____________________________________________
What
is Beneath the Sunspots?
By:
Mahmoud E. Yousif
e-mail: yousif@exmfpropulsions.com
C/O Physics
Department - The University of Nairobi
P.O.Box 30197
Nairobi-Kenya
ABSTRACT
Sunspots continued to
represent enigma phenomena. The recent detection and measurement
of sunspot magnetic
field region, while emerging from solar interior, lead
to suggestion of an elongated plasma body model composed of oppositely gyrating
electrons and protons. It is thought to produce the Plasma Body External
Magnetic Field (PBEx). Magnetic field emanating
from PBEX is thought to interacts
through Active Region External Magnetic Field (BAREx),
with the granules and photosphere constituents, magnetizing these layers, and
forming patches or sunspots. Produced magnetic force resulted from that, pulls
the granules forming Wilson depression. An inter-atomic mechanism that
decreased granules (sunspots) temperature due to BAREx interaction
with atomic magnetic field, is proposed. The knowledge of these mechanisms may
help to understand the solar activities and how it should be predicted to
protect humanity from any hazardous consequences.
Key words:
Sun activity; granulation; photosphere; sunspots; Sunspot Model; surface
magnetism
1: Introduction
The sunspot phenomenon,
with its reduced temperature and intense magnetic field, continued to be
without scientific explanation, until now [1], but recent developed
technologies had improved specialized satellites studying the sun [2], with
ability to convey above and sub-surface solar activities data in several
wavelengths [3], that had opened the Heliospheric to in-depth solar data
activities, making possible to conceive sunspots as a block unit [4].
Sunspots are the dark
spots seen on sun’s surface [5], they are regions where strong magnetic fields
emerge from solar interior and where major eruptive events occurs [6], it was studied
individually as a phenomenon with strong magnetic field [5].
Until now, sunspots are
conceived as a magnetic flux entity that emerged from sun’s interior [7], but
the Helioseismology–methods allowed for in-depth analyses of sun’s interior
[8], while the Solar Dynamic Observatory (SDO) footages clarify many
obscurities [9], but the ignorance of the subsurface structure of sunspots, had
led to arbitrary interpretations for the magnetic field conditions underlying
the sunspot [10], which had led to such many approaches and theories tackling
sunspots concentrating on magnetic flux tubes perspectives [1].
There are two main
hypotheses for the structure of the subsurface magnetic configuration of the
spot: the monolithic model and the jellyfish/cluster/spaghetti model [11], and
although there are several existing classes of sunspot models, but they are
more or less suited to local helioseismology [11], and as new sunspots images
may bring challenge to solar physics such as treatment of penumbra filaments as
“convection cells” [12], or the twisting motions of penumbral
filaments [13], and realization of existence of several sunspots penumbras
in photosphere layers [14]. With many examples demonstrate that, and
that, the numerical simulations are capable of reproducing many features of
the helioseismic measurements [11], but it was found
that, the simulations models, cannot address fundamental questions
regarding the subsurface structure and origin of sunspots [11],
and with current universal invocation of magnetic field in the
theoretical interpretation of nearly all anomalous or active stars and
galaxies, it was suggested that, some attentions are to be given to the
development of the basic physics of the magnetic fields themselves [1], and
although some simulations were carried out, but still they didn’t address the
question of the nature of the deep structure of sunspots [11]. Therefore, if
any advancement is thought to be achieve within the solar physics studies, the
plasma body responsible of producing that magnetic field must be investigated,
together with the mechanism producing sunspot magnetic field.
This paper analyzed the
detected and emerged sunspot underneath sun surface [6] together with
the ultraviolet footage of sunspot drifting beneath photosphere in
synchronization with effects on solar surface[15], these had lead to a proposal
of a shape for a plasma body beneath the sunspot, a body which is responsible
of generating intense Plasma Body External Magnetic Field (PBEx).
Although the production of external magnetic field (ExMF) outside
an atom was previously suggested [16], but the formula used is to obtained the PBEx,
when the Sunspot External Magnetic Field (BSEx), together
with the radial distances (rpp), from middle of the
plasma body to the measured point are known, (this could be adjusted to be
known at any photosphere altitude).
The Active Region
External Magnetic Field (BAREx) emerging from PBEx,
is thought to magnetized the known changes on the granules and upper
photosphere [14], while the decrease in granules (sunspots) temperature is
thought to take place due to interaction of the BAREx with
granules atoms on micro-levels, leading to reduction in excitation energy, and
temperatures of these atoms, hence sunspot temperature. Interaction of the
resulted magnetization with BAREx, produced
Wilson Depression Magnetic Force (FWD), pulling the
granules within the BAREx radius.
