6. The meaning of
We know the meaning of in statistical physics; it is equal to , where is Boltzmann's constant, and T is the absolute temperature. In the large-scale (or any other) structure we can establish a similar meaning by developing a kinetic theory, in which the particles are the galaxies themselves (or other particles).
If we integrate expression ( 2 ) over position space, we get
The mean value of the peculiar velocities for all clustering galaxies is
We can also express this as
where and C represent the same constant as in the force equation for the Newtonian case. Hence, note that the parameter C, which we could obtain in the equality ( 21 ), will give information about the velocity field of the particles, or, vice-versa, we could obtain C for ( 21 ) from the mean velocity.
The parameter is even more directly related to the kinetic energy. An analogous derivation leads to
a fundamental result of statistical mechanics.
© European Southern Observatory (ESO) 1997
Online publication: October 15, 1997