SOLAR PROMINENCE
MODELS
tical threads frequently seen in quiescent prominences
above the limb. It is unclear, for example, whether the
magnetic eld in these vertical threads is vertical or
horizontal.
Magnetic elds play an key role in many aspects
of prominence physics, including their support against
gravity and thermal insulation from the surrounding
corona. It the following we discuss some of these aspects
in more detail.
Solar prominences are ribbons of cool dense gas embedded in the hot tenuous corona, which forms the outer
atmosphere of the Sun. Prominence models aim to describe the physical conditions in and near prominences,
and the physical processes involved in their formation,
maintenance, and disappearance.
Prominences are located tens of thousands of kilometers above the visible \surface" of the Sun (the photosphere) and have temperatures 104 K, a hundred
times lower than the temperature of the surrounding
corona. The particle densities in prominences range
from 1016 to 1017 m;3 , a hundred times greater than
coronal values. When viewed above the solar limb,
prominences appear as bright features against the dark
background. They can also be observed on the solar
disk by taking images of the Sun in certain narrow
wavelength bands corresponding to strong Fraunhofer
lines in the solar spectrum. The higher opacity of the
solar atmosphere in a spectral line allows observers to
see structures higher up in the atmosphere which are
not visible in broad-band \white" light. One spectral
line often used for such studies is the hydrogen H line
at a wavelength of 6563 A, which is formed in the solar chromosphere. When observing in H on the disk,
prominences show up as dark laments overlying the
chromosphere. In the following we refer to these laments as \prominences" since they really are one and
the same phenomenon.
Prominences are always located at the polarity inversion lines separating regions with opposite magnetic
polarity in the photosphere (i.e., lines where the radial component of the photospheric eld changes sign).
They form in so-called lament channels, regions where
the chromospheric brils (thread-like ne structures in
the chromosphere) are aligned parallel to the inversion
line (see SOLAR FILAMENT CHANNELS and SOLAR PROMINENCE FORMATION). The magnetic
eld in a lament channel is mainly horizontal and directed along the polarity inversion line. Filament channels can be classied as dextral or sinistral, depending
on the direction of the axial eld as seen by an observer standing on the positive-polarity side. Quiescent
prominences in the northern hemisphere are predominantly dextral, while those in the south are predominantly sinistral (see SOLAR PROMINENCE CHIRALITY).
Prominences are large, long-lived structures which
can persist for many days, but they usually contain
thread-like ne structures which last only a few minutes
(see SOLAR PROMINENCE FINE STRUCTURE).
Some of these threads are clearly aligned with the local
magnetic eld, but this is not so obvious for the ver-
Prominence Support
The outer atmosphere of the Sun is permeated by magnetic eld, and this eld is also present within prominences, where it provides the magnetic force necessary
to support the dense prominence gas against gravity.
This magnetic force is made possible by the fact that
prominences (and the surrounding corona) consist of
partially ionized gas, or plasma, in which there is a
high concentration of unbound electrons. The electrical
conductivity of this plasma is very high, and electric
currents can easily ow through the plasma. In such a
highly conducting medium the plasma is forced to move
along magnetic eld lines and cannot easily cross from
one eld line to another. Therefore, a parcel of dense
prominence plasma will stay on the eld line on which
it was originally located. Under the inuence of gravity, the parcel will slide down along the eld line until
it reaches the chromosphere or encounters a \dip" in
the eld line where the eld is locally horizontal and
curved upward. Various models of magnetic congurations with dipped eld lines have been proposed (see
Fig. 1). Prominences are thought to be cool plasmas
which have come to rest in such dipped (or nearly horizontal) eld lines.
Kippenhahn and Schluter (1957) were the rst to develop a model of the equilibrium and stability of prominence plasma in a magnetic conguration with dipped
eld lines. They assumed a so-called normal polarity
conguration in which the eld lines pass through the
prominence from the region of positive polarity (radially
outward magnetic eld in the neighboring photosphere)
to the region of negative polarity (Fig. 1a). Kuperus
and Raadu (1974) later proposed a dierent model in
which the prominence has inverse polarity compared to
the neighboring elds (Fig. 1b). These gures show vertical cross-sections of a prominence in a plane perpendicular to the long axis of the prominence. It should be
kept in mind that in general there is also a component
of magnetic eld along the prominence (into or out of
the plane), which often is stronger than the component
within the plane. However, as we will see below, this
axial component of the eld is not essential for prominence support.
