Flare of
17
July 1 9 8 2
Flare in the eastern part of the large complex active region of July 1982. Observations made with the 53-cm Nikolsky-type coud6-coronagraph of the Debrecen Observatory through a 0.5 A Halle filter. Observers O. Gerlei and I. Nagy. North to the top, east to the left.
220
HORST BALTHASAR
at 7699 fi, which is formed in very high layers of the solar atmosphere, has not significant asymmetry, but in a recent paper, Roca Cortes et al. (1983) report about asymmetries of 200 m s - 1 for this line. A systematic investigation of the depth dependence of a lot of lines has not been done before the now presented work. Instead of the depth dependence of the asymmetries it was searched for a dependence on the excitation potential, the central intensity or the equivalent width of the lines. Kostik and Orlova (1977) found a decreasing asymmetry with increasing equivalent width at the disk center. Near the limb broad lines show the inverse asymmetry. Barambon and MOiler (1979) found larger asymmetries for broader lines. These authors did not find a dependence of the asymmetries on the excitation potential, in contradiction to Dravins et aL (1981), who found larger asymmetries for iron lines with higher excitation potentials, if lines with comparable central intensities were investigated. Lines with smaller central intensities show larger asymmetries than lines with higher. Preliminary results about the center-to-limb variation of the line asymmetries are given by Balthasar and Wrhl (1983). A review about solar line asymmetries is given by Dravins (1982). The necessary determination of absolute solar wavelengths of high accuracy is ditticult, if no reference source can be used. Due to gravitation a redshift of 2.12 x 10 - 6 of the laboratory wavelength is expected. Convection causes a blueshift of a still unknown amount. St. John (1928) found that this amount is about one half of the gravitational shift. Lopresto et al. (1980) found smaller values: nearly no convectional blueshift for most of the lines and only one quarter of the gravitational shift for weak lines. Keil (1980a, b) found a depth dependence for these differences; the velocity increases by an amount of 138 m s - 1 per unit oflg z, in contrast to Durrant et al. (1979) who found only 50 m s - 1. A missing limb effect for several lines formed in very high layers was reported by SchrOter (1959), Appenzeiler and SchrOter (1967) and Roca Cortes etal. (1983). Bruning (1980) found a stronger limb effect for the deeper formed iron line at 5250 fit than for the higher formed line at 5576 A. In recent years it was also searched for different limb effects on the polar and the equatorial diameter. While Appenzeller and SchrOter (1967) found none, Beckers and Taylor (1980) obtained at cos0 = 0.5 smaller wavelengths on the polar than on the equatorial radius, but no difference at cos0 = 0.2. Brandt and Schrrter (1982) found that the limb effect is more pronounced along the equatorial than along the polar diameter. Such differences may be explained by meridional motions as predicted by theories for the differential rotation. 2. The Observations
The observations were performed at the McMath Telescope and its Fourier-TransformSpectrometer (FTS) of the Kitt Peak National Observatory (KPNO) by H. Wrhl and the K P N O staff(cf. Acknowledgement)in August 1980 and November 1981.54 spectra at different positions along the polar and equatorial diameter of the solar disk each one
ASYMMETRIES, WAVELENGTHS, AND ROTATION
221
covering the range from 4800 to 6300 ~ were obtained, including five spectra at the disk center and two spectra of the integrated solar disk. Magnetic active regions, where different asymmetries occur (Kaisig and Schrrter, 1983; Koch, 1984), have been avoided. Most of the spectra were recorded with an exposure time of 29 min and 10 s, hence the influence of the five minute oscillation is minimized. The entrance slit had a length of 10 mm and a width of 2 mm, corresponding to 25 × 5 arc sec. The longer side was parallel to the nearest solar limb. As wavelength reference 12 telluric oxygen lines between 6278 and 6307 A have been used. The wavelengths of these lines have been determined by Babcock and Herzberg (1948) and by Pierce and Breckinfidge (1973). A correction for telluric wind streams described by Balthasar et aL (1982) has been applied. The solar wavelengths have been corrected for the Earth's motions. For 61 lines from neutral iron occurs a wavelength depending difference - expressed in velocities - between the solar and the laboratory wavelengths measured by Crosswhite (1975). Since this trend is different for the individual spectra, it seems to be of instrumental origine. Hence, the given dispersion was slightly changed to avoid these trends. For more details concerning the observations see the thesis of Balthasar (1984). Wavelengths have been determined by the minimum of a fourth order polynomial fit to the lower ten percent of the line. From these spectra 143 solar lines with different central intensities have been selected. These lines are not recognizable blended below 80~o of the continuum intensity and have at this intensity a width of less than 300 mA in the disk center spectra. The lines are listed in Table I. The formation heights of the line cores are calculated using the LTE-program of H. Schleicher with the model atmosphere H M A of Holweger and MOiler (1975).
