The Universe is not empty but filled with Cosmic Microwave
Background (CMBs). For **very high energy** (VHE) -rays
and electrons, our Universe is not transparent any more but
rather opaque because
they yield electromagnetic (EM) cascades in extragalactic space
as the electrons and photons collide further with
the CMB photons.
A high energy photon pair-produces
electrons in the CMB photon field. An electron kicks out
a CMB photon to high energy range via the inverse Compton
scattering. These two channels mainly drive the EM (electro-magnetic)
cascade recycling energies to much lower energies with growing
number of photons and electrons. Schematically,

The CMB is not only the universal diffuse radiation backgrounds
which are involved in the EM cascades but the radio and infrared-optical
(IR-O) backgrounds also play an important role in the cascade
depending on energies of high energy particles in the cascade.
The threshold energy of pair production is given by

In case of the collisions between VHE -rays and CMB photons,
the differential cross section of pair creation can be rather easily
obtained. Not let us calculate the cross sections to see the general
characteristics of the EM cascades driven in the Universe.
The energy of pair-produced electron in CMS, ,
is equivalent to .
Using Eq. 27 and the fact that
energy of
is orders of magnitude higher than
that of CMB
, we find

Here is the dimensionless energy of the electron normalized by primary energy of VHE -ray . Then Eq. 32 reads

Pair-produced electrons are subject to the inverse Compton scattering with the background photons. The differential cross section is given by Eq. 30.

FIG. 7 shows the attenuation length calculated by the cross sections of the relevant reactions, indicating how long VHE -rays can travel in the extragalactic space. One can see that VHE -rays with energies of eV can only run over kpc that is equivalent to the dimension of out Galaxy. It implies that we are not able to see an extragalactic part of the Universe in the VHE energy range by photons. The structures seen in the figure at and eV are formed by interactions with IR-O and radio photons, respectively, as described above. It should be remarked, however, that, energies of ultra-high energy (UHE) photons above eV would not be degraded rapidly in the EM cascade. As the pair production cross section has local maximal at and , either of pair-produced electrons carries most fraction of energy of primary UHE -ray. The leading electron transfer most of its energy again to the photon via the inverse Compton scattering as you see the cross section becomes larger in regime in Eq.30. Thus leading photons and electrons would maintain their energies longer than nucleons do.

2002-07-18