PASJ: Publ. Astron. Soc. Japan 51, 553-563 (1999)
A Quadruple Magnetic Source Model for Arcade Flares
and X-Ray Arcade Formations outside Active Regions
I. Dark Filament Suspension and the Magnetic Structure
in the Pre-Event Regions
Yutaka UCHIDA, 1 Shigenobu
Masaya T O R I I , 1 Shuhei
1
H I R O S E , 1 Samuel CABLE, 2 Satoshi M O R I T A , 1
U E M U R A , 1 and Tomotaka YAMAGUCHI 1
Department of Physics, Science University of Tokyo, Shinjuku-ku, Tokyo 162-8601
2
Physics Department, Auburn University, Alabama, USA
E-mail (YU): [email protected]
(Received 1999 April 9; accepted 1999 June 3)
Abstract
The high-sensitivity, wide dynamic-range observations by the Soft X-ray Telescope (SXT) aboard
Yohkoh has enabled us to look into the faint pre-event structures of arcade flares, and of even fainter
X-ray arcade formation events outside active regions. What we have found in the pre-event structure of
the latter, however, was not a sagged simple (bipolar) arcade, as expected in the classical model, but a
"dual-arcades" type structure in which the inside legs of each "arcade" cross with the other's, landing at
the closer part of the domain of the other. Similar features, together with some other features inexplicable
in the classical arcade flare model, were also found in strong arcade flares in active regions seen axis-on at
the limb. These features raised a severe problem with the classical "reclosing of the once opened simple
arcade" model(s). In the present paper, we propose interpretations of what we discovered by Yohkoh-SXT
by reviving a quadruple source model proposed by one of the authors (YU) years ago, pointing out a serious
difficulty in the classical model(s). This model, based on the quadruple magnetic sources in the photosphere, has a "neutral sheet" already in the pre-event phase in the corona above the field polarity-reversal
line in the photosphere, and turns out to explain quite nicely the structures of both faint pre-event corona
before arcade formation events, and that of arcade flares discovered by Yohkoh-SXT. A dynamic model
of arcade flares and arcade formation events based on this dark filament model will be discussed in the
forthcoming Paper II of this series.
K e y words: Sun: flares — Sun: magnetic field — Sun: prominences — Sun: X-rays
1.
Introduction
The magnetic structure surrounding a dark filament is
of intrinsic relevance to the understanding of the physics
of arcade flarings (energetic arcade flares in active regions, and large-scale weaker X-ray arcade formation
events outside active regions).
A model of mass suspension in a dipped magneticfield configuration has been discussed by Kippenhahn
and Schluter (1957), and many authors have assumed
that such a mass suspension could occur due to sagging of
the field lines, even at the top of a convex magnetic field
arching over the field-polarity reversal lines in the photosphere (see Tandberg-Hanssen 1974; Pickelner 1971;
Priest 1989). A model for arcade-type flares (Carmichael
1964; Sturrock 1966; Hirayama 1974; Kopp, Pneuman
1976) was developed based on this type dark-filament
model: When a dark filament is somehow destabilized
and flies away, it drags the arcade field with it into interplanetary space. Magnetic reconnection occurs between
the antiparallel fields at the leg parts of this stretched
fieid. A reclosed arcade in the low corona and a detached
c i o s e d loop field surrounding a flying blob will be formed
as the result of magnetic reconnection. The energy released in the flare is interpreted as being the difference
'm the energies in the stretched and reclosed magnetic
n e lds, a substantial part of which is liberated in the rec i o s e d arcade during the process. The magnetic energy
[s converted into kinetic and thermal energies of the gas
ejected downward from the reconnection site and the energy of high-energy particles accelerated in the reconnect ion process, and transported down to the chromosphere
a i o n g the magnetic fields. The soft X -ray emitting mass
in the reclosed arcade is considered to be chromospheric
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
554
Y. Uchida et al.
mass "evaporated" by being given excess energy via heat
conduction and/or electron bombardment from above.
Some researchers (e.g., Shibata et al. 1995) refer to this
model as the CSHKP model, taking the initials of the
above authors.
A difficulty with this model of dark filament came to
light in the observations by Leroy et al. (1983). Using
the Hanle effect to observe the magnetic field in dark filaments, they showed that the direction of the field perpendicular to the dark filament is opposite to the direction
expected from the simple connection of the bipolar field
below. A solution of this dilemma has been proposed, for
example, by introducing the Kuperus and Raadu (1974)
type model with a field configuration having an inverted
circular sub-connection at the top of the convex arcade
(cf., Priest 1989). However, no sufficiently persuasive
physical explanation has been given for the creation and
stability of such an intricate configuration.
A more basic question about this classical model of
arcade flares was raised (Uchida 1980) concerning the
kinetic energy of the rising dark filament. In order to
stretch the strong field (whose magnetic energy ultimately should explain the large energy of flares in the
reconnection process) and eventually cut it open, the energy in the rise of the dark filament should be larger than
the energy of the flare itself. [This point, which was the
motivation for the work of Uchida and Jockers (1979),
and Uchida (1980), was later formulated in a clearer form
by Aly (1991).] It should be pointed out here that there
would be no magnetic neutral sheet in the classical model
if the process of cutting the field open could not actually
take place due to the energy problem. This is a more
severe dilemma. If the classical picture is correct, what
requires a more serious investigation is the dark filament
rise, not the flare itself, because the flare is then merely
a repairing process of a more energetic break-up caused
by the rise of the dark filament.