3. Asymmetries of Solar Spectral Lines For the investigation of line asymmetries the bisector method is used. Wavelength reference is the minimum of the line. Line bisectors are determined at every percent of the continuum intensity above the minimum. The median value C of all these bisectors is used as a measure of the asymmetry of the whole line profile. The median value is preferred with respect to the mean value because it is not influenced by some extremely large bisectors in the wings of the lines. In addition the bisectors at one quarter of the line depression above the minimum, C¼, are regarded. When calculating averages of more lines, mean values are determined from individual values reduced to a wavelength of 5000 A. 3.1. CENTER-TO-LIMB VARIATION OF THE ASYMMETRIES At the disk center all lines show the well known C-shape, except for some weak lines showing red asymmetries (see also Dravins et aL, 1981). Near the limb, at cos0 = 0.194, three classes of lines are distinguished. The 89 lines of class I show still blue asym-
222
HORST BALTHASAR TABLE I T h e lines
2 (A)
X (eV)
W~ ( m A )
R
lg z
Class
4999.5 T i l 5001.7 Fe I
0.83 3.88
117 170
0.15 0.16
- 3.10 - 2.90
2 2
5002.8 5010.9 5012.4 5014.9 5016.2 5022,2 5022.9
Fel NiI Ni I Fe I Ti: Fe I TiI
3.40 3.63 3,70 3,94 0,85 3,98 0.83
100 57 76 144 72 124 79
0.26 0.44 0.35 0.18 0.29 0.19 0.24
-
1.80 0.90 1.20 2,60 1,70 2.40 2,00
1 1 1 1 1 1 1
5024.8 5028.1 5036.5 5039,9 5072.1
Ti I Fel Ti: TiI FeI
0,82 3,57 1.44 0.02 4.28
81 102 108 83 138
0.28 0.23 0.27 0.23 0.25
-
1,75 2,00 1.80 2.10 1.80
1 1 1 1 1
5074.7 5079,7 5080.5 5081.1
FeI Fel Nil NiI
4.22 0.99 3.65 3.85
155 132 154 116
0.18 0.18 0.20 0.22
-
2,60 2.70 2.50 2.10
2 3 1 1
5082.3 N i I 5083.3 F e I 5102.9 N i I
3,66 0.96 1.68
74 119 53
0.34 0.15 0.44
- 1.30 - 3.30 - 1.20
1 3 1
5115.4 5123,7 5127.4 5137.1 5137.4
Ni I FeI Fel Ni: Fe I
3.83 1.01 0.91 1,68 4,18
90 122 112 115 148
0.27 0.17 0,18 0.22 0.20
-
1.70 3.10 2,70 2,20 2,50
1 3 3 3 2
5145,1 5146.5 5159.1 5185.9 5192.9
FeI Ni: Fe~ TiII Ti I
2,20 3,70 4,28 1.89 0.02
59 122 84 80 90
0.39 0.25 0.31 0.34 0.22
-
1.30 1.85 1,40 1.15 2,30
3 t 1 1 1
5194.9 F e I 5195.5 F e I
1.56 4.22
139 124
0,16 0.21
- 3,20 - 2.40
3 1
5196.1 F e I 5197.6 F e l l 5210.3 Ti I
4.26 3.23 0,05
85 95 99
0.29 0.27 0.20
- 1.60 - 1.60 - 2.50
1 3 1
5216.3 5217.4 5225.5 5228.4 5234.6 5242.5 5243,8 5247.0 5247.6 5250.2 5250.6 5253.5 5275.7
FeI FeI Fe: FeI Fell Fe I Fe: Fe I Crl Fe: Fe I FeI Cr!
1.61 3.21 0.11 4,22 3,22 3,63 4,26 0.09 0,96 0, t 2 2.20 3.28 2.89
167 135 79 71 105 99 72 74 94 74 118 90 120
0,17 0.19 0.24 0.38 0.26 0.23 0.36 0.28 0,25 0.25 0.19 0.27 0.34
-
3,20 2.70 2.20 1.15 1.80 2.10 1,20 2,00 2,00 2,20 2,80 1.80 1.40
3 1 3 1 3 1 1 3 1 3 3 1 3
5284.1 F e I l
3.24
77
0.40
- 0.90
3
ASYMMETRIES, WAVELENGTHS, AND ROTATION
223
Table I (continued) •~ ( ~ )
X (eV)
W~ (m/~)
R
lg ~
Class
5288,5 F e I
3.69
66
0.38
- 1,20
1
5296.7 C r I 5297.9 C r I
0,98 2.90
105 110
0,20 0.32
- 2.60 - 1,60
2 3
5300,7 C r t
0,98
66
0.37
- 1,55
3
5322.0 5329.1 5329.9 5332.9
Fe I CrI FeI FeI
2,28 2,91 4.07 1,56
68 86 85 108
0.34 0,35 0.39 0.20
-
1.60 1,40 1.20 2.80
3 3 1 3
5336.8 5339.9 5345.8 5348.3 5349.5 5364.9 5365.4 5373.7 5379.6 5389.5 5393.2
TilI Fex CrI CrI Cal FeI FeI FeI Fe I Fel Fe I
1.58 3.26 1.00 1.00 2.71 4.44 3.57 4,47 3,69 4,41 3.24
83 192 131 113 111 161 88 75 71 101 182
0.32 0.18 0.17 0.21 0.22 0.21 0.28 0.37 0.36 0.27 0,19
-
1.35 3,10 3,20 2,60 2.20 2.50 1.80 1.30 t,30 1,90 2.90
1 2 2 2 1 2 1 1 t 1 2
5395,2 5398.3 5410,9 5412.7 5417.0
Fe I FeI Fe I Fe I Fel
4.44 4.44 4.47 4.43 4.41
23 88 165 22 39
0,77 0.3I 0,21 0.78 0.63
-
0,40 1,60 2.60 0.40 0,60
1 1 2 1 -
5434.5 5435.8 5436.6 5441.3
Fe I NiI FeI Fe I
1.01 1.99 2.28 4.31
206 59 47 37
0.13 0.45 0.50 0.66
-
4,80 1.30 1.10 0.60
3 1 3 3
5445.0 F e I 5461.6 F e I 5463.3 F e ]
4.39 4.44 4.43
149 29 148
0.22 0.72 0.23
- 2.50 - 0.60 - 2,40
2 1 -
5464.3 5470.1 5473.2 5483.1 5487.2 5487,7 5493,5 5501,4 5506.7 5512.9 5517.1 5522.5 5526.8 5534.8 5539.3 5543.9 5565.7
4,14 4,44 4,19 4,15 4,41 4,14 4,10 0.96 0.99 2,93 4.21 4.21 1.77 3.24 3.64 4.22 4.61
44 29 21 61 42 118 46 t33 135 105 20 50 89 80 19 75 116
0.57 0.72 0.78 0.50 0.61 0.27 0.58 0.18 0.17 0.31 0.80 0.53 0.32 0.43 0.80 0.38 0.29
-
0.80 0,40 0,40 0,90 0,60 2,00 0,80 3,50 3,60 1.60 0,40 0.90 1,60 0.90 0,60 1,30 1.80
1 1 1 1 1 1 3 3 1 1 1 1 3 1 1 1
3.42 3.43 1,68
198 142 65
0.19 0.21 0.43
- 3.20 - 2.85 - 1,40
2 3
Fel Fe I Fe ) Fel Fe I Fe I Fe I FeI FeI Cal FeI Fel ScII Fe 1I FeI FeI FeI
5569.6 F e I 5576.1 F e I 5578.7 Ni ~
224
HORST BALTFIASAR
Table I (continued) 2 (h).