The knowledge of such
plasma body and the PBEx would change many
perceived ideas about sunspots, solar interior and will help building logical
theory about sunspots, solar flares and the solar activities in general, with
ability to predict the solar storms in advance, which in final analysis will
reflects positively on human ability to regulate environments and safeguard human
and technologies in Earth and space.
2: Emerged Sunspots and Measured
Magnetic Fields
The study of sun’s
interior, using acoustic waves, in time-distance helioseismology, detected
sunspots, 65,000 km while submerged deep inside the sun [6], as shown
in Fig.1 [17].
The study, also showed
simultaneous changes on both the photosphere and the detected magnetic fields
intensity, where the magnetic flux rate of Active Region (AR) 8164, steeply
increased when it started emerging from deep inside the sun, as shown in
Fig.2-D by the red line [6], this also brings to attention that, since the
detected flux reflects intensity and location of the internal magnetic field on
the solar photosphere [18], therefore the magnetic field as shown in Fig.2, was
attained gradually while the sunspot is raising towards the photosphere, as
shown in Fig.1.
3: An Elongated Submerged Body
An elongated sunspot
body was detected by SOHO at lesser depth, as shown in Fig.3, in
which the distance between the surface and the end of the submerged body
is 24 Mm [4]. Relative measurements of this distance within the figure,
gives the distance between the top of the plasma body and the umbra
and penumbra on the surface as 6.5 Mm, and the radial distance from the middle
of the plasma body to the photosphere (rpp) as 15.2
Mm, from Fig.3. the object clearly shows the elongated nature of the plasma
body.
The plasma body
structure of Fig.3, is in contrary to the notion that both umbra and penumbra
are part and parcel of sunspots entity, that constitute an integral part of
sunspot body as depicted by the raising flux tube [19], although studies
were carried on the physical characteristics of umbral dots (UD) such
as temperature stratification, magnetic field vector, and line-of sight (LOS)
velocity to understand the nature of UDs [20], and number of simplified (and
partly conflicting) models have been suggested to explain the structure and
outflows of penumbrae [4], but a comprehensive theoretical understanding of the
basic mechanisms does not exist [10], therefore the true picture and nature of
sunspots not yet been elaborated .
4: Sunspots: The Elongated Body Verses
the Magnetic Effects
In the two snap
shots shown in Fig.4, from UV and light wavelength movie by Solar
Dynamics Observatory (SDO), sunspot group is shown moving westwards of the
solar disk [15], from Fig.4-B, some observations were made that, the
leading negative (-Ve), Blue color sunspot rotate clockwise, while the positive
(+Ve) Magenta color sunspot rotates counterclockwise, this is also seen in a
continually play short part of the movie [21], and as shown in Fig.4-A, and
regardless of the movements in the movie, that both the leading –Ve Blue
color and the lagging +Ve Magenta color sunspots are connected by closed
magnetic lines of force, while an open magnetic lines of force emerged from
both the encircled leading –Ve Blue color and the lagging +Ve Magenta
color sunspots. The magnetic lines of force connecting both the leading
–Ve Blue color and the lagging +Ve Magenta color sunspots, rotates
along what seem to be an imaginary axis joining the –Ve Blue color sunspot
and the +Ve Magenta color sunspot, as shown in Fig.4-A.
Therefore from these
observations and descriptions, and as the main footage shows a rotation along
an imaginary axis [21] and as from direct surface measurements, it is well
known that active regions rotate faster than quiet ones, which was confirmed
with helioseismology [12], therefore, it is clear that, an elongated body
of plasma connecting both the negative and the positive poles, this body is
depicted in Fig.4-A by the violet color body, it is thought to consist of
plasma joining both the –Ve-1 with +Ve-1 poles and –Ve-2 with the +Ve-2 poles
therefore, these submerged plasma bodies depicted in Fig.4-A are the one
producing the magnetic field that caused effects on the photosphere shown in
Fig.4-B.
