*Astron. Astrophys. 326, 433-441 (1997)*
## 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
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