ON THE S T R U C T U R E OF THE MAGNETIC FIELD OF
E.I.
(Institute
M O G I L E V S K Y , L.B.
of Terrestrial
DEMKINA, B.A.
Magnetism,
USSR
Ionosphere
Academy
IOSHPA, and
V.N.
and Radio-Wave
of Sciences,
SUNSPOTS
OBRIDKO
Propagation
of
the
Moscow)
ABSTRACT
The model of the magnetic field of sunspots, taking account of fine structure of magnetic field
in solar plasma, is considered. Small-scale subgranules with their o w n field form magnetic filaments
in the external current-free field. T h e filaments are vertical in the umbra, while in the penumbra they
run along the surface with sharp bends. In a number of spot umbra the relation between D o p p l e r
velocity and the field is established o n polarized spectrograms. The 7r-component splitting in
umbra is interpreted as a result of a weak background magnetic-field existence together with a large
field of magnetic filaments. Spectrographic definition o f the magnetic field in spot umbra is ac­
complished o n the effect o f magnetic-lines intensification and directly o n spectrograms of lowexcitation (Fe i, Ti i) and high-excitation ( F e n) lines. Magnetic field measured in low-excitation lines
exceeds twice the field value obtained in high-excitation lines. This result has been considered in the
light of the proposed model of sunspot field.
By s t u d y i n g t h e m a g n e t i c
field
of a s u n s p o t o n e c a n o b t a i n the m o s t c o m p r e ­
h e n s i v e i n f o r m a t i o n o n t h e s m a l l - s c a l e s t r u c t u r e of t h e s o l a r m a g n e t o p l a s m a . T h i s is
p r i m a r i l y d u e t o t h e fact t h a t t h e p h o t o g r a p h i c m e t h o d is t h e m o s t efficient in m e a s u r i n g
s u n s p o t fields, s i n c e it y i e l d s a h i g h r e s o l u t i o n a n d g o o d g u i d i n g . O n t h e o t h e r h a n d ,
i n v e s t i g a t i o n o f t h e m a g n e t i c - f i e l d d i s t r i b u t i o n s e p a r a t e l y in t h e u m b r a a n d p e n u m b r a
o f a s u n s p o t m a k e s it p o s s i b l e t o s t u d y t h e s t r u c t u r a l e l e m e n t s in t w o p r o j e c t i o n s , a s
it w e r e , i.e. f r o m a b o v e in t h e u m b r a , w h e r e t h e field is p r e d o m i n a n t l y v e r t i c a l , a n d
f r o m t h e s i d e in t h e p e n u m b r a , w h e r e t h e field is n e a r h o r i z o n t a l . F i n a l l y , t h e s u n s p o t
field d e v e l o p s r a t h e r r a p i d l y a n d e v i d e n t l y r e m a i n s l a r g e l y u n a f f e c t e d b y t h e m a g n e t i c
fields of n e i g h b o u r i n g a c t i v i t y p h e n o m e n a . A w o r k i n g m o d e l o f a m a g n e t i c field o f a
sunspot, which takes i n t o a c c o u n t the small-scale structure of the m a g n e t o p l a s m a a n d
s o m e s p e c t r a l o b s e r v a t i o n s s h e d d i n g l i g h t u p o n t h e fine s t r u c t u r e of t h e m a g n e t i c
field of a s u n s p o t w i l l b e c o n s i d e r e d b e l o w .
The
model
of t h e
magnetoplasma
structure
considered
by
Mogilevsky
and
Shelting (1968) implies the existence of small-scale ( ~ 1 0 c m ) elements (so-called
7
sub-granules) with a closed magnetic
c u r r e n t - f r e e m a g n e t i c field H=H
0
field
field
+ Y tHh
J
surrounded
where H
0
by a
quasi-homogeneous
is t h e h o m o g e n e o u s m a g n e t i c
a n d £ / / , is t h e t o t a l field ( a t t h e given p o i n t ) of t h e e n t i r e e n s e m b l e of s u b -
granules.
D u e t o t h e i n t e r a c t i o n b e t w e e n t h e i r m a g n e t i c m o m e n t s , s u b - g r a n u l e s t e n d t o line
Kiepenheuer
(ed.),
Structure
and Development
of Solar Active
Regions, 215 229. r
l.A.U.
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E.I. M O G I L E V S K Y
216
u p in l o n g c h a i n s ( m a g n e t i c
filaments)
ET AL.
whose space distribution
determines
the
o b s e r v e d l a r g e - s c a l e field o f t h e s p o t . I n t h e u m b r a w e s h o u l d o b s e r v e a r e c e d i n g
ensemble of vertical m a g n e t i c
filaments
which can group together into convection
cells o w i n g t o c o n v e c t i v e s u b - p h o t o s p h e r i c m o t i o n s ( w h i c h o b v i o u s l y t a k e t h e f o r m
of oscillatory convection). T h e
extending of a m a g n e t i c
first
filament
appearance
of a p o r e c o r r e s p o n d s t o
cell w i t h a m e a n i n t e n s i t y o f
the
> 1200-1500 oe.