Z (eV)
Wx ( m ~ )
R
lg z
Class
5581.9 c a l 5587.8 Ni I 5590.1 Cal 5619.6 FeI 5633.9 FeI 5635.8 FeI 5636.7 FeI 5638.3 FeI 5650.0 Fel 5650.7 Fe I 5651.5 Fe I 5652.3 Fel 5662.5 FeI 5679.0 FeI 5688.2 Na I 5701.6 FeI 5731.8 FeI 5753.1 FeI 5754.7 NiI 5775.1 FeI 5862.4 FeI 5930.2 Fel 5934.6 Fel 5948.5 SiI 5952.7 Fe I 5983.7 Fe I 5984.8 Fe I 6065.5 Fe I 6102.2 Fe! 6108.1 NiI 6125.0 Sil 6136.6 FeI 6145.0 SiI 6166.4 CaI 6173.3 Fe I 62t3.4 Fel 6219.3 FeI 6243.8 SiI 6246.3 Fe I 6265.t Fe! 6301.5 Fel 6302.5 FeI
2.52 1.93 2.52 4.39 4.99 4.26 3.64 4.22 5.10 5.08 4.47 4.26 4.18 4.65 2.10 2.56 4.26 4.26 1.93 4.22 4.55 4.65 3.93 5.08 3.98 4.55 4.73 2.61 4.83 1.68 5.61 2.45 5.61 2.52 2.22 2.22 2.20 5.61 3.60 2.18 3.65 3.69
114 64 106 44 85 43 24 96 44 46 21 31 111 72 157 95 68 93 87 69 104 106 90 107 73 81 103 134 96 73 35 156 45 80 76 95 t01 59 142 95 147 101
0.23 0.40 0.25 0.64 0.39 0.62 0.76 0.33 0.62 0.62 0.79 0.71 0.27 0.43 0.23 0.27 0.44 0.32 0.35 0.43 0.31 0.31 0.38 0.42 0.45 0.39 0.36 0.24 0.37 0.41 0.76 0.23 0.70 0.42 0.38 0.32 0.30 0.64 0.28 0.31 0.26 0.34
-
1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 3 2 1
2.20 1.40 2.10 0.60 1.20 0.60 0.60 1.60 0.60 0.60 0.40 0.60 2.10 1.10 2.60 2.20 1.10 1.70 1.80 1.20 1.90 2.00 1.50 1.10 1.20 1.40 1.60 2.90 1.60 1.70 0.40 3.40 0.40 1.30 1.75 2.20 2.30 0.60 2.60 2.20 2.90 2.00
m e t r i e s , b u t a n i n v e r s e c u r v a t u r e o f t h e b i s e c t o r line. T h e 14 l i n e s o f c l a s s I I a r e s i m i l a r t o t h o s e o f c l a s s I, b u t t h e y h a v e r e d a s y m m e t r i e s in t h e l o w e r p a r t o f t h e fine, I n c l a s s I I I w e find fines s h o w i n g a similar C - s h a p e as t h a t at the disk center. Six lines r e m a i n unclassified. It should be mentioned
that FeI
5 5 7 6 A is o n e o f t h e m , t h i s l i n e is
s y m m e t r i c at c o s 0 = 0.2 a n d m a y be a t r a n s i t i o n b e t w e e n class I a n d II. O t h e r lines m a y be slightly b l e n d e d . F i g u r e 1 s h o w s typical lines o f e a c h class.
ASYMMETRIES,
e I
1.0
HI= 4. 22 ,,,~,..
7
0.19qE
--4
, rTn-~
, L . . . .
,
o.8
>--
z 0 . Lt
@.Li
Z
].
0.2
1 9qE1
0.2
'i2
0.@
, , , I=
@.6
60 Z bA b--
Z IM %-
b. 2 ,~
1.Oj
222j
[email protected]
J
bA
~Z 0 . Li
LASS I I I e I 5079. 7 HI= 0. 99
7
t--
J
c~O.6 Z
225
ROTATION
>_0.8
I
F-
, I , i ,
'J'"
M;
@.0
2 6 -10 -6 -2 DELTA LAMBDA EM~]
2 S 0 -6 -2 DELTA LAMBOR EM~]
Fig. 1.
507q.
I
>_0.8 ~
0.0
AND
CLASS I I
CLASS I Fel 52q2.5 CHI= 3.63
1.0
WAVELENGTHS,
r i ~ I f ~ , I ,
-10 -6 -2 BELTA L R M B D R
s
6 EM~]
Typical examples of the three classes of lines. The bisector lines of the disk-center measurement M2 and of the measurement at cos~ = 0.194 of the eastern radius are shown.
From Figure 2 it can be seen that these differences depend on the formation heights and on the excitation potentials of the lines. The lines of class II are systematically formed in higher layers than those of class I. Many lines of class III have lower excitation potentials than those of class I and II formed in comparable heights of the solar atmosphere.
x Class I
-5-
o C l a s s II
• C l a s s III
--4-
o~
--3-
,,
o ×
x
•
•
00<
)¢4
× --2"
x
Xx
@
IXX
x@
x x • x
•< @x x
•
x
o
o
x
×
X
0. W ×
X
x •
o
o
xXx
X
x
x
x
•
Xx
X
•
X X
x
x
X
X~ Xx
X
XX
XX
•
X X
--.1."
× •
NI>X
x
x<
c h i [eV] Fig. 2.
Excitation potentials and formation heights of the lines.
226
HORST BALTHASAR
-5
-4.
-3
•~
0
0~
• o x 2
c l a s s III c l a s s II class I
1~o
d.8
d.6
d~
dz
oo
cos theta Fig. 3.
