Американский Научный Журнал QUANTUM TEORY OF SOLAR CORONA HEATING

74 American Scientific Journal № ( 29 ) / 20 19
отмеченных позиций на сегодняшний день активно
обсуждаются вне взаимосвязи межд у собой,
причем последняя из них отвечает известному
требованию (1), предъявляемому к физическим
моделям, которые ориентированы на объяснение
происхождения ос таточного фотонного излучения.
На вопрос о том, является ли идея о первичном
термоядерном взрыве адекватной реальности, в
настоящее время однозначного ответа нет,
поскольку непосредственные экспериментальные
свидетельства в пользу каждого из возможных
вари антов рождения вселенной отсутствуют.

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QUANTUM TEORY OF SO LAR CORONA HEATING

Mirzoeva Irina
Cand. Sc. Physics, Space Research Institute,
Russian Academy of Sciences,
Moscow
Chefranov Sergey
Dr. Sc. Physics, Obukhov Institute of Atmospheric Physics,
Russian Academy of Sciences,
Moscow

Ab stract. Data obtained in the framework of the INTERBALL -Tail Probe (1995 –2000) and RHESSI (from
2002 to the present) projects have revealed variations in the X -ray intensity of the solar corona in the photon energy
range of 2 −15 keV during the period of th e quiet Sun. Previously, a hypothesis was proposed that this phenomenon
could be associated with the effect of coronal heating. In the present study, a new mechanism of coronal plasma
heating is proposed on the basis of the experimental data and the quantu m theory of photon pairs that are produced
from vacuum in the course of the Universe’s expansion. A similar mechanism based on the splitting of photon
pairs in the interplanetary and intergalactic space is also proposed to explain the observed microwave ba ckground
radiation.
Keywords: photons, photons pairs, solar corona, coronal plasma heating

INTRODUCTION
In the previous studies [1, c.57], [2, c.316], [3,
c.92] variations in the intensity of solar X -ray emission
in the photon energy range from 2 to 15 k eV during the
period of the quiet Sun were investigated. The
phenomenon of a decrease in the intensity of solar
emission in narrow subranges of the X -ray spectrum in
the photon energy range of 2 −15 keV was revealed in
2005 [1, c.57] by analyzing the data o f the
INTERBALL -Tail Probe project. Further, this
phenomenon was confirmed by the data of the RHESSI
project. In [2, c.316], [3, c.92], the total range of soft
X-ray (SXR) emission from 3 to 11 keV was divided
into narrow subranges of w idth 1 keV, i.e., th e X -ray
spectrum was separately analyzed in the following
subranges: 3 –4, 4 –5, 5 –6, 6 –7, 7 –8, 8 –9, 9 –10, and 10 –
11 keV. Such a partition of the spectrum made it
possible to observe a drop (in some cases, an increase)
in the X -ray intens ity of microflares a nd thermal
background radiation of the solar corona. In some
cases, the maximum drop in the X -ray intensity was
shifted toward harder spectral range. Detailed analysis

American Scientific Journal № (2 9) / 2019 75

of the observational data revealed the subranges in
which the X -ray intensity most often decreased: these
are the subranges of 3 –4 and 4 –5 keV and, in some
cases, the subranges of 7 –8 and 8 –9 keV. Along with
this drop, an increase in the X -ray intensity was also
observed in the spectral subrange of 10 –11 keV
compared to th e other subranges in the total spectral
range of 3 –16 keV.
Let us consider an example of an atypical energy
spectrum of the thermal X -ray background of the solar
corona [3, c.92]. Figure 1 shows almost quiet thermal
X-ray background of the solar corona rec orded during
7 min o n March 10, 2003. In the figure, one can see the
above -mentioned drop in the X -ray intensity in the
subrange of 3 –4 keV and, simultaneously, an increase
in the intensity in the subrange of 10 –11 keV. This
phenomenon is well illustrated in Fig. 2, which sho ws
the energy spectrum of the thermal background of the
solar corona measured in time interval from 13:44 to
13:51 UT on March 10, 2003. The photon energy (in
keV) is plotted on the abscissa, and the intensities of
each component in the energy range from 3 to 11 keV
(in counts per second) are plotted on the ordinate. The
plot is compiled from the data presented in Fig. 1. A
typical descending X -ray spectrum in the photon
energy range from 4 to 10 keV is disturbed by a sharp
drop in the X -ray intensity in th e subrange of 3 –4 keV
and by an increase in the subrange of 10 –11 keV.