Some researchers, accordingly, have tried to explain the
dark filament as a high-stress structure having a highly
sheared field (cf., Moore, Roumeliotis 1992). The dark
filament in this type model is an extremely energetic entity, because if, for example, an initially current-free arcade with a 10 G field in a high latitude dark filament
case, is sheared to produce a structure (a dark filament)
with an aspect ratio of 10-100, the field strength in the
long dark filament should become 10 2 - 3 G in the corona
by a simple argument, and this is difficult to hold down.
(This is a simplified argument. In actuality, the coronal
part of the field may expand, but then it does not explain
the thin partition-like shape of the dark filaments). In
this connection, it should also be noted that there is no
evidence for an actual very long and systematic antiparallel excursion of the photospheric footpoints along the
field-polarity reversal line to consistently shear a simple
arcade structure to produce an elongated dark filament
[Vol. 51,
with an aspect ratio of 10-100. Also, there is no reason for the photospheric motion to follow the polarity
reversal line, if the field is thought to be a passive entity
down in the photosphere. Comparing this type model
with the observations, the greatest difficulty is that the
observed dark filaments are an intrinsically passive entity
easily shaken by the influence of some other disturbance,
and, on the other hand, are quite stable as a whole until they are disturbed by some newly emerged magnetic
patches appearing nearby. The highly sheared appearance is better interpreted as in our model discussed later
in sections 2 and 4.
In section 2, some explanation is given about a quadruple photospheric magnetic source model that one of us
proposed years ago after being motivated by the difficulty of the classical models as mentioned above.
2.
Quadruple Magnetic Source Model to Solve
the Difficulty
One suggestion that explains the elongated magnetic.
structure along the "polarity reversal line" in a more
natural way was proposed by Uchida (1980), based on
Uchida and Jockers (1979), to avoid the energy paradox
mentioned above, with a related proposal for a mechanism to produce arcade-type flares from such a configuration. Their proposal was that the magnetic structure
involving a dark filament may be due to a quadruple array distribution of the magnetic field (elongated regions
of +,—,+, — polarities side by side, referred to as A, B, C,
and D) in the photosphere below. In that case, there appears a "neutral line" (the locus of the "neutral points",
which will become a vertical "neutral sheet" if the photospheric footpoints are squeezed towards the central line)
in the planar component of the magnetic field, B± (the
field components in the xz-plane perpendicular to the
central polarity-reversal line in the photosphere which is
taken to be the y-axis), in the corona above the central
polarity reversal line. We refer to this symbolically as
the "neutral sheet" in the following, although it is actually a current sheet with the y-component of the field
lying in it. The longitudinal component along the y-axis,
Byi is dominant in the "neutral sheet", because B± is
close to zero there. In our model, By, which may be relatively week initially, but will become of the same order of
magnitude as B± at certain distance on both sides when
squeezed, is what is suspending the dark filament gas lying in the thin, high and long vertical "neutral sheet",
and is supported, in turn, by the gradient in B± a^ciiscussed later in section 4.
j
This model proposed by Uchida (1980) is a natural
one for the suspension of dark-filament material, compared with the Kippenhahn-Schluter model. When the
Kippenhahn-Schluter model is applied to the top of a
convex arcade, the material initially loaded at the top of
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
No. 4]
Quadruple Source Model for Arcade Flarings
a convex loop will readily slip down, and it would be hard
to produce a dip at the top of the arcade. If one looks
into Kippenhahn-Schluter's treatment, it would be readily seen that their treatment is for a concave field with
current flowing on the side boundaries in an appropriate
direction to support it, and does not apply to the convex
loop top situation.
The quadruple-array source model, in contrast, can
sustain the dark filament mass in the thin neutral sheet,
thus explaining the observed very thin vertical partitiontype structure of the dark filament. The quadruple
source model, however, was not accepted too well when
proposed by Uchida (1980) when there were no sufficiently precise X-ray observations to compare with it.
Many years after our proposal (Uchida 1980), the
quadruple source characteristics have attracted increasingly greater attention, and have been discussed
by Dahlburg and Antiochos (1991), Demoulin, Priest
(1993), Hundhausen, Low (1994), Antiochos et al. (1994),
and Sciffer (1997).
In the following, we first summarize what we obtained
from the observation by Yohkoh in section 3, and describe
our theoretical model in section 4. Comparisons between
the observation and the model will be given in section 5.
Finally, some discussion will be given in section 6.
3.
Coronal Structure Surrounding a Dark Filament, or Features in the Pre-Event Region
of Arcade Formation and Arcade Flares, Observed by Yohkoh
It is not necessary to say that the information about
the structure and its change of the magnetic field (represented by coronal X-ray loops) in the still faint preflare
and initial stages is vital for clarifying the flare mechanism from the point of view of causality. But this information could not be obtained before Yohkoh. We first
concentrate on the pre-event structure of X-ray arcade
formation outside of the active regions in subsection 3.1,
since the details are more clearly observable in those
large-scale, slowly developing fainter version of arcade
flares outside of the active regions, and then come to the
case of arcade flares in active regions in subsection 3.2.
3.1.
Large Scale Arcade Formation outside Active Regions
McAllister et al. (1992) reported on a detailed observation of this type event obtained on 1991 September 28 by
Yohkoh. The observed behavior, however, was quite different from what was expected from the classical model,
and people thought that it might have been an exceptional event. It turned out, however, from analyses of
several more events (Uchida 1996a, 1996b, 1996c; Uchida
et al. 1999a; Fujisaki et al. 1999) that what was ob-
555
served in this event was common for arcade formation
events. Namely, a bundle of bright threads (we referred
to this as a "spine") rises together with the arcade of
loops, sometime after the dark filament has disappeared.
