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Dark matter, the pulsars and the neutron stars
© Sergey G. Burago
D.Sc., Prof.
Email: [email protected]
Site: http://buragosg.narod.ru/
Abstract
In science is gaining the assumption that in the universe there are the two kinds of
matter. One of them is ordinary an baryonic matter, and the other is a dark matter. . It is
assumed that this the two kinds of matter do not interact together. In contrast to these views,
we assume that the dark matter between the stars, the planets and other objects in the
universe is in a gaseous state and is actively cooperating with a baryonic matter. The atoms
baryonic matter continuously absorb the dark matter, increasing its a mass. As a result, nearly
the all baryonic bodies, including the pulsars is implemented the radial flow directed to their
centers.
This view of the nature of the interaction of pulsars with a dark matter allowed to
formulate a new condition in order to prevent the destruction of these stars by centrifugal
forces. Now it is accepted that the periodic signals emitted by these stars is arise as a
consequence of rapid rotation of the radiation source located on the surface of pulsar. In
order to the centrifugal forces would not destroy the rotating stars the scientists had to admit
that a pulsars are very dense neutron star with a radius of 10 km to 20 km.
The neutron pulsars can not be measured. Therefore, their sizes and weight is represent
the purely speculative. On the basis of the developed theory of the gaseous dark matter this
paper is shows that the white dwarfs can be by pulsars. The existence of such objects in the
universe is undisputed and more natural than the existence of hypothetical neutron pulsars.
What do we know about the pulsars?
The stars are called by pulsars , if they are sources of short periodic pulses of radio
and X-rays. Most of pulsars, theirs are about 400, emit the pulses with a very short period
of Т1s.. (in the range of (T = 1-3s). But also the short-period pulsars are known:
PSR0835-45 with period T = 0,089s and PSR0531 + 21 c period T = 0,033s. The pulsar
is situated in a center of Crab Nebula. The pulsar-рекорд with smallest period T =
0,00155s was discovered in 1982 in the constellation Vulpecula. The discovery of the
pulsars has been awarded in 1972 the Nobel Prize.
The frequency of radio signal is associated with the rapid rotation of neutron stars. It
is believed that the star-the source of radiation is rotates like a lantern of lighthouse. It
creates a discontinuity of radiation. In order to explain the smallest period T = 0,00155s
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it assumed that star is rotating with a large number of revolutions n = 645 r/s. In this
case, there is a danger that it will be broken by centrifugal forces. The force of gravity is
opposes to the centrifugal forces. In order to prevent the destruction of stars, we have to
assume that a radius of pulsar is less than 20 km. The matter density of such star is close
to matter density of the atomic nucleis . These stars are called by neutron stars. Their a
weight is estimated to range from 1,4 to 3 mass of the suns.
The scientists have developed a theory of the neutron pulsars. They suggest that the
substance is compressed to a high density. It is converted into a mixture of neutrons with
small amount of protons and electrons. The internal structure of stars is described very
roughly.The physics does not have the necessary knowledge about properties of
neutrons, which are highly compressed. Nevertheless, it is believed that the neutron star
is not a gas but a liquid sphere. Would otherwise have to assume that the gas in a center
of star is compressed to more dense state than a substance of atomic nuclei. This,
apparently, is beyond a scope of the most incredible fantasies. It is also believed that the
neutron fluid is devoid of viscosity.
We will develop the our an attitude towards the neutron stars. The discontinuity of
radiation of pulsar is explained a rapid rotation of star. Only a force of gravity could to
keep the star from destruction by the centrifugal forces. This is required a very small
radius of star. It should be remembered that a density and a mass of these hypothetical
stars no one and ever was not measured. This is a purely theoretical star. Its role in an
implementation and a recognition of neutron pulsar has played the desire of number of
influential scientists to materialize a theoretical model of neutron star.
Therefore, we try to make up their own idea about these star. The such small sizes of
these stars is real whether they? Can whether be the some of observed stars "white
dwarfs" in order to act as pulsars? To answer this question we consider the most common
period of rotation short-period pulsars T=1s. If a white dwarf Wolf-457
( m = 1,01 ⋅ 10 30 kg , ro = 0,7 ⋅ 10 6 m ) revolved and radiated the radio frequency energy
with such period, then a force of the gravity is five times higher than the centrifugal
forces.
Fтяж
f ⋅ mo 6,7 ⋅ 10 −11 ⋅ 1,01 ⋅ 10 30
≥ 3 2 =
=5
Fцб
ro ⋅ ω
6,28 2 ⋅ (0,7 ⋅ 10 6 ) 3
(1)
This the example shows that some white dwarfs with the parameters close to Wolf457 may be by the short-period pulsars. The most common in nature a pulsation period,
and hence a rotation period can not lead to destruction of their by the centrifugal forces.
