced above, has different spectral indices. For young supernovae (massive stars exploding at the end of their lifetimes), α ∝ -0.5 is measured. Much later, when the synchrotron plasma from supernovae has lost part of its energy, values in the range of -0.8 to -1.0 are measured. Far away from the sites of supernovae, for example in halos of galaxies, α ∝ -1.5 can be found. Here the spectral index value can tell us about the nature of the synchtrotron plasma, which makes spectral indices a powerful diagnostic tool.

Radio spectral energy distribution of the spiral galaxy NGC 891

The radio spectral energy distribution of NGC 891 shown above, with its spectral index in the regime of -0.7, is a good indicator of the fact that most of the electrons emitting radio photons must be nonthermal, relativistic electrons.

Radio spectral index as a function of distance from the disk plane of NGC 891

In the graph above one can see how the radio spectral index becomes more negative ("steepens") away from the disk plane of NGC 891. This indicates that cosmic-ray electrons, when leaving their birth sites in the disk plane, incur energy losses. This leads to more photons at lower energies being emitted as the cosmic-rays propagate through the interstellar medium. The observed spectral index slope can then be used to study how much energy the cosmic-rays lose and which mechanism(s) cause(s) the losses.