Fig 1. Data from the rhessi experiment

Fig 2. Energy spectrum

It was ascertained in [2, c.316], [3, c.92] that such
behavior of the X -ray spectrum was independent of the
solar flares and other events that took place in the active
flare regions of the solar corona. It was also supposed
that the physical mechanism for the observed
phenomena was associated with quantum processes
and, in turn, this mechanism could be responsible fo r
the anomalous heating of the solar corona plasma. For
better understanding of what follows, let us make some
digressions. In this paper, we will repeatedly use the
following conce pts and terms: axions, the Primakov
effect (direct and inverse), conversion of axions, etc.
Let us briefly explain their meanings.
The most challenging problem of modern
astrophysics is the search for dark matter. As one of the
candidates for the elementar y particles that form dark
matter, axions are considered. They are hypothet ical
electrically neutral pseudoscalar elementary particles
that can be involved in the electromagnetic and
gravitational interactions. In the original theory, the rest
mass of an a xion (in energy units) was assumed to be
fairly large (100 keV). Later, it was suggested that the
axion mass should be as low as 0.02 eV and this became
the main difference of axions from the so -called
“weakly interacting massive particles” (WIMPs),
which are another candidate for the elementary
particles forming dark matter. All particles that are
similar to axions and unified by the general term
“weakly interacting slim particles” (WISPs) are
assumed to have a very low mass and weakly interact
with other particles [4, c.116]. Initially, axions were
introduced rather artificially to explain the violation of
the СР -symmetry in strong interactions [5].
Theoretically, under the effect of a static electric or
magnetic field, axion should spontaneously decay int o
two photons. This effect was called the inverse
Primakov effect. Accordin gly, the direct Primakov
effect is the resonance conversion of photon into a

76 American Scientific Journal № ( 29 ) / 20 19
pseudoscalar particle (axion) in the electric or magnetic
field. Such conversions of axions into photons and back
are often called the conversion of axions. Figure 3
shows the Fey nman diagram that illustrates the
conversion of an axion into a pair of photons and bach,
i.e., the inverse and direct Primakov effects. In theory,
due to the conversion of axions i nto photons, “vacuum”
should acquire certain optical properties (birefringe nce
and dispersion) in the magnetic or electric field. Many
experiments on the search of axions are based on the
Primakov effect (direct and/or inverse). It is proposed
to consider the cores of stars (in particular, the Sun’s
core) to be sources of axions. In theory, there are a
number of processes that should contribute to the
formation of the axion flux from the Sun: the Primakov
effect, Compton scattering, scattering of electrons by
electrons and ions, recombination, and deexcitation.