5: The External Magnetic Field (ExMF)
and the Magnetization Effects
As an
elongated plasma body detected by SOHO and shown in
Fig.3 [4], and as suggested, in Fig.4-A, that an elongated plasma body
links poles of opposite magnetic fields, and since the Maps of the travel-time
anomalies showed the signatures of emerging flux that are mostly concentrated
in circular areas with a typical size of 30 to 50 Mm [6], and the
field lines at these points are usually directed away from the surface, or
vertical field [22], and that, while the main plasma body raises
towards the surface or drifts westwards, it continually produced intense
magnetic fields as shown in Fig.4-A by the magnetic lines of force emerging or
entering -Ve-1, +Ve-1, -Ve-2 and +Ve-2 poles, and since an intense magnetic field
was detected and measured raising in linear proportionality with the raises of
the plasma body as shown in Fig.2-D [6], and also measurement
analysis showed that the longitudinal component of these magnetic fields change
with the height, where the umbrae and penumbrae of sunspot exhibits
longitudinal magnetic fields that decrease with height, as shown in Fig.5 [23],
which imply an increase of the magnetic field inward to the plasma body in the
sun interior.
Therefore, as it was
suggested, an intense External Magnetic Field (ExMF) could be
produced by a plasma body [16], thus an ExMF is
also produced by plasma body shown in Fig.4-A, and such fields is the one
measured in Fig.2-D and other figures [23], the intensity of which is
strongest at the body center, and is designated as the Plasma Body
External Magnetic Field (PBEx), hence the radial
magnitude of this field as measured from the sunspot is designated as
the Sunspot External Magnetic Field (BSEx), and
it is given by
Where, PBEx is
the Plasma Body External Magnetic Field in Tesla, rpp is
the radial distance from the middle of the plasma body to the granules or the
interaction distance as shown in Fig.3, θ is the angle of the detected magnetic
field at the photosphere, and the measured Sunspot External Magnetic Field (BSEx),
is in Tesla.
The total produced
Plasma Body External Magnetic Field (PBEx), at the
center of the plasma body, is given by
Where, BSEx is
the Sunspot External Magnetic Field, is in Tesla, and the total produced Plasma
Body external magnetic field PBEx is in
Tesla.
Since a physical
similarity of convection existed between the granulation and penumbra [10], and
that the measured value of magnetization depends on the value of applied
magnetic field [24], therefore, it is suggested that, the magnetic field
produced by the plasma body shown in Fig.4-A, the magnitude of which is given
by Eq.{1} above, interacts and magnetized different layers of the
photosphere starting with the granules, as shown in Figs.1, 3, 4 and different
other layer as shown by Figs.6 & 7, [25, 14], the magnetization is
given by
Where, BAREx is
the Active Region external magnetic field, it is the field produced by the
plasma body Plasma Body External Magnetic Field (PBEx)
in Tesla, H is the H-field it is ampere-turn per meter or Tesla, the μ0 is
the permeability of free space (4π×10−7 V·s/(A.m),
and the magnetized Sunspot Field MSS, or the
sunspot external magnetic field (BSEx) in Tesla.
The magnetization is
also given by [24].
Where, χm is
the volume magnetic susceptibility and H is the applied magnetic field.
As the magnetized
Sunspot External Magnetic Field (BSEx) given in
Eqs.{3&4} is not the Active Region external magnetic
field (BAREx), produced by the plasma Body and shown
in Eq.{3}, and as clearly seen, BSEx is only
a reduced magnitude of BAREx, therefore, BSEx given
by Eq.{1}, becomes
Where, M% is
the percentage of Magnetization loss of the original BAREx,
in Tesla.
From the above
discussion, the total magnitude of the of the Plasma Body External
Magnetic Field (PBEX), given by Eq.{2}, becomes
Therefore from Eq.{5},
the Active Region external magnetic field (BAREx), is
given by
6: The Wilson Depression
As the polarity of
detected and measured magnetized sunspot field (MSS),
or the Sunspot external magnetic field (BSEx) is
opposite to the Active Region external magnetic field (BAREx),
therefore both fields interacts and resulted in the attractive magnetic
force [26] or the Wilson Depression force (FWD), the FWD polls
the magnetized granules, and it is given by
Where, BSEx is
sunspot external magnetic field, BAREx is
the Active Region External Magnetic Field at the lower edge of the
granules, rPS2 is the radial
distance from the Plasma Body to the granule’s sunspot center, c is the speed
of light, θ is the angle between both magnetic fields, and the Wilson
Depression magnetic force FWD is in Newton.
If the Sunspot
external magnetic field (BSEx) is equal in magnitude
to the established field, or the un-magnetized Active Region external magnetic
field (BAREx), therefore Eq{8} becomes
7: The Plasma Body
As given by
Eqs.{3&4}, appearance and sunspots patches movements on solar surface
doesn’t always reflects the true shape of the internal body creating the
sunspots, rather it reflects some of features it posses, such as the ability to
magnetized umbra and penumbra as shown in Figs.1,2,3,4,6 and 7.
