Sp.-V/AQuan/1999/10/10:10:02 Page 339
14
Sun
14.1
14.2
14.3
14.4
14.5
14.6
Basic Data
. . . . . . . . . . . . . . . . . . . . . . . . .
340
Interior Model
. . . . . . . . . . . . . . . . . . . . . . .
341
Solar Oscillations
. . . . . . . . . . . . . . . . . . . . .
342
Photospheric–Chromospheric Model
. . . . . . . . . .
348
Spectral Lines
. . . . . . . . . . . . . . . . . . . . . . .
351
Spectral Distribution
. . . . . . . . . . . . . . . . . . .
353
14.7
Limb Darkening
. . . . . . . . . . . . . . . . . . . . . .
355
14.8
14.9
Corona
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
357
Solar Rotation
. . . . . . . . . . . . . . . . . . . . . . .
362
14.10
Granulation
. . . . . . . . . . . . . . . . . . . . . . . . .
364
14.11
Surface Magnetism and its Tracers
. . . . . . . . . . .
364
14.12
Sunspots
. . . . . . . . . . . . . . . . . . . . . . . . . . .
367
14.13
Sunspot Statistics
. . . . . . . . . . . . . . . . . . . . .
370
14.14
Flares and Coronal Mass Ejections
. . . . . . . . . . .
373
14.15
Solar Radio Emission
. . . . . . . . . . . . . . . . . . .
375
339

Sp.-V/AQuan/1999/10/10:10:02 Page 340
340 / 14 S
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Solar radius
Volume
Surface area
Solar mass
Mean density
Gravity at surface
Moment of inertia
Angular rotation velocity at equator
Angular momentum (based on surface rotation)
Work required to dissipate solar matter to infinity
Sun’s total internal radiant energy
Escape velocity at solar surface
R
=
6
.
955 08
±
0
.
000 26
×
10
10
V
=
1
.
4122
×
10
33 cm
3
6
.
087
×
10
22
M =
1
.
989
×
10
33
ρ =
1
.
409 g cm
−
3
2
.
740
×
10
4 cm g
2 cm s
−
2
5
.
7
×
10
53
2
.
85
×
10
−
6
1
.
63
×
10
48
6
.
6
×
10
48 g cm
2 rad s g cm erg
−
1
2 s
−
1
2
.
8
×
10
47
6
.
177
×
10
7 erg cm s
−
1 cm [1]
Mean equatorial horizontal parallax [2]
Surface area of sphere of unit radius
In heliographic coordinates
At mean distance A
8
.
794 18
=
4
.
263 54
×
10
−
5
1 AU
=
1
.
495 979
×
10
13 rad cm Mean distance from Earth
(A
=
AU
= astronomical unit)
Distance at
Perihelion
Aphelion
Semidiameter of Sun
At mean Earth distance
Oblateness: Semidiameter equator–pole difference [3, 4]
Solid angle of Sun, mean distance
1
.
4710
×
10
13
1
.
5210
×
10
13
959
.
63 cm cm
0.004 652 4 rad
0
.
0086
6
.
8000
×
10
−
5
A
/
R
=
214.94
(
A
/
R
) 2 sr
(
A
/
R
) 1
/
2
4
π
A
2
=
46 200
=
14.661
=
2
.
8123
×
10
27
1
◦ =
12 147 km
1 of arc
=
4
.
352
×
10
1 of arc
=
725.3 km
4 cm km
2
Solar constant S (total solar irradiance)
= flux of total radiation received outside the Earth’s atmosphere per unit area at the mean Sun–Earth distance [5–9]:
Radiation from whole Sun
Radiation per unit mass
S
=
1
.
365–1
.
369 W m
L
=
3
.
845
×
10
26
L
/ M =
1
.
933
×
10
−
4
−
2 =
1
.
365–1
.
369
×
10
6
W
=
3
.
845
×
10
33
W kg
−
1 erg s
=
1
.
933 erg s
−
1
−
1 g
.
−
1
.
erg cm
−
2 s
−
1
,

Sp.-V/AQuan/1999/10/10:10:02 Page 341
Radiation emittance at Sun’s surface
Mean radiation intensity of Sun’s disk
14.2 I
NTERIOR
M
ODEL
/ 341
F =
6
.
312
×
10
7
W m
−
2 =
6
.
317
×
10
10 erg cm
−
2 s
−
1
.
F
= F /π =
2
.
009
×
10
7
=
2
.
009
×
10
10
W m
−
2 sr
−
1 erg cm
−
2 s
.
−
1
.
Magnitudes of the Sun in three wavelength bands and the bolometric magnitude are given in
Table 14.1 [10–13].
Visual
( m v )
Blue
Ultraviolet
Bolometric
Table 14.1. Solar magnitudes.
Apparent
V
= −
26
.
75
B
= −
26
.
10
U
= −
25
.
91 m bol
= −
26
.
83
Modulus
31.57
Absolute
M
M
V
B
M
U
= +
4
.
82
= +
5
.
47
= +
5
.
66 m bol
= +
4
.
74
Color indices [10–14]:
B
−
V
= +
0
.
650,
U
−
B
= +
0
.
195,
U
−
V
= +
0
.
845,
V
−
R
= +
0
.
54,
V
−
I
= +
0
.
88,
V
−
K
= +
1
.
49.
Bolometric correction
Spectral type
Effective temperature
Velocity relative to near stars
Solar apex
BC
= −
0
.
08.
G2 V.
L
5777 K.
19.7 km s
A
=
271
=
57
◦
,
◦
,
−
1
(4.5–4.7)
×
10
9
B
D
=
30
◦
=
22
◦
.
(1900), yr.
Age of Sun [15, 16]
Mean magnetic field [17]
Average
Peak
0 G,
±
1 G.
The tabulated data in Table 14.2 are for a standard model of the Sun (no rotation, no diffusion), from
Table 3B in [18]. This model was constructed using opacities from [19] and the solar mixture from [20].
Other similar recent models can be found in [21] and [22].