The magnetic force in a plasma is given by the
Lorentz force, j B, where B(r) is the magnetic in1
+
+
+
+
-
-
-
+
(a)
+
-
-
(b)
Figure 1: Two models of the magnetic eld supporting a solar prominence: (a) Kippenhahn-Schluter model (b)
Kuperus-Raadu model. These gures show the projection of the eld lines onto the plane perpendicular to the long
axis of the prominence (shaded region). The horizontal line at the base indicates the solar photosphere.
duction and j(r) is the electric current density, i.e., the
electric current per unit area perpendicular the to current. Hence, to support the weight of the prominence in
the dips of eld lines, there must exist an electric current which ows through the prominence in a horizontal direction which crosses the magnetic eld lines. An
important dierence between the Kippenhahn-Schluter
and Kuperus-Raadu models is the direction of this electric current: in Fig. 1a the current ows out of the
plane of the gure (toward the observer), whereas in
Fig. 1b the current ows into the gure (away from
the observer). Moreover, in the Kuperus-Raadu model
the current is present not only inside the prominence,
but also in the \magnetic island" just above the prominence, as indicated by the cross in Fig. 1b.
The plasma within the prominence is subject to
three forces: (1) the Lorentz force, j B (2) the gravitational force, ;gz^, where (r) is the mass density,
g is the acceleration of gravity, and z^ is the radially
outward direction on the Sun and (3) the force due to
the gradient of gas pressure, p(r). In equilibrium these
forces must balance each other:
;rp ; g^z + j B = 0:
between 0.6 and 1.3 times the proton mass, depending on composition and ionization state of the plasma).
Kippenhahn and Schluter (1957) modeled the prominence as a thin vertical sheet in which the pressure p(x),
density (x) and vertical magnetic eld Bz (x) depend
only on the horizontal coordinate x perpendicular to
the sheet. The temperature T and horizontal eld components Bx and By are assumed to be constant. Then
the x- and z -components of Eq. (1) reduce to
2
(3)
(4)
The boundary conditions far away from the sheet (x !
1) are p ! 0 and Bz ! Bz1 . Integrating equation
Eq. (3) yields
2
2
(5)
p = Bz12; Bz and using Eqs. (2) and (5), equation (4) yields a dierential equation for Bz which has the following solution:
(1)
Bz (x) = Bz1 tanh 2BBz1Hx x p
Using Ampere's law, the electric current density can
be written as j = ;1 r B, where is the magnetic
permeability. The mass density can be written as
= mp
kT d p + Bz = 0
; dx
2
B
z
;g + x dB
dx = 0:
;2
2
B
B
z1 x
z1
p(x) = 2 cosh 2B H
:
x p
Here Hp kT=(mg) is the so-called pressure scale
(2)
height which describes how rapidly the pressure and
density fall o with height along the eld lines (Hp
200 km within the prominence). Note that the plasma
pressure at the center of the prominence sheet is equal
where T (r) is the temperature, k is the Boltzmann constant, and m is the mean mass per particle (m lies
2
to the external magnetic pressure associated with the
vertical component of the magnetic eld, and that the
width of the sheet is of order 4(Bx=Bz1 )Hp . The observed widths of quiescent prominences ( 8000 km)
can be reproduced with Bz1 0:1Bx, in other words,
the support of the prominence requires only a minor
perturbation of the surrounding magnetic eld.
In general there is also a component of magnetic eld
along the prominence (By ), so the normal polarity eld
shown in Fig. 1a is actually a sheared arcade (with dips
at the loop tops), and the circular eld lines in Fig. 1b
are actually helical windings which are wound around
a horizontal axis that runs parallel to and above the
prominence. Therefore, to obtain a more accurate picture of the prominence magnetic eld we must consider
its full three-dimensional structure.
+
+
-
-
Figure 2: Twisted ux tube model for solar prominences. The prominence sheet is indicated by the
shaded region.
Prominence Magnetic Structure
ing this helical eld is an coronal arcade, which likely
plays an important role in the equilibrium and stability of the eld. Cool prominence plasma is supported
at the troughs of the helical windings where the eld
lines are curved concave-upward. This twisted ux tube
model has many features which agree with observations,
including the inverse polarity of the magnetic eld in
the prominence and the fact that when a prominence
erupts it sometimes looks like a twisted tube (see SOLAR PROMINENCE ERUPTION).
How does the Sun produce such helical elds? One
possibility is that the twist is produced by vortical motions of the photospheric footpoints of the tube, but this
would require persistent twisting over several revolutions, which is not observed. Another possibility is that
the twisted ux rope is created in the convection zone
below the photosphere, and emerges through the photosphere with its twisted structure already formed (e.g.
Rust & Kumar 1995). A third possibility is that the helical eld is produced by magnetic reconnection, i.e., the
reconguration of magnetic eld lines due to plasma resistivity eects (see MAGNETIC RECONNECTION).