It should be emphasized that it is real and observable stars, rather than the invented stars
The theory of gaseous dark matter of pulsars
2
Developed in [1,2,3] theory of gaseous dark matter makes us to doubt in the
correctness of conventional explanations of blinking pulsars, their masses, densities and
sizes (radii). According to this theory, a radii of neutron stars were much smaller of radii
than the minimum radius of visible stars.
The fact that star - pulsar, like any other star, is a sink for dark gas [1,2,3]. Dark gas
flows to a center of star evenly along a radius. Therefore, a photons of light have to travel
against radial flow a dark gas towards a center of star. It reminds a swimming of
swimmer on a river against a current. If a speed of swimmer does not exceed the speed
of water, you can go as long as you want, but no one meter does not move forward with
respect to a banks.
The radiation from pulsars is captured with instruments on Earth. Therefore, we
believe, that a radial velocity of flow of dark gas [1,3] to star, was not exceed the speed
of the light m / s, emitted by star
Vro =
α ⋅ mo
<C
4πρ e ro2
(2)
If this condition is violated a star could not be seen. Let us take as the parameters of
pulsars a values: the radius ro = 20km = 2 ⋅ 10 4 m and the mass equal to the 3 solar masses
mo = 6 ⋅ 10 30 kg . The density of gaseous dark matter ρ e = 1,19 ⋅ 10 9 kg / m 3 . According to
[1,3] coefficient α = 1c −1 . The calculation of equation (2) gives a following values of
radial velocity on surface of star
Vro =
α ⋅ mo
6 ⋅ 10 30
=
= 1012 m / s
2
9
4 2
4πρ e ro
4 ⋅ 3,14 ⋅ 1,19 ⋅ 10 (2 ⋅ 10 )
(3)
The calculation result of equation (2) shows that a velocity of jets of gaseous dark
matter significantly (333 times) greater than a velocity of light. Consequently, the
pulsars would have been impossible to see if, they have mass and size such, what they
was rewarded by the astrophysics. The stars of this size are only suitable for the role of
"black holes" [5].
From the equation (2) we can to write an expression for a minimum radius at which star
is not visible
ro min =
α ⋅ mo
=
4π ⋅ ρ e ⋅ C
f ⋅ mo
α ⋅C
(4)
The minimum radius of star with mass of Sun and with a decrease in which a star
disappears from view according to expression (4) is
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ro min = 668,6 км.
As you can to see, this radius more than 30 times is greater than a maximum radius of
neutron star. So, out of 400 known pulsars only three pose is a problem if you count their
by white dwarfs. In this case the pulsars PSR0845-45 with the period T = 0,089s and
PSR0531 + 21, with the period T = 0,033s and, especially, the pulsar in the constellation
Vulpecula with period T = 0,00155s does not satisfy a criterion (1). Can not to ignore
this. Therefore, you should to find another an explanation for observed phenomena.
In modern astrophysics in order to explain this phenomenon had no other choice
exept to reduce a radius of pulsars before 20 km. The reason for this was the idea that a
space around star is empty. A radiation from other stars and the weightless
electromagnetic fields there is around it. Only a gravity can to counteract a centrifugal
forces. Therefore, the astrophysicists used a condition of equilibrium between centrifugal
force and force of gravity acting at pulsar.
In theory of gaseous dark matter, a neutron stars, as well as all the other stars, is
surrounded by an enough dense dark gas. In a dark gas there is a high pressure and this
pressure also is counteracts the tearing rotating stars. For the conventional gas-stars this
effect is small and it can be neglected. It is noticeable, and even is a decisive factor if a
star's surface is surrounded by a continuous layer of dense material. This is a continuous
layer of dense material which is discarded to periphery by a centrifugal forces and
compacted with a rapid rotation. We believe that this layer is able to perceive a pressure
of surrounding gaseous dark matter and that a pressure of gaseous dark matter is
counteracted to centrifugal forces.
Based on these considerations, arising from theory of gaseous dark matter [1,2,3],
we find a new condition of equilibrium of stars, rotating with high angular velocity. For
this we turn to fig.1. We shall have to select the segment of star by unit width. The mass
of this segment is
dmo = ρ o ro2
dθ
2
(5)
2
ro from the axis of
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rotation ω o = r ⋅ ω ), rotating with the angular velocity ω , centrifugal force is
For this mass (the center of mass is located at a distance rcg =
dFcg =
U o2 ⋅ dmo ρ o ⋅ ro3 ⋅ ω 2 ⋅ dθ
=
2
3
ro
3
(6)
This force is balanced by external pressure, acting on a surface of segment
dFp=perodθ
(7)
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In order to the segment of star was not taken out of star by centrifugal force, the
inequality must be satisfied
dFцб/dFp<1.