Sp.-V/AQuan/1999/10/10:10:02 Page 342
342 / 14 S
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Central values
Temperature
Density
Pressure
T c
=
15
.
7
×
10
ρ c
P c
Central hydrogen content by mass X c
=
0
.
355.
6
=
151 g cm
−
3
.
=
2
.
33
×
10
17
K.
dyn cm
−
2
.
Surface composition parameters
X
=
0
.
6937,
Z
=
0
.
0188.
The fraction of the radius at the base of the surface convection (SCZ or surface convection zone) can be determined by helioseismology [23, 24], which is within 1% of model [18]: r
SCZ
/
R
=
0
.
71
.
r
(
R
) r
(cm)
0.007
4.87
×
10
8
0.02
1.39
×
10
9
0.09
6.24
×
10
9
0.22
0.32
0.42
0.52
0.60
0.71
0.81
0.91
0.96
1.53
×
10
10
2.23
×
10
10
2.92
×
10
10
3.62
×
10
10
4.18
×
10
10
4.94
×
10
10
5.64
×
10
10
6.33
×
10
10
6.68
×
10
10
0.99
6.89
×
10
10
0.995
6.93
×
10
10
0.999
6.95
×
10
10
1.000
6.96
×
10
10
(10
T
15.7
15.6
13.6
8.77
6.42
4.89
3.77
3.15
2.23
1.29
6
0.514
0.208
K)
150
146
9.77
3.22
1.05
Table 14.2. Model of solar interior.
ρ
(g cm
− 3 )
95.73
28.72
0.500
0.177
0.0766
0.0194
4.85
×
10
−
3
0.004 41 2.56
×
10
−
4
0.002 66 4.83
×
10
−
5
0.001 35 1.29
×
10
−
6
0.000 60 2.18
×
10
−
7
M r
( M )
Lr
0.00003
1.01
×
10
30
0.001
3.97
×
10
31
0.057
1.39
×
10
33
0.399
0.656
0.817
0.908
0.945
0.977
0.992
0.999
0.9999
1.0000
1.0000
1.0000
1.0000
(erg s
− 1 )
3.72
×
10
33
3.85
×
10
33
3.85
×
10
33
3.85
×
10
33
3.85
×
10
33
3.85
×
10
33
3.85
×
10
33
3.85
×
10
33
3.85
×
10
33
3.85
×
10
33
3.85
×
10
33
3.85
×
10
33
3.85
×
10
33
Lr
(
L
)
P
(dyn cm
− 2
0.0002
2.33
×
10
17
0.010
2.27
×
10
17
0.361
1.50
×
10
17 log P
) (dyn cm
− 2 )
17.369
17.355
17.177
0.966
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
3.35
×
10
16
5.29
×
10
15
2.10
×
10
15
5.28
×
10
14
2.10
×
10
14
5.26
×
10
13
1.32
×
10
13
1.32
×
10
12
1.31
×
10
11
1.31
×
10
9
1.31
×
10
8
1.31
×
10
6
8.27
×
10
4
16.525
15.724
15.324
14.722
14.322
13.721
13.119
12.119
11.118
9.118
8.118
6.118
4.918
R = solar radius.
g
= gravitational acceleration at solar surface.
= spherical harmonic degree of mode of oscillation.
m
= spherical harmonic azimuthal degree of mode.

Sp.-V/AQuan/1999/10/10:10:02 Page 343
14.3 S
OLAR
O
SCILLATIONS
/ 343 n
= radial order of mode.
k
ν = frequency of mode.
ω = angular frequency of mode,
ω =
2
πν
.
h
= horizontal wave number of mode, k
P i
=
Legendre polynomial of degree i .
A
(ν, ) = amplitude of mode.
h
=
√
( +
1
)/ R
.
(ν, ) = full width at half maximum of mode.
Characteristic period of p (pressure) modes 5 min.
Characteristic photospheric amplitude of p modes 10 cm s
−
1
.
Characteristic lifetime of p modes
Estimated number of excited p modes
7 days.
10
7
.
n
,
=
0) p
(a) Tassoul first-order asymptotic approximation for low-degree modes with
≤
3 and 11
≤ n
≤
33 [25]:
ν( n
, ) = ν
0 n
+
2
+ δ with measured coefficients in Table 14.3 [26] and accuracy of 2.8–4.1
µ
Hz.
Table 14.3. Fit values.
ν
0
(µ
Hz)
2
3
0
1
135
135
135
135
.
.
.
.
4
7
4
7
δ
1
.
43
1
.
36
1
.
36
1
.
24
(b) Tassoul second-order asymptotic approximation for low-degree modes with
≤
3 and 11
≤ n
≤
33 [25]:
ν( n
, ) = ν
0 n
+
2
+ δ −
( +
1
)α − β n
+ /
2
+ δ
, with measured coefficients in Table 14.4 [26] and accuracy of 1.4–2.0
µ
Hz.
2
3
0
1
Table 14.4. Second-order fit values.
ν
0
(µ
Hz)
α β δ
137.0
137.9
137.4
137.0
5.6
0.90
0.20
7.8
0.62
0.15
7.8
0.70
0.20
7.4
0.80