C e n t e r - t o - l i m b v a r i a t i o n o f the m e d i a n v a l u e o f the a s y m m e t r i e s ,
Figure 3 shows the center-to-limb variation of the median value of the bisectors, the three classes being separated. For the lines of class I the blue asymmetry decreases in the range 1.0 >__cosO> 0.7, increases for 0.7 >__cos~ > 0.3 and decreases then very rapidly toward the limb. The lines of class III show a similar behaviour, but the asymmetries are larger and the decrease near the limb is much weaker, if it is real at all. For the lines of class II a monotonous decrease of the asymmetries to cos0 = 0.2 is found. Near the limb they show an increasing red asymmetry. Similar curves are derived for the C¼-values. 3.2.
DEPTH
DEPENDENCE
OF THE ASYMMETRIES
The depth dependence of the median values of the line asymmetries at the disk center is shown in Figure 4. Lines formed in higher layers show larger asymmetries. Some lines formed in very deep layers have red asymmetries. If blue asymmetries are considered to be negative and red asymmetries to be positive, this dependence can be expressed by the following regression line: C(z, 1.000) = (+0.09 + 0.25) + (1.62 + 0.13) lgz
[mA],
ASYMMETRIES,
WAVELENGTHS,
227
AND ROTATION
-0.0
-7.0-
-6.0-
Median asymmetry
×x
i
i
X X
X
~
o
0
Q
¢'
-5.0~ xx X ii ::0(
x× ~××~
~ -a.o~ •
<>
x°
xX
X
<~
o I
~')
II
•
~ X
X
"
xX
• •
~'0
.
g
o
e
-I.0=
0,0x
o
1.0-
:~.0
¢
0,0
-1.o
I
-L0
-~.o
-3.0
-5.0
LG TAU 5000 Fig. 4. Depth dependence of the median asymmetries at the disk center. Lines of class I are marked by crosses, lines of class II by rhombs, lines of class III by full circles and unclassified lines by open circles. The regression line is given.
Since many lines of class I and II show larger asymmetries than those of class III, also separate regression lines for these two groups are given: C(z, 1.000, I + II) = (+0.56 + 0.24) + (1.99 _+ 0.13)lgz
[m,~],
C(z, 1.000, III) = ( - 0 . 5 6 + 0.71) + (1.17 + 0.31)lgz [rm~], For the Cl-values a similar dependence is found; these values are slightly smaller and the scatter is less. In Figure 5 the depth dependence of the median asymmetries near the limb, at cos 0 = 0.194 are shown. Now the lines are formed in layers higher by about A lg z = 1 as compared to the disk center. Using all lines, the following regression line is derived:
C(z, 0.194) = ( - 0 . 5 8 +_ 0.40) + (0.44 + 0.14)lgz [m]k]. This regression line describes also an increasing asymmetry with increasing formation height, but the coefficient of this increase is smaller than that at the disk center. However, it is not justified to use all lines for a regression fit, as the figure shows. In accordance with the definition of the three classes of lines there are clear differences between the classes. Separate regression lines have to be given:
C(z, 0.194, I + II) = ( - 2 . 1 1 +_ 0.26) - (0.29 + 0.10)lgz [rn~], C(z, 0.194, I I I ) = (+0.29 + 1.01) + (1.15 + 0.31)lgz
[mA].
228
BALTHASAR
HORST
-8.0-
-7.0"
Median asymmetry
(0.194)
--6.0" o • -5.0" o
©
--4,0
5'}
Z
o -3,0-
J
x
i×× x
/
~ xo
XX
~
•
x
X
~ X . . x ~ ~ Xxx
XO
•
x,
X•
x
× ×
2.0
t
o0
Fig. 5.
X
0
°8o O
0,0~
t.O
x
x
X
~
o
~ -
° ¢, o
o o
"
-io
-L0
,,. . . . . . -3.0
,,.....
'
- 4 ,' 0
-5.0
LG T A U 5 0 0 0
Depth dependence of the median asymmetries at cos,9 = 0,194. S a m e symbols as in Figure 4.
Only for the lines of class III an increasing asymmetry with increasing formation height similar to that at the disk center is found. The lines of class I and II show a decreasing asymmetry with increasing height, whereby some lines of class II show red asymmetries. The C¼-values show less scatter at this position too, and the differences between the classes are more pronounced. The lines of class II have positive C¼-values. These values yield the following regression lines: C¼(z, 0.194, I + II) = ( - 1.28 + 0.16) - (0.24 + 0.06)lg~ C¼(~,0.194, I I I ) = ( + 0 . 7 6 + 0 . 6 1 ) + ( 1 . 0 0 + 0 . 1 9 ) 1 g ~
[mA], [m/~].
3.3. DEPENDENCEOF THE ASYMMETRIES ON THE EXCITATIONPOTENTIAL Investigating the dependence of the asymmetries on the excitation potentials, the strong dependence on the formation heights has to be considered. For this purpose, the value of the corresponding regression line determined above has been subtracted and then the mean value of all lines has been added. In Figure 6 the median asymmetries altered in this way are plotted against the excitation potential. There is only a slight and not significant increase of the asymmetries with increasing excitation potential. This tendency is in accordance with that found by Dravins etaL (1981), but due to the missing significance it is not in contradiction to Barambon and Mt~ller (1979). Here, it seems not to be necessary to distinguish between the three classes of lines, hence only one
229
ASYMMETRIES, WAVELENGTHS, AND ROTATION
-8.0!1
--7,0 -
Median asymmetry
--6.0-
X x
-5.0-
x
x
O "5<
iii
0
x
x. Z
-3.0-
~
-g,O-
tl
x
o
x x
~" •
x
x °I
x x x x
II
"
o
Z" _~.o
~
x
lr'--'-----
O
x
x
X
E-,
x
o xx
x
Xx
~
x)
@
34
xo
xX*x x~x
x
x~,,,,
•
x
xx
........
x
XxX'-
x
o
X
x
o
•
o o
x
o.o Z
• @
1.0-
a,O 010
L0
0
;o
110 cm [Ev]
;0
5'o
Fig. 6. Dependence of the median asymmetries at the disk center on the excitation potential after correcting for the depth dependence. Same symbols as in Figure4.
regression line is given: C(Z, 1.000) = ( - 2 . 3 6 + 0 . 2 6 ) - (0.14 _+ 0.08)Z
[mA].
