12.5.4. Effect of Absorption by Ionized Hydrogen
The observed radio spectrum may differ from the radiated spectrum owing to the influence of the medium between the source and the observer. If a cold cloud of ionized gas is located in front of the source, then the observed flux density will fall off sharply below the frequency, 0, where the optical depth is unity. For an electron temperature Te,
where = ne dl is the emission measure, and ne the density of thermal electrons. The observed spectrum is then
If the ionized medium is mixed with the synchrotron source, then for << 0
If the density of thermal electrons is sufficiently great, then at frequencies where the index of refraction, , becomes less than unity, the form of the spectrum will differ from that in vacuo. When < 1, the velocity of a relativistic electron is less than the phase velocity of light in the medium; the radiation is no longer so highly concentrated along the electron trajectory, and the energy no longer appears in the high-order harmonics of the gyrofrequency. This is commonly called the Razin, or Tsytovich, effect and is important below a frequency r given by
For < r the spectrum cuts off very sharply (see Chapter 3).