**4.2. Relativistic Beaming?**

Radiation from relativistically moving matter is beamed in the
direction of the motion to within an angle
^{-1}.
In spite of
this the radiation produced by relativistically moving matter can
spread over a much wider angle. This depends on the geometry of the
emitting region. Let
_{M} be the
angular size of the
relativistically moving matter that emits the burst. The beaming
angle will be
_{M} if
_{M} >
^{-1}
and
^{-1}
otherwise. Thus if
_{M} =
4 - that is if the emitting
matter has been accelerated spherically outwards from a central source
(as will be the case if the source is a spherical fireball) - the
burst will be isotropic even though each observer will observe
radiation coming only from a very small region (see
Fig. 11). The radiation will be beamed into
^{-1}
only if the matter has been accelerated along a very narrow beam. The
opening angle can also have any intermediate value if it emerges from
a beam with an opening angle
>
^{-1},
as will be the case if the source is an anisotropic fireball
[222,
223] or an
electromagnetic accelerator with a modest beam width.

Beaming requires, of course, an event rate larger by a ratio
4 /
^{2} compared to
the observed rate. Observations of about one
burst per 10^{-6} year per galaxy implies one event per hundred
years per galaxy if
^{-1}
with given by
the compactness limit of ~ 100.