N e g l e c t i n g t h e p r o b l e m o f t h e g e n e r a t i o n o f s u b - g r a n u l e s w i t h a force-free m a g n e t i c
field*,
o n e m a y a s s u m e t h a t t h e s u b s e q u e n t g r o w t h o f t h e p o r e is a p r o c e s s o f t h e
successive extending of vertical c h a i n s of sub-granules g r o u p e d t o g e t h e r i n t o convection
cells. I t f o l l o w s f r o m o b s e r v a t i o n s (Vasilieva, 1963) t h a t t h i s p r o c e s s o f t h e i n i t i a l
g r o w t h o f t h e s p o t is p r e c e d e d b y t h e egress o f t h e g a s - d y n a m i c s h o c k - w a v e t o t h e
p h o t o s p h e r e . * * T h e w a v e , p r o p a g a t i n g p a r t l y u p w a r d s , c a r r i e s t h e initial
weak
m a g n e t i c field of t h e f u t u r e s p o t o u t i n t o t h e c h r o m o s p h e r e . E x t e n d i n g v e r t i c a l m a g ­
netic tubes can extend i n t o t h e c h r o m o s p h e r e a n d c o r o n a t h r o u g h the initial
field,
b e c a u s e t h e diffusion o f s u b - g r a n u l e s o v e r t h e g r a d i e n t field is m u c h m o r e r a p i d ( b y
a factor of the o r d e r of t h e R e y n o l d s ' m a g n e t i c n u m b e r ) t h a n o r d i n a r y m a g n e t i c field diffusion ( S y r o v a t s k y a n d Z h u g z h d a , 1967).
T h e u m b r a will c o n t i n u e g r o w i n g u n t i l p a r t o f t h e o u t e r m a g n e t i c t u b e s b e g i n t o
d e v i a t e f r o m t h e v e r t i c a l , d u e t o r e f r a c t i o n w h e n t h e field p r o p a g a t e s i n t o t h e c h r o m o s ­
p h e r e w h e r e t h e c o n d u c t i v i t y i n c r e a s e s . T h i s d e v i a t i o n will r e s u l t in t h e b e n d i n g o f
t h e o u t e r filaments a n d l a t e r i n t h e i r r e t u r n i n t o t h e p h o t o s p h e r e ( t h e o u t e r b o u n d a r y
of the p e n u m b r a ) . These magnetic
a relatively thin ( ~ 5 x l 0 c m )
7
filaments,
creeping through the photosphere, form
translucent magnetic surface, the p e n u m b r a .
The
q u a l i t a t i v e r e p r e s e n t a t i o n o f t h i s s c h e m e is g i v e n in F i g u r e 1. I n t h i s w o r k i n g m o d e l ,
t h e u m b r a o f t h e s p o t is a n i n h o m o g e n e o u s ( d u e t o c o n v e c t i v e p e r t u r b a t i o n s ) b a n d
consisting of sub-granule
filaments
w h o s e v e r t i c a l field m a y r e c e d e i n t o t h e r e g i o n of
t h e c h r o m o s p h e r e a n d c o r o n a a n d later close u p o n t h e u m b r a (or u m b r a s ) of o t h e r
s p o t s o f t h e g r o u p , w h i l e t h e p e n u m b r a is a relatively t h i n l a y e r o f m a g n e t i c t u b e s
d e t a c h e d f r o m t h e u m b r a w h i c h y i e l d a n e a r h o r i z o n t a l field a n d c l o s e e i t h e r u n d e r
t h e p h o t o s p h e r e o r u p o n t h e d a r k i n t e r g r a n u l a r a r e a s o f t h e p h o t o s p h e r e . T h e es­
s e n t i a l p o i n t in t h i s ' m u s h r o o m - l i k e ' s c h e m a t i c m o d e l o f t h e s p o t is t h a t t h e f o r m a t i o n
of the p e n u m b r a d u e to the b e n d i n g of the magnetic tubes s h o u l d be a c c o m p a n i e d by
s u b s t a n t i a l c h a n g e s in t h e m a g n e t i c flux a n d b y t h e g e n e r a t i o n o f a r i n g c u r r e n t in t h e
s u r f a c e l a y e r o f t h e p h o t o s p h e r e w i t h a finite c o n d u c t i v i t y . T h e field o f t h i s t o r o i d a l
c u r r e n t , l o c a t e d u n d e r t h e p e n u m b r a a r o u n d t h e u m b r a , d e t e r m i n e s t h e s t a b i l i t y of
t h e s u n s p o t u m b r a a t t h e p h o t o s p h e r e level. T h e r i n g - c u r r e n t e n e r g y , w h i c h is e q u a l
t o o r less t h a n t h e e n e r g y o f t h e p e n u m b r a field, m a y b e e s t i m a t e d b y c a l c u l a t i n g t h e
* That the field in sub-granules tends to become force-free follows from the condition of magneticenergy extremum in the sub-granule.
** This is accompanied by the appearance of a bright-point floccule and then of a small ringlike
one.
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S T R U C T U R E
O F
T H E
M A G N E T I C
F I E L D
O F
S U N S P O T S
217
F I G . 1 . Structural scheme of the magnetic field of a sunspot: I = photosphere;
2 = penumbra field;
3 = induced ring current restraining
the umbra field; 4 = umbra field; 5 = sub-granules in various
convection cells; 6 = current-free background magnetic field.
field of t h e r i n g a t t h e c h a r a c t e r i s t i c v a l u e s g i v e n in F i g u r e 2. I t w a s a s s u m e d t h a t
t h e m e a n field v a l u e in t h e p e n u m b r a w a s < 0 - 2 5 H ,
max
a n d therefore the ring was
l o c a t e d a t a d e p t h o f a b o u t 0-2 u m b r a r a d i u s ( K o l p a k o v , 1966). T h e a d d i t i o n of t h e
' t a b l e - s h a p e d ' u m b r a field, t h e p e n u m b r a field a n d t h a t o f t h e ' h o l d i n g ' r i n g o p p o s i t e
in sign y i e l d s a s u n s p o t field s i m i l a r t o t h e o b s e r v e d d i s t r i b u t i o n ( F i g u r e 2 ) . H e r e w e
o n l y c o n s i d e r t h e m a g n e t i c - f i e l d i n t e n s i t y d i s t r i b u t i o n . I t is k n o w n , h o w e v e r ( S e v e r n y ,
1964) t h a t t h e o b s e r v e d d i s t r i b u t i o n o f t h e s u n s p o t - f i e l d v e c t o r is n o t a p p r o x i m a t e d
b y t h e d i p o l e field, n o r is it a p o t e n t i a l o n e , b e c a u s e t h e o b s e r v a t i o n s p o i n t t o t h e
existence of a n a z i m u t h a l c o m p o n e n t . Restricting ourselves t o t h e general structural
scheme of the s p o t a n d w i t h o u t going into the n a t u r e of the
field-vector
distribution,
w e will n o t e t h a t t h e set o f v e r t i c a l m a g n e t i c t u b e s o f t h e u m b r a s h o u l d a c q u i r e t h e
g e n e r a l a z i m u t h a l c o m p o n e n t d u e t o t h e helical i n s t a b i l i t y o f t h e p l a s m a w i t h t h e
field ( K a d o m t z e v , 1962). I n t h i s c a s e t h e g e n e r a l m a g n e t i c field o f t h e u m b r a (especial­
ly in t h e c h r o m o s p h e r e ) will a l s o b e force-free ( M o g i l e v s k y a n d S h e l t i n g , 1966). W i t h
t h e g r o w t h of t h e u m b r a a r e a ( ' s u r f a c i n g ' o r ' s i n k i n g ' o f i d e n t i c a l - t y p e m a g n e t i c
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E. I. M O G I L E V S K Y
218
ET AL.
