The Sunyaev-Zeldovich (S-Z) effect can be understood in a qualitative sense
by considering the interaction of photons in the 2.73 K black body distribution
with much more energetic electrons, with an energy of 5 keV and density of
102 cm3.
References 331
(a) What is the energy of photons with a wavelength of 1.6 mm (the peak of the
background distribution)? Compare to the energy of the electrons.
(b) Obtain the number of 2.73 K photons per cm3 from Problem 20c of Chap. 1.
(c) Assume that the interaction of the 2.73 K black body photons with the electrons
(assumed monoenergetic) in the cluster will lead to the equipartition of energy.
Make a qualitative argument that this interaction leads to a net increase in the
energy of the photons. Justify why there is a decrease in the temperature of the
photon distribution for wavelengths longer than 1.6 mm and an increase shorter
than this wavelength.