Spectral index

In radio astronomy, the spectral index of a radio source can hint at its physical properties. The spectral index is calculated from an assumed power law dependence for flux given by $S\propto \nu ^{\alpha }$ where $S$ is flux and $\nu$ is frequency. A more direct formula is: $\alpha ={\frac {\log(S_{1}/S_{2})}{\log(\nu _{1}/\nu _{2})}}$

Note: Alternatively, the spectral index can be defined in terms of wavelength according to $S\propto \lambda ^{n}$, instead of frequency (see Kraus, Radio Astronomy). In that case, the so-called direct relationship becomes:

$n={\frac {\log(S_{1}/S_{2})}{\log(\nu _{2}/\nu _{1})}}$

A spectral index of −0.1 typically indicates thermal, or free-free (bremsstrahlung) emission, while a steep spectral index of −0.7 indicates synchrotron emission.

Thermal emission

Blackbody radiation

Thermal emission is perhaps the most basic form of emission for EM radiation. Any object or particle that has a temperature above absolute zero emits thermal radiation. The temperature of the object causes the atoms and molecules within the object to move around. For example, the molecules of a gas, as in a planet's atmosphere, spin around and bump into one another. When the molecules bump into each other, they change direction. A change in direction is equivalent to acceleration. As stated above, when charged particles accelerate, they emit electromagnetic radiation. So each time a molecule changes direction, it emits radiation across the spectrum, just not equally. As a result, the amount of motion within an object is directly related to its temperature.

You can explore this for yourself by placing a cast-iron pan on a stove, heating it for a few minutes, and then placing it to the side. It is hot enough to be emitting a noticeable amount of infrared radiation (or heat), which you can detect by placing your hands near it. If you were to put more heat into the iron, it would eventually emit higher and higher energy wavelengths, until it would glow on its own, emitting visible light as well as infrared radiation.

Scientists call this blackbody radiation. A blackbody is a hypothetical object that completely absorbs all of the radiation that hits it, and reflects nothing. The object reaches an equilibrium temperature and re-radiates energy in a characteristic pattern (or spectrum). The spectrum peaks at a wavelength that depends only on the object's temperature. All objects in the universe behave this way. The image at left shows blackbody spectra for objects at three different temperatures: 5000 K, 4000 K, and 3000 K. It is apparent from the image that objects at lower temperatures emit more radiation at longer wavelengths. The objects in the image emit at or near the visible range of the electromagnetic spectrum; in order for an object to emit thermal radiation at radio wavelengths, it must be much colder than these objects.

The unit of temperature that astronomers typically use is called the kelvin, and its symbol is K (no degree symbol is used). To convert from degrees Celsius to kelvins, add 273 to the temperature in Celsius. So, if an object has a temperature of 100 °C, its temperature in kelvins is 100 + 273 = 373 K. Objects that are cooler than about 1000 K emit more infrared than visible light, such as the Earth or brown dwarfs (dim, cool objects too massive to be planets but not massive enough to be stars). Hotter objects, like stars, emit mostly optical light. Very hot objects emit mostly ultraviolet radiation, such as white dwarfs (dying stars that have burned up all of the hydrogen in their cores). The major difference in the type of energy emitted by these objects is their temperature. 3k

The Sun and other stars are, for all intents and purposes, considered blackbody radiators. By looking at the frequency or "color" of the radiation they emit, scientists can learn about the temperature of these bodies. For example, cooler stars appear red and hotter stars appear bluish-white.

One of the most famous examples of a "perfect" blackbody is known as the Cosmic Microwave Background (CMB) radiation. The CMB is a redshifted picture of the universe as it appeared 379,000 years after the Big Bang. Today it appears as a blackbody radiator at 2.725 Kelvin.

Free-free emission

Another form of thermal emission comes from gas which has been ionized. Atoms in the gas become ionized when their electrons become stripped or dislodged. This results in charged particles moving around in an ionized gas or "plasma", which is a fourth state of matter, after solid, liquid, and gas. As this happens, the electrons are accelerated by the charged particles, and the gas cloud emits radiation continuously. This type of radiation is called "free-free" emission or "bremsstrahlung". The image at left shows the emission of a photon when a negatively charged electron (green particle) changes direction or accelerates due to the presence of a nearby positively charged ion (red particle). Some sources of free-free emission in the radio region of the EM spectrum include ionized gas near star-forming regions or active galactic nuclei (AGN).

Spectral line emission

Spectral line emission involves the transition of electrons in atoms from a higher energy level to lower energy level. When this happens, a photon is emitted with the same energy as the energy difference between the two levels. The emission of this photon at a certain discrete energy shows up as a discrete "line" or wavelength in the electromagnetic spectrum.

