Thermal vs. Synchrotron Radiation

The emission from ordinary galaxies is dominated by thermal radiation from stars and dust. Active galaxies are dominated by
non-thermal processes like synchrotron radiation and thermal processes characterized by exceedingly high temperatures not found in
stars (i.e. large energies). Below we outline some of the character of each.


Thermal Emission

In normal galaxies, the temperatures found usually vary from about 10 K for the coldest dust and gas in the interstellar medium to
several thousand kelvin for stellar photospheres. Stars generally fall in the range between 3000 and 30000 K (the sun has a surface
temperature near 6000 K), and so they emit most of their energy near the visual wavelength region. The type of radiation emitted by
stars is called Planck radiation, or sometimes black body radiation. Max Planck first explained such radiation from a theoretical
basis in 1900. He found that the distribution of energy with wavelength of such an object depends on temperature alone, and not on
composition, size, phase or other properties. This is why Planck emission is referred to as a type of thermal emission (there are
others as well). Of course, black body emitters are an idealization, and stars are really just very good
approximations to them. Nonetheless, the Planck radiation law predicts extremely well that the hottest stars will have their peak
emission in the UV while the emission of the coolest stars will peak in the near to mid-IR. Example spectra for Planck emitters are
given below (at right) for three temperatures: 3000K, 6000K and 30,000K.

The Wien displacement law describes the relationship between the temperature of a Planck emitter and the wavelength of the peak
of the Planck curve describing its spectrum. The table below lists the peak wavelength of the Planck emission for four temperatures,
corresponding to the Planck curves in the figure to the right. Note that the curve for 100K falls outside the boundaries of the plot
and so cannot be seen.

max (in microns) = 2898 / T

Here T is the temperature in kelvin.

T (K)

lambda max (microns)








Planck Curves

At wavelengths longer than the peak the radiation emitted decreases slowly with increasing wavelength. (At wavelengths shorter
than the peak there is a rapid decrease.) At radio wavelengths (or frequencies) we are observing on the long wavelength tail of
the energy distribution for ordinary stellar and galactic sources. Thus, in the radio region, ordinary astronomical sources which
are thermal emitters are brighter at higher frequencies (shorter wavelengths).


Synchrotron Emission

Synchrotron radiation is produced when energetic charged particles (electrons in this context) move through a region of space
containing a magnetic field. The motions of the particles are deflected by the magnetic field, causing them to gyrate around the
magnetic field in a plane perpendicular to the direction of the field lines. Since accelerating charged particles causes them to
radiate (according to the Larmor radiation formula), these particles will radiate as they gyrate around the magnetic field. When the
energy distribution of the radiating particles follows a “power law” (see below) which is often true, the
spectral distribution of this radiation at long wavelengths is described by the following relation:

Synchrotron Power Law Synchrotron Power Law Plot

Example of power law spectra for three spectral indices, s = 0.5, 1.0 and 1.5

Here s is is called the spectral index of the radiation, the Greek letter nu is the frequency and F is the
flux. This type of relation is called a power law relation because the flux varies with a constant power, s, of the
frequency. The equation relates the flux at some particular frequency nu, to that at a reference frequency nu_zero. The spectral index
is related to the index describing the energy distribution of the electrons producing the radiation, though it is not the same. Radio galaxies and quasars
have similar radio properties and have spectral indices between s = 0.7 and s = 1.2. Compact radio sources have a flatter spectrum and
tend to have a spectral index near s = 0.4.

The image at right shows the synchrotron spectrum for the Milky Way. At short wavelengths (high frequencies) the emission has a power
law index s = 0.6. Note the turnover in the power law at low frequencies. This is caused by a turnover in the number of relativistic
electrons at low energies. Figure from Cummings, Stone and Vogt, 13th International Cosmic Ray Conference, Denver, 1973.

Milky Way Synchrotron Spectrum

Non-thermal radio emission from Milky Way. Note the break in the power law near 3 MHz