G. S. GOLITSYN

1528

Figure 1. The virial similarity parameter П1 = MG/RU2 for

the 21 galactic clusters from the table versus the ratio of the

cluster age T0 to its dynamic relaxation time Td = (ρG)−1/2, ρ

being the cluster mass density.

needed for the Boltzmann thermal equilibrium, but in

collisionless plasma [16] several dynamic time scales are

needed as well for reaching an equilibrium among vari-

ous degrees of freedom.

6. Conclusions

In astrophysics four quantities can be measured of an

object: mass M, luminocity W, velocity U, size R. There

is also the gravitational constant G, five quantities with

dimensions out of three dimension units: mass, time, and

length. Therefore two non-dimensional similarity criteria

can be formed and various scales. We start to explain

turbulent velocity and magnetic fields. For our Galaxy on

the base of supernova explosions we explain the structure

and intensity of these fields.

As the first similarity criterium we use the well known

virial ratio between potential and kinetic energies:

2

GRU

0.6z

z

T

d

T

. For 21 cluster of galaxies from [1] it is found

that this ratio is close to unity for really clusters with

redshift . The 20 per cent scatter may be under-

stood to measurement inaccuracies. The same is for 11

nearly clusters from [2]. The clusters [1] with

have lesser and lesser degree of virial relaxation the

younger they are. A notion of interaction time d is

introduced and it is concluded that of order 10 time

is needed to reach a relaxation for a cluster.

0.6

The second criterium 15

UWG

1.8

is found to be con-

stant at for all 21 clusters from [1] including

not yet relaxed ones and for 11 relaxed clusters from [2].

This unpexected finding needs a model explanation to-

gether with an old Tully-Fisher [8] relation for radiogal-

axies that .

0.02

5

WU

The reasons for this paper to be written are exposed in

the abstract and in the Introduction. I may add two re-

frences for Wesson [17,18] on the application of dimen-

sional analysis to cosmology, which could be a good

starting point in this direction. It should begin, as in any

other case, with an analysis of what the problem is phys-

ically, what is measured and/or should be measured and

how everything is interconnected. Of course, it would not

solve the whole problem of cosmology but may reveal

some important and/or interesting aspects.

7. Acknowledgements

As a student of Moscow University I visited in midfifties

a special lecture course on astrophysics by Prof. A. I.

Lebedinsky. My later work was in environmental physics

in a broad sense, lately there were occasionally a few

specific astrophysical problems, like cosmic rays energy

spectrum, or analogy between earth- and star-quakes.

Sporadic meetings and discussions with I. S. Shklovsky,

Ya. B. Zeldovich, R. A. Syunyaev and some others kept

alive my interest in astrophysics. I am grateful to all

these people and their memories, though occasional talks

with Rashid Syunyaev, Alexey Starobinsky and Alexey

Vikhlinin still continue.

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