%1
F- cowA.
0.1
OA
01
0.6
F I G . 2. Distribution
of magnetic field H in sunspot: H
H k = ring-current field, H m a x = maximum intensity in sunspot
u
filaments
,
10
= umbra field, H m = penumbra
umbra.
n
field,
o f t h e s u b - g r a n u l e s ) t h e specific t e n s i o n (stress p e r u n i t l e n g t h ) o f t h e r i n g
is r e t a i n e d , w h i c h is in a c c o r d w i t h its s t a b i l i t y . T h e d i s s i p a t i o n t i m e o f t h e r i n g
c u r r e n t , p r i m a r i l y d u e t o J o u l e losses ( t a k i n g i n t o a c c o u n t t h e c o n d u c t i v i t y a c c o r d i n g
t o K u k l i n , 1966, in p a r t l y i o n i z e d s u b - p h o t o s p h e r i c l a y e r s ) will b e o f t h e o r d e r of
5 x 1 0 - 1 0 sec, w h i c h c o r r e s p o n d s t o t h e lifetime of t h e s p o t . T h e o b v i o u s i m p l i c a t i o n
6
7
o f t h i s s u n s p o t m o d e l is t h e p o s s i b i l i t y o f a c o n s i d e r a b l e p e n e t r a t i o n o f t h e u m b r a
field i n t o t h e c h r o m o s p h e r e a n d t h e s m a l l h e i g h t o f t h e p e n u m b r a . T h e relatively
s m a l l ( < , 1 0 c m ) t h i c k n e s s o f t h e p e n u m b r a n a t u r a l l y e x p l a i n s its s h a r p l y defined
8
boundaries (photosphere-penumbra, penumbra-umbra), whose contrast does not
v a r y w i t h t h e shifting of t h e s p o t f r o m t h e c e n t r e t o w a r d s t h e l i m b . T h e
filamentary
s t r u c t u r e o f t h e p e n u m b r a a l i g n e d a l o n g t h e field a n d t h e n e a r - r o u n d g r a n u l e s in t h e
u m b r a , t h e n a t u r e o f t h e g a s m o t i o n w i t h i n t h e u m b r a a n d p e n u m b r a , a n d finally t h e
p o s s i b i l i t y o f e x p l a i n i n g t h e s p o t e v o l u t i o n , a s well a s s o m e m o r p h o l o g i c a l f e a t u r e s
o f c o m p l e x ( m u l t i - n u c l e u s ) s p o t s w i t h i n t h e f r a m e w o r k o f t h i s m o d e s p e a k in f a v o u r
of t h e w o r k i n g m o d e l u n d e r review.
T o o b t a i n additional i n f o r m a t i o n o n the structure of the s u n s p o t m a g n e t i c
field,
d e t a i l e d p h o t o g r a p h i c m e a s u r e m e n t s o f t h e magnetic-field d i s t r i b u t i o n in a g r e a t
n u m b e r ( a b o u t 50) o f l a r g e ( S p > 2 5 0 u n i t s ) , p r e d o m i n a n t l y q u i e t s p o t s w e r e c a r r i e d
o u t w i t h t h e t o w e r s o l a r t e l e s c o p e I Z M I R A N in 1 9 6 6 - 6 7 ( Z h u l i n et a/.,
1966). F o r
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STRUCTURE
OF THE
MAGNETIC
FIELD OF
SUNSPOTS
219
t h i s p u r p o s e p a i r e d p o l a r i z a t i o n s p e c t r o g r a m s n e a r line F e I k 6302-508 A w e r e o b ­
t a i n e d by t r a v e r s i n g t h e s p o t 1 5 - 2 5 t i m e s with t h e s p e c t r a l slit. S i m u l t a n e o u s l y w i t h
t a k i n g t h e s p e c t r o g r a m s , a series of p i c t u r e s o f t h e s p o t o n t h e s p e c t r o g r a p h slit w e r e
t a k e n , a n d t h i s e n a b l e d u n a m b i g u o u s ' g u i d i n g ' . T h e o b s e r v a t i o n s w e r e c a r r i e d o u t in
the Cassegrain focus of t h e telescope ( F = 2 7 m ) . O n each pair of s p e c t r o g r a m s of a
g i v e n c r o s s - s e c t i o n of t h e s p o t , m e a s u r e m e n t s of t h e l o c a t i o n o f t h e n- a n d a - c o m p o n e n t s r e l a t i v e t o t h e t e l l u r i c line w e r e m a d e in 2 0 - 2 5 different p o i n t s a l o n g t h e
h e i g h t of t h e slit. T h u s , f o r e a c h s p o t t h e m a g n e t i c fields a n d l i n e - o f - s i g h t velocities
w e r e m e a s u r e d in s e v e r a l h u n d r e d p o i n t s of t h e s p o t , w h i c h c h a r a c t e r i z e d t h e d i s t r i ­
b u t i o n of the H a n d V
D
values comprehensively e n o u g h a n d with a high resolution.
