Adapted from P. Coles, 1999, The Routledge Critical Dictionary of the New Cosmology, Routledge Inc., New York. Reprinted with the author's permission. To order this book click here:

When the theory of the gravitational Jeans instability is applied in the context of the Big Bang theory as part of a theory of structure formation, it is essential to take into account a number of physical processes that modify the evolution of density fluctuations. The phenomenon of Silk damping, named after Joseph Silk, is one such effect that applies when we are dealing with adiabatic fluctuations in a medium comprising of baryonic matter and radiation.

During the plasma era of the thermal history of the Universe, the baryonic matter was fully ionised. Under these conditions, free electrons were tightly coupled to the cosmic background radiation by a process known as Thomson scattering. Although this coupling was very tight because the collisions between electrons and photons were very rapid, it was not perfect. Photons were not scattered infinitely quickly, but could travel a certain distance between successive encounters with electrons. This distance is called the mean free path.

According to the classic theory of Jeans instability, fluctuations would have oscillated like acoustic waves when they are shorter than the so-called Jeans length. These waves were longitudinal, and corresponded to a sequence of compressions and rarefactions of the medium through which the waves were travelling. Acoustic waves persisted because there was a restoring force caused by pressure in the regions of compression, which eventually turned them into rarefied regions. In the plasma era most of this pressure was supplied by the photons.

Consider what would have happened to a wave whose wavelength was smaller than the mean free path of the photons. The photons would have leaked out of a compressed region before they had a chance to collide with the electrons and produce a restoring force. This is called photon diffusion. The photons moved out of the compression region and into the neighbouring regions of rarefaction, thus smoothing out the wave. Rather than oscillating as acoustic waves, small-scale fluctuations therefore became smoothed out, and this is what is termed Silk damping.

A similar phenomenon occurs with sound waves in air. Here the restoring force is caused by the air pressure, but because air is not a continuous medium, but is made of molecules with a finite mean free path, any wave which is too short (i.e. of too high a frequency) will not be able to sustain oscillations. High-frequency oscillations in air therefore get attenuated, just as acoustic waves do.

Silk damping causes the smoothing of primordial density fluctuations on length scales smaller than those of clusters of galaxies. The implication for a theory of structure formation based on this idea is therefore that individual galaxies must have formed in a `top-down' manner by the fragmentation of larger objects. Modern theories of structure formation which include non-baryonic dark matter do not suffer greatly from this effect, so that galaxies can form from smaller objects in a `bottom-up' fashion.


Silk, J., `Fluctuations in the primordial fireball', Nature, 1967, 215, 1155 Coles, P. and Lucchin, F., Cosmology: The Origin and Evolution of Cosmic Structure (John Wiley, Chichester, 1995), Chapter 12.