For example, Pneuman (1983) proposed that the radial
outward distention of a bipolar region by gas pressure
gradients could lead to an inward collapse of the region,
causing the eld lines to reconnect. If the initial eld
is signicantly sheared along the polarity inversion line,
reconnection produces helical eld lines in the region
above the reconnection site.
Observations indicate that prominences tend to
form in regions where opposite polarity ux is cancelling
at the polarity inversion line. In a sheared coronal arcade magnetic ux cancellation can proceed only if reconnection occurs in the region just above the inversion
line (van Ballegooijen & Martens 1989). The process
is illustrated in Fig. 3, which shows the evolution of a
sheared arcade in response to converging motions of the
photospheric footpoints. The initial eld is assumed to
There exist a variety of methods for measuring the magnetic elds in and around prominences, most of which
are based on the Zeeman eect (the splitting of atomic
energy levels in the presence of a magnetic eld). The
Zeeman eect causes the light emitted in a spectral line
to become circularly polarized. By measuring the degree of circular polarization it is possible to deduce the
component of magnetic eld along the line of sight in a
prominence. Another method is based on the fact that
much of the light emitted by a prominence above the solar limb is actually scattered light which originates from
the chromosphere below. The magnetic eld aects the
scattering properties of the atoms, and manifests itself
as a change in the state of linear polarization of the scattered light in certain spectral lines. This so-called Hanle
eect allows observers to deduce both the strength and
direction of magnetic elds in prominences. Observational studies have shown that the magnetic elds in
quiescent prominences are in the range (3 ; 30) 10;4
T, and that the eld is mainly directed along the length
of the prominence: the magnetic vector is inclined to the
prominence axis at an average angle of about 25 degrees
(Leroy 1989). Most quiescent prominences have inverse
polarity, i.e., the magnetic eld traverses the prominence from the region of negative polarity to the region
of positive polarity, opposite to what would be expected
for a coronal arcade. The eld strength increases with
height in the prominence.
These observations are consistent with the idea that
a quiescent prominence is located within a large, twisted
ux tube or ux rope (see Fig. 2). A number of authors have developed prominence models based on this
idea (e.g. Priest, Hood & Anzer 1989). According to
these models, an arched ux tube is anchored in the
photosphere at two ends, and the eld lines in the coronal portion of the tube make one or two revolutions
about the tube axis, forming a helical eld. Overly3
1
0
11
00
00
11
C
B
1
0
1
0
1
0
C
1
0
0
1
(a)
G
B
0
A1
0
1
1A
0
11 11
00
00 D00
11
00 H
11
1D
0
D
1
0
0
1
100
A
E0
11
(b)
(c)
1 11
0
0 D00
1
00 H
11
11
00
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1 00
0
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F
G
F
00
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0000
A
E11
11
(d)
Figure 3: Flux cancellation in a sheared coronal arcade. The rectangle represents the solar photosphere, and
the dashed line is the polarity inversion line. (a) Initial sheared eld subject to converging ows. (b) Reconnection
produces a long loop AD and a shorter loop CB, which subsequently disappears below the photosphere. (c) Overlying
loops EF and GH are pushed to the inversion line. (d) Reconnection produces the helical loop EH and a short loop
GF, which again submerges.
be sheared (Fig. 3a), which may have been caused by
ows along the inversion line or by some other eect.
When the footpoints of the coronal loops are pushed
to the inversion line, the loops become more and more
aligned with the inversion line, eventually causing different loop systems to reconnect (Fig. 3b). The model
assumes that the short, highly curved loops produced by
such reconnection are pulled below the photosphere by
magnetic curvature forces, causing magnetic ux to disappear from the photosphere (ux cancellation). However, the reconnection also produces longer loops which
remain in the corona because their curvature radii are
too large to overcome the buoyancy forces at and below the photosphere. As overlying loops are pushed to
the inversion line, further reconnection produces helical
loops in which a prominence can form (Figs. 3c and 3d).
As more and more ux is forced to reconnect at the inversion line, the width of the helical ux tube gradually
increases and the axis of the tube slowly rises. Eventually the magnetic structure becomes unstable, causing
the helical eld to erupt.
depends on atomic parameters and the chemical composition of the plasma. In a coronal loop these radiative losses are balanced by heating due to dissipation of
magnetohydrodynamic (MHD) waves or other disturbances. Electron thermal conduction plays an important role in redistributing this heat along the coronal
loop. However, as coronal conditions change, the density and/or loop length may slowly increase with time,
causing radiative losses to become more important relative to conduction. Eventually, the coronal loop may
reach a point where a stable equilibrium between energy gains and losses is no longer possible. The plasma
then rapidly cools and settles into a new equilibrium
with much lower temperature but higher density. This
condensation process occurs for a wide range of forms
of the heating function.