Sp.-V/AQuan/1999/10/10:10:02 Page 344
344 / 14 S
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(c) Polynomial approximation for low-degree modes with
≤
3 and 11
≤ n
≤
33 [27]:
ν( n
, ) = ν ν n
+
2
− n
0
+ γ n
+
2
− n
0
2
, using n
0
=
22 as a reference order, measured coefficients listed in Table 14.5 in
µ
Hz [26] and accuracy of 1.0–1.2
µ
Hz.
Table 14.5. Polynomial fit values.
ν ν γ
0 3169.4
135.31
0.090
1 3166.2
135.52
0.105
2 3160.5
135.35
0.085
3 3150.8
135.52
0.070
The quantities
ν and
¯ are linear functions of
( +
1
)
:
ν
ν
= ν
0
= ν
0
+
− (
( +
+
1
)
1 d
)
0
D
,
0
, with fitted values [26]
ν
0
=
3169
.
4
µ
Hz
,
ν
0
D
0
=
135
.
35
µ
Hz
,
=
1
.
54
µ
Hz
, d
0
=
0
.
012
µ
Hz
.
(d) Parabolic fit for intermediate-degree modes with 4
≤ ≤
100, 3
≤ n
≤
24, and accuracy of
1–10
µ
Hz [26]:
ν( n
, ) = a
0
( n
) + a
1
( n
) + a
2
( n
) 2 , where coefficients a i are fitted to second-order polynomials in n expressed in matrix form as a a a
0
1
2
=


643
8
.
6
101
2
.
.
3
9
−
0
0
.
.
71
047
−
0
.
025
−
0
.
008
−
0
.
0002

 n
1 n
2
.
(e) Empirical fit for low- and intermediate-degree modes with 1
≤ ≤
200, 1
.
7 mHz
≤ ν ≤
5
.
0 mHz,
R in km, and accuracy of 10
µ
Hz [28]:
ν( n
, ) =
2354
.
2
( n
+
1
.
57
) e
0
.
2053
( ln x
−
14
.
523
) 2 +
4
.
1175 x
= ( n
+
1
.
57
)π R
[
( +
1
)
]
−
1
/
2 .
1
/
2 − ln x µ
Hz
,
The Duvall dispersion law [29] collapses all p-mode ridges in an k h
–
ω diagram to a single ridge via a transformation of coordinates. This transformation is
( n
+
ω
α)π
= f
ω k h

Sp.-V/AQuan/1999/10/10:10:02 Page 345
14.3 S
OLAR
O
SCILLATIONS
/ 345 with fitted value
The dependence of
ν on m for p modes is [30]
α =
1
.
67
.
ν(, m
, n
) = ν(, n
) + ( +
1
) i
=
5 a i
(ν, )
P i i
=
1 where the splitting coefficients a i depend on
ν( n
, )
, in mHz [31]: a i
(ν, ) = a i
∗ () + b i
∗ ()
[
ν( n
, ) −
2
.
5]
.
√
− m
( +
1
)
,
Some of these coefficients are given in Table 14.6.
Table 14.6. Selected splitting coefficients [1]. All coefficients in nHz. a
∗
1 b
∗
1 a
∗
2 b
∗
2 a
∗
3 b
∗
3 a
∗
4 b
∗
4 a
∗
5 b
∗
5
11 436.7
−
1.0
−
3.5
−
1.7
12.0
−
2.1
1.3
20 438.4
−
0.7
−
0.9
0.2
16.9
0.3
0.8
6.8
1.3
−
1.3
3.1
29 439.5
−
0.5
−
0.5
−
0.5
19.9
−
5.1
1.2
−
1.1
−
3.4
38
47
56
440.7
441.4
441.5
0.3
−
0.1
−
0.8
21.3
−
2.0
0.9
0.1
−
0.3
−
1.0
21.5
−
0.7
0.4
0.7
0.2
0.6
22.3
−
0.5
0.4
1.4
1.9
1.3
−
−
−
2.5
3.3
3.5
−
3.2
2.2
1.0
0.1
0.5
0.3
Reference
1. Libbrecht, K.G. 1989, ApJ, 336, 1092
The dependence of p-mode frequency change
ν of
ν(, n
) on area-weighted average full-disk absolute magnetic field B in Gauss [32] is
ν = a
(
B
−
7
), with fitted value a
=
0
.
027
µ
Hz
/
G
.
The approximate formulas for amplitude A
(ν, ) of p modes [33, 34]
A
(ν, ) =
10
( b
+ c
)/
2 cm
/ s
, with fitted values b
=
2
.
2
ν −
3
.
5
,
= −
0
.
9
ν +
5
.
6
, c
= −
8
.
8
×
10
−
4
= −
3
.
1
×
10
−
3
,
+
0
.
75
,
ν <
2
.
9 mHz
,
ν >
2
.
9 mHz
,
<
340
,
>
340
.
The observed estimate of absorption fraction
α of p-mode power by sunspots is discussed in [35] and listed in Table 14.7.

Sp.-V/AQuan/1999/10/10:10:02 Page 346
346 / 14 S
UN
Table 14.7. Sunspot absorption. k h
(
Mm
−
1 ) α
0.2
0.3
0.4
≥
0
.
5
0.10
0.18
0.34
0.42
Approximate formulas for the full width at half maximum (FWHM)
(ν, ) of p modes
[33, 36, 37] are
(ν, ) =
1
.
7
×
10
−
2 ( −
20
) +
10 d µ
Hz
, with fitted values d
= ν −
2
.
3
,
=
0
.
1
,
= ν −
3
.
0
,
=
0
.
4
ν −
0
.
6
,
The dispersion relation for f (fundamental) mode is
ν <
2
.
4 mHz
,
2
.
4 mHz
≤ ν ≤
3
.
1 mHz
,
3
.
1 mHz
≤ ν ≤
4
.
3 mHz
,
4
.
3 mHz
< ν.
ω = gk h
, or equivalently
ν =
99
.
8569[
( +
1
)
]
1
/
4 µ
Hz
.
The first-order asymptotic approximation for period P
( n
, ) of g (gravity) mode with n [25] is
P
( n
, ) =
P
0
2
2n
+ + φ
[
( +
1
)
] 1
/
2
.
Theoretical estimates of period spacing P
0 and phase
φ from standard solar models [38] are
P
0
=
33
.
9 to 38
.
0 min
,
φ = −
0
.
42 to
−
0.25.
Observational estimates [38] are
P
0
=
29
.
9 to 42
.
6 min
,
φ = −
0
.
35 to
+
2.
Properties of “160-min” oscillation [38] are period
=
160
.
010 min
, amplitude
=
54 cm
/ s
.
Table 14.8 gives zonal p-mode frequencies for selected n and values.

