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 T_e,

(12.16)

where = n_e dl is the emission measure, and n_e the density of thermal electrons. The observed spectrum is then

(12.17)

If the ionized medium is mixed with the synchrotron source, then for << ₀

(12.18)

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

(12.19)

For < _r the spectrum cuts off very sharply (see Chapter 3).