For the C¼-values the following regression line is derived, also corrected for the depth dependence: C¼(Z, 1.000) = ( - 2 . 1 4 + 0.15) - (0.03 + 0.05)Z
[mA].
This equation yields an independence on the excitation potential. Figure 7 shows the dependence of the median asymmetries on the excitation potential at cos 0 = 0.194. Using all lines and correcting for the depth dependence, the following regression line is derived:
C(Z, 0.194)
= ( - 2 . 6 5 + 0.27) + (0.27 + 0.08)Z
[m~].
The increase of this regression line is obviously due to the large scatter of the asymmetries of the lines in class III. Hence separate regression lines at this position are also given: C(Z, 0.194, I + II) = ( - 1.19 + 0.25) - (0.06 + 0.07)Z C(Z, 0.194, III) = ( - 3.89 + 0.62) + (0.39 + 0.29)Z
[m~],
[mA].
6.0
230
HORST
BALTHASAR
-8.0
-7.0
Median asymmetry
(0.~94)
--6,0 -
--5.0o
•
O
© --4.0-
o
EO
z
o
--3.0-
•
×
• x
x
--2.0-
-~x-.~
r_)
xx
x~>~ x x
• -
--l.0-
×
xxx
x
•
×
o
o
0.0-
o
x
x
90
o
o
o o
o o
o
o
o o
1.0-
8.0
Lo
0.0
n
' f """ .
z.o
3.0
.
.
.
;.o
.
~.o
"
CHI [EV] Fig. 7. Dependence of the median asymmetries at cos ~ = 0.194 on the excitation potential after correcting for the depth dependence. Same symbols as in Figure 4. class 1
-4,0
-3.0
-8,0
-I,0
0.0
o w
eE oS xN LO 1.0
cos theta
Fig. 8.
Dependence of the C¼ asymmetry values on the direction on the solar disk.
6.0
ASYMMETRIES, WAVELENGTHS, AND ROTATION
231
F o r class I and II there is no dependence on the excitation potential, and for class III the dependence is not significant. The C¼-values yield again a similar result. 3.4. O T H E R RESULTS OF THE ASYMMETRY I N V E S T I G A T I O N S Figure 8 shows the center-to-limb variation of the C¼ asymmetries o f the lines o f class I along the four radii separated. N o systematic dependence of the asymmetries on the direction is recognizable. Similar small differences occur for the lines o f class II a n d III. In Table II the asymmetries at the disk center are compared with those from the spatially integrated spectra. In the integrated light also blue asymmetries are found similar to Dravins et al. (1981), but they are much smaller than at the disk center for all three asymmetry classes. For the simulation of integrated spectra by the superposition of line profiles from different positions on the disk, the wavelength shifts have to be taken into account. Comparisons to stellar spectra have to be done using the integrated spectra. TABLE II Comparison of the asymmetry parameters at the disk center and in the spatially integrated spectra Median asymmetries
Disk center Integrated light
Class I
Class II
Class III
- 2.3 + 0.2 - 1.1 + 1.1
- 4.2 _+0.3 -2.6 + 0.3
- 2.8 + 0.3 - 1.4 + 0.3
Asymmetries at 1/4 of the depth
Disk center Integrated light
Class I
Class II
Class III
- 1.8 + 0.1 -0.8 + 0.1
-3.3 + 0.1 - 1,9 + 02
-2.7 _+0,3 - 1.2 + 0.2
4. Wavelength Shifts at the Disk Center Figure 9 shows the wavelength shifts o f 59 iron lines with respect to the laboratory wavelengths determined by Crosswhite (1975). For this figure the measurement M2 from August 29, 1980 has been chosen. The other measurements at the disk center look very similar. The wavelength shifts depend strongly on the formation depth of the lines: lines formed in higher layers show larger shifts. Lines formed in layers above lg z = 3.0 have shifts of about the gravitational redshift. About one half of this amount is found for lines formed at - 1.5 < lg z < 1.0. The first result is in agreement with Lopresto et al. (1980), the second one is in agreement with St. John (1928), but contradicts Lopresto et al. (1980).
232
HORST
BALTHASAR
800 700 i X
X
600
. . • • ~
5O0
;R
X'"
400 -
v
X
x ~ ~...f~x
/
~
X
~
.............
i
._
×
x
.... .
x
/~ ×
/ X/' X
< 300
-
200
-
I00
-
:'"
,." t }
.' .'
0-
/ /
/
: / : / :: / t
x
-100 t0 :' ' ...: . . ." .
21
. . . .
2 z
'
-'3
. . . .
-'4
. . . .
-5
LG T A U Fig. 9. Differences between solar disk center and laboratory wavelength m e a s u r e m e n t s o f iron lines by Crosswhite (1975). The horizontal line is the gravitational redshift. The solid line is a regression line, the dashed line is a second order polynomial and the dotted line is an exponential fit.