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14.3 S
OLAR
O
SCILLATIONS
/ 347

Sp.-V/AQuan/1999/10/10:10:02 Page 348
348 / 14 S
UN
Table 14.9 gives a model of the average quiet solar atmosphere, from [39]. The height h is the distance above
τ
500
=
1, where
τ
500 is the radial optical depth in the continuum at 500 nm. Hydrostatic equilibrium is assumed so that m
=
P tot
/
g, where m is the column mass, P tot is the total pressure, and
g is the gravitational acceleration at the solar surface. In the photosphere (
−
100
< h
<
525 km) and in the chromosphere (525
< h
<
2100 km) the temperature T has been adjusted empirically so that the computed spectrum is in agreement with the spatially averaged spectrum from quiet areas (away from sunspots and active regions). The temperature distribution in the transition region above h
≈
2100 km
(up to T
=
10
5
K) has been determined theoretically by balancing the downflow of energy from the corona (due to thermal conduction and diffusion) with the radiative energy losses. The microvelocity v t roughly accounts for the Doppler broadening that is observed to exceed the thermal broadening of lines formed at various heights (see [40, 41]). The total pressure P tot and the turbulent pressure
ρv t
2 /
2, where
ρ is the gas density.
The table also lists the total hydrogen density n
H is the sum of the gas pressure P and the proton and electron densities n p gas and n e
.
The number densities and other quantities are determined by solving the coupled radiative transfer and statistical equilibrium equations [without assuming local thermal equilibrium (LTE)], given the T and v t distributions. The helium to hydrogen abundance ratio is assumed to be 0.1. The abundances of the other contributing elements are from [42].
See [43] and [44] for similar empirical models of the photosphere. Models for faint and bright components of the quiet Sun and for a plage region are given in [39]. See [45] for a theoretical lineblanketed LTE photospheric model, and [46] for theoretical non-LTE line-blanketed chromospheric models. Bifurcated chromospheric models based on a combination of hot and cool components are given in [47] and [48]. Papers in [49] and [50] discuss related studies and include references to earlier work.
Other aspects of the chromosphere, such as infrared and radio data, are referred to in [51–53].

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HOTOSPHERIC
–C
HROMOSPHERIC
M
ODEL
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PECTRAL
L
INES
/ 351
Selected Fraunhofer absorption features are given in Table 14.10. Equivalent width refers to disk center. Cycle variability, where known, refers to solar irradiance, or Sun as a star [54–64].
Wavelength
(nm)
279.54
280.23
388.36
587.56
589.00
589.59
612.22
630.25
656.28
676.78
769.89
777.42
854.21
393.36
396.85
430.79
517.27
518.36
525.02
537.96
538.03
557.61
868.86
1006.37
1083.03
1281.81
1564.85
1565.29
2231.06
4652.55
4666.24
12318.3
Name
(CN band head)
K
H
G band b
2 b
1
D
3
D
2
D
1
C (H
α
H Pasch
H Pfund
)
β
β
Species
Table 14.10. Absorption features.
Equiv. width
(nm)
2.2
Cycle var.
[% ( p-to- p)]
10
Comment
UV emission, high chromosphere Mg II
Mg II
CN 0.03 (index) 3 Photosphere, magnetic field tracer
Ca II
Ca II
2.0
1.5
CH (Fe I , Ti II ) 0.72
Mg I 0.075
Mg I
Fe I
Fe I
C I
Fe I
0.025
0.0070
0.0079
0.0025
H I
Ni I
K I
O I
Ca I
He I
Na I
Na I
Ca I
Fe I
0.075
0.056
0.0083
0.40
0.0066
0.37
0.014
Fe I
FeH
He I
H I
Fe I
Fe I
Ti I
H I
CO
Mg I
0.003
0.19
0.0035
0.003
15
10
0.3
0.3
0.0
6
−
1
200
Chromosphere
Magnetic field tracer
Low chromosphere
Photo. magnetic fields
( g
=
3
)
Medium photosphere
Low photosphere
Photo. velocity fields
( g
=
0
)
Chromo., flares, prominences
Upper photo., low chrom., prom.
(same except water blend free)
Photo. magnetic fields
( g
∼
1
.
5
)
Photo. magnetic fields
( g
=
2
.
5
)
Chromo., prom., flares
Photo. oscillations
Photo. oscillations
High photo. (?) (NLTE?)
Low chromo., prom.
Photo. magnetic fields
( g
=
1
.
7
)
Umbral (only) mag. fields
( g
=
1
.
22
)
High chromosphere
Chromosphere
Photo. magnetic fields
( g
=
3
)
Photo. magnetic fields
( g
=
1
.
8
)
Umbral (only) mag. fields
( g
=
2
.
5
)
Chromo., electric fields
High photo. thermal structure
High photo., magnetic fields
( g
=
1
)
Table 14.11 gives absolute spectral irradiances at the Earth for the UV and EUV with estimates of solar cycle variability where known. Irradiances from both individual lines and integration over bands are given in the table. The irradiance for all entries identified as a “line” in column 3 (bandwidth) is the integral for the line, and is in units of mW m
−
2
. In contrast, irradiances for the “bands” are mean fluxes per nanometer wavelength interval for that band [65, 66].

