**Stellar Dirac
constant**

The **stellar Dirac constant**, denoted as ħ_{s}, is a
physical constant, a natural unit of angular momentum and action for the
objects of the stellar level of matter.

**Содержание**

- 1 Origin
- 2 The stellar Dirac
constant in various relations
- 3 See also
- 4 References
- 5 External links

**Origin**

The introduction
of the stellar Dirac constant was one of the consequences of the development of
the theory of __Infinite Hierarchical Nesting of Matter__.
In 1999, while Sergey Fedosin studied __similarity of matter
levels__ and __SPФ
symmetry__, he determined the values of the __stellar
Planck constant__ h_{s}, which was related to the stellar Dirac constant
by a factor 2*π* : h_{s}
= 2π ħ_{s}.

At each
level of matter we can distinguish objects that have similar mass, but have
different sizes and matter densities. This is possible if the stability of
matter is maintained by various mechanisms. Thus, in the main sequence stars
the stability is maintained by the pressure of non-relativistic plasma, in
white dwarfs – by the pressure of electrons, and in neutron stars – by the
pressure of degenerate nucleon gas. Hence it follows that in order to establish
similarity between the stars and elementary particles, depending on the types
of stars, different sets of similarity coefficients can be used. In addition,
the stars of different types must have noncoincident values of characteristic
angular momentum.

For ordinary
stars and for planets, revolving around them, it is assumed that ħ_{s} =
2.8∙10^{41} J∙s. For degenerate objects, such as neutron stars, the
stellar Dirac constant is greater in magnitude:
ħ’_{s} = 5.5∙10^{41} J∙s. ^{[1]}
^{[2]}

The values
of the corresponding stellar Dirac constant can be obtained with the help of
the known coefficients of similarity between the levels of stars and elementary
particles. At the level of elementary particles the standard unit of angular
momentum is the Dirac constant ħ. Taking
into account the dimensional analysis, in order to determine ħ_{s} and ħ’_{s} we
must multiply ħ by the corresponding coefficients of similarity in mass, size
and speeds (more detailed information about it can be found in the articles __similarity
of matter levels__, __discreteness of stellar
parameters__, __stellar constants__, __hydrogen
system__).

In the hydrogen
atom the orbital angular momentum of the electron is quantized and is
proportional to ħ, and the nuclear spin
is assumed to be equal to the value ħ/2.
Similarly, the value ħ_{s} for planetary
systems specifies the characteristic orbital angular momentum of a typical
planet, ^{[3]} and the
value ħ_{s}/2 is close to the limiting angular momentum of
the low-mass main-sequence stars. ^{[1]} At the same time, the value ħ’_{s}/2 describes the angular momentum of rapidly
rotating neutron stars, such as PSR 1937+214, for which the angular momentum,
as the product of their inertia moment by the angular speed of rotation, can
reach L = 4∙10^{41} J∙s. ^{[4]} In white dwarfs the proper angular momenta
also do not exceed the value ħ’_{s}/2.

The analysis
of the orbital rotation of moons near planets shows that their angular momentum
was determined by the angular momentum of protoplanets during the formation of
the Solar system. The same applies to the orbital angular momentum of planets,
which have obtained their angular momentum from the rapidly rotating shell of
the Sun at the stage of compression of a gas-dust cloud into a star. The
discovered quantization of the specific orbital and spin angular momenta of
planets and planets’ moons supports the fact that __quantization in atomic
and stellar systems__ has the same mechanism that is
associated with equilibrium of energy fluxes in the matter of electrons and
protoplanetary clouds, respectively, at certain distances from the central
objects. ^{[2]}

**The stellar Dirac constant in
various relations**

1) For
elementary particles, the Chew-Frautschi plots are
known, ^{[5]} which correspond
to Regge trajectories in quantum mechanics and relate
the spin of particles in units of Dirac constant and the squared mass-energy of
these particles. Passing from the nucleon Chew-Frautschi
trajectory to the corresponding trajectory for neutron stars, taking into
account the data on the limiting rotation of neutron stars, ^{[6]} we obtain the following estimate: ħ’_{s} <
1.2∙10^{42} Дж∙с. ^{[1]}

2) The
coefficient of similarity in size Р’ can be found as the ratio of
the neutron star radius to the proton radius. If we now multiply the Bohr
radius (this is the most probable location of the electron in the hydrogen
atom) by Р’, we will obtain the value of
the order of 10^{9} m. The Roche limit (the distance, within which any
planet near a neutron star must disintegrate due to the gravitational force
gradient) has the same value. Observations show that at the given radius disks
of scattered matter are found near a number of neutron stars. ^{[7]} In
the theory of Infinite Hierarchical Nesting of Matter, such disks are assumed
to be the analogues of electrons in atoms. If we calculate the angular momentum
of these disks, it appears to be close in value to the stellar Dirac
constant ħ’_{s},
similarly to the angular momentum of the electron in the hydrogen atom, which
is equal to ħ.

3) The
stellar Planck constant and the stellar Dirac constant are related by a
numerical factor, therefore, in order to estimate the latter constant the
methods can be used, which are described in the article __stellar Planck constant__.
They include:

a) The ratio
based on the __de Broglie waves__:

J∙s,

where M_{s} and R_{s} are
the mass and radius of the neutron star, C_{s} is the __characteristic speed__
of the particles in the neutron star.

b) The
statistical angular momentum for a black hole as a measure of ħ’_{s}/2.

c)
Calculation of ħ’_{s} as a coefficient of proportionality between
the natural oscillation frequency and the excitation energy in the black hole.

**See**** also**

- Uncertainty principle
__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 Boltzmann constant
- Stellar Stefan–Boltzmann constant

**References**

- Fedosin S.G. (1999), written at Perm,
pages 544, Fizika i filosofiia podobiia ot preonov do metagalaktik, ISBN 5-8131-0012-1.
- Comments
to the book: Fedosin S.G. Fizicheskie
teorii i beskonechnaia vlozhennost’ materii. – Perm, 2009, 844 pages, Tabl.
21, Pic. 41, Ref. 289
__. ISBN 978-5-9901951-1-0__. (in Russian). - Fedosin S.G. Sovremennye problemy fiziki:
v poiskakh novykh printsipov. Moskva: Editorial URSS,
2002, 192 pages. ISBN 5-8360-0435-8.
- Шапиро С., Тьюкольски
С. Чёрные дыры, белые карлики, нейтронные звёзды. В 2 частях. – М., Мир,
1985.
- Коллинз П. Введение в реджевскую
теорию и физику высоких энергий. – М.: Атомиздат,
1980.
- Friedman J.L., Ipser J.R., Parker L. Rapidly rotating neutron star
models. – ApJ, 1986, Vol. 304, P. 115-139.
- Wang Zhongxiang,
Chakrabarty Deepto,
Kaplan David L. A Debris Disk Around An Isolated Young
Neutron Star. arXiv: astro-ph / 0604076 v1, 4 Apr 2006.

**External**** links**

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