Evolution of large-scale magnetic fields in the Sun
A scenario of evolution of the large-scale magnetic fields in the Sun is proposed. The analysed models of the Sun allow one to accept the shearing of the poloidal field by differential rotation, helical turbulence and also the advective transport of the magnetic flux by meridional circulation as the...
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Головна астрономічна обсерваторія НАН України
2005
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irk-123456789-796372015-04-04T03:02:26Z Evolution of large-scale magnetic fields in the Sun Brayko, P.G. MS2: Physics of Solar Atmosphere A scenario of evolution of the large-scale magnetic fields in the Sun is proposed. The analysed models of the Sun allow one to accept the shearing of the poloidal field by differential rotation, helical turbulence and also the advective transport of the magnetic flux by meridional circulation as the main processes of the solar activity. We found that toroidal magnetic field (TMF) was more effectively generated in the strong radial shear layer (tachocline). It has a small value of diffusion and is carried out by meridional circulation toward the equator, where diffusion of the fields with different signs takes place. Casual force takes away the partial TMF in the solar convective zone and magnetic buoyancy sends the field to the surface. Using the Babcock–Leighton idea, we give confirmation of the generation of the poloidal magnetic field only near the surface and poles. The approximate decisions enable one to build the model of the solar dynamo in accordance with the observations. 2005 Article Evolution of large-scale magnetic fields in the Sun / P.G. Brayko // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 176-178. — Бібліогр.: 13 назв. — англ. 0233-7665 http://dspace.nbuv.gov.ua/handle/123456789/79637 en Кинематика и физика небесных тел Головна астрономічна обсерваторія НАН України |
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MS2: Physics of Solar Atmosphere MS2: Physics of Solar Atmosphere |
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MS2: Physics of Solar Atmosphere MS2: Physics of Solar Atmosphere Brayko, P.G. Evolution of large-scale magnetic fields in the Sun Кинематика и физика небесных тел |
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A scenario of evolution of the large-scale magnetic fields in the Sun is proposed. The analysed models of the Sun allow one to accept the shearing of the poloidal field by differential rotation, helical turbulence and also the advective transport of the magnetic flux by meridional circulation as the main processes of the solar activity. We found that toroidal magnetic field (TMF) was more effectively generated in the strong radial shear layer (tachocline). It has a small value of diffusion and is carried out by meridional circulation toward the equator, where diffusion of the fields with different signs takes place. Casual force takes away the partial TMF in the solar convective zone and magnetic buoyancy sends the field to the surface. Using the Babcock–Leighton idea, we give confirmation of the generation of the poloidal magnetic field only near the surface and poles. The approximate decisions enable one to build the model of the solar dynamo in accordance with the observations. |
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Article |
| author |
Brayko, P.G. |
| author_facet |
Brayko, P.G. |
| author_sort |
Brayko, P.G. |
| title |
Evolution of large-scale magnetic fields in the Sun |
| title_short |
Evolution of large-scale magnetic fields in the Sun |
| title_full |
Evolution of large-scale magnetic fields in the Sun |
| title_fullStr |
Evolution of large-scale magnetic fields in the Sun |
| title_full_unstemmed |
Evolution of large-scale magnetic fields in the Sun |
| title_sort |
evolution of large-scale magnetic fields in the sun |
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Головна астрономічна обсерваторія НАН України |
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2005 |
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MS2: Physics of Solar Atmosphere |
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http://dspace.nbuv.gov.ua/handle/123456789/79637 |
| citation_txt |
Evolution of large-scale magnetic fields in the Sun / P.G. Brayko // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 176-178. — Бібліогр.: 13 назв. — англ. |
| series |
Кинематика и физика небесных тел |
| work_keys_str_mv |
AT braykopg evolutionoflargescalemagneticfieldsinthesun |
| first_indexed |
2025-07-06T03:39:55Z |
| last_indexed |
2025-07-06T03:39:55Z |
| _version_ |
1836867331214540800 |
| fulltext |
EVOLUTION OF LARGE-SCALE MAGNETIC FIELDS IN THE SUN
P. G. Brayko
Kirovohrad National Technical University
3 Universytetsky Avenue, 25006 Kirovohrad, Ukraine
A scenario of evolution of the large-scale magnetic fields in the Sun is proposed. The analysed
models of the Sun allow one to accept the shearing of the poloidal field by differential rotation,
helical turbulence and also the advective transport of the magnetic flux by meridional circulation
as the main processes of the solar activity. We found that toroidal magnetic field (TMF) was more
effectively generated in the strong radial shear layer (tachocline). It has a small value of diffusion
and is carried out by meridional circulation toward the equator, where diffusion of the fields with
different signs takes place. Casual force takes away the partial TMF in the solar convective zone
and magnetic buoyancy sends the field to the surface. Using the Babcock–Leighton idea, we give
confirmation of the generation of the poloidal magnetic field only near the surface and poles.
