**Stellar Boltzmann
constant**

**Stellar Boltzmann constant**, denoted as *K*_{ps}_{
}, is a physical constant that connects the average energy of motion in a
certain set of typical objects of the stellar level of matter with the kinetic
temperature characterizing this set. This constant was introduced by Sergey
Fedosin in 1999. ^{[1]} In the framework
of the theory of __Infinite Hierarchical Nesting of Matter__, Fedosin proved the theorem of __SPФ
symmetry__ and
determined the similarity coefficients between different __levels of matter__. This allows us to move from the values of the
fundamental physical constants, inherent in the level of elementary particles,
to the physical constants of other scale levels.

Since the
temperature does not undergo scale transformation, the Boltzmann constant is
transformed between the matter levels in the same way as energy. From the
theory of dimensions of physical quantities it follows that the Boltzmann
constant for the main-sequence stars is *K*_{ps}
= *k*_{m} ∙ *Ф* ∙ *S*^{2},
where *Ф* = 6.654∙10^{55} is the
coefficient of similarity in mass, *S *= 7.34∙10^{-4} is the coefficient of similarity in speeds, *k*_{m} is the Boltzmann's constant for the objects at
the level of elementary particles, similar in their properties to the
main-sequence stars. For neutron stars *K' *_{s} = *k* ∙ *Ф**' *∙ *S' *^{2} = 1.18∙10^{33}
J/K, where *k* is the Boltzmann constant as the constant for the nucleon matter, *Ф**' *= 1.62∙10^{57} is the coefficient of similarity in mass, *S' *= 0.23
is the coefficient of similarity in speeds.

In the first
approximation we can assume that *K*_{ps} and *K' *_{s} are equal to each other.

**Содержание**

- 1 Application
- 2 See also
- 3 References
- 4 External links

**Application**

In space the
most common chemical element is hydrogen. The abundance of other elements is
much less, for example, the number of silicon atoms is less than that of
hydrogen atoms tens of thousands of times. The same holds true for the
abundance of stars of different masses. In accordance with the __discreteness of stellar parameters__, the abundance of stars fully copies the abundance of
chemical elements, ^{[1]} and
low-mass stars prevail in our Galaxy. In this case, the typical objects
characterizing the Galaxy in general must be the stars with minimum mass *М*_{ps} = 0.056 *М*_{c} (*М*_{c} is the Solar
mass), which are brown dwarfs and correspond to hydrogen according to the __similarity
of matter levels__. For the set of these stars, the value of the stellar Boltzmann
constant is *K*_{ps}. If the Galaxy
consisted only of identical more massive main-sequence stars, the stellar
Boltzmann constant for them would be *K*_{s} = *А* *K*_{ps}, where *A*
would be the mass
number
corresponding to these stars.

For the average
kinetic energy of the stars’ motion in space, we can write the following:

where and are the mass and root-mean-square velocity of
the stars’ motion, is the kinetic temperature.

Hence, taking
into account the relation at the velocity km/s we
can determine the effective temperature of our Galaxy:

K.

The effective
temperature of the Galaxy can also be estimated using other methods, for
example, with its integral luminosity using the Stefan–Boltzmann law for the radiation from a perfect
black body, in this case the __stellar Stefan–Boltzmann
constant__
should be used. ^{[1]} Another
method involves calculation of the gravitational energy of the Galaxy and its
total internal kinetic energy, which is approximately equal to J. ^{[2]} If we calculate the total number of nucleons *N* in all the stars of the Galaxy, then from the
formula:

where is the number of nucleons per gas particle,
we can find the temperature K.

The effective
pressure of the *gas*, consisting
of a set of stars, is calculated by the formula:

where is the concentration of stars found from
observations.

The stellar
Boltzmann constant can be introduced into the equation of the state of matter
inside the star (the matter is considered as a gas, consisting of nuclei, ions
and electrons, which is held by the proper gravitational force; the thermal
energy of the gas is approximately equal to half the gravitational energy
according to the virial theorem). In this case the
formula is valid:

where is the number of nucleons per gas particle, , and are the volume of the star, its average
pressure and internal temperature, is the internal thermal energy of the star.
This formula holds with an accuracy up to a coefficient of the order of unity,
because the star cannot be uniform, the pressure and temperature increase in
its interior. We can take the Sun as an example, in which the average pressure
reaches almost 10^{14} Pa, and the average temperature is about 8
million degrees at .
^{[3]}

Hence it
follows that the stellar Boltzmann constant represents both the intrinsic
properties of the stellar objects, describing the relationship between the
energy and temperature of the matter, and the relationship between the energy
and temperature of the interacting stellar objects in the aggregate. The same
conclusion can be made about the physical meaning of the ordinary Boltzmann
constant, with substitution of the stellar objects by elementary particles.

**See**** also**

__Infinite Hierarchical Nesting of Matter____Similarity of matter levels____SPФ symmetry____Discreteness of stellar parameters____Quantization of parameters of cosmic systems____Stellar constants____Hydrogen system____Stellar Planck constant____Stellar Dirac constant____Stellar Stefan–Boltzmann constant__

**References**

^{1,0}^{1,1}^{1,2}Fedosin S.G. (1999), written at Perm, pages 544, Fizika i filosofiia podobiia ot preonov do metagalaktik, ISBN 5-8131-0012-1.- Нарликар Дж. Неистовая Вселенная. М.:
Мир, 1985.
- Мартынов
Д.Я. Курс общей астрофизики. М.: Наука, 1988.

**External**** links**

Source: http://sergf.ru/spben.htm