The "spine" is definitely not the locus of the reconnecting
points in the reclosing process of the once-opened arcade,
as suggested by the classical model, because the "spine"
consists of multiple longitudinal threads coming up from
below! The locus of the reconnecting points can not form
multiple threads. The "spine" eventually balloons up on
one end, and forms a large cusp-like shape. Considering that these X-ray arcade formations are larger scale
fainter versions of arcade flares occurring outside active
regions with a weaker magnetic field, we examined their
pre-event structure in detail.
An important result of this investigation reported separetely by Uchida et al. (1999b) is that the faint pre-event
structure of these X-ray arcade formations were found to
be "dual-arcades", one on respective sides of the "field
polarity reversal line" in the photosphere (figure la). The
inside legs of each arcade land in the domain of the other
arcade in an intermingled way, and the dark-filament lies
in the region in which the legs are crossing, quite unlike
what was expected from the classical model.
Upon examining the Kitt Peak magnetogram, rotated
precisely to the time of the X-ray observation, we found
that the "field polarity reversal line" is not at all a clearly
definable line as assumed by previous reporters, but is a
belt of mixed polarity regions extending to both sides of
such an imaginary line (figure lb. Jack Harvey immediately endorsed what we found as true, and said he always
noted it. Also see Uchida et al. 1999b). The assumption
in the classical model that the parts closer to the polarity reversal lines are preferentially connected to the
corresponding closer parts of the opposite polarity side,
while the distant parts are preferentially connected to
the distant parts of the opposite polarity side, and form
a familiar simple arcade, does not actually hold. Distant
parts are connected to the close parts of opposite polarity
region, and vice versa, quite unlike the classical model.
The observed coronal structure, "dual-arcades", whose
inside legs cross, just looks like the flux separatrix surfaces seen in the quadruple source model proposed by
Uchida and Jockers (1979) and Uchida (1980) (see figures 3 and 4 later).
The situation with a considerable number of flux
patches transported into the opposite polarity region can
be approximated by four belt of regions with different
field intensities; especially when the density of the transported opposite polarity flux exceeds that of the normal
flux in that locality, the situation may be represented by
belts of sources +,—,+,—, quadruple array sources, if
approximated in 2.5 D.
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
556
Y.
Fig. 1. Coronal structure surrounding a dark filament:
(a) Faint structure-enhanced SXT image around
a high-latitude dark filament on southern hemisphere (16:44 UT, 1992 January 18). The white
curve is the locus of the top of the corresponding
dark filament (16:40 UT, 1992 January 16) taken at
BBSO, rotated to the exact time of the SXT observation by using a technique described in Uchida
et al. (1999b).
(b) Kitt Peak magnetogram of
16:16 UT, 1992 Jan 18 (not rotated because the
time is close enough to the time of the SXT observation). The white curve is the same as in (a),
but down-projected to the photosphere to compare
with the photospheric magnetic field, (c) The relevant Ha dark filament observed at BBSO, 16:40
UT, 1992 January 16. The height of the top of the
dark filament is determined as 1.2 x 10 5 km in the
method of matching the down-projected white locus to the border of the opposite polarity fields in
the photosphere which is not a well-defined line as
presumed before (Uchida et al. 1999b).
3.2. Arcade Flares in Active Regions
The first example of the case of an arcade flare in active
regions suggesting quadrupolarity, was, to our surprise,
the famous flare of 1992 February 21 (GOES class M2).
This flare, seen at the east limb, showed us for the first
time the clear structure of an arcade flare seen axis-on
(Tsuneta et al. 1992). The first report said that Yohkoh
confirmed what the magnetic reconnection model predicted. What the young Yohkoh colleagues had in mind
in writing their reports was the CSHKP model mentioned
in section 1 (the "reclosing of the once opened simple
bipolar arcade" model), without knowing about the debates on the energy difficulty of that model. Their con-
a et al.
[Vol. 51,
elusion was derived a bit too hastily, because the quadruple source model, an opponent of the CSHKP model, can
also explain the observed behavior of the cusp, for example, that their foot point distance increases with time,
etc., equally well. The difference can be found (1) in
the structures above the top of the cusp, which are faint,
and could not be seen easily before, but possibly can be
seen by Yohkoh, and (2) in the energy aspect that we
claimed to be fatal, but did not attract much general
attention when first claimed. Those could not be made
clear due to the absence of precise enough observations,
and we noted that Yohkoh would be able to contribute
essentially to this point.
We therefore pursued observational evidence that
could discriminate those models by using Yohkoh-SXT.
We tried to look into the faint pre-event phase of the
1992 February 21 event, and actually found that (a)
there exist overlying structures connecting the top of
the "pre-flare core" (which developed into the flare cusp
later) back to the photosphere on both sides at several
times of the width of the core structure (figure 2a). We
also found (b) a bright structure existed near the axis
of the dark tunnel, together with a vertical partition-like
structure in the middle of the dark tunnel, below the
pre-flare cusp (figure 2a). There was in this event a faint
rising blob ejected from the region of the pre-flare core
before the flare started. It is worth noting that this did
not pull up and stretch the arcade, but rather, seemed
to be pulled out by the rising "dual-loops" (back connections on both sides mentioned above) from the valley
right above the pre-flare core (S. Morita et al. 1999, in
preparation), and continued to be pulled up rather than
making the loop into a sharply tipped shape by pulling
it. All of these are not in agreement with what the classical model predicts, but in good agreement with what a
quadruple source model suggests.
Exactly similar features were found in another event,
the 1991 December 2 flare of GOES class Ml.5 (Tsuneta
1993). Namely, there appeared clear quadruple connections in the flare site with the central X-shape (figure 2b).