T h e r e s u l t s o f t h e d e t e r m i n a t i o n o f line-of-sight velocities a r e a s f o l l o w s :
( a ) F o r m o s t of t h e u m b r a s m e a s u r e d , w i t h a field o f 2 0 0 0 - 3 5 0 0 o e , t h e velocity
o f g a s ' s i n k i n g ' a t t h e p h o t o s p h e r e level w a s a b o u t
1 k m / s e c * ( F i g u r e 3). S u c h
velocities w e r e o b s e r v e d b o t h for t h e a (0)- a n d n ( V ) - c o m p o n e n t s .
3000
-0 5
1
-10
-i
c
-2.0
F I G . 3. Dependence of line-of-sight velocities VD in sunspots defined from a (0)- and n (V') -com­
ponents, on magnetic field H (taking account of polarity 4- S, —N).
* The sign of the velocity (descent or ascent) may depend on the phase of sunspot development.
Since we used only spots of large area, we were able to observe mainly the descent of the gas which
is characteristic of the period of the post-maximum development of the group.
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220
E.I. M O G I L E V S K Y
ET AL.
( b ) T h e feasibility of d e f i n i n g t h e line-of-sight velocities b y t h e a- a n d ^ - c o m p o n e n t s
is i l l u s t r a t e d in F i g u r e 4 . A l i n e a r r e l a t i o n s h i p of t h e t y p e V = V — 0-26 k m / s e c w a s
a
f o u n d b e t w e e n t h e s e velocities (V
n
a n d V ). T h e r a y shift o f t h e lines i n d i c a t e s t h a t ,
a
n
a t l e a s t i n t h e u m b r a , t h e r o l e o f t h e s c a t t e r e d l i g h t w h i c h w o u l d yield u n s h i f t e d lines
is n o t g r e a t .
1,0
0,3
-
•
•
/
/
-0,9
-i,0
•
-of
I
•
V
*
jr
*
/
•
•
•i.O
*
•
•
•
•
•
•
•
•
•
•
•
•
F I G . 4. Comparison of line-of-sight
and a (Va)
-components.
velocities
in sunspot umbra obtained by measurements
in n ( V.-t)
(c) T h e e x i s t e n c e of r e l a t i v e l y h i g h v e r t i c a l velocities in t h e u m b r a , o b t a i n e d by
p h o t o g r a p h i n g , was confirmed by photoelectric m e a s u r e m e n t s of the s a m e spot with
a m a g n e t o g r a p h (for a l a r g e s p o t o f J u l y 19, 1966, w h i c h w a s l o c a t e d n e a r t h e c e n t r a l
m e r i d i a n of t h e S u n ) .
A n o t h e r i m p o r t a n t result p r o m o t i n g the u n d e r s t a n d i n g of the sunspot-field structure
a n d o b t a i n e d f r o m t h e s a m e m a t e r i a l s , w a s t h e effect o f t h e 7 r - c o m p o n e n t s p l i t t i n g i n t o
t w o s u b - c o m p o n e n t s d i s p l a c e d r e l a t i v e t o t h e c e n t r e of t h e line ( F i g u r e 5). A s i m i l a r
effect w i t h a c o m p l e t e s p l i t t i n g o f t h e line in t h e u m b r a w a s o b s e r v e d b y a n u m b e r of
a u t h o r s (for e x a m p l e , S e v e r n y , 1 9 5 9 ; B u m b a , 1 9 6 2 ; C h i s t j a k o v , 1 9 6 7 ; a n d o t h e r s ) . It
is a l s o r e v e a l e d b y e x a m i n i n g p h o t o c o p i e s of s p e c t r o g r a m s of l a r g e s p o t s f r o m t h e
M o n t e M a r i o O b s e r v a t o r y . T h i s effect c a n n o t b e a t t r i b u t e d t o i n s t r u m e n t a l p o l a r ­
i z a t i o n , it r e m a i n s a t a c o n s i d e r a b l e t u r n of t h e s p e c t r o g r a p h g r a t i n g , for
instance
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S T R U C T U R E OF THE M A G N E T I C
FIELD OF
SUNSPOTS
221
u p o n t r a n s f e r f r o m t h e f o u r t h r i g h t s p e c t r a l o r d e r t o t h e s e c o n d left o n e ( C h i s t j a k o v ,
1967). C o n s i d e r a t i o n o f t h i s effect o f t h e
rc-component
s p l i t t i n g in t h e u m b r a s for 34
S o u t h e r n - p o l a r i t y a n d 10 N o r t h e r n - p o l a r i t y s p o t s ( o b s e r v a t i o n s of 1 9 6 6 - 6 7 ) l ead s t o
the following conclusions:
( a ) T h e v a l u e o f s p l i t t i n g , o b t a i n e d f r o m a g r e a t n u m b e r of p o i n t s , is 0 - 0 0 8 - 0 - 0 2 0 A,
t h u s c o n s i d e r a b l y e x c e e d i n g t h e p o s s i b l e m e a s u r e m e n t e r r o r ( r . m . s . e r r o r is 0-003 A
±
10%).
( b ) T h e d i s p l a c e m e n t o f t h e s p l i t 7 i - c o m p o n e n t r e l a t i v e t o t h e c e n t r e o f t h e l i n e in
e a c h s p e c t r u m is i n d e p e n d e n t o f t h e field sign a n d a p p e a r s t o b e o p p o s i t e t o t h e
displacement of the c - c o m p o n e n t (Figure 6). T h e value of the 7r-component splitting
i n t o t w o s u b - c o m p o n e n t s w a s f o u n d t o b e a b o u t o n e o r d e r less t h a n t h e d i s t a n c e
between the ^-components.