The depth dependence is best represented by an exponential fit, but approximations by a regression line and a second order polynomial fit are also given in Table III. The regression lines are comparable to that found by Keil (1980a, b), although Keil used another model atmosphere. T A B L E III Coefficients for the three different fits to the depth dependence o f differences between solar and laboratory wavelength measurements: A V = a + b lg v, A V = c + d lg z + e lg 2 z, A V = f + g exp (h lg z), for the five disk-center spectra M1
M2
M3
M4
450
M5
a (ms -1) b (ms -l )
294
194
281
- 116
- 139
- 132
-64
- 140
257
c (ms -l ) d (ms -1) e (ms -1)
-78 -439 - 64
- 151 -439 -59
-68 -435 - 60
+42 -418 -70
-62 -418 - 55
f (ms -1) g (ms -a ) h
718 -509 0.69
680 - 810 0.89
737 -959 1.00
767 - 170 0.15
745 -3192 1.48
ASYMMETRIES, WAVELENGTHS, AND ROTATION
233
5. The Limb Effect Investigating the limb effect, two corrections are necessary. On the north-south diameter, Doppler shifts due to the variation of the angle B o of the solar axis have to be considered, as found by Kubi6ela and Karabin (1977). This effect amounts to 3.5 m s - 1 southward in August 1980 and to 16.3 m s - l northward in November 1981. On the equatorial diameter a correction for the rotation velocity of 1971 m s - l, determined in Section 6, is required. All wavelength differences are reduced to 5000 ,~. First the mean wavelength for the five measurements at the disk center is determined. For positions outside the disk center the wavelength differences with respect to that disk center value are calculated. The limb effect is described by a second order polynomial fit with (1 - cos0) as variable in order to obtain the best representation at the disk center. A deviation of the fit from zero is possible for this position. Figure 10 shows the limb effect of 96 fines of neutral iron. In the range 0.5 < c o s O < 1.0 the wavelengths are shorter than at the disk center confirming the result of Schr0ter (1959). Between cos0 = 0.5 and the limb an increasing redshift is found. The limb effect is described by the following polynomial fit: A2(0) = - 0 . 2 7 - 3.20 (1 - cos0) + 12.12 (1 - cos0) 2 . The scatter is similar for every individual line and seems therefore to be due to solar velocity fields, e.g. supergranulation (Kttveler, 1983).
I0.0
-
8.0-
x/
6.0
4.0-
f
0,0-
-2,0-
-4,0
-6,0
1,o
~.8
6,6
................ ~.~ cos theta
Fig. 10,
L i m b effect of 96 lines of neutral iron.
&~
0.0
234
HORST BALTHASAR
For comparison of absolute wavelengths only the 59 lines of Section 4 should be used. For these lines the following polynomial fit is derived: A2(0) = - 0 . 3 2 - 1.50 (1 - cos0) + 9.96 (1 - cos0) 2 . This fit is rather similar to that for all 96 lines. After subtracting the gravitational redshift, a blueshift of - 1.2 m A at the disk center is found. At cos0 = 0.2 there is a redshift of + 3.7 mA. Extrapolating the fit to the limb, the redshift amounts to 7.0 mA. The wavelength accuracy is about _+ 1 m]~, hence the redshifts near the limb are real. Hints to such a redshift have been given before by Adam (1959), Schr6ter (1959), and Higgs (1962). An explanation is possible by horizontal motions, as calculated by Beckers and Nelson (1978). The depth dependence of the limb effect of neutral iron lines is given in Figure 11. Conspicuous deviations are only found for fines with cores formed above lg z = - 3: these lines show redshifts with respect to the disk center at all positions outside the disk center. The coefficients for the polynomial fits are given in Table IV. 10.0
- . - o.o / -1.o - * -1.o / -1.5 +
8.0 ¸
-+-
-t.5/,-2.0
/
-z.o x - 2 . ~
~
• .'~-- - 2 , 5 / - 3 . 0
+
4.0
~
2.0
.~/' /
o.,-*"
o
,.Q
,,,,
./..../
~/...._
- 3 . 0 / -~.o
6,0
•
/ /,
...............
i
o
................ ~
i
-2.0
-4.0
-6,0
cos theta Depth dependence of the limb effect of iron lines. The lg z-ranges are given in the top left corner Fig. 11. of the figure.
In Figure 12 the dependence of the limb effect on the excitation potential is shown. Lines with low excitation potentials have larger redshifts than others, but it has to be considered that most of these lines are formed in high layers of the atmosphere, so that this difference may be due to the depth dependence.
ASYMMETRIES, WAVELENGTHS, AND ROTATION
235
TABLE IV Coefficients for polynomial fits A2 = a + b(1 - cos9) + c(1 -cosO) 2 for the depth dependence of the limb effect tg z 0.0/- 1.0/1.5/2.0/2.5/- 3.0/-
-
-
1.0 1.5 2.0 2.5 3.0 5.0
a (m s - i)
b (m s - 1)
c (m s - 1)
Number of lines
- 0.00 -0.32 - 0.45 - 0.42 - 0.36 - 0.02
- 6.24 -6.54 - 4.76 - 4.65 + 1.54 + 5.33
+ 16.04 + t6.75 + 13.88 + 13.71 + 4.95 + 3.28
21 16 16 16 17 10
10.0 ---x-- 0 - - 2 e V
-o-- 2 8.0-
'
///,"" x/,'"
~,., /,,,,'~ /
3 eV
--o- 3 - 4 e V +4--6eV
6+0-
4.0
Z
0.0
+
~
-2.0
-4.0
-6,0
1.o
+
0.8
d.6
&+
d.z
o.o
cos theta
Fig. 12. Dependence of the limb effect of iron lines on the excitation potential.
T h e d e p e n d e n c e o f t h e l i m b effect o n t h e a s y m m e t r y c l a s s e s is p r e s e n t e d in F i g u r e 13. L i n e s o f c l a s s I I I s h o w l a r g e r w a v e l e n g t h s t h a n lines o f c l a s s I a t all p o s i t i o n s o u t s i d e t h e d i s k c e n t e r . B o t h c l a s s e s s h o w b l u e s h i f t s in t h e i n n e r p a r t s o f t h e d i s k a n d i n c r e a s i n g r e d s h i f t s w h e n a p p r o a c h i n g t h e limb. L i n e s o f c l a s s II, w h i c h a r e f o r m e d i n h i g h layers, h a v e a less p r o n o u n c e d
l i m b effect. A l s o t h e s e d i f f e r e n c e s m a y b e d u e t o t h e d e p t h
d e p e n d e n c e o f t h e l i m b effect. I n F i g u r e 14 t h e l i n e s o f n e u t r a l i r o n a n d t i t a n i u m a r e c o m p a r e d t o t h e l i n e s o f t h e ionized elements. The latter show smaller blueshifts at the inner parts of the disk and
236
HORST BALTHASAR
I0,0
--x-- c l a s s I -,~- c l a s s II
fl
/
8,0
/.¢):
6.0
4.0-
8.0-
×
×
-2,0
-4.0-
~6,0
........,,,, 1,0
d.6
dis
d,
da
O,O
cos theta Fig. t3.