a- axion, γ- photons
Fig 3. Feynman diagram

To detect solar axions, a number of experiments
were performed. In particular, the CAST (CERN Axion
Solar Telescope) experiment is being conducted in
CERN since 2003. The CAST experiment is aimed at
detecting axions that ar e assumed to be emitted (due to
the Primakov effect) by the solar core plasma with a
temperature of ~15 × 10 6 K [6]. No axions or expected
effects that could confirm their existence have been
observed in any experiment [7, c.10], [8], [9, c.6].
However, in 2014, J. Fraser et al. [10], scientists
from the XMM -Newton International Space
Observatory, reported on the indirect d ata that
evidenced in favor of the existence of axions. The main
idea of the XMM -Newton experiment was to attempt
detecting solar axions that, in accordance with the
Primakov effect, should convert into photons in the
Earth’s magnetic field. Of course, it is possible to detect
only these resulting X -ray photons, which are a kind of
marker indicating the presence of axions. The authors
of t he experiment believed that, in order to see these
photons, the telescope should not be directed straight to
the Sun, be cause several conversions have time to occur
in the Earth’s magnetosphere. Due to the motion of the
Earth around the Sun, the mutual ori entation of the
geomagnetic field lines, the direction of observations,
and the direction to the Sun changes throughout the
year. Therefore, the telescope should detect seasonal
variations in the X -ray background in the Earth’s
magnetosphere. The backgroun d associated with
distant galaxies, interstellar gas, and cosmic radiation
passing through the solar system should remai n
approximately constant, while the part of the
background associated with axions should vary
seasonably. In addition, for the purity of the
experiment, the brightest X -ray sources (such as stars,
star clusters, and other compact X -ray objects) were
exclud ed from observations. Thus, a “clean X -ray sky”
was obtained. Against this “cleaned” background, the
desired seasonal variations in the X-ray background in
the Earth’s magnetosphere were observed. On the basis
of the XMM -Newton experiment, it was concluded
[10] that axions (the candidates for the dark matter
particles) are actually produced in the Sun’s core and
converted into SXR emission in the Earth’s magnetic
field, which leads to seasonal variations in the X -ray
background in the spectral range of 2 –6 keV.
Additionally, narrow axion lines associated with
silicon, copper, and iron were detected in the same
energy range.
Let us now retur n to the previously discussed
results. In [2, c.316], [3, c.92] atypical behavior of the
energy spectrum of the thermal X-ray background of
the solar corona was analyzed. In narrow bands of the
energy spectrum, drops and, in some cases, rises of the
X-ray intensity were observed. Recall that we speak
about the same photon energy range of 2 –6 keV as in
the XMM -Newton experim ent. The difference is that
variations in the X -ray intensity were found in the solar
corona, whereas in the XMM -Newton experiment, the
X-ray background of the Earth’s magnetosphere was
investigated. Similarly to the XMM -Newton
experiment, the data on the X-ray background of the
solar corona were carefully selected. Data from large -
scale solar events were excluded to obtain pure X -ray
back ground of the solar corona. The coincidence of the
energy ranges and the presence of variations in the X -
ray background intensity in both experiments cannot be
accidental. Most likely, these experiments indicate that,
in both cases, there is a common reaso n for the
observed X -ray events.
One can see some contradictions that occur in the
course of the long search for one of the candidates for
the dark matter particles. On the one hand, the main
evidence in favor of the existence of axions is the
experimental ly proved variations in the X -ray
background intensities of the solar corona and the
Earth’s magnetosphere. On the other hand, axions
themselves were not detected in any of the numerous
experiments carried out in ground -based laboratories.
The situation is strange because there is indirect
evidence of the effect, but the axions themselves that
are responsible for this effec t have not been detected.
This work is intended to eliminate this contradiction.
PHOTON PAIRS
Photons are the most widespread particles in the
Universe. They have a zero rest mass and can propagate
at a speed of с = 300 000 km/s. However, such a speed
can be achieved only in absolute vacuum, which can be

American Scientific Journal № (2 9) / 2019 77

found almost nowhere in nature. In fact, the photon
properties commonly postulated in classical physics are
a simplified model.
In [11, c.731], [12], a generalization of the Gliner –
Sakharov hydrodynamic va cuum theory [13, c.378],
[14, c.559], [15, c.70] was obtained in the framework
of the modified general theory of relativity (MGTR),
whic h is in good agreement with the observational data
on the accelerated expansion of the Universe. In [11,
c.731], [12], i t was shown that the exact solution to the
MGTR equations has a structure corresponding to the
quantum theory of gravitation generalized to the case
of a finite value of the cosmological constant [16, c.82].
From the condition of their exact coincidence, t he mass
of ultralight scalar bosons continuously produced due
to the polarization of vacuum in the course of expansion
of the Universe w as found to be g. In
this case, the possibility was considered to identify
these scalar bosons with photon pairs that are produced
from vacuum, have a zero total helicity and (similar to
axions) can be dark matter particles.
If w e assume that the observed coronal produc tion
of photons with energies of keV is due to the
splitting of photon pairs in the magnetic field of the
solar corona ( G). Then, from the relation
, we can determine the magne tic moment
M of photons in the splitting photon pairs (the volume
density of which is determined by the energy density in
the corona),
(1)
Estimate (1) of the photon magnetic moment can
be taken into account when interpreting the
observational data from full -scale and laboratory
experiments, e.g., experiments on the Faraday effect.
We also note that, in [17], the electric dipole
moment associated with each photon pair was also
estimated to explain the observed bary on asymmetry
(in [17], such photon pairs were called gravitons).
According to the theory proposed in [11, c.731],
the Universe existed for unlimited time in the past, with
no singularities associated with the Big Bang or its
infla tionary modifications. By this theory, the photon
pairs are continuously produced all over the space and
the observed microwave background radiation (MBR)
should also be a consequence of this process of
production of photon pairs from vacuum in the course
of expansion of the Univer se (which, according to the
estimate obtained in [11, c.731], should last for another
38 billion years and then change for its compression).
In this case, the MBR can be formed due to the
splitting of photon pairs in the interplan etary and
intergalactic ma gnetic field. Indeed, for a typical
magnetic field of G and the
magnetic moment given by expression (1), the theory
yields K.
In the photon pair under consideration, the two
constituent photons (similarly to a single photon)
display both the particle and wave properties,
depending on their energies and the properties of the
ambient medium. The lower the frequency (i.e., the
longer the wavelength and the lower the energy), the
closer the propertie s of the photon pair to the wave
ones. The higher the frequency (i.e., the shorter the
wavelength and the higher the energy), the closer the
properties of the photon pair to the particle ones. In this
case, it is the photon pair that serv es as the quantum of
electromagnetic interaction. Figure 4 illustrates a
photon pair in terms of the conventional oscillating
electric and magnetic field vectors ( Е1 and Е2, and Н1
and Н2, respectively). Each photon in the pair has its
own pair of the Е and H vectors, which oscillate at an
angle of 90° relative to one another. It is well known
that a photon can have either right - or left -handed
helicity. Therefore, each photon in this pair can also
have right - or left -handed helicity. However, the pair