A s w a s s h o w n i n R a c h k o v s k y ' s (1962) p a p e r , s u c h a n effect o f t h e 7 r - c o m p o n e n t
s p l i t t i n g c o u l d h a v e b e e n o b s e r v e d d u e t o t h e r o t a t i o n o f t h e p o l a r i z a t i o n p l a n e in a n
i n h o m o g e n e o u s m a g n e t i c field. O n e m u s t a s s u m e t h a t t h e s e n s e o f t h e r o t a t i o n of t h e
p o l a r i z a t i o n p l a n e a n d , a c c o r d i n g l y , t h e s i g n o f t h e r o t a t i o n o f t h e field's t a n g e n t i a l
c o m p o n e n t , reverse with d e p t h simultaneously with t h e c h a n g e of t h e sunspot-field
p o l a r i t y . B e s i d e s , s u c h a n effect s h o u l d b e e q u a l i n v a l u e a n d sign f o r all u m b r a
p o i n t s , w h i c h often b e l o n g t o a m a r k e d l y i n h o m o g e n e o u s field o f t h e u m b r a . A t t h e
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E.I. M O G I L E V S K Y ET AL.
222
s a m e t i m e , S e v e r n y ' s ( 1 9 6 4 , 1965) o b s e r v a t i o n s r e v e a l e d a s u b s t a n t i a l i n h o m o g e n e i t y
o f t h e r o t a t i o n effect of t h e p o l a r i z a t i o n p l a n e .
A n o t h e r i n t e r p r e t a t i o n o f t h i s effect p r o c e e d i n g f r o m m o r e g e n e r a l p o s s i b l e c o n ­
c e p t i o n s o f t h e s t r u c t u r e o f t h e m a g n e t o p l a s m a field ( M o g i l e v s k y a n d S h e l t i n g , 1968)
is t h a t t h e 7 t - c o m p o n e n t s p l i t t i n g s h o u l d b e a t t r i b u t e d t o t h e r e a l b a c k g r o u n d m a g n e t i c
field,
w h o s e sign s h o u l d b e o p p o s i t e t o t h a t o f t h e s u b - g r a n u l e field a n d
whose
i n t e n s i t y is m u c h l o w e r ( d e p e n d i n g o n t h e g e o m e t r y o f t h e s u b - g r a n u l e s , t h e i r sizes,
e t c . ) t h a n t h e m a x i m u m i n t e n s i t y o f t h e field i n s i d e t h e s u b - g r a n u l e s . H e r e , s o m e
r e l a t i o n s h i p s h o u l d exist b e t w e e n t h e field o f t h e s u b - g r a n u l e s {H )
a
g r o u n d (H )
n
and the back­
m a g n e t i c fields, in a c c o r d a n c e w i t h o b s e r v a t i o n s ( F i g u r e 6 ) , w h e r e a s in
t
•
•
2000
2S00
3000
tSOO
•
•
••
*
-40
I
•
-10
t
•
•
•
-50
•
-1,0
F I G . 6.
Splitting
of n-component
of line Fe i 6302-5 A as a function of sunspot umbra field H.
t h e g e n e r a l c a s e t h e r o t a t i o n o f t h e p o l a r i z a t i o n p l a n e is i n d e p e n d e n t o f t h e v a l u e a n d
direction of the
field.
O n e c o u l d t r y t o c l e a r u p t h e q u e s t i o n o f t h e r e a l i t y o f t h e b a c k g r o u n d field b y
c o n s i d e r i n g t h e effect o f t h e 7 r - c o m p o n e n t s p l i t t i n g f o r t h e u m b r a s o f s p o t s l o c a t e d a t
different d i s t a n c e s f r o m t h e c e n t r a l m e r i d i a n o f t h e S u n . U n l i k e all o t h e r p o s s i b l e
effects, t h e v a l u e o f t h e b a c k g r o u n d field s h o u l d d e p e n d o n l y slightly o n t h e l o n g i t u d e
o f t h e s p o t . M e a s u r e m e n t s in 4 4 s p o t s ( w i t h o u t d i s t i n c t i o n o f p o l a r i t i e s ) w e r e u s e d .
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STRUCTURE OF THE M A G N E T I C FIELD OF SUNSPOTS
223
T h e r e s u l t o f t h e s t a t i s t i c a l a n a l y s i s is p r e s e n t e d in F i g u r e 7. T h e c u r v e o b t a i n e d b y
t h e l e a s t - s q u a r e s m e t h o d h a s t h e f o r m Ak = 0-64 c o s 0 + 0-03 sin 0 + 0-44. I n s p i t e of
n
t h e c o n s i d e r a b l e s c a t t e r o f t h e p o i n t s o n e c a n see t h a t , a l o n g w i t h c o s 0 t e r m s , n e a r l y
h a l f of t h e m e a n v a l u e o f s p l i t t i n g is i n d e p e n d e n t o f t h e l o n g i t u d e .
-90 - J O - 7 0 - 6 0 SO
F I G . 7.
the disc.
Dependence
-40
"30 - 2 0 -i0
of n-component
0
(AX )
n
W
10
30
td
SO
60
10
fa
90
- e n
splitting in line Fe I X 6302-5 A on location of spots in
N o t e t h a t t h e d e t e c t i o n o f s u c h a relatively w e a k b a c k g r o u n d field is p o s s i b l e o n l y
b y t h e p h o t o g r a p h i c m e t h o d b e c a u s e of t h e a v e r a g i n g o f t h e s e fields by t h e m a g n e t o ­
g r a p h . * S i n c e t h e effect o f t h e 7 r - c o m p o n e n t s p l i t t i n g is of g r e a t i m p o r t a n c e for defining
t h e s u n s p o t - f i e l d s t r u c t u r e , it is n e c e s s a r y t o c o n t i n u e d e t a i l e d i n v e s t i g a t i o n s u c h a s
m e a s u r e m e n t s w i t h i n v a r i o u s lines a n d a t v a r i o u s h e i g h t s , t h e u s e o f a p h o t o e l e c t r i c
m a g n e t o g r a p h for d e t e r m i n i n g t h e v a r i a t i o n o f p o l a r i z a t i o n a l o n g t h e c o n t o u r o f
lines within the u m b r a of spots with a m a x i m u m intensity, etc.