Limb effect of iron lines separated for the three asymmetry classes.
lO.O-
8.0-
FeI - o - F e iI - ~ - Ti I -+~ Ti II
,,
/
/,Q" •
/ /
S.O-
4,0-
7j
0,0-
x
o
-;LO-
-4,0
jj
o
o o
o
-
-6.0 0.0
1,0
cos t h e t a Fig. 14.
Limb effect o f neutral and ionized iron and titanium lines.
237
ASYMMETRIES, WAVELENGTHS~ AND ROTATION
10.0
-x- North -o-- South
// /
oo.
× /
4-,0-
Z a)
~
-
+
- --
-~,Oq-
o +
-4.0
- 8.0
"j
1.0
dB
...... "
06
d~
0,2
0,0
cos t h e t a Fig. 15.
Limb effect of iron lines on different radii.
much larger redshifts near the limb. This may be caused by a larger abundancy of the ionized elements in the hot ascending gas. A comparison of the limb effect on the different radii shall be tried, although mostly only one measurement at one cos 0-value is available, which is strongly influenced by local velocity fields like supergranulation. The results are given in Figure 15. Because the influence of the supergranulation is not known for the single measurements, the differences between the northern, the eastern and the western radius can not be regarded as significant. Only the inner parts of the southern radius seem to show real differences: her the wavelengths are larger than on the other radfi. A justification for combining the northern and southern resp. the eastern and western radii as done by Brandt and SchrOter (1982) can not be drawn by these observations. Some different trials to determine potential meridional motions lead to very different results, so it is concluded that such a determination is not possible from this material. Similar trials by other authors have to be regarded with some doubts. 6. The Solar Rotation The data of this paper have been used for a preliminary determination of the solar rotation and its depth dependence by Balthasar (1983). In that paper only 63 lines have been considered, and the final correction for the wavelength trends discussed in
238
HORST BALTHASAR
Section 2 has been performed later. The small influence of the angle B o of the solar axis has again been neglected. For all 143 lines the mean rotation velocity amounts to 1971 + 1 m s - 1. The error represents that of the mean and does not consider the error of the rotation velocities of the individual lines which is between 29 and 97 m s - 1. The value of 1971 m s - ~ is 15 m s - 1 smaller than the preliminary determination, but it is still comparable to those of Duvall (1982), Ktlveler and WOhl ( 1983 ), Prrez et aL ( 1981), or H o w a r d and Harvey (1970). The depth dependence of the rotation is shown in Figure 16. Fitting a regression line, the following result is derived: V(z) = (1971 _+ 3 ) - (0.4 +_ 1.2)lgz
[ms-l].
The coefficient of the lg z-term is very small and not significantly different from zero. It corresponds to solid rotation. Omitting the five lines with rotation velocities below 1940 m s - 1 and above 2000 m s - 1, the sign of this coefficient changes. By this new reduction the results of Livingston (1969a, b) and Gasanalizade (1980) are confirmed, but not those of Aslanov (1964) or Solonsky (1972). It should be mentioned that this fit is only valid within the solar photosphere.
0
100
HEIGHT [KM] 300 400
200
500
600
700
2.00-
7 1,98-
0
>
1,96-
;.~.
N ©
,
•
.
•
• •
•
1.94
1.92
1.90
0,0
-~.o
&o
-~.o LG TAU 5000
Fig. 16. Depth dependence of the rotation velocity.
-;.o
-5.0
ASYMMETRIES, WAVELENGTHS, AND ROTATION
239
7. Conclusions One of the main items of this work was to investigate the depth dependence of the asymmetries and the limb effect of a great number of lines. The dependence on the formation height of the lines is stronger than the dependence on any other parameter like excitation potential, central intensity or equivalent widthm. It can be concluded that asymmetries and limb effect originate in the photospheric line formation layers and not in chromospheric layers as suggested by some authors. An explanation by convective motions is suggestive, if the ascending matter is decelerated and if horizontal motions occur.
Investigating the center-to-limb variations of the asymmetries three classes of lines have to be distinguished. The difference between the first and the second class is only due to the different formation height of the lines, while lines of class III have lower excitation potentials than those of the other classes formed in comparable heights. However, the formation heights are calculated using a homogenous atmosphere. It seems possible that different weights have to be given to the ascending and the descending matter when calculating the line profiles of the three classes. This may also be the reason for the different limb effect of neutral and ionized elements. The determination of absolute wavelengths is still difficult, because the problem of the wavelength calibration of the FTS is not yet perfectly solved. A reference source in the solar spectra is required. Hence only telluric atmospheric lines could be used. A better wavelength determination for the oxygen lines than that of Babcock and H erzberg (1948) or Pierce and Breckinridge (1973) would be desirable. But the oxygen lines occur only at wavelengths greater than 6000 A, so the dispersion of the FTS has to be known very accurately. The alternative is to use water vapor lines, but for these no satisfactory wavelength determination is known to the author. In addition, these lines change strongly due to different air humidity. Nevertheless the wavelength differences for the minima of the lines at the disk center are found to be closer to the gravitational redshift than found by St. John (1928). Near the limb redshifts are found which are larger than the possible wavelength error. For a detailed explanation of the present results new theoretical calculations are required. The next step in observation should be a spatial resolution of single granules for spectra. It seems that therefore a spectrograph in an Earth orbit is necessary. The depth dependence of the solar rotation velocity is found to be a solid rotation within the solar photosphere. For a determination of the absolute rotation velocity, measurements on the solar equator and not on the east-west diameter would be better. For a determination of the rotation velocity in deeper layers, e.g. the convection zone, other methods are required.