A di#culty with the above scenario is that the mass
of a quiescent prominence ( 1012 kg) typically exceeds
the mass available in the surrounding corona before the
prominence is formed. Therefore, additional mass must
somehow be supplied to the prominence. One possibility is that the mass is injected along the eld lines
that connect the prominence with the chromosphere below. This could be in the form of a siphon ow driven
by a possible pressure dierence between the chromosphere and the prominence. Another possibility is that
cool plasma is lifted up by magnetic elds as they rise
through the chromosphere. For example, in the ux
rope model of Rust & Kumar (1995), the twisted ux
rope emerges from the convection zone and sheds most
of its mass on it way up into the corona (the density
in the corona is much less than that in the convection
zone). However, a small fraction of the initial mass remains trapped in the troughs of the helical windings.
This remnant is believed to form the prominence.
Observations suggest that prominences are very dynamical structures, with plasma continually draining
downward and new material being injected into the
Origin of Prominence Plasma
How do prominences acquire their mass? One viewpoint is that prominences are formed by the cooling and
\condensation" of plasmas from the surrounding corona
(see Priest 1982, Chapter 11). To understand how this
happens, we must consider the energetics of the coronal
plasma. A hot gas such as the corona is subject to radiative cooling, i.e., the loss of thermal energy due to collisional excitation of ions by electrons and the subsequent
emission of radiation at Extreme Ultraviolet and X-ray
wavelengths (the corona is optically thin, so this radiation can freely escape into space). The rate of energy
loss per unit volume is approximately given by n2e !(T ),
where ne is the electron density, T is the temperature,
and !(T ) is the so-called radiative loss function, which
4
Leroy J L 1989 Observation of prominence magnetic
elds In: Priest, E R (ed.) Dynamics and Structure of
Quiescent Solar Prominences (Dordrecht: Kluwer) pp
77-113
Pneuman G W 1983 The formation of solar prominences
by magnetic reconnection and condensation Solar Phys.
88 219-239
Priest E R 1982 Solar Magnetohydrodynamics (Dordrecht: Reidel)
Priest E R, Hood A W and Anzer U 1989 A twisted ux
tube model for solar prominences: I general properties
Astrophys. J. 344 1010-1025
Priest E R, van Ballegooijen A A and Mackay D H
1996 A model for dextral and sinistral prominences Astrophys. J. 460 530-543
Rust D M and Kumar A 1995 Helical magnetic elds in
laments Solar Phys. 155 69-97
van Ballegooijen A A and Martens P C H 1989 Formation and eruption of solar prominences Astrophys. J.
343 971-984
prominence. Priest et al (1996) propose a model in
which the prominence is maintained by a continual input of mass and magnetic ux from below. In this
model the correct dextral and sinistral patterns for
high-latitude, east-west prominences are produced by
the combined eects of dierential rotation acting on
subphotospheric ux, its subsequent emergence by magnetic buoyancy, and its rearrangement by reconnection
to form a lament channel with magnetic ux oriented
along its axis. Continual emergence and reconnection
creates a prominence as a ux tube along the lament
channel and lled with cool plasma which is lifted up
from the photosphere and chromosphere by the reconnection process. According to this model, reconnection
occurring in the chromosphere yields prominence densities in rough agreement with observations.
Thermodynamic Modeling
The temperature within a prominence is determined by
the balance between heating and cooling of the prominence plasma. There are several possible contributions
to the heating: (1) energy may be transported into the
prominence by thermal conduction from the hot corona,
but this is not very eective in the low-temperature
prominence material (2) the plasma can be heated by
dissipation of MHD waves or other disturbances which
propagate into the prominence from the sides and (3)
the prominence may be heated by absorption of ultraviolet radiation from the chromosphere. The energy
losses occur mostly in the form of radiation in hydrogen spectral lines and continua (Lyman and Balmer series). The radiation transport is complicated by the
fact that prominences are optically thick at these wavelengths, which means that the ultraviolet radiation is reabsorbed and reemitted many times before it nally escapes. Another complication is that prominences have
a lamentary structure, with thin (sometimes vertical)
threads of dense plasma embedded in a much more tenuous medium. This allows the ultraviolet radiation to
penetrate deep into the prominence, greatly enhancing
the excitation rate compared to models without such
ne-scale structures (Heasley and Mihalas 1976). The
cause of these ne structures is not yet understood.
A A VAN BALLEGOOIJEN
Bibliography:
Heasley J N and Mihalas D 1976 Structure and spectrum of quiescent prominences: energy balance and hydrogen spectrum Astrophys. J. 205 273-285
Kippenhahn R and Schluter A 1957 Eine Theorie der
solaren Filamente Zeitschrift fur Astrophysik 43 36-62
Kuperus M and Raadu M A 1974 The support of prominences formed in neutral sheets Astron. & Astrophys.
31 189-193
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