The approximate decisions enable one to build the model of the solar dynamo in accordance with
the observations.
INTRODUCTION
The basic models of the solar dynamo established that the solar cycle involves a recycling of two main components
of the Sun’s large-scale magnetic field [10]. The toroidal component of the magnetic field is generated by
the shearing of the poloidal field in a region of strong radial gradient in the rotation known as the tachocline,
located at the base of the solar convection zone (SCZ), from where it erupts to the surface due to magnetic
buoyancy and gives rise to bipolar sunspot pairs. It was believed that propagation of this toroidal field wave
at the base of the SCZ manifested itself on the surface as the migration of the sunspot activity belt toward
the equator. But some problems exist in description of this process.
Firstly, the polar weak magnetic field of the Sun is of order 10G, whereas the toroidal magnetic field at
the bottom of the convection zone has been estimated to be 105 G. Simple order-of-magnitude estimates show
that the shear in the tachocline is not sufficient to stretch a radial field into a high mean TMF [4]. Stretching by
shear in the tachocline is then expected to produce a highly intermittent magnetic configuration at the bottom
of the convection zone. The meridional flow at the bottom of the convection zone should be able to carry this
intermittent magnetic field equatorward [9]. In avoidance of buoyancy, the analysis and calculations confirmed
the possibility of the TMF generation in the SCZ and pushing down the field into the stable radiative layers.
There the TMF is formed completely and is transported by the meridional circulation equatorward through
this stable region. The TMF produced at high latitudes cannot erupt there if it is pushed down into the stable
layers. But when the meridional flow rises at low latitudes, the toroidal field can come out through the base
of the SCZ and be subjected to magnetic buoyancy, erupting outward to form sunspots. Possibly, the toroidal
field emerging is related to the radial gradient of angular speed, which at the negative value does not give
the magnetic tubes to approach the SCZ bottom, while at the negative value such possibility is more credible.
This scenario is explicitly shown through the results of the dynamo simulations and it is remarkably successful
in giving a consistent description of the observations of sunspots at low latitudes in light of recent developments
[2, 5, 6, 9, 13].
When a flux tube from the bottom of the convection zone rises to a region of pre-existing poloidal field at
the surface, we point out that it picks up a twist in accordance with the observations of current helicities at
the solar surface.
The poloidal component of the magnetic field (identified with the weak diffuse field observed outside
sunspots) is regenerated from the toroidal field by a process known as the α-effect, in which the toroidal
field is lifted and twisted into the meridional plane. Contrasting mechanisms have been proposed to explain
the origin of this α-effect, for example helical convection [10]; decay of tilted bipolar sunspot pairs [1]; buoyancy
instability coupled with rotation [3]; hydrodynamic instability of the differential rotation [5]. First two models
explain the mechanism of transformation of the poloidal fields, last two give a substitution to a source of alpha-
effect. Although these various mechanisms differ in their nature and location, one common feature is that all of
c© P. G. Brayko, 2004
176
them predict positive α-effect in the northern hemisphere of the Sun and negative α-effect in the southern hemi-
sphere. The author supports the Babcock–Leighton idea, which was developed by Nandy and Choudhuri [8],
that the poloidal field is generated at the surface of the Sun from the decay of active regions.
PRELIMINARY NOTES
So, the large-scale magnetic field is in a nonconvective environment of the overshoot layer. This means that
TMF can exist there for the time long enough, but certain force compels magnetic tubes to appear in the SCZ.
