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3.5. Energy Density and Pressure

The standard minimum-energy calculation due to Burbidge (1956) is generally used to estimate energy densities for synchrotron-emitting material (convenient formulae are given in Hughes 1991). There are many reasons to suspect these estimates, for example:

  1. The filling factor f may be << 1, rather than = 1 as is generally assumed.

  2. Parts of the source can be overpressured for various reasons (Begelman 1993).

  3. The upper and lower limits of the electron energy distribution are not well known and may vary systematically across a source (e.g. as a result of adiabatic expansion; Scheuer 1989). In most applications, the lower limit is the important one. It is known to correspond to a frequency < 10 MHz in many cases, but lower-frequency emission cannot be measured from the ground.

  4. The observed radiation may be affected by Doppler beaming if the bulk flow velocities are relativistic.

  5. The proton/electron ratio is unknown.

The conclusion, as for the thermal matter density, is that minimum energy and pressure arguments are of limited usefulness. The best of a bad lot are the estimates of minimum energy density made using the most conservative assumptions and treated as lower limits.