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

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6. The meaning of [FORMULA]

We know the meaning of [FORMULA] in statistical physics; it is equal to [FORMULA], where [FORMULA] 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

[EQUATION]

[EQUATION]

The mean value of the peculiar velocities for all clustering galaxies is

[EQUATION]

[EQUATION]

We can also express this as

[EQUATION]

where [FORMULA] 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 [FORMULA] is even more directly related to the kinetic energy. An analogous derivation leads to

[EQUATION]

a fundamental result of statistical mechanics.

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© European Southern Observatory (ESO) 1997

Online publication: October 15, 1997
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