**Stellar Stefan–Boltzmann constant**

**Stellar Stefan–Boltzmann constant**, denoted as , is a constant that relates the average luminosity of
a sufficiently large stellar system with the area of its outer surface and the
average temperature of the kinetic motion of stars in this system.

The
definition of the stellar Stefan–Boltzmann constant was made in 1999 in the
works of Sergey Fedosin. ^{[1]}
Using the __similarity of matter levels__, __SPФ symmetry__ and the theory of __Infinite Hierarchical Nesting of Matter__, Fedosin calculated the similarity coefficients
between the atomic and stellar levels of matter. This allowed finding various __stellar constants__ based on the dimensional equations.

For the
main-sequence stars of minimum mass the stellar Stefan–Boltzmann constant is:

where is the Stefan–Boltzmann constant for the
objects at the level of elementary particles, similar in their properties to
the main-sequence stars, is the coefficient of similarity in mass,
and is the coefficient of similarity in time.

If we assume
that is equal to the Stefan–Boltzmann constant, then we obtain W/(m^{2}∙K^{4}).

In case if
the stellar system consists of more massive stars, the effective stellar
Stefan–Boltzmann constant increases by a factor equal to , where and are the mass and charge numbers of stars,
which characterize the stellar system on the average and are found from the
similarity between stars and chemical elements (more about it in the article __Discreteness of stellar parameters__).

**Содержание**

- 1 Theory
- 2 Application
- 3 Stellar matter
- 4 See also
- 5 References
- 6 External links

**Theory**

According to
the Stefan–Boltzmann law, the radiation power of a black body is proportional to
the surface area and to the fourth power of the body’s temperature:

,

where is the emissivity (for all substances , for a perfect black body ), is the body’s surface area, is the body’s temperature.

To apply this
formula at the level of stars, we need to pass from the atomic systems to the
stellar systems, which implies we need to use the constant instead of
.

**Application**

The stellar
Stefan–Boltzmann constant allows us to relate the luminosity (the radiation
power) of the galaxy, its surface area and the average kinetic temperature of
stars. There are various methods for estimating the luminosity of galaxies.
Similarly, the average kinetic temperature of stars in galaxies can be found in
different ways, for example, by the velocities of stars in the galaxy and the __stellar Boltzmann
constant__, or by the
total energy and the number of nucleons in the galaxy. ^{[1]} If we substitute in the formula:

the integral
luminosity of our Galaxy, the Milky Way, W, ^{[2]} and the area of the galaxy m^{2}, with the galaxy’s form of a
flat disk with the radius of about 15 kpc, we obtain the estimate of the
effective kinetic temperature of the stellar “gas” of the galaxy: K.

**Stellar matter**

After the
long-time evolution of stars, they must turn into white dwarfs and neutron
stars. The latter will cluster into star systems, similar in their properties
to atoms and molecules. Thus the stellar matter emerges, the basis of which are
neutron stars and magnetars as the stars that carry a strong magnetic field and
an electric charge.

The stellar
Stefan–Boltzmann constant for neutron stars is:

W/(m^{2} ∙K^{4}),

where W/(m^{2} ∙K^{4}) is the Stefan–Boltzmann constant as the constant characterizing the
nucleon level of matter, is the coefficient of similarity in
mass, is the coefficient of similarity in
time, is the coefficient of similarity in sizes,
and is the coefficient of similarity in speeds.

The
constant must be included in the formula for the power
of radiation from the stellar matter, heated to the temperature . The Stefan–Boltzmann constant exceeds the value of the stellar constant , which reflects the fact that the
energy density increases with transition to the lower levels of matter. In the
limiting case, the area of the stellar matter must not be less than the surface
area of one neutron star . For a neutron star RX
J1856.5-3754, radiating approximately as a black body with the temperature of
the order of K, at the radius of km, ^{[3]} the formula for luminosity leads to the
following:

W or ,

where denotes the luminosity of the Sun. In fact, a
neutron star radiates almost 300 times more, and to calculate the star’s
luminosity we must use the value instead of
. This difference is due to the
difference in temperatures: if in the Stefan–Boltzmann law the kinetic
temperature of the moving particles of the black body’s surface is used,
averaged due to a number of interactions, then applying the law to one matter
particle leads to inaccuracy, since the temperature of the particle’s surface
is related to its internal processes and may not be equal to the kinetic
temperature, arising from the motion of a set of 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 Boltzmann constant__

**References**

^{1,0}^{1,1}Fedosin S.G. (1999), written at Perm, pages 544, Fizika i filosofiia podobiia ot preonov do metagalaktik, ISBN 5-8131-0012-1.- Мартынов
Д.Я. Курс общей астрофизики. М.: Наука, 1988.
- Wynn C. G. Ho. Constraining the geometry of
the neutron star RX J1856.5−3754. Monthly Notices of the Royal
Astronomical Society (2007) 380 (1): 71-77. DOI:
__https://doi.org/10.1111/j.1365-2966.2007.12043.x__.

**External**** links**

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