(8)
Substituting (6) and (7) in (8), we obtain
dFцб
dF p
=
ρ 0 ⋅ ro2 ⋅ ω 2
3 ⋅ pe
≤1
(9)
The average value of density of a matter star can be
estimated as a ratio of its mass to volume
Fig.1
ρ o = 3 ⋅ mo / 4π ⋅ r
3
o
(10)
Substituting this value into (9), we obtain a condition of failure star by centrifugal
forces
m0 ⋅ ω 2
=
≤1
dF p 4π ⋅ ro ⋅ p e
dFцб
(11)
The pressure [1,2,3] in a gaseous dark matter is . Further, we note that a density of
stars to white dwarfs is located within interval
ρ o = 0,4 ⋅ 10 8 kg / mo3 − 0,9 ⋅ 1012 kg / mo3
(12)
For our the white dwarf we select a density
ρ o = 10 8 kg / mo3
(13)
When such a density the radius of pulsar can be determined from formula (10)
ro = 3
3 ⋅ mo
4π ⋅ ρ o
(14)
We believe that condition (11) is holds for pulsar. We assume that an angular
velocity of pulsar was considered by the same as that of most rapidly rotating pulsar in a
constellation Vulpecula
ωo =
2π
6,28
=
= 4,05 ⋅ 10 3 s −1
T
0,00155
(15)
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From a condition of destruction of stars from by centrifugal forces (11) we have
mo 4π ⋅ p e 4 ⋅ 3,14 ⋅ 6,426 ⋅ 10 25
=
=
= 4,92 ⋅ 1019 кг/м
2
3 2
ro
ω
(4,05 ⋅ 10 )
We will replace in this expression
determine its a mass
mo =
(16)
a value of radius of pulsar (14) and then
3
(4,92 ⋅ 1019 ) 3 = 1,686 ⋅ 10 25 kg
4π ⋅ ρ o
(17)
From (16) we shall be to determine a radius of studied pulsar
ro =
1,686 ⋅ 10 25
= 0,343 ⋅ 10 6 m = 343км
4,92 ⋅ 1019
(18)
Thus, we have obtained the material object of universe with a density of white dwarf
with mass mo = 1,686 ⋅ 10 25 kg and radius ro = 343км . This radius is exceeds in 15 times
the radius recognized today a pulsars by the astrophysics ( ro ≤ 20km .). This is a visible
object, but is not a black hole. This pulsar is spinning as fast as a pulsar in the
constellation Vulpecula. Despite, what its have large size compared to size of neutron
stars, the centrifugal forces can not break it.
The sources of short periodic radio and X-ray pulsations
Such a high speed of rotation of pulsar possibly was acquired during a collapse
(disastrous compression) of large sparse space object. We can also to assume that a very
bright spot on its surface is a volcano. A volcano is erupted parallel to surface. As a
result this a jet was ejected and was action which is resulted to unwinding of pulsar.
Whatever it was, it is clear that a theory of gaseous dark matter is expands an
opportunity to explain a phenomenon of very rapid pulsations, which is observed by the
astronomers in the constellation Vulpecula. Not necessarily, to come up the neutron stars,
which can not be seen, which can not be measured, which can not be understood how
they work. Besides, their the dimensions match the dimensions of the black holes.
Therefore, they could not be seen. But the astronomers see them. Therefore they should
not be sized smaller than the size of white dwarfs. Apparently, mainly in recognition of
their to the real objects was a desire of number of the influential scientists to materialize a
theoretical model of neutron star.
It must be remembered that the pulsars-champions are extremely rare in a universe.
This is an unusual star. It not easy to find in a nature of real space object, in order to it
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rotates at speed n = 645 rps. But it was not torn by the centrifugal forces. These forces
are large even for the terrestrial mechanisms which is made by the people from the most
durable materials. It rotates with a number of revolutions .n=645 rps. But it can to
withstand an action of centrifugal forces
As an object of research we choose the cosmic body of type Jupiter. Jupiter is
characterized by the following parameters: a weight range moю = 1,89 ⋅ 10 27 кг , radius
roю = 7 ⋅ 10 7 м , a average density ρ ю = 1,32 ⋅ 10 3 kg / m 3 . Own an angular velocity of
Jupiter is ω ю = 1,76 ⋅ 10 −4 s −1 ( full circulation around its axis Jupiter makes in just 9
hours 55 minutes).
