Synchrotron Self Absorption

If the intensity of synchrotron radiation within a source becomes sufficiently high, then re-absorption of the radiation by the synchrotron electron themselves becomes important. This re-absorption of radiation is termed as 'synchrotron self absorption'. Synchrotron self-absorption will drastically modify the spectrum of the source at low frequencies.

When the apparent source brightness temperature approaches the equivalent kinetic temperature of the relativistic electrons, synchrotron self absorption becomes important, and part of the radiation absorbed by the relativistic electrons along the propagation path.

For a source of maximum flux density , magnetic field, B, angular size $\theta$ and redshift z, the cutoff frequency $\nu_c$ is given by

$$\rm {\nu_c \approx 34 {({S_m \over \theta^2})}^{2/5} B^{1/5} (1+z)^{1/5}}$$ (5..7)

Where the constant has been chosen so that $\nu_c$ is in MHz, when is in flux units(Jy), $\theta$ in seconds of arc and B is in gauss. Observations of the maximum flux density, cutoff frequency and angular size of many compact radio sources indicate that $B = 10 ^{-4\pm1}$ gauss, if the observed low frequency cutoff in their spectra is due to synchrotron self absorption.
(Ref : K.R.Lang, Astrophysical formulae).

The magnetic field in a compact radio source can be determined directly by equation 5.7, from the observables $\theta$, , and $\nu_c$. For an example we would calculate the magnetic field for the source 0240-231 for which a turn in the spectra is seen due to synchrotron self absorption. From the spectra shown in the figure 5.2, we can calculate the value of $\nu_c$, the cutoff frequency in MHz to be 1420 MHz, the value of , the maximum flux density to be 6.30 Jy. We assume the angular size of the source to be 1 milli-arcsecond i.e 0.001 arcsecond. Using these values and the equation 5.7, the magnetic field in the source 0240-231 is 1.6008 micro-gauss.

Figure 5.2: Spectra of the Source 0240-231.