3.5. Energy Density and Pressure
The standard minimum-energy calculation due to
is generally used
to estimate energy densities for synchrotron-emitting material
(convenient formulae are given in
There are many reasons to suspect these estimates, for example:
- The filling factor f may be << 1, rather than = 1 as is generally
- Parts of the source can be overpressured for various reasons
- 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
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.
- The observed radiation may be affected by Doppler beaming if the
bulk flow velocities are relativistic.
- 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.