We have explored the implications of radio source intermittency on source
statistics. To do this, we have developed a simple model for the evolution
of a cocoon/shocked-shell system which is expanding supersonically into an
ambient medium that possesses a power-law density profile. The cocoon is
assumed to be fed energy at a rate
. This model is
integrated numerically for the case of a periodic source which has active
phases (with constant
) separated by inactive, or coasting,
phases in which
. During the first few periods of inactivity,
the radio luminosity will fade rapidly. However, these young sources can
maintain highly supersonic expansion during their coasting phases and,
hence, will remain intact throughout the inactive periods. Once a source
has grown large enough such that the expansion timescale is longer than the
recurrence timescale, the intermittency will not affect its subsequent
evolution. The fading of small, inactive sources, and the effect of
intermittency on the expansion velocity of the sources, produce a
double-break in the size distribution. This can be readily identified with
the plateau found in the size distribution of OB97.
There are two clear predictions of this model. First, one could search for
the faint, inactive sources. These sources might reveal themselves in
deep, low-frequency radio surveys. Alternatively, they could be detectable
via the X-ray signatures or H
emission accompanying the coasting
ISM/ICM shock front. Secondly, statistically complete radio samples of
small sources (
and smaller), once corrected for absorption
effects, should show these sources to be very overluminous as compared with
an extrapolation from larger sources. Since this is essentially reflecting
the high pressure of these small sources, this prediction should be
independent of the precise form of the radio emissivity.