We suppose that a pulsar was formed due to explosion of cosmic body type Jupiter
with same mass moю = 1,89 ⋅ 10 27 kg and same angular speed ω ю = 1,76 ⋅ 10 −4 s −1 . The
radius is increased to values roю = 1,54 ⋅ 10 8 m . This is a real cosmic body, similar to
Jupiter. We believe that an explosion of cosmic body led to a collapse of masses. The rest
mass of the pulsar was mopul = 1,69 ⋅ 10 25 kg .
As a result of explosion of pulsar a density is increased and is amounted the value
ρ pul = 10 8 kg / m 3 . The radius of pulsar has become ropul = 0,34 ⋅ 10 6 m . From the law of
conservation of angular momentum of pulsar we can calculate a new value of angular
velocity. It is equal to angular velocity of pulsar in the constellation Vulpecula
ω pul =
moюω ю ro2ю 1,89 ⋅ 10 271,76 ⋅ 10 −4 (1,54 ⋅ 10 8 ) 2
=
= 4,05 ⋅ 10 3 s −1
2
25
6 2
mopul ropul
1,69 ⋅ 10 (0,34 ⋅ 10 )
In resulting a pulsar density is increased and became as a density of white dwarfs.
Therefore now a force of pressure on its surface is counteracted to destruction of pulsar
by centrifugal forces. Therefore, we must have a implementation of equation (11). The
calculation of this expression shows that a centrifugal force is less than a pressure force
restraining a destruction.
dFцб
dF p
=
m0 ⋅ ω 2
1,89 ⋅ 10 27 ⋅ (4,05 ⋅ 10 3 ) 2
=
= 0,25
4π ⋅ ro ⋅ p e 4π ⋅ 1,54 ⋅ 10 8 ⋅ 6,426 ⋅ 10 25
(17)
Thus, we see that a high speed of rotation of pulsar in the constellation Vulpecula
could be formed as a result of disastrous contraction (collapse) of real body such as
Jupiter. In this case, the resulting pulsar is not broken by the centrifugal forces.
An objection soon may be followed that Jupiter is not a star but is a planet
However, it is known that Jupiter radiates into a space twice more a heat than is receives
it from the sun. This is a sign of star and is unlikely to be challenged by a fact that over
4.5 billion years it is still hot. Too much time has passed. Studies have shown that Jupiter
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as the sun is composed of hydrogen and helium. From this perspective, Jupiter is a little
star. She did not self-luminous due to a fact that an energy of gravitational contraction
was insufficient for an appearance in it to the stable thermonuclear reactions. Jupiter, like
other a massive bodies of universe, eventually will be heats and in the future, increasing
its a mass and an energy reserves, could erupt as brightly as the sun.
We note in passing that a fairly large radio emission.there is from Jupiter. Jupiter was
first recognized by radio-emitting object at beginning of 1955 years, when the members
of Carnegie Institution B.F. Berk and F.L. Franklin have tied with Jupiter the strong
periodic bursts of radio noise at wavelength of 13.5 m. A little later, a radio astronomer
S.A.Shayn found that a frequency of bursts to radio emission is corresponds to period of
rotation of Jupiter on its axis. This relationship is well within by an assumption of
astrophysicists about interconnection of period of radio frequency of pulsars with a
rotation period of star.
A model of star has a right to exist and could to explain a nature of pulsar in the
constellation Vulpecula with a record number of revolutions n = 645 rps. Similarly, the
rapid rotation of two other anomalous pulsars PSR0845-45 and PSR0531 + 21, with the
rotation periods 0,089s and 0,033s. is explained in a same way
It can be argued that all the "white dwarfs" is rotated at high the angular velocities
around their axes. If, for example, to compress the Sun (roС=7⋅108m, ωС=2,9⋅10-6s-1) to
the size of star Wolf-457 (roВольф=0,7⋅106m), the period of rotation on the basis of law of
the conservation angular momentum would
Т=
2π 6,28
=
=2,165с,
ω
2,9
(19)
tthat fits a most widespread range of rotation periods of pulsars Т=1÷3 s.
Of course, it is difficult to imagine such a large reduction in size to value of 700 km.
But even more difficult to imagine how these stars have shrunk to a size of 10-20 km,
which today the astrophysics appropriated to neutron stars, or to a size of "black holes"
less than 3 km. Although there is no limit of human imagination. For example, the theory
of "big bang" implies that the entire universe was condensed into small elementary
particle with a negligible dimensions
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