I n v e s t i g a t i o n s o f t h e m a g n e t i c field w i t h i n t h e s u n s p o t u m b r a u s i n g ' h i g h - t e m p e r ­
a t u r e ' ( F e II, S r II, C r n , e t c . ) a n d ' l o w - t e m p e r a t u r e ' ( T i I , F e I , e t c . ) * * lines m a y b e
a n o t h e r p o i n t in f a v o u r of t h e inhomogeneous-field m o d e l . T o m a k e s u r e t h a t lines
F e II in t h e s u n s p o t u m b r a a r e n o t a s s o c i a t e d w i t h t h e s c a t t e r e d l i g h t f r o m t h e p h o t o s ­
p h e r e as claimed b y Z w a a n (1965), a n u m b e r of p o l a r i z a t i o n s p e c t r o g r a m s in a large
* The systematic understating of the field value o n a magnetograph as compared with p h o t o ­
graphic determinations and which cannot be prevented by calibration may possibly be explained by
the effect of averaging the fields H and H in the magnetosphere.
** 'High-temperature' lines need practically photospheric conditions for excitation, whereas 'lowtemperature' ones, 1500-2000 °K less.
n
a
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in lines Til, Tin, Fe I and Fe 11 according
to Fricke and Elsasser
(a) and separately
in umbra and penumbra
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https://doi.org/10.1017/S0074180900021550
F I G . 8. Magnetic intensification
Ti i according to Makita
(b).
in
225
STRUCTURE OF THE MAGNETIC FIELD OF SUNSPOTS
'quiet' spot were obtained with t h e I Z M I R A N solar tower telescope ( J u l y - A u g u s t
1967) i n lines F e n ( / U 5 0 1 8 - 4 5 a n d 4 9 2 4 A), F e I (15016-86
A), a n d T i i ( ^ 5 0 2 0 - 0 3 A)
s i m u l t a n e o u s l y . I t w a s f o u n d t h a t t h e m a g n e t i c field i n lines F e i a n d T i i a n d F e H
a r e s i m i l a r i n t h e n a t u r e o f s p l i t t i n g , s h o w i n g m a x i m u m field v a l u e s a t t h e s a m e p o i n t s
of t h e s u n s p o t u m b r a . This indicates that, within t h e r a n g e of possible spatial reso­
l u t i o n , lines w i t h different e x c i t a t i o n t e m p e r a t u r e s d o c o e x i s t i n t h e u m b r a , a n d t h e
t w o - c o m p o n e n t m o d e l o f t h e s p o t is q u i t e p r o m i s i n g ( M a k i t a , 1963). T h e r e f o r e , o n e
c o u l d e x p e c t t h a t t h e m a g n e t i c fields d e t e r m i n e d b y t h e l i n e s T i i a n d F e i w o u l d b e
different a s well. T h i s q u e s t i o n c o u l d b e c o n s i d e r e d b y i n v e s t i g a t i n g t h e m a g n e t i c
i n t e n s i f i c a t i o n effect i n t h e s u n s p o t l i n e s . A c c o r d i n g t o B o j a r c h u k et al. ( I 9 6 0 ) , t h e
l o g a r i t h m o f m a g n e t i c i n t e n s i f i c a t i o n lg W*/W
Q
i n c r e a s e s l i n e a r l y w i t h nAg, t h e s l o p e
being p r o p o r t i o n a l t o t h e magnetic-field strength. H e r e n = n u m b e r of a-sub-comp o n e n t s , a n d A g = difference o f t h e L a n d e f a c t o r s o f t h e u p p e r a n d l o w e r levels. U s i n g
t h e d a t a of Fricke a n d Elsasser (1965) we plotted such a r e l a t i o n s h i p for l o g
W*/W
Q
( w h e r e W a r e e q u i v a l e n t w i d t h s ) f o r a n u m b e r o f lines T i i, T i n , F e i, a n d F e n .
F o r the purpose of control, a similar relationship w a s plotted for t h e u m b r a a n d
p e n u m b r a f o r lines T i i f r o m t h e d a t a o f M a k i t a ( 1 9 6 3 ) . T h e r e l a t i v e l y l a r g e s c a t t e r i n g
o f t h e p o i n t s is o b v i o u s l y d u e n o t o n l y t o e x p e r i m e n t a l e r r o r s o r t h e difficulty o f t a k i n g
i n t o a c c o u n t t h e s c a t t e r e d l i g h t , b u t a l s o t o t h e d e p e n d e n c e o f l g W*/W
Q
on the space
o r i e n t a t i o n o f t h e field, line s t r e n g t h , t u r b u l e n t v e l o c i t y , t e m p e r a t u r e a n d p r e s s u r e
r e l a t i o n s i n t h e u m b r a a n d t h e p h o t o s p h e r e . A c e r t a i n d e c r e a s e in t h i s s c a t t e r w a s
a c h i e v e d b y s e l e c t i n g m e a n - i n t e n s i t y lines l o c a t e d i n t h e m i d d l e p a r t o f t h e g r o w t h
curve for spots.*
F i g u r e 8 d e p i c t s t h e r e l a t i o n s h i p s t h u s o b t a i n e d , a n d T a b l e 1 gives t h e n u m b e r o f
Table 1
Fricke and Elsasser 1965
Ti i
N
a
b
Ti II
Fe i
32
20
17
0-086 ± 0-045
0-031 ± 0-027 0-067 ± 0 - 0 1 2
0-553 ± 0-077 - 0-050 ± 0-030 0-218 ± 0 - 0 1 9
Makita 1963
Fe n
Ti i, umbra
Ti i, penumbra
11
11
0-041 ± 0-032 0-077 ± 0-035
- 0-210 ± 0-043 0-395 ± 0-041
21
0-024 ± 0-020
0-144 ± 0-024
p o i n t s u s e d (N) a n d t h e coefficients a a n d b f o r e x p r e s s i n g \gW*/W =anAg+
0
b,
w h i c h w e r e o b t a i n e d b y t h e l e a s t - s q u a r e m e t h o d . T h e coefficient a c h a r a c t e r i z e s t h e
m a g n e t i c i n t e n s i f i c a t i o n , a n d is p r o p o r t i o n a l t o t h e m a g n e t i c - f i e l d s t r e n g t h i n t h e l i n e f o r m a t i o n r e g i o n , w h i l e b defines t h e i n c r e a s e ( o r d e c r e a s e ) o f t h e l i n e s t r e n g t h n e g ­
l e c t i n g t h e m a g n e t i c i n t e n s i f i c a t i o n . T h e i n t e n s i f i c a t i o n i n l i n e s T i l is close t o t h a t
e x p e c t e d in a field o f a b o u t 2 5 0 0 - 3 0 0 0 o e ( B o j a r c h u k et al., 1960). I n t h e p e n u m b r a
* For such lines magnetic intensification is determined with a high certainty and changes little with
small changes in the line strength.