Fig 4. Photon pair

as a whole should have a zero total helicity, i.e.,
the photon pairs are composed of photons of opposite
helicity. It is due to this structure that a photon pair
splits in a magnetic field. The properties of a photon
pair can be revea led from indirect indications that
manifest themselves in the interaction with ambient
particles or due to the splitting in a magnetic field.
SOLAR CORONA HEATING
Since photon pairs should split i n any magnetic
field, such splitting should also occur in th e solar
corona. It was experimentally ascertained that the
spectral intensity of the X -ray background of the solar
corona in the photon energy range of 2 –6 keV decreases
or increases in time. In o ur opinion, this is a result of
the splitting of photon pair s, accompanied by an energy
release, which, in turn, results in an increase in the
coronal plasma temperature. However, this increase is
limited and the temperature of the solar corona plasma
is m aintained at a constant level of Т = 1.5 × 10 6 K. This
may b e due to the fact that, after splitting, photon pairs
can recombine again and also interact with ions and
electrons of the hot plasma. A fraction of the energy is
radiated from the solar corona in to open space, due to
which the temperature balance is maint ained. Due to
the high matter density inside the Sun, the radiation
generated in the solar core and propagating through the 66 0 3 10 m −  3 E 100 H = E HM= 14 4.8 10 J/T. M − = 5 0.765 10 H −  2.725 T 

78 American Scientific Journal № ( 29 ) / 20 19
zone of radiation energy transport toward the solar
surface very slowly diffuses through the inner layers of
the Sun, because it is permanently absorbed and
reradiated by heavy atoms and ions. It is for this reason
that the processes of splitting of photon pairs are almost
absent inside the Sun and practically do not affect th e
distribution of temperature, which, as is well known, is
maximal in the core and gradually decreases toward the
photosphere. When the solar radiation escapes from the
photosphere, the matter density drops and the radiation
begins to propagate relatively freely. In the
chromosphere and, then, in the corona, the fl ux of
photon pairs enters the region with a strong magnetic
field, where they split and an energy is released, due to
which the coronal plasma is heated to a temperature of
1.5 × 10 6 K. Further, d ifferent interaction scenarios for
the split photon pair can take place: recombination;
various types of interactions with ions and electrons of
the hot coronal plasma, followed by the emission of
secondary photon pairs; etc.
CONCLUSIONS
Experimental data obtained in the INTERBALL -
Tail probe, GOES , RHESSI , and XMM -Newton projects
made it possible to analyze a number of physical
phenomena that occur in the solar corona and Earth’s
magnetosphere and derive the following estimates and
conclusions.
1. The observed variations in the intensity of the
X-ray background of t he solar corona in the photon
energy range of 2 –6 keV were confirmed by
observations of the X -ray background of the Earth’s
magnetosphere performed in the XMM -Newton
International Space Obser vatory. A conclusion is made
on the common mechanism of these phe nomena.
2. To explain the mechanism for variations in the
X-ray background intensities in both the solar corona
and the Earth’s magnetosphere, the quantum theory of
photon pairs produced from vacuum of the expanding
Universe, as well as in the processes oc curring in the
solar core, is involved. A hypothesis on the splitting of
photon pairs in the interplanetary and intergalactic
magnetic fields, as well as in the magnetic field of the
solar co rona, is proposed.
3. For the energies of photon pairs in the ran ge of
2–6 keV, the photon magnetic moment is estimated for
a nonzero mass of ultralight scalar bosons (photon
pairs).
4. Assuming that the MBR of the Universe is
caused by the splitting of ph oton pairs and taking into
account the magnitudes of the interpla netary and
intergalactic magnetic fields and the obtained estimate
for the photon magnetic moment, the obtained radiation
temperature is found to agree with the well -known
MBR temperature K.
5. It is hypothesized that the mechani sm of coronal
plasma heating is due to the slitting of photon pairs in
the magnetic field of the solar corona.

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