There was also a brightening right at the axis of the dark
tunnel below the "candle flame" shaped cusp of the flare
in this case. There was a rising blob from the valley part
of the "dual arcades" type structure above the top of the
cusp, leaving the X-shape behind, without pulling the
loop into a sharp-tipped shape.
These examples clearly showed similar structures connecting the top of the pre-flare core back to the photosphere on both sides, together with the low-lying activities near the axis of the dark tunnel, and a rising blob
from the top part of the cusp ejected without pulling the
loop into a sharply tipped shape.
The classical model(s) have difficulties in providing the
model counterparts for these newly discovered features,
in addition to the energy paradox. We are convinced
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
Quadruple Source Model for Arcade Flarings
No. 4]
557
Fig. 2. Pre-flare structure above the core of arcade flares seen at the limb: (a) Time development of the 1992 February 21
flare. There are clear high loops connecting the top of the pre-flare core back to the photosphere on both sides, as well as
a bright structure at the axis of the dark tunnel below the "candle flame" type flare cusp, that are not explicable in the
classical models. A blob rises prior to the start of the flare, but it is being pulled up by the expanding "dual-loops", rather
than pulling the arcade into a tipped shape as expected from the classical model, (b) The same of the 1991 December 2
flare. Corresponding features that can not be explained by the classical model, and supporting the quadruple source
model, are seen clearly.
that the situations for arcade flares and arcade formations are better represented by our quadruple magnetic
source model to be shown in section 4.
4. Magnet ohydrost at ic Configuration due to
Quadruple Array Sources in the Photosphere
(2.5 D Model)
We next discuss a 2.5 D solution of magnetohydrostatics in order to look into some basic properties of a model
having a neutral point in B±, in order to better understand what occur in flares.
We deal with the equation of magnetohydrostatics,
1 .
j x B -gmdp + pg = 0,
(1)
where B is the magnetic field, j = (c/47r)rot B is the current flowing in the plasma, p is the pressure and p is
the density of the plasma, and g is the gravity directed
downward to the — z direction. B is assumed to have the
form
B =
dz'"y'
dx)'
(2)
where ip is the magnetic stream function in the xz-plane,
and this, as well as Byj the field component in the ydirection (taken along the polarity-reversal line in the
photospheric plane), is assumed to be independent of y
(so-called 2.5 D approximation). Equation (1) is then
written as
'dtp
dx
2
±<P +
J_ /dipdBy
An \ dx dz
l^\
2 dx I
+
dP
dx
0,
d(p dBy
dz dx
dp
1- ^vi^ + i ^ + ~d~z
4TT I dx
^ 2 dz
(3)
(4)
-pa,
(5)
where V^_ = d2/dx2 + d2/dz2. Equation (4) can be
written as B± - \7±By — 0, where B± — (BX,BZ), and
indicates that By is constant along the field line JB_L, or
By is constant along the curve ip =constant in the xzplane.
By assuming that the temperature T is constant and
that p and p depend on (p and z in a separable way like
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
H
2a(z + l)
[x2 + (z + l)2Y
i p = f(<p)F(z), then
the equations (3) and (5) reduce respec5 tively to
S
[Vol. 51,
Y. Uchida et al.
5 5 8
/
I
2
^
1 dB2y
2 dip
Equation (9) is accordingly transformed into
ox
d<p ox
(6)
and
V#
w%% + «rfi; + ™-
(7)
If we further assume that the dependence of p on z
fulfills a hydrostatic distribution with a scaleheight z s =
?RT/g where 5ft is the gas constant, or
dlnF
dz
(14)
1
zs'
2a 2
d
V| c ^ + [xi2 + (C - a) 2 ] 2 d<p [£>)]
4a(C - a)
+ l)/zt
+8-rrp0((p)exp
2
£ + (C - a)2
0,
(15)
where V | c = d2/d£2 + d2/dC,2 .
We solved this transformed equation by extending the
Jockers'(1977) numerical code, which is a three-level
sc heme of relaxation by Marder and Weitzner (1970).
As f o r t h e boundary conditions, Jockers (1976, 1977)
chose the following for a simple bipolar array situation:
a
9 U=o= x 2 + l , ( a > 0 ) ,
(16)
we have from equations (6) and (7)
2
2
V ^ + \^[B V{<P) + 87rp 0 (^)e-
z/z
'] = 0,
(9)
which is a two-dimensional Poisson's equation with a
source distribution that depends on ip itself. We solve
this equation by giving the distribution of ip on the
boundary, together with the dependence of By and po
on (p.
Jockers (1977) had developed a numerical scheme to
solve the equation for the force-free field case for which
equation (1) simplifies itself into ( l / c ) j X B — 0 with a
simple arcade-like geometry. Uchida and Jockers (1979)
extended the scheme and took into account the pressure gradient force and gravity terms as in equations (1)
through (9), and further, dealt with a different type
boundary distribution of the field (quadruple array) for
which a neutral sheet structure in B± appears in the
corona above.
By a conformal transformation from the half plane xz
to the inside of a circle on the ££-plane by the use of a
complex mapping function,
W = ai^A,
Z + i'
(10)
where
Z
x + iz,
(11)
and
W = £ + iC.