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226
E.I. M O G I L E V S K Y
ET AL.
t h e i n t e n s i f i c a t i o n is a p p r o x i m a t e l y o n e - t h i r d t h a t in t h e u m b r a , as c o u l d b e e x p e c t e d .
F r o m t h e p o i n t o f view of t h e p r e s e n t w o r k , a c o m p a r i s o n o f t h e m a g n e t i c intensifi­
c a t i o n s a n d t h e m a g n e t i c fields o b t a i n e d f r o m ' c o l d ' ( T i l , F e i ) a n d ' h o t ' ( T i n , F e n )
lines, is o f special i n t e r e s t . I t c a n b e seen f r o m T a b l e 1 t h a t in ' h o t ' r e g i o n s t h e m a g ­
n e t i c field is a p p r o x i m a t e l y h a l f t h a t in ' c o l d ' o n e s . I g n o r i n g s o m e w e a k p h o t o s p h e r i c
lines T i l ( w i t h a n e q u i v a l e n t w i d t h o f < 1 0 m A ) , w h i c h c a n n o t b e m e a s u r e d w i t h
sufficient c o n f i d e n c e , w e o b t a i n a n e v e n g r e a t e r m a g n e t i c i n t e n s i f i c a t i o n for lines T i l ,
a n d t h e field r a t i o will b e c o m e a b o u t 3 . * A n a n a l o g o u s r e l a t i o n s h i p ( F i g u r e 9) is
o b s e r v e d in 9 lines of m u l t i p l e t N o . 38 T i l (a = 0 . 0 8 5 , £ = 0-35) a n d , w i t h less c e r t a i n t y ,
in 5 lines o f m u l t i p l e t N o . 4 9 F e n (a = 0 0 2 0 , b=
i
I
i
-0-31).
k
Tl I (Mult
F I G . 9.
Magnetic
intensification
from
multiplets
sHit)
Ti i and Fe II according
to Fricke
and
Elsasser.
T h e s a m e difference in t h e v a l u e s o f t h e m a g n e t i c fields in ' h o t ' a n d ' c o l d ' lines
w a s o b t a i n e d b y d i r e c t m e a s u r e m e n t s o f t h e m a g n e t i c field s e p a r a t e l y in lines F e n
^ 5 0 1 8 - 4 5 A a n d 4923-93 A, F e i >U5016-86 a n d 4927-78 A, a n d T i l ; U 5 0 2 0 - 0 3 a n d
5016-17 A.
F o r this purpose, polarization spectrograms were obtained with
the
I Z M I R A N t o w e r s o l a r t e l e s c o p e f o r a n u m b e r o f s e c t i o n s in l a r g e s p o t s ( A u g u s t 1, 2,
a n d 7, 1967).
* A n identical ratio is obtained (naturally, with a large scatter) by taking into account all the
lines measured in the work (Fricke and Elsasser, 1965), as well as when using data uncorrected for
scattered light.
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S T R U C T U R E
O F
T H E
M A G N E T I C
F I E L D
O F
227
S U N S P O T S
A l l t h e s e lines w e r e o b t a i n e d in o n e s p e c t r o g r a m , t h u s p e r m i t t i n g a c o m p a r i s o n of
m a g n e t i c fields m e a s u r e d f r o m different lines a t t h e s a m e site. M e a s u r e m e n t s w e r e
c a r r i e d o u t in 4 0 i n d e p e n d e n t p o i n t s o f t h e s u n s p o t u m b r a a n d p e n u m b r a . F i g . 10a
displays t h e results of these m e a s u r e m e n t s . It also s h o w s t h e h i s t o g r a m s for the
o c c u r r e n c e of v a r i o u s v a l u e s o f t h e r a t i o H /H .
Fcll
H ^H ,
Fell
O n l y in 4 o f t h e 4 0 c a s e s w a s
Tll
w h e r e a s in 7 0 % of t h e c a s e s t h e r e s u l t w a s 0 - 4 ^ H
Tll
Fe
/H ^0'6.
u
The mean
Til
Hr.z
1000
li­
a
5
^
5
ft
iZ\
i0<
01
06
0k
02
0
N
Hr.
t
FIG. 1 0 .
7, 1967.
