(Submitted May 30, 1996)
We understand that in recent years discovery of intense 511-keV
lines from black holes indicate that steady-state thermal annihilation
plasmas may exist and that there is a fundamental limit to the
above which pair creation can no longer be balanced by annihilation and
this limit is referred to as the BKZS limit. Can you let us know the
derivation of the letters B, K, Z & S in the naming of this limit?
Could you give us a reference to some place where we can get more
information on this subject?
Thank you very much for your interesting, very high level, question.
We could not answer your question ourselves, but we have managed to find
expert, Dr. Charles Dermer of Naval Research Laboratory, who could.
His answer is given here.
The questioner is quite right about what he has heard.
There is a fundamental limiting temperature above which
steady thermal plasmas cannot exist. The limit is named
after the authors of the paper which points out this limit,
and the complete reference is:
Bisnovatyi-Kogan, G. S., Zel'dovich, Ya. B., and
Sunyaev, R. A., 1971, Soviet Astronomy, AJ, vol. 15, p. 17.
The question outlines the essential reason for this limit: at
high temperatures, there is a competition between two-body processes.
On the one hand, collisions of electrons with other particles
(such as electrons, positrons, or protons), makes electron-positron
pairs through the process:
At sufficiently high temperatures, the addition of electron-positron
through process (1) makes additional electron-positron pairs through
process (1) and so on, and this cannot be balanced
by the pair annihilation rate. The result is unlimited production of
if one requires the system to remain at a fixed temperature. In reality,
course, energy cannot be continuously injected and the system cools, so
the runaway pair production is quenched.
- particle 1 + particle 2 --> particle 1 + particle 2 + electron +
The electrons and positrons are made at the expense of the kinetic energy
of particles 1 and 2.
- On the other hand, pair production is balanced by the pair
electron + positron --> two gamma-ray photons.
BKSZ calculated a maximum temperature of about 20 MeV; subsequent
revised that maximum to about 12 MeV (see, for example, A. A. Zdziarski,
1982, Astronomy and Astrophysics Letters, vol. 110, p. L7). This is for
completely transparent medium, and the maximum temperature is even less
the system is opaque (i.e., has finite optical depth).
The discovery of time-variable sources of 0.511 MeV annihilation
the impetus for this work, although the reality of black hole sources
of annihilation radiation is now in dispute (although diffuse
radiation in the galaxy and on the Sun from radioactive beta-emitters is
beyond question). A Scientific American article by Gehrels, et al.
(December 1993, page 68) discusses cosmic annihilation radiation, though
in great detail.