**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).