(12)
The photospheric boundary in the xz-plane is mapped
to a circle of radius a with the origin mapped to (£ = 0,
( — —a) and the infinity to (£ = 0, ( = a) by means of
equation (10) through the relations
C
_
2ax
" [X2 + (Z + l) 2 ] '
(13)
3v(w)
'dip
8TT
= -P<pn
(/?,n>0),
(17)
in his calculation of a force-free field satisfying ( l / c ) j X B
= 0, in place of our (1). Equation (16) has a positivesloped region in x < 0 and a negative-sloped region in
x > 0, implying that he considered extended negative
and positive polarity regions lying side by side divided
by x — 0. He treated a sheared simple arcade.
In the present paper in which we deal with the nonforce-free field having a neutral sheet structure in JB_L, we
use a more general boundary distribution for ip (x, z — 0),
which results in a neutral sheet structure in JB_L, and
takes a dependence of j y on ip more suitable to our situation corresponding to the physical circumstance of the
dark filament to be considered.
We consider a magnetoplasma system in equilibrium
which fulfills equation (1). We must note that the time
history of the system before attaining the equilibrium
under consideration is relevant in specifying the boundary condition on ip and jy(ip). In our case, we consider
two systems of closed magnetic flux initially independent
from each other like two pairs of extended magnetic regions (for the case of a quiescent dark filament), or two
pairs of sunspots or two sets of spot-plage combinations
(for the case of an active region dark filament), and assume that these are brought into contact by a systematic
motion of the photospheric footpoints of lines of force
approaching each other (Tang 1987).
Corresponding to this process, we assume that initially
*.<*-<»~S
z=0
=£*o, exp
(x - x 0 J 2
(18)
and thus
<P
£^Bb,{Erf
(x - x0i)
+ 1},
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
(19)
No. 4]
Quadruple Source Model for Arcade Flarings
where B^ is the local peak of the field in each of
the two-dimensional magnetic belts at x — xoi with
a Gaussian widths c^, and Erf(x) is the Gauss' error
function, Erf(x)= (2/V5F) /0* exp(-t2)dt.
We assume
that the pairs of magnetic fluxes were initially self-closed
within them and that the net total flux vanishes at ±00.
The condition is ip (x — +00, z = 0) = 0, or
] P ViBoi
(20)
0
with (p(x = - 0 0 , z = 0) = 0 automatically fulfilled. A
simplest example fulfilling equation (20) is a pair of extended field regions antisymmetric with respect to the
central field polarity-reversal line x = 0 in the photosphere.
By giving the boundary values for ip(x) on the lower
boundary, we can solve equation (15) numerically by a
relaxation method, as mentioned above, if we specify po
and By as functions of <p, as in the next section.
5.
A Solution and Its Characteristic Features to
Compare with Observations
If we consider a case with p0 and By independent of ip,
the source term in equations (9) and (15) is identically
zero and the equations reduce to the two-dimensional
Laplace's equation. The solution is then a potential field
for the given distribution of the sources on the boundary,
equation (18) for our quadruple sources. We, however,
consider here the source term for equations (9) and (15),
for example, with
P o M = Po c exp
(<P ~ Vc)
21
+ P00
(21)
distributed around the critical lines of force, <p — tpc,
passing through the neutral point in B±. A constant
background pressure does not affect the solution. As for
the dependence of By on y?, we also assume a function of
the form
By(ip)
=BVcexp
(<P - Vcf
(22)
with a2B — 2a2. This may well be the case if the weak
background field with plasma which pre-existed between
the flux regions is squeezed together with the plasma
frozen to it by the approaching motion of the two systems towards each other, and some part of it remains
confined in the intervening region within the sheet-like
structure.
In order to reproduce the process of the squeezing of
the two field systems, we here move the distribution of
the footpoints of the potential field lines towards x — 0,
for example, by
dtanh f — J ,
(23)
559
with appropriate values of d and h. The magnetic lines of
force in initially different regions can not penetrate into
each other's region if there are plasmas frozen-in to them.
Therefore, a sheet current is formed on the interface of
these regions by this squeezing in order to maintain the
identity of the field lines in each region.
An example of the solution for the case in which the
photospheric footpoints are moved from x to x' is given.
Figure 3a shows the field with the thus-formed current
sheet, and figure 3b is the same one, but seen from a
different angle in order to show the 3 D structures of
the field. In this squeezed state, energy is stored in the
distorted magnetic field, and we propose this to be the
source of energy to be released in the process of flaring
when the relaxation to a lower energy configuration is allowed via magnetic reconnection at the "neutral points".
The first thing to note from figure 3b is a pattern similar to the characteristic pattern of the observed dark
filaments as seen from above (Martin, Levi 1992; Martin
et al. 1994). This pattern was commonly attributed to
the sheared arcade (the By field produced from a simple
arcade by a shear due to a footpoint motion to a large aspect ratio, however, should be unreasonably strong, and
also no observational evidence for such a shearing motion
exists as noted in section 1). It is now quite naturally
explained by a reasonable By imbedded along the neutral sheet of B± in our model. In the neutral sheet in
JB_L, even a By of a modest strength can dominate, and
the field pattern is elongated into the y-direction without actually shearing the structure. By in the thin neutral sheet may be considered to be the original weak field
which pre-existed in the intervening region, strengthened
by being squeezed between the two approaching field regions, and has a considerable value to render magnetohydrostatic equilibrium together with B± and the pressure
of the dark-filament gas. The plasma may initially be
the plasma frozen-in to the squeezed field, but it will be
supplemented by a plasma flowing into the region by a
mass-supply mechanism, which will be mentioned later.