The authors of [8] believe that the dynamo generated magnetic fields are of limited value. They found that
critical fields for eruption should be more than 105 G limiting the magnitude and distribution of the magnetic
field generated within the overshoot layer. Another part of the TMF continues motion along the meridional
direction. In this study it was not examined. We were interested in expression of α-effect in the SCZ. We will
notice that a convective environment has the asymmetrical field with small-scale casual speeds and convective
elements carry out radial motions, which are collinear with the direction of emerging. On identical depths these
motions have characteristic speeds and length scales:
l =
(
αMLT
γ
)
Hρ, (1)
where αMLT is characteristic value of the model (it is 5/3 for the Stix model SCZ), γ is the adiabatic index
(it is approximately 7/5), Hρ =
∣∣∣∣ρ∂r
∂ρ
∣∣∣∣ is a density height scale. The presence of TMF in the SCZ cannot
be fixed because the force tube emerges, though there can be nonlinear effects which compel it to remain
long time at the bottom of SCZ [7]. Speed of emerging is characterized by constant Alfen speed [10] and
Bϕ/
√
ρ = const, where Bϕ is TMF intensity. At a motionless force magnetic tube the curvature occurs due to
movements, which have turbulent character and are described by parameter turbulent helicity (α-parameter).
This parameter has been offered by Rädhler and Krause, and then specified by Rüdiger and Kichatinov. But
the analysis of contribution of the relative velocity to α-parameter is not essential and we can neglect it. Using
some suppositions, we get:
α = −2
3
Ω l 2
(
∂ρ
ρ∂r
+
∂V
V ∂r
)
cos θ =
2
3
Ω l 2
∣∣∣∣∣
∂B2
ϕ
B2
ϕ∂r
∣∣∣∣∣ cos θ, (2)
where Ω is the angular velocity of the SCZ rotation,
∂ρ
ρ∂r
+
∂V
V ∂r
is the sum of gradient rates of a natural logarithm
of a density and the relative velocity of turbulent oscillations. This means that the sign of α-parameter is positive
in the northern hemisphere and negative in the southern hemisphere, as suggested by Rüdiger et al. [11].
BASIC EQUATIONS
The large-scale magnetic fields in the spherical coordinates (r, θ, φ) have the form:
{
∂
∂t
− η
(
∇2 − 1
r2 sin2 θ
)}
Bϕ +
1
r
[
∂
∂r
(rvrBϕ) +
∂
∂θ
(vθBϕ)
]
= r sin θ
(
Br
∂Ω
∂r
+ Bθ
1
r
∂Ω
∂θ
)
, (3)
{
∂
∂t
− ηΔ
}
Br,θ +
1
r
[
∂
∂r
(rvrBθ) +
1
sin θ
∂
∂θ
(vθBr sin θ)
]
= α rotBϕ + gradα · Bϕ, (4)
where Br, Bθ, Bφ are the components of the magnetic induction, η is coefficient of turbulent magnetic diffusivity,
vr and vθ are the components of meridional velocity, including the radial magnetic buoyancy. Thus, we have non-
homogeneous equations (3) and (4) with the zero initials and boundary conditions for the northern hemisphere,
where the lowest bounder TMF-penetrating equals 0.6 of the solar radius.
177
RESULTS
The straight order of the equation (3) and (4) with initials and boundary conditions was used. We obtained:
Bϕ(r, θ, t) =
∞∑
n,m=1
⎡
⎣
t∫
0
e
−η2π2
[
4n2
π2r2
0
+ m2
(0.3R)2
]
(t−τ)
fmn(τ)dτ
⎤
⎦
× sin
(
2nθ +
2nvθt
0.7Rπ
)
sin
(
r − 0.7R + vrt
0.7R
)
, (5)
where m, n ∈ N ; R is the solar radius.
We believe that poloidal field is created near the surface from the decay of titled active regions. It should
be noted that α-coefficient in the Babcock–Leighton dynamo is not given by the mean helicity of turbulence
as in conventional mean-field MHD. It was confirmed by Vainstein et al. [12] that TMF spread in the SCZ
without dissipation right up to the top of SCZ. In this approach the α-effect generating the poloidal field results
phenomenologically; we consider it to be essential for the formulation of the Babcock–Leighton dynamo for
the mean field. The angular factor cos θ arises from the angular dependence of the Coriolis force, which causes
the tilts of active regions. Our results confirm the idea of Babcock–Leighton on maximal transformation of
TMF to weak meridional magnetic fields near the Sun’s surface. This hypothesis also takes place in the theory
of the turbulent dynamo, suggested on the basis of many models of the SCZ.
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