Sp.-V/AQuan/1999/10/10:10:02 Page 352
352 / 14 S
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Band
34
35
36
37
27
28
29
33
21
22
24
25
17
18
19
20
GOES a
4
5
6
10
11
12
14
15
7
8
9
Band center
(nm)
62.97
62.50
70.33
72.50
77.04
78.94
77.50
97.70
97.50
102.57
103.19
102.50
121.50
150.00
32.50
36.81
37.50
46.52
47.50
55.44
58.43
57.50
60.98
0.50
22.50
25.63
28.42
27.50
30.33
30.38
5 line line
5
1
1 line
5 line
5 line line
5 line
5 line
5 line
5 line line
5 line
0.6
5 line line
5 line line
Table 14.11. Solar spectral irradiances: 0.5–300 nm.
Bandwidth
(nm)
Solar irradiance
Solar cycle variability
I max
/
I min
Solar max.
Solar min.
1.9
×
10
− 2
6.5
×
10
−
2
2.6
2.9
8.6
×
10
−
3
1.6
7.4
6.9
×
10
−
2
1.2
1.5
×
10
−
2
7.1
×
10
− 1
3.0
×
10
−
3
1.7
3.5
×
10
−
1
1.1
×
10
− 2
9.8
×
10
−
1
1.5
×
10
−
1
9.3
×
10
−
3
1.2
×
10
−
1
3.9
×
10
−
3
4.1
×
10
−
1
5.5
×
10
−
1
2.2
×
10
−
3
9.0
×
10
− 1
5.4
×
10
−
2
1.8
1.7
5.1
×
10
− 2
1.0
×
10
1
1.0
×
10
− 1
0
1.6
×
10
−
2
7.7
×
10
− 2
5.9
×
10
−
1
3.9
×
10
−
3
1.6
×
10
−
1
3.9
1.1
×
10
−
2
1.1
×
10
− 1
7.8
×
10
−
3
1.3
×
10
− 1
1.5
×
10
−
3
5.7
×
10
− 1
1.6
×
10
−
1
5.5
×
10
− 3
4.9
×
10
−
1
5.5
×
10
−
2
2.9
×
10
−
3
4.8
×
10
−
2
2.1
×
10
−
3
2.0
×
10
−
1
2.2
×
10
−
1
1.0
×
10
−
3
3.6
×
10
− 1
2.4
×
10
−
2
6.2
×
10
− 1
7.0
×
10
−
1
1.7
×
10
− 2
2
3
2
3
1.5
1.15
2
2
2
3
3
2
3
3
2
2
3
2
6
10
2
5
2
4
34
5
2
10
2
Note a
Geostationary Operational Environmental Satellite.
Species
He II , Si X
Fe XV
Si XI
He II
Mg IX
Ne VII
O IV
He I
Mg X
O V
O III
Ne VIII
O IV
C III
H I (Ly
β
)
O VI
H I (Ly
α
)
See [67] for a detailed description of curve-of-growth analysis techniques. These yield the following results [68–74]:
Atomic thermal velocity
= (
2kT
/ m
Microturbulence (
ξ
Macroturbulence (
ξ mi
) ma
)
=
=
1.4 km s
1.1 km s a
)
−
1
−
1
1
/
2
.
=
1.6 km s
−
1
.
(vertical)
=
2.8 km s
−
1
Velocity for line breadth
= (ξ 2 th
+ ξ
=
2.4 km s
2
−
1
=
3.3 km s
−
1
(horizontal).
+ ξ 2 ma
) 1
/
2 at center of disk at limb.

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PECTRAL
D
ISTRIBUTION
/ 353
Table 14.12 gives heights of formation of spectral lines [75, 76]:
Line
(nm)
Table 14.12. Spectral line heights of formation.
Optical depth
τ
(FWHM)
Height (km)
(FWHM)
Continuum (388.385)
CN 388.33
Continuum (500.0)
Fe
C
H
Fe
Fe
I
I
I
I
I
537.9
538.0
656.0
1564.8
1564.8 (spot)
3.2 to 0.32
−
45 to 60
0.003 to 0.000039
370 to 740
2.5 to 0.25
−
35 to 90
0.35 to 0.0025
1.6 to 0.16
60 to 400
−
20 to 110
2000 to 3000
−
20 to
−
30
20 to 80
(
F λ
±
= intensity of the mean solar disk per unit wavelength with spectrum irregularities smoothed
50 ˚
F
λ f λ
= π
= F
F
λ
λ
(
R
= emittance of the solar surface per unit wavelength range.
/
=
A
) 2
F λ d
λ
.
=
6
.
80
×
10
−
5
F λ wavelength range. A
= astronomical unit.
solar flux outside the Earth’s atmosphere per unit area and
F
λ same as for F λ but referring to the continuum between the lines. The curve joining the most intense windows between the lines is regarded as the continuum. This may differ appreciably from the continuum in the entire absence of absorption lines. F
λ
Balmer limit).
does not have any sudden changes (e.g., at the
F
λ
I λ
(
0
) = intensity at the center of the Sun’s disk with spectral irregularities smoothed (
±
50 ˚
I
λ
I λ
(
0
) = intensity of the center of the Sun’s disk between spectrum lines. This is obtained by interpolation from the most intense windows, as for F
λ
.
F λ
/
I
λ
( 0 )/ I
/
I λ
(
0
λ
)
( 0 ) represents the observed line blanketing for the center of the Sun’s disk.
A) disk-to-center ratio. It is approximately equal to
(0). The solar spectrum is given in Table 14.13.
Table 14.13. Solar spectral distribution, 0.2–5.0
µ m [1–3].
λ
(
µ m)
F λ
(10
3
F
λ
W m
−
2
I λ (0) sr
−
1
I
λ
(0)
A
−
1
)
0.20
0.01
0.014
0.014
0.22
0.07
0.10
0.13
0.24
0.08
0.13
0.26
0.19
0.27
0.28
0.34
0.68
0.13
0.37
0.60
0.30
0.83
1.48
0.32
1.12
1.97
0.34
1.34
2.39
0.36
1.42
2.56
1.34
1.67
1.89
1.96
0.02
0.19
0.21
0.53
1.21
2.39
2.94
3.30
3.47
(10
−
3 f λ
W m
−
2
A
−
1
) I λ
(
0
)/
I
λ
(
0
)
F λ
/
I λ
(
0
)
56
76
91
97
0.65
4.5
5.2
13
23
0.7
0.7
0.6
0.7
0.5
0.56
0.57
0.57
0.56
0.7
0.5
0.6
0.5
0.56
0.62
0.67
0.71
0.72