With lack of recognized
sunspot model, that could withstand scientific credibility, and based on the
analysis carried on Fig.4, and since sunspot is an ideal situation to
guide the theoretical development because the spot is observable down to the
small details [1], therefore the plasma body beneath the surface is
thought to consist of two inter-related charged particles, capable of
producing ExMF [16] or the PBEx,
the electrons structure in front, followed by the protons structure, as shown
in Fig.8, the plasma body is characterized by the followings:
The PBEx produced
by the sunspot in Fig.8, is in line with the conventional idea of the magnetic
field configuration of a sunspot [1].
The red plasma body
structured formed by gyrating electrons, spinning clockwise, while the lower
blue plasma body formed by gyrating protons, that spinning counterclockwise.
The intense magnitude
of produced PBEx is at the center of the
plasma body.
The intense portion of
the field is the polar field (θ factor) which first interacts and
magnetized the Granules forming the umbra, hence designated as umbra zone.
In Fig.8, the closed
field, which interacts with the Granules and upper photosphere’s layers
(Eq.(4)) forming the penumbra, it is designated as penumbra zone.
The upward movements of
the plasma body, as shown in Fig.8-A, represented by the small radius at the
top, occurred during the photosphere raises, as detected and shown in Fig.1,
and Fig.2-D.
The poleward or
westwards movement, shown in Fig.8-B, is where the plasma body inclined while
drifting, the heavy protons at lower end and at rear, while the lighter
electrons on top and in front, similar to westwards movement shown in Fig4-A.
Due to imbalance
between the heavy protons and lighter electrons constituents, the whole
spinning of the plasma body is so strange.
8: The Magnetic Effects
When the plasma
body raises towards photosphere, BSEx intensity
as given by Eq.5, increased, hence the polar field, shown in Fig.4-A and Fig.8,
it interacts with the granules according to Eqs.{3&4},resulting in the
magnetization and formation of magnetic patches on the granules [10],
afterwards the less nonpolar field, also interacts with photosphere
materials and magnetized them accordingly, forming patches, which could
also be formed at upper layers within the photosphere [14] depending on existed
elements types, as shown in Fig.6 [25] and Fig.7 [14] or only on the
granules as shown in Figs.1, 3, and 4.
Since
the photosphere elements are known [27], and that the interaction
increased with the materials susceptibility in each layer as given in Eq.{4},
hence this re-shaped the penumbra to trace the open magnetic lines of
force as shown in Fig.6-C and Fig.7, thus the created sunspot effects, is
similar in process to iron filings attracted to horseshoe magnetic fields or
lodestone field [28], which also explained the seen twisted motion of
the filaments as an actual twisting motion or turn of individual filaments
about their axis [13], as a process within line of force.
Therefore, it could be
stated that, the Umbra and Penumbra reprepresents the level at which the
granules or different photosphere constituents can be magnetized by the raising
intense plasma body magnetic field.
From observations of
pores and their transformation into sunspots [11], pores are low degree of
magnetization due to low intensity of BAREx, this
occurred when the plasma body in Figs.3 & 4 are raising to the surface, and
the interaction distance rpp is less than to
trigger the magnetization effects. If the closed (horizontal) field angle
increased to θ (γ) ≥ 35◦ [11], this lead to increase in
magnetization, hence penumbra appeared and pore transformed into sunspot.
Since the intense open
magnetic field produced by the plasma body is circular around the poles,
therefore, the magnitude of magnetic field towards the closed field, decreased,
reducing magnetization given by Eq.{3}, this explained observed bright rings
around sunspots [11].
9: Sunspots Temperature Phenomenon
Knowing that,
the detailed structure of granulation is not as
simple as suggested by its convective origin [29], therefore
the raising magnetic field, such as detected and shown in
Figs.1&2. [9] and proposed by Fig.8, interacts (in addition to
Eqs.{3&4}) with the granules in accordance to Eq.(3), together with the
first law of thermodynamic [24], the resulted energy is given by
Where, Q is the heat
added to the system, W is the work done by the system, and the change in the
internal energy ±dU is in Joule.
Since
the photosphere is one of the coolest regions of the Sun (6000 K), and
only a small fraction (0.1%) of the gas is ionized (plasma state) [30], this
imply that almost all photosphere elements are in a continual excitation
state, therefore the atom’s energy at such state is given by [26]
Where, B1U is the
nucleus spinning magnetic field (SMF) [26], vD is the
excitation velocity, rn is the excited
orbital radius, q is electric charge, and the
energy En is in Joules.