Variation in magnetic-field
ratio from lines Fe N, Til,
Fe I in sunspots
of August
1, 2, and
v a l u e of t h i s r a t i o is 0-55. T h u s , a s well a s in t h e c a s e of d e t e r m i n i n g t h e field f r o m
t h e difference in m a g n e t i c i n t e n s i f i c a t i o n , t h e m a g n e t i c field in ' h o t ' r e g i o n s is, o n t h e
a v e r a g e , h a l f t h a t in ' c o l d ' o n e s . W e m a y a l s o n o t e t h a t , d e s p i t e t h e s m a l l n u m b e r
o f p o i n t s u s e d , t h e r a t i o H /H
Fell
Til
also exhibits a t r e n d t o w a r d s t h e g r o u p i n g of points
a r o u n d a v a l u e o f t h e o r d e r o f 0-25, w h i c h m e a n s a f o u r - f o l d excess of t h e field of
' c o l d ' r e g i o n s o v e r t h a t o f ' h o t ' o n e s . T h i s is c l o s e ( w i t h s o m e s c a t t e r ) t o t h e a b o v e m e n t i o n e d v a l u e s o f t h e m a g n e t i c field m e a s u r e d b y u s f r o m n- a n d
c-components
i n l i n e F e i X 6302-5 A. T h e r a t i o s o f t h e m a g n e t i c fields m e a s u r e d in t h e s a m e s p e c t r o ­
g r a m s f r o m lines F e i a n d T i l a r e p r e s e n t e d in F i g u r e 1 0 b . A l t h o u g h in t h i s c a s e t h e
s c a t t e r of p o i n t s is c o n s i d e r a b l e , in 7 0 % of t h e c a s e s H
F e I
/jF/
T i I
^ 1-0, a n d t h e m e a n
v a l u e is 0-83. H e r e , t o o , t h e h i s t o g r a m r e v e a l s t h a t t h e p r e d o m i n a n t v a l u e s a r e
H /H &
Fel
Til
\ a n d H /H ^0-6.
Fel
Til
F r o m all t h e s e s p e c t r o p h o t o m e t r i c d a t a it follows
t h a t t h e r e is a n a p p r e c i a b l e i n h o m o g e n e i t y in t h e v a l u e s o f t h e m a g n e t i c fields, w h i c h
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228
E.I. M O G I L E V S K Y
ET AL.
h a v e different v a l u e s a t t h e s a m e p o i n t s o f t h e s p o t ( m a i n l y in t h e u m b r a ) , if t h e field
is d e f i n e d f r o m ' c o l d ' a n d ' h o t ' l i n e s .
I n t h e l i g h t of t h e m o d e l b e i n g c o n s i d e r e d , t h i s r e s u l t o f s p e c t r o p h o t o m e t r i c o b s e r ­
v a t i o n s p o i n t s t o t h e e x i s t e n c e o f a s p a c e g r o u p i n g of s u b - g r a n u l e c h a i n s w i t h i n w h i c h
t e m p e r a t u r e c o n d i t i o n s a r e different. S u c h a difference in t e m p e r a t u r e s a n d d e n s i t i e s
( a t e q u a l g a s p r e s s u r e ) m a y a r i s e , f o r e x a m p l e , d u e t o t h e o s c i l l a t o r y c o n v e c t i o n in
s u b - p h o t o s p h e r i c l a y e r s ( S y r o v a t s k y a n d Z h u g z h d a , 1967). I n s u c h c o n v e c t i o n cells
t h e sizes a n d , p e r h a p s , s h a p e s o f t h e s u b g r a n u l e s will b e different.* T h e n , e v e n if t h e
t o t a l e n e r g y o f t h e s u b - g r a n u l e m a g n e t i c field is c o n s e r v e d * * , t h e m a x i m u m v a l u e s o f
t h e field i n t e n s i t y in t h e s u b - g r a n u l e s o f ' h o t ' cells will b e less t h a n t h o s e in ' c o l d ' o n e s .
A p p a r e n t l y , in o b t a i n i n g a s p e c t r o g r a m in t h e s u n s p o t u m b r a , a c e r t a i n s p a c e a v e r ­
a g i n g o f t h e effects, i n t r o d u c e d b y t r a n s l u c e n t ' h o t ' a n d ' c o l d ' cells, t a k e s p l a c e .
A l t h o u g h n o t y e t sufficiently c o m p l e t e , t h e a c c o m p l i s h e d i n v e s t i g a t i o n s s h o w t h a t in
t h e s u n s p o t field t h e r e m a y exist s o m e s m a l l - s c a l e m a g n e t i c e l e m e n t s ( s u b - g r a n u l e s )
w i t h a l a r g e field a n d w i t h a n i n t e r m e d i a t e b a c k g r o u n d ( s m a l l ) field o f o p p o s i t e sign
b e t w e e n t h e m . T h e d i s t r i b u t i o n o f t h e s u b - g r a n u l e c h a i n s , a s well a s t h e g e o m e t r y of
i n d i v i d u a l s u b - g r a n u l e s (i.e. t h e t o t a l e n e r g y a n d m a x i m u m i n t e n s i t y o f t h e field),
w h i c h d e t e r m i n e t h e a v e r a g e d field o b s e r v e d , is d u e t o t h e s u b - p h o t o s p h e r i c m o t i o n s
( p r i m a r i l y c o n v e c t i o n ) in t h e p a r t i c u l a r site of t h e s u n s p o t .
References
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Astron. J., 37, 812.
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Bull. astr. Inst. Csl., 13, 42.
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Private c o m m u n i c a t i o n .
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Solnechnie dannie, 9, 78.
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* This follows from the generalized expression o f the Bernoulli integral for the sub-granule chain
in the outer field H. In our case, this relation will have the form P + pv + pgh 4 - xH = const, where
p = density, g = gravity acceleration, x = effective 'magnetization'.
** A t relatively slow deformations the dissipation of the currents flowing inside the sub-granules
may occur as well.
2
2
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available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S0074180900021550
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OF THE
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SUNSPOTS
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available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S0074180900021550