Sp.-V/AQuan/1999/10/10:10:02 Page 354
354 / 14 S
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(
µ
λ m)
F λ
(10
3
F
λ
W m
−
2
I λ (0) sr
−
1
I
λ
(0)
A
−
1
)
2.0
2.5
3.0
4.0
5.0
0.37
1.67
2.67
0.38
1.58
2.99
0.39
1.52
3.21
0.40
2.17
3.35
0.41
2.50
3.42
0.42
2.54
3.47
0.43
2.34
3.50
0.44
2.71
3.49
0.45
2.94
3.47
0.46
3.01
3.41
0.48
2.99
3.28
0.8
0.9
1.0
1.1
1.2
0.50
2.83
3.20
0.55
2.76
2.93
0.60
2.61
2.67
0.65
2.34
2.41
0.70
2.08
2.13
0.75
1.87
1.92
1.4
1.6
1.8
1.68
1.38
1.11
0.90
0.76
0.51
0.37
0.25
1.71
1.39
1.12
0.90
0.76
0.17
0.076
0.039
0.0130
0.0055
2.28
2.16
2.08
2.97
3.38
3.45
3.12
3.61
3.87
3.95
3.84
3.61
3.43
3.17
2.81
2.46
2.18
1.94
1.57
1.25
1.01
0.84
Table 14.13. (Continued.)
0.56
0.40
0.27
0.18
0.081
0.041
0.0135
0.0057
3.60
4.14
4.41
4.58
4.63
4.66
4.67
4.62
4.55
4.44
4.22
4.08
3.63
3.24
2.90
2.52
2.24
1.97
1.58
1.26
1.01
0.84
(10
−
3 f λ
W m
−
2
114
94
75
61
52
35
25.5
16.9
11.6
5.2
2.6
0.9
0.4
205
203
192
188
177
159
141
127
113
107
103
148
170
173
159
184
200
A
−
1
) I λ
(
0
)/
I
λ
(
0
)
F λ
/
I λ
(
0
)
0.63
0.52
0.47
0.65
0.73
0.74
0.67
0.78
0.85
0.89
0.91
0.88
0.94
0.98
0.97
0.975
0.975
0.983
0.993
0.995
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.87
0.88
0.89
0.89
0.90
0.91
0.92
0.92
0.93
0.94
0.95
0.96
0.96
0.76
0.78
0.78
0.80
0.82
0.83
0.85
0.86
0.73
0.73
0.73
0.73
0.74
0.74
0.75
0.75
0.76
References
1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London), Secs. 81
& 82
2. Labs, D., Neckel, H., Simon, P.C., & Thuiller, G. 1987, Solar Phys., 90, 25
3. Neckel, H., & Labs, D. 1984, Solar Phys., 90, 205
Brightness temperatures for two optical wavelengths are given in Table 14.14, and Table 14.15
gives them for the infrared.
Table 14.14. Brightness temperatures.
F λ
F
I λ
λ
I
λ
5850 K
6125 K
6165 K
6465 K
5860 K
5940 K
6155 K
6240 K

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14.7 L
IMB
D
ARKENING
/ 355
Mean intensity and brightness temperature in mid- and far-infrared regions with heights from the
Vernazza, Avrett, and Loeser (VAL-C) model [77–79]:
λ (µ m)
5
10
20
50
100
200
1000
=
1 mm
1 cm
Table 14.15. Infrared brightness temperatures.
h (km) log F λ
(
(W m
I
− 2
λ sr
− 1
F
λ
µ m)
I
λ
)
T b
(K)
70
160
240
340
410
450
4.77
3.57
2.36
0.76
−
0.45
−
1.67
−
4.31
5 730
5 140
4 820
4 500
4 340
4 200
5 920
(temp min.)
10–23 000 (transition)
I
λ
(θ) = intensity of the solar continuum at an angle the Sun’s radius vector and the line of sight.
θ from the center of the disk;
θ = angle between
I
λ
(
0
) = continuum intensity at the center of the disk.
The ratio I
λ
(θ)/
I
λ
(
0
)
, which varies with the wavelength
λ
, defines limb darkening. As far as possible, measurements are made in the continuum between the lines (hence the primes in the notation).
The results may be fitted to the following expressions:
I
λ
(θ)/
I
λ
(
0
) =
1
− u
2
− v
2
+ u
2 cos
θ + v
2 cos
2 θ, or
I
λ
(θ)/
I
λ
(
0
) =
A
+
B cos
θ +
C[1
− cos
θ ln
(
1
+ sec
θ)
]
, where
A
+
B
+ (
1
− ln 2
)
C
=
1
.
The ratio of the mean to central intensity is
F
λ
/
I
λ
(
0
) =
1
− 1
3 u
2
− 1
2 v
2
, or
F
λ
/
I
λ
(
0
) =
A
+
C
+ 2
3
B
−
2C
( 2
3 ln 2
=
A
+
0
.
667B
+
0
.
409C
.
− 1
6
)
The ratio of the limb-to-central intensity is
I
λ
(
90
◦ )/
I
λ
(
0
) =
1
− u
2
− v
2
≈
1
− u
1
=
A
+
C
.
Table 14.16 presents limb darkening details, and the fit constants are given in Table 14.17.