Acknowledgements I have to thank Dr H. W6h] from the Kiepenheuer-Institutftlr Sonnenphysik at Freiburg for many discussions and suggestions and for doing a part of the observations. I also
240
HORST BALTHASAR
thank the KPNO-staff, especially Dr J. Brault, Mr L. Testerman, Mr J. Wagner, and Mr G. Ladd for performing the observations and for additional support. For their computer programs I thank Dr H. Schleicher and Mr U. Thiele. For cooperation in computer problems I thank my collegues Dr A. Koch and Dr G. Kt~veler. A part of the numerical reductions have been done using the SPERRY 1100/83 of the Gesellschaft for wissenschaftliche Datenverarbeitung m.b.H. G~Sttingen. References Adam, M. G.: 1959, Monthly Notices Roy. Astron. Soc. 119, 460. Adam, M. G., Ibbetson, P. A., and Petford, A. D.: 1976, Monthly Notices Roy. Astron. Soc. 177, 687. Appenzeller, I. and Schrrter, E. H.: 1967, Astrophys. J. 147, 1100. Aslanov, I. H.: 1964, Soviet Astron. 7, 794. Babcock, H. D. and Herzberg, L.: 1948, Astrophys. Y. 108, 167. Balthassar, H.: 1983, Solar Phys. 84, 371. Balthasar, H.: 1984, Thesis, Grttingen (in german). Balthasar, H., Thiele, U., and Wrhl, H.: t982, Astron. Astrophys. 114, 357. Balthasar, H. and WON, H.: 1984, 'An Atlas of Spectral Line Asymmetries and their CLV from Solar FTS Spectra', in S. L. K eil (ed.), Sac Peak Conference on Small-Scale Dynamical Processes in Stellar Atmospheres, (in press). Barambon, C. and Mftller, E.: 1979, Solar Phys. 64, 201. Beckers, J. M. and Nelson, G. D.: 1978, Solar Phys. 58, 243. Beckers, J. M. and Taylor, W. R.: 1980, Solar Phys. 68, 41. Brhm, K. H.: I954, Z. Astrophys. 35, 179. Brandt, P. N. and SchrOter, E. H.: 1982, Solar Phys. 79, 3. Brault, J.: 1979, in G. Godoli, G. Noci, and A. Righini (eds.), Proceedings of the JOSO Workshop Future Solar Optical Observations -Needs and Constraints, Osservazioni e Memorie dell' Osservatorio Astrofisico di Arcetri, Vol. 106, p. 53. Bruning, D. H.: 1980, Solar Phys. 71,233. Crosswhite, H. M.: 1975, J. Res. N.B.S. 79A, 17. Dravins, D.: 1982, Ann. Rev. Astron. Astrophys. 20, 61. Dravins, D., Lindegren, L. and Nordlund, ~.: 1981, Astron. Astrophys. 96, 345. Durrant, C. J., Mattig, W., Nesis, A., and Schmidt, W.: 1979, Solar Phys. 61, 259. Duvall, T. L. Jr.: 1982, Solar Phys. 76, 137. Erikson, G. und Maltby, P.: 1967, Astrophys. J. 148, 833. Gasanalizade, A. G.: 1971, Solar Phys. 20, 507. Gasanalizade, A. G.: 1980, PubL Obs. Pulkovo 197, 145. Gingerich, O., Noyes, R. W., Kalkofen, W., and Cuny, Y.: 1971, Solar Phys. 18, 347. Hatm, J.: 1907, Astron. Nachr. 173, 273. Hart, M. H.: 1974, Astrophys. J. 187, 393. Higgs, L. A.: I962, Monthly Notices Roy. Astron. Soc. 124, 51. Holweger, H. and Mtiller, E.: 1975, Solar Phys. 39, 19. Howard, R. and Harvey, J. W.: 1970, Solar Phys. 12, 23. Kaisig, M. and Schr6ter, E. H.: 1983, Astron. Astrophys. 117, 305. Keil, S. L.: 1980a, Astrophys. J. 237, 1024. Keil, S. L.: 1980b, Astrophys. aT. 237, 1035. Koch, A.: 1984, Solar Phys. 93, 53. Kostik, R. I. and Orlova, T. V.: 1977, Solar Phys. 53, 353. Kubirela, A. and Karabin, M.: 1977, Solar Phys. 52, 245. Kiiveler, G.: 1983, Solar Phys. 88, 13. Kiiveler, G. and Wrhl, H.: 1983, Astron. Astrophys. 123, 29. Livingston, W. C.: 1969a, Solar Phys. 7, 144. Livingston, W. C.: 1969b, Solar Phys. 9, 448.
ASYMMETRIES,WAVELENGTHS,AND ROTATION
241
Lopresto, J. C., Chapman, R. D., and Sturgis, E. A.: 1980, Solar Phys. 66, 245. Missana, M.: 1975, Astrophys. Space Sci. 33, 239. Nordlund, ~.: 1980, in D. F. Gray and J. L. Linsky (eds.), 'Stellar Turbulence', IAU Colloq. 51,213. Nordlund, ~.: 1982, Astron. Astrophys. 107, 1. P~rez Garde, M., Vfizquez, M., Schwan, H , and W~hl, H.: 1981, Astron. Astrophys. 93, 67. Pierce, A. K. and Breckinridge, J. B.: 1973, KPNO Contr. 559. Plaskett, H.H.: 1956, The Observatory 76, 216. Roca-Cortes, T., V~zquez, M., and W6hl, H.: 1983, Solar Phys. 88, 1. Rudkj~bing, M.: 1978, in A. Reiz and T. Andersen (eds.), Astronomical Papers dedicated to Bengt Str6mgren. Copenhagen, p. 125. St. John, C. E.: 1928, Astrophys. J. 67, 195. SchrOter, E. H.: 1957, Z. Astrophys. 41, 141. Sehr6ter, E.H.: 1959, Mitt. Potsdam, No. 83. Solonsky, Y. A.: 1972, Solar Phys. 23, 3. Voigt, H. H.: 1956, Z. Astrophys. 40, 157.