Secondly, the thin partition-like structure of the Ha
dark filament, which is difficult to explain in the previous
models, because of rather slight sagging of strong fields
due to the relatively small gravitational force on the dark
filament material (Low 1975) for the classical model, is
now naturally explicable because the thin partition-like
structure is basically the vertical shape of the squeezed
neutral sheet in B± in our model, as can be seen in the
lower-middle of figure 3a. If we look at the field structure
from the sides, it is seen to be nested in this thin sheet,
because the field at the center of the sheet is horizontal,
while the field in the region on both sides are gradualy
tilted toward the vertical with distance according to the
nature of the solution. The line-of-sight field component
in the dark filament in this case is nicely opposite from
what the polarities of the "bipolar regions" predict. Also,
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
560
Y. Uchida et al.
[Vol. 51,
(a)
Fig. 3. A solution of magnetohydrostatic equation (15): (a) A mildly squeezed solution described in the text, seen almost
axis-on. An X-point-like structure is seen near the center, and the magnetic fluxes from each one of the sources are (i)
fluxes connecting the source A to B and D, (ii) fluxes connecting the source B to C and A, (iii) fluxes connecting the
source C to B and D, and (iv) fluxes connecting the source D to C and A. The part in the low central part will show
up as an X-ray cusp when the reconnect ion takes place at the "neutral point" right above it, and various characteristic
behavior, like the widening of the footpoints of the cusped arcade etc., take place just as observed. The difference from
the classical model is that the strong part of the field is already "opened" by the effect of the second pair of magnetic
fields, (b) A bird's-eye view of the same solution. The B y component dominates in the neutral region in -Bj_, and the
structure appear as if highly sheared in the middle into which the lines of force coming from A and D flow into, and then
leave from it after running some distance along the valley where the neutral line in B± is located. (In 3 D, B y is likely
due to the presence of a flux pair at skewed positions outside of the finite region in which the elongated inner pair of
sources exist.)
there can be vertically flattened helices in the neutral
sheet region corresponding to the "island" between the
oppositely directed fields on both sides, explaining the
observed helical field in the eruptive prominences.
Thirdly, our model has simply-connecting high loops
over this neutral sheet region of B±. The presence of
such overlying loops are noted in soft X-ray observations
(Vaiana et al. 1973), and thought of as evidence for the
simply-connected configuration in favor of the classical
picture. It is interesting to note that in some cases the
overlying loops are not affected by the disappearance of
the dark filament (Serio et al. CfA Preprint No. 935,
1978). In our present picture, the mass in the dark filament has been pumped in along the field lines which connect the dark filament to the hot coronal regions on both
sides in skew (see figure 3b) by the "syphon" mechanism
(Meyer, Schmidt 1969) due to the decrease of the pressure
caused by the radiative cooling in the high density dark
filament. The direction of the flow can be inverted without interfering the overlying loops if heating, rather than
cooling, takes place in the dark filament. If, however, the
heating is too violent, or some mechanism of eruption operates, for example, due to some magnetic instability, as
in large flares exerting a force on the dark filament in the
perpendicular direction to By, the dark filament as well
as the overlying loops may also be disturbed, and pushed
upward. We will present in a following paper a magnetohydrodynamic treatment of the 2.5 D dark filament
model by dealing with the magnetodynamical simulation
of the processes following a trigger destabilizing the system (Hirose et al. 1999 in preparation). The expansion
of such large scale loops is actually observed by Yohkoh,
but a noticeable point is that they are not made to be
sharp-tipped as they would be if pulled by the rising dark
filament as in the classical model, but rise without changing their initial rounded shape of the overlying loops. A
simulation of the quadruple source model shows the loop
behavior just as observed (Hirose et al. 1999 in preparation), and provides an inclusive interpretation of the
phenomena associated with flarings much better.
Fourth, we have a longitudinal field lying along the
neutral sheet (mainly By) supporting the radiativelycooled dense plasma held down by gravity; this massloaded By) in turn, is supported in the gradient in the
structure of JB_L- Our configuration is equipped with a
structure supporting these mass-loaded field lines in the
sheet from below. This is an array of small-scale loop
structures lying below, directly bridging both sides of
the "central polarity reversal line" in the photosphere,
as can be seen in figure 3a (strong field connecting the
region B to C). Such a structure is actually observed in
the low corona, and was often erroneously thought to
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
Quadruple Source Model for Arcade Flarings
evidence against the existence of a physical neutral
structure in association with the "polarity reversal
. The neutral sheet in B± (with By lying in it) exght above this in the corona in our model. The lowlying structure plays an important role in supporting the
mass-loaded field lines lying inside the neutral sheet by
providing the gradient in B±, providing the model counterpart of "barbs" (Martin et al. 1994), whereas none of
the previous models supporting the gas above the convex arcade could explain the "barbs". The lower part of
the dark filament is considered to show up as a heated
S-shaped feature pressed down on the structure below,
while the upper part of it is squeezed out and flies away
as an erupting dark filament before arcade flarings. The
major antiparallel vertical fields can come into contact
and are allowed to reconnect after the dark filament with
By is expelled out. It will be shown in Paper II that
the presence of the dark filament containing By prevents
the antiparallel field from contacting, and stabilizes the
system before the dark filament is squeezed out. Anomalous resistivity can only set in when the current density
that drives plasma turbulence can get high after the antiparallel fields can be squeezed together after the dark
filament is gone.
Finally, it should be mentioned that the structure in
the central part of figure 3a below the "neutral sheet"
shows up as an X-ray cusp when the reconnection takes
place in the "neutral point" right above it, and various
characteristic behavior like the widening of the footpoints
of the cusped arcade etc., take place just as observed.