Sp.-V/AQuan/1999/10/10:10:02 Page 356
356 / 14 S
UN
Table 14.16. I
λ
(θ)/
I
λ
(
0
)
[1–16]. cos
θ
1.0
0.8
0.6
0.5
0.4
0.3
0.2
0.1
0.05
0.02
λ (µ m) sin
θ
0.000
0.600
0.800
0.866
0.916
0.954
0.980
0.995
0.9987
0.9998
1.5
2.0
3.0
5.0
10
20
Total
0.35
0.37
0.38
0.40
0.45
0.50
0.55
0.60
0.80
1.0
0.20
0.22
0.245
0.265
0.28
0.30
0.32
[9]
[9]
[9]
[8]
[8]
[8]
[9]
[9]
[9]
[9]
[9]
[9]
[9]
[9]
[9]
[9]
[7]
[7]
[7]
[7]
[7]
[7]
[9]
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.85
0.74
0.69
0.65
0.61
0.58
0.58
0.71
0.68
0.72
0.33
0.49
0.42
0.47
0.26
0.42
0.32
0.38
0.21
0.36
0.24
0.29
0.16
0.31
0.19
0.22
0.12
0.25
0.14
0.16
0.77
0.57
0.48
0.39
0.30
0.22
0.14
0.809
0.623
0.532
0.438
0.347
0.262
0.17
0.837
0.665
0.579
0.487
0.397
0.306
0.21
0.851
0.83
0.687
0.66
0.603
0.58
0.513
0.48
0.421
0.39
0.332
0.30
0.23
0.22
0.19
0.18
0.835
0.663
0.585
0.490
0.403
0.308
0.222
0.18
0.860
0.714
0.637
0.556
0.468
0.378
0.278
0.21
0.877
0.744
0.675
0.599
0.513
0.425
0.323
0.26
0.890
0.769
0.703
0.633
0.556
0.468
0.371
0.31
0.900
0.788
0.727
0.664
0.587
0.508
0.412
0.35
0.924
0.843
0.793
0.744
0.681
0.615
0.533
0.47
0.941
0.870
0.828
0.783
0.731
0.675
0.59
0.54
0.957
0.902
0.873
0.831
0.789
0.735
0.65
0.966
0.922
0.896
0.865
0.826
0.780
0.70
0.976
0.944
0.922
0.902
0.873
0.835
0.78
0.986
0.963
0.949
0.937
0.916
0.890
0.84
0.992
0.981
0.973
0.964
0.956
0.937
0.90
0.58
0.61
0.67
0.76
0.87
0.994
0.983
0.975
0.970
0.964
0.957
0.95
0.93
0.898
0.787
0.731
0.669
0.602
0.525
0.448
0.39
0.14
0.19
0.24
0.28
0.32
References
1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London), Sec. 81
2. Pierce, A.K., McMath, R.R., Goldberg, L., & Mohler, O.C. 1950, ApJ, 112, 289
3. Pierce, A.K., & Waddell, J.H. 1961, MNRAS, 68, 89
4. Gaustad, J.E., & Rogerson, J.R. 1961, ApJ, 134, 323
5. Mouradian, Z. 1965, Ann. d’Astrophys., 28, 805
6. Heintz, J.R.W. 1965, Rech. Astron. Obs. Utrecht, 17/2
7. Bonnet, R. 1968, Ann. d’Astrophys., 31, 597
8. Lena, P. 1970, A&AS, 4, 202
9. Pierce, A.K., & Slaughter, C.D. 1977, Solar Phys., 51, 25
10. Neckel, H., & Labs, D. 1987, Solar Phys., 110, 139
11. Neckel, H., & Labs, D. 1994, Solar Phys., 153, 91
12. Neckel, H. 1996, Solar Phys., 167, 9
13. Neckel, H. 1997, Solar Phys., 171, 257
14. Pierce, A.K., Slaughter, C.D., & Weinberger, D. 1977, Solar Phys., 52, 179
15. Petro, C.D., Foukal, P.V., Rosen, W.A., Kurucz, R.L., & Pierce, A.K. 1984, ApJ, 283, 462
16. Elste, G.H. 1990, Solar Phys., 126, 37
λ
0.20
0.22
0.245
−
0.1
0.30
u
+
−
1.3
0.265
−
0.1
0.28
+
0.90
−
1.9
+
0.38
+
0.57
−
1.3
+
2
0.12
0.74
Table 14.17. Limb darkening constants. v
+
+
1.6
+
0.85
−
1.9
+
2
0.33
0.20
A
−
−
3.4
−
0.2
0.4
B
0.9
2.9
2.0
2.1
1.8
1.2
C
+
+
+
+
+
+
0.9
5
3
2.7
1.8
0.5
I
F
λ
λ
(
0
)
I
λ
(
90
◦
I
λ
(
0
)
)
0.79
0.54
0.51
0.61
0.06
0.20
0.540
0.08
0.588
0.10
0.648
0.06