An important spectral line that radio astronomers study is the 21 cm line of neutral hydrogen. This line is emitted by the following transition: the hydrogen atom consists of one electron orbiting one proton in the nucleus. Both the electron and the proton have a "spin". In the lowest energy state, or "ground" state, the spins of both particles are in opposite directions. When the atom becomes excited, either by absorbing a photon of energy, or by bumping into other atoms, the electron absorbs a small amount of energy, and the spin of the electron "flips," so that the spins of both particles are in the same direction. When the atom reverts back to its natural state, it loses this energy by emitting a photon with a wavelength of 21 cm, in the radio region of the electromagnetic spectrum.

Non-thermal emission

Synchrotron emission

Non-thermal emission does not have the characteristic signature curve of blackbody radiation. In fact, it is quite the opposite, with emission increasing at longer wavelengths.The most common form of non-thermal emission found in astrophysics is called synchrotron emission. Basically, synchrotron emission arises by the acceleration of charged particles within a magnetic field. Most commonly, the charged particles are electrons. Compared to protons, electrons have relatively little mass and are easier to accelerate and can therefore more easily respond to magnetic fields.

As the energetic electrons encounter a magnetic field, they spiral around it rather than move across it. Since the spiral is continuously changing the direction of the electron, it is in effect accelerating, and emitting radiation. The frequency of the emission is directly related to how fast the electron is traveling. This can be related to the initial velocity of the electron, or it can be due to the strength of the magnetic field. A stronger field creates a tighter spiral and therefore greater acceleration.

For this emission to be strong enough to have any astronomical value, the electrons must be traveling at nearly the speed of light when they encounter a magnetic field; these are known as "relativistic" electrons. (Lower-speed interactions do happen, and are called cyclotron emission, but they are of considerably lower power, and are virtually non-detectable astronomically).

As the electron travels around the magnetic field, it gives up energy as it emits photons. The longer it is in the magnetic field, the more energy it loses. As a result, the electron makes a wider spiral around the magnetic field, and emits EM radiation at a longer wavelength. To maintain synchrotron radiation, a continual supply of relativistic electrons is necessary. Typically, these are supplied by very powerful energy sources such as supernova remnants, quasars, or other forms of active galactic nuclei (AGN).

It is important to note that, unlike thermal emission, synchrotron emission is polarized. As the emitting electron is viewed side-on in its spiral motion, it appears to move back-and-forth in straight lines. Its synchrotron emission has its waves aligned in more or less the same plane. At visible wavelengths this phenomenon can be viewed with polarized lenses (as in certain sunglasses, and in modern 3-D movie systems).

Gyrosynchrotron emission: pulsars

A special form of synchrotron emission is known as gyrosynchrotron emission which is emitted by pulsars. Pulsars result from the deaths of massive stars (stars with about 8–15 times the mass of the Sun). As a massive star runs out of nuclear fuel, its core begins to collapse. When the outer layers of the star collapse onto the core, a shock wave is produced that results in a massive explosion called a supernova. After the supernova explosion, an extremely dense neutron star is left behind, containing mostly neutrons, measuring a few kilometers in diameter, and containing 40 percent more mass than the Sun. As the core of the star collapses to vastly increase the density, the magnetic field of the star is also tremendously intensified.

A rapidly rotating neutron star is known as a pulsar. A typical pulsar has a magnetic field a trillion times stronger than the Earth's, which accelerates electrons and other subatomic particles to nearly the speed of light, causing them to emit beams of radiation, including radio waves. When these beams sweep across the Earth, we see a "pulse" of radiation from the pulsar. As the pulsar rotates, the radiation appears to flash on and off, similar to a lighthouse. Some pulsars rotate relatively slowly, such as the pulsar in the center of the supernova remnant called the Crab Nebula (M1), which rotates 33 times per second. Other pulsars, known as millisecond pulsars, can rotate hundreds of times per second.

Masers

Another form of non-thermal emission comes from masers. A maser, which stands for "microwave amplification by stimulated emission of radiation", is similar to a laser (which amplifies radiation at or near visible wavelengths). Masers are usually associated with molecules, and in space masers occur naturally in molecular clouds and in the envelopes of old stars. Maser action amplifies otherwise faint emission lines at a specific frequency. In some cases the luminosity from a given source in a single maser line can equal the entire energy output of the Sun from its whole spectrum.

Masers require that a group of molecules be pumped to an energized state (labeled E₂ in the diagram at right), like compressed springs ready to uncoil. When the energized molecules are exposed to a small amount of radiation at just the right frequency, they uncoil, dropping to a lower energy level (labeled E₁ in the diagram), and emit a radio photon. The process entices other nearby molecules to do the same, and an avalanche of emission ensues, resulting in the bright, monochromatic maser line. Masers rely on an external energy source, such as a nearby, hot star, to pump the molecules back into their excited state (E₂), and then the whole process starts again.

The first masers to be discovered came from the hydroxl radical (OH), silicon oxide (SiO), and water (H₂O). Other masers have been discovered from molecules such as methanol (CH₃OH), ammonia (NH₃), and formaldehyde (H₂CO).