The essential difference from the classical model is (a)
that the strong part of the field is already "opened" by
the effect of the second pair of magnetic field, removing
the difficulty in energy in our model, while there does not
exist any neutral sheet in the classical model unless the
dark filament opens up the strong part of the closed magnetic arcade. This causes the energy difficulty. And (b)
the actual structure above the "neutral sheet" revealed
by the observations by Yohkoh, favoring our model, as
mentioned in section 3.
All the features from the quadruple source model summarized above seem to explain the characteristics of the
observed dark filaments, as well as the characteristic preevent X-ray coronal structures very well.
6.
Conclusion and Discussion
We have revisited the quadruple magnetic source
model for the magnetic field surrounding dark filaments
(Uchida, Jockers 1979). The model was not well accepted
at the time of its proposal, and was not published. Some
figures and explanations, however, are found in the Proceedings of the Skylab Workshop as a part of the Reports
of the Working Groups, reported by Uchida (1980). It is
now revived because the results of the new observations
561
of the pre-event coronal structure around the dark filaments from Yohkoh seem to suggest that quadruple photospheric magnetic source model explains the observation quite well (Uchida et al. 1994; Uchida 1996; Uchida
et al. 1999a). The long-conceived bipolar arcade model
of the dark filament suspension, which provided the basis of the " reclosing of the once opened simple bipolar
arcade" model (so-called CSHKP model) for the arcade
type flarings, not only have a difficulty with respect to
energy, but can not provide model counterparts for various new features discovered by Yohkoh.
6.1.
Separatric Surfaces for a More Realistic Case with
Magnetic Patches Exchanged to the Opposite Polarity Regions
We claim that what are observed in X-rays in the preevent state (figure la) are the flux separatrix surfaces in
the quadruple source model. This is plausible because
the contact line of the two branches of the separatrix
surfaces is the magnetic neutral line in that case, and it
is quite possible that the neutral line provides the separatrix surfaces with some mass and heat already in the
pre-event phase of the flaring event that starts there one
or two days later.
We first show a set of two separatrix surfaces for the
quadruple array magnetic sources in the photosphere, for
the cases of a potential field in 2.5 D, as a reference, in
figure 4a. If we name the four sources A, B, C, and D
as before, it is seen that the near-critical lines of force
coming from source A, for example, go either to source B
or source D, but together with the part of other critical
lines connecting D to C, they seem to land at source C
of the same polarity as A. This explains the seemingly
paradoxical fact that the observed pre-event loops in the
"dual-arcades" seem to connect a region to the patches of
the same polarity on the other side (precise comparison
of figures la and b suggest this), though not very clear,
due to the lowering of the temperature of the loop near
the footpoints. Although the elongated field in the ydirection will give an impression of a highly sheared field,
we now know that this is due to the dominance of By
in the "neutral sheet" of B±, and no actual mechanical
shearing is necessary.
Next, in a more realistic situation, in which the exchanged patches of one polarity are transported into the
opposite side, and vice versa, are taken into account, the
magnetic configuration is no longer 2.5 D but 3 D. The
critical lines of force in such a case in the potential field
state are shown in figure 4b. Here, we can see in figure 4b
that the configuration explains even better the observed
features of "dual-arcades with crossed legs", seemingly
connecting to the same polarity parts, as seen in figure la.
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
562
[Vol. 51,
Y. Uchida et al.
(b)
^^^^^^^fe^^j
ifflm
/ /1'
"^flM
^^^WjF^
&
^''S^TBH
Sni^l
Fig. 4. Flux separatrix surfaces for 2.5 D and 3 D cases: (a) The separatrix surfaces are in the form of "dual-arcades" shape
as seen from figures 3a and 3b with critical lines of force spanning the surfaces. The contact line of the two surfaces is the
neutral line (figures 4a,b are the potential field cases, for simplicity), (b) Critical lines of force for a case with exchanged
patches of oppsite polarity sources. These critical lines of force, corresponding to the critical lines in figure 3b, seemingly
connecting source A to C and B to D spanning on the separatrix surfaces, represent the observed "dual-arcades" quite
well (cf., Uchida et al. 1999a).
6.2.
Relation of Our Global Model to the Local X-Point
Reconnection Models
Finally, we would like to point out that the local
treatment of the reconnection problem, started by Sweet
(1958) and treated by many authors, has not really been
solved yet.
The huge discrepancy in the time scales between the
rise time of flares, on the order of 102 s, and the magnetic
diffusion time scale, on the order of 10 12 s, has annoyed
researchers, and various kinds of trials have been made
to resolve the discrepancy without any real success. For
example, an introduction of anomalous resistivity, or an
enhancement of the resistivity by an order of 10 6 , still
leaves a 4-5 orders of magnitude discrepancy.
In the model proposed by Uchida (1980), the rapid
flare rise is attributed to a rapid dynamical collapse to
the intervening lower energy interchanged state through
an interchange instability after the longitudinal field (By
with dark filament) which stabilized the configuration
against this instability in the neutral sheet with some
asymmetry in general, is lost with the dark filament rises.
The long-endured energy release in the later phase of arcade flares for hours to one day has been identified with
dissipation enhanced through an increase in the contact
surface of the opposite-polarity fields by a large factor as
the result of this interchange collapse, thus producing a
highly interleaved state of opposite polarity fields.
One of the most important findings from the dynamical
simulations is that the energy release comes from a relax-
ation of the magnetic stress all over the squeezed magnetic field below the separatrix surfaces. This relaxation
is allowed by the occurrence of magnetic reconnection at
the "neutral points". The release of the magnetic stress
and mass stored within this structure contained below
the separatrix surfaces can exceed by considerable factors the energy and mass directly released in the locality
of the critical point. This may solve the riddle that the
total release of mass and energy in CME's (corresponding to the mass and energy released dynamically from
the stressed region under the separatrix surfaces in our
model) exceeds those liberated in the flare itself (corresponding to the direct release of the mass and energy in
the locality of reconnection site), and they seem to provide a consistent explanations for this. Actual results of
our MHD simulations of the dynamical energy and mass
releases will be discussed in Paper II of the series (Hirose
et al. 1999 in preparation).