The balance of energy for Eq.{11}, is given by
Where, me is electron
mass in kg, and the nucleus SMF is given by
The deduced BAREx given
by Eq.{7}, effected the granules’ inter-atomic parameters, and interacted with the nucleus SMF or B1U of granules,
as given by Eq.{13}, therefore subtracting BAREx from B1U,
thus Eq.{13} becomes
Reduction in B1U lead
to reduction of the
excitation velocity vD, increase in the excited
orbital radius rn, hence reduction in the atomic
excitation energy, therefore based on Eq.{13}, the balance of energy given by
Eq.{12} becomes
But the formula
of heat energy [31] is given by
Where, Cp is the
Specific heat in J/kg x degrees C, m is the mass in kilograms, delta T is the
change in temperature in Celsius, the Heat energy (H) is in Joules.
We assumed that, Heat
energy produced by Eq.(16) is equivalent to that produced by Eq.{15} multiply
by number of electrons involved in that, thus
Where, ne is
the number of electrons in unit volume.
It was proved that,
there is strong relation between Umbral normalized continuum
intensity vs. umbral field strength BSex [32],
therefore from Eq.{17}, the field strength is proportional to
lose in intensity or the temperature, and the change in
temperature ΔT is given by
The number of electrons
to produce that heat is given by
Equation {18},
explained reduction in granules temperature, after been magnetized by Eq.(3) or
Eq.(4) to form what is known as the sunspot.
10: Discussion
- Observations
confirmed noticeable differences in the temperature and field strength of umbra
of large and small spots [11], this is due to that, the magnetic field obtained
in Eq.{6} is related to the plasma size, while Eq.{18} which explain the
decreased in temperature, is also depends on Eq.{6} which depends on plasma
size.
- The
current suggested sunspot plasma body model, is to replace the previous one
[33], and the new model will slightly altered some of the pre-conceived ideas
about solar flare mechanism [34].
- The
distance between the end of plasma body and umbra surface, in Fig.3. is 24 Mm
[4], as shown relative distances in Fig.3, in relations to that distance, gives
the interaction radius, or rpp at 15,243. If
the measured sunspot magnetic field intensity (BSEx)
at the umbra is 200 gauss. Using Eq.{2}, therefore:
o when
the BSEx = 200 gauss = 0.02 Tesla, and rpp =
15.2 Mm, therefore, the total produced Plasma Body External Magnetic Field (PBEx)
= 1.4 x 1018 Tesla.
o If
the BSEx = 500 gauss = 0.05
Tesla, therefore, AREX = 1.7 x 1019 Tesla!
11: Acknowledgments
Special gratitude to
the Late Prof. B.O. Kola, Prof. John Buers Awuor,
Dr Lino Gwaki, Prof. P. Baki, Prof, Bernard
O. Aduda, Prof. J. Otieno Malo and staff of Physics
Department University of Nairobi.Dr Ali Khogali, Late Yousif Kuwa Makki.
Brothers and sisters, Mustafa, Halima, Hukmala, Asha, Arfa,
Mohamed, Ahmad, Esmaiel, Sophya and her husband the
late Abubakar Mohammad their family and Mr. Paul E Potter.
12:0 Glossaries
BAREx:
The Active Region External Magnetic Field detected at lower edge of the
granules
BSex:
The Sunspot External Magnetic Field
B1U = SMF: The nucleus spinning
magnetic field
BSEx :
The Sunspot External Magnetic Field
C: The speed of light
Cp: The Specific
heat in J/kg x degrees C
±dU : The change in the internal energy
ExMF External
Magnetic Field
En is Atom’s energy at
excitation state
FWD Wilson
Depression magnetic force is in Newton.
LOS: The Line-of
sight
M: The mass in kilograms
M% : The
percentage of Magnetization loss of the original BAREx,
in Tesla.
me : The electron mass in kg
MSS :
The Magnetized sunspot field
ne :
The number of electrons in unit volume
PBEx :
The Plasma Body External Magnetic Field
Q : The heat added
to the system
q : The electric charge
rn : The excited orbital radius
rpp :
The radial distances
rPS2 :
The radial distance from the Plasma Body to the granule’s sunspot center
SDO : The
Solar Dynamic Observatory
UD :
The Umbral Dots
vD : The excitation velocity
-Ve : Negative
+Ve : Positive
W : The work done
by the system
:
Delta Heat energy (H)
θ : The
angle between two magnetic fields
μ0 :
The permeability of free space (4π×10−7 V·s/(A.m)
χm :
The volume magnetic susceptibility
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