We acknowledge that this work was made possible
through the results of observations by Yohkoh, and thank
all the team members who made the successful satellite possible through hardware and software construction,
continued successful operation of the satellite, and the
collaborative data analysis and scientific discussions.
References
Aly J.J. 1991, ApJ 375, L61
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
No. 4]
Quadruple Source Model for Arcade Flarings
Antiochos S.K Dahlburg R.B., Klimchuk J.A. 1994, ApJ
420, L41
Carmichael H. 1964, in Proc. NASA Symp. on the Physics of
Solar Flares, ed W.N. Hess (NASA SP-50) p451
Dahlburg R.B., Antiochos S. 1991, ApJ 383, 420
Demoulin P., Priest E.R. 1993, Sol. Phys. 144, 283
Pujisaki K., Uchida Y., Morita S., Tsuneta S., Hirose S., Cable
S. 1999, PASJ submitted
Hirayama T. 1974, Sol. Phys. 34, 323
Hundhausen A., Low B.C. 1994, ApJ 429, 876
Jockers K. 1976, Sol. Phys. 50, 405
Jockers K. 1977, Sol. Phys. 56, 35
Kippenhahn R., Schluter A. 1957, Z. Astrophys 43, 36
Kopp R.A., Pneuman G.W. 1976, Sol. Phys. 50 85
Kuperus M., Raadu M. 1974, A&A 31, 189
Leroy J.-L., Bommier V., Sahal-Brechot S. 1983, Sol. Phys
83, 135
Low B.C. 1975, ApJ 198, 211
Marder M.B., Weizner H . 1970, Plasma Phys. 12, 435
Martin S.F., Bilimoria R , Tracadas P.W. 1994, in Solar Surface Magnetism, ed R.J. Rut ten, C.J Schrijver (Springer,
New York) p303
Martin S., Levi S. 1992, in Eruptive Solar Flares, ed Z.
Svestka, B. Jackson, M. Machado (Springer, Berlin) p33
McAllister A.H., Uchida Y., Tsuneta S., Strong K., Acton L.,
Hiei E., Bruner E., Watanabe Ta. et al. 1992, PASJ 44,
L205
Meyer F., Schmidt H.U. 1968, Z. Angew. Math. Mech. 48, 218
Moore R., Roumeliotis G. 1992, in Eruptive Solar Flares, ed
Z. Svestka, B. Jackson, M. Machado (Springer, Berlin)
p69
Pickelner S.B. 1971, Sol. Phys. 17, 44
Priest E.R. 1989, Dynamics and Structure of Quiescent Solar
Prominences (Kluwer, Dordrecht)
Sciffer M. 1997, Thesis, University of New Castle, Australia
Shibata K., Masuda S., Shimojo M., Hara H., Yokoyama H.,
Tsuneta S., Kosugi T., Ogawara Y. 1995, ApJ 451, L83
563
Sturrock P A . 1966, Nature 221, 695
Sweet P A . 1958, in Electromagnetic Phenomena in Cosmic
physics, ed B. Lehnert (Cambridge University Press) pi23
Tandberg-Hanssen E. 1974, Solar Prominences (D. Reidel,
Dordrecht)
Tang F. 1987, Sol. Phys. 107, 203
Tsuneta S. 1993, in The Magnetic and Velocity Fields of Solar
Active regions, ed H. Zirin, G.-X. Ai, H. Wang, ASP Conf.
Ser. 46, p239
Tsuneta S., Hara H., Shimizu T., Acton L.W., Strong K.T.,
Hudson H.S., Ogawara Y. 1992, PASJ 44, L63
Uchida Y. 1980, contributions by Uchida, printed in the
Reports of Working Groups, in Sky lab Workshop, Solar
Flares, ed P.A. Sturrock (University of Colorado Press)
pp67, 110
Uchida Y. 1996a, Adv. Space Res. 17, 19
Uchida Y. 1996b, in The Structure of the Sun, ed T.R. Cortes,
F. Sanchez (Cambridge University Press) p355
Uchida Y. 1996c, in Magnetodynamic Phenomena in the Solar
Atmosphere-Prototypes of Stellar Magnetic Activity, ed
Y. Uchida, T. Kosugi, H.S. Hudson (Kluwer, Dordrecht)
p295
Uchida Y., Fujisaki K., Morita S., Torii M., Hirose S., Cable
S. 1999b, PASJ 51, 53
Uchida Y., Hirose S., Morita S., Fujisaki K., Torii M., Tanaka
T., Yabiku T., Miyagoshi T., Uemura S., Yamaguchi T.
1999a, Ap&SS in press
Uchida Y., Jockers K. 1979, presented at the Skylab Workshop in 1980 (Uchida 1980)
Uchida Y., McAllister A., Khan J., Sakurai T., Jockers K.
1994, in X-ray Solar Physics from Yohkoh, ed Y. Uchida,
T. Watanabe, K. Shibata, H. Hudson (Universal Academy
Press, Tokyo) pl61
Vaiana G.S., Krieger A.S., Timothy A.F. 1973, Sol. Phys. 32,
81
Webb D.F., Krieger A.S., Rust D.M. 1976, Sol. Phys. 48, 159
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System