Sp.-V/AQuan/1999/10/10:10:02 Page 357
14.8 C
ORONA
/ 357
λ
0.60
0.80
1.0
1.5
2.0
3.0
5.0
10.0
Total
0.32
0.35
0.37
0.38
0.40
0.45
0.50
0.55
Table 14.17. (Continued.) u
2 v
2
A B C
I
F
λ
λ
(
0
)
I
λ
(
+
0.88
+
0.03
−
0.02
+
0.98
−
0.10
+
0.25
+
1.03
−
0.16
+
0.42
+
0.92
−
0.05
+
0.26
+
0.91
−
0.05
+
0.20
+
0.99
−
0.17
+
0.54
+
0.97
−
0.22
+
0.68
+
0.93
−
0.23
+
0.74
+
0.88
−
0.23
+
0.78
+
0.73
−
0.22
+
0.92
+
0.64
−
0.20
+
0.97
+
0.57
−
0.21
+
1.11
+
0.48
−
0.18
+
1.09
+
0.35
−
0.12
+
1.04
+
0.22
−
0.07
+
1.02
+
0.15
−
0.07
+
1.04
0.97
+
0.1
0.79
−
0.3
0.68
−
0.4
0.78
−
0.2
0.685
0.705
0.08
0.11
0.13
0.71
0.13
0.81
−
0.1
0.718
0.13
0.60
−
0.44
0.755
0.11
0.39
0.25
0.18
0.08
0.07
0.06
0.05
0.00
−
−
−
−
−
−
−
−
0.57
0.56
0.53
0.61
0.49
0.34
0.18
0.22
0.71
0.49
−
0.56
0.782
0.16
0.43
−
0.56
0.803
0.20
0.817
0.862
0.886
0.916
0.932
0.948
0.964
0.982
+
0.84
−
0.20
+
0.72
+
0.42
−
0.45
0.82
0.24
0.39
0.48
0.56
0.60
0.72
0.81
0.87
0.32
90
◦
I
λ
(
0
)
)
Optical radiation from the corona contains three components:
K
= continuous spectrum due to Thomson scattering by electrons of the coronal plasma,
F
=
Fraunhofer spectrum diffracted and/or scattered by interplanetary dust particles [81],
L
= coronal emission of forbidden lines; L is negligible for coronal photometry (about 1%).
The total coronal light beyond 1.03R (for typical lunar disk at eclipse) [82–84] is at sunspot maximum
=
1
.
5
×
10
−
6 at sunspot minimum
=
0
.
6
×
10
−
6
Total F corona
=
0
.
3
×
10
−
6 solar flux 0
.
66 full Moon
, solar flux 0
.
26 full Moon
.
solar flux
.
Earthshine on Moon at total eclipse [85]
=
2
.
5
×
10
−
10 mean Sun brightness.
The brightness of the sky near the Sun during a total eclipse [82, 84, 86] is
6
×
10
−
10 <
S
<
10
−
8 ×
[mean Sun brightness
( ¯ )
]
.
The spectral distribution of K components is similar to the solar spectrum, with B
−
V
=
0
.
65
.
The
F component is slightly redder in the outer corona [87], with B
−
V 0
.
75. The base of corona may be taken as the transition region at r
=
1
.
0025R from the visible limb. Chromospheric extensions are seen up to r
=
1
.
015R .
The coronal ellipticity from isophotes [83, 88, 89] is
= (
A
3
−
P
3
)/
P
3
(
A
1
−
P
1
)/
A
1
,

Sp.-V/AQuan/1999/10/10:10:02 Page 358
358 / 14 S
UN where A
1 and P
1 are equatorial and polar diameters, and for A
3 averaged with those oriented 22
.
5
◦ on either side.
,P
3 the corresponding diameters are at sunspot max.
0
.
06
, at sunspot min.
0
.
26 near r
=
2R (extrapolated values; the a
+
b index).
Values are tabulated against r
(
R
)
.
The polarization of coronal light
(
K
+
F
)
[82, 90, 91] is p tot
= (
I t
−
I r
)/(
I t
+
I r
), where I t and I r are intensities polarized in the tangential and radial direction.
p max
=
50%
.
Other values tabulated against r
/
R are listed in Tables 14.18 and 14.19.
p k
A most relevant parameter to describe the distribution of electron densities in the plasma corona is
= (
I t
−
I r
)/
K with K
= (
I t
+
I r
) −
F ; see [90].
x
Density irregularities in the corona may be specified approximately by an irregularity factor
=
N e
2 /(
N e
) 2
, where N e is the electron density. Then rms N e
= ¯ e x
1
/
2
. In the striated outer corona one might write x 1
/ f
.
f
., where f.f. is the filling factor, which could be very small indeed. Only approximate data exist (see
Table 14.18). x varies with r
/
R
.
Temperature of corona:
Loops
Quiet corona T max at r 2R
Coronal condensation
Coronal hole
(1.0–3.0)
×
10
6
1
.
6
×
10
6
K.
3
×
10
6
1
×
10
6
K.
K.
K .
Table 14.18. Radial variations of p, , and x for homogeneous and minimum cycle corona at 0.55
µ m [1–3]. r
/
R 1.0
1.2
1.5
2 3 5 10 20 25
Polarization in % p tot at equator p tot at pole
Ellipticity , minimum corona
Irregularity x
20
20
0.06
35
25
0.10
41
17
0.16
>
38
10
0.13
2.5
21
3
0.11
4
10
<
1
0.12
8
4
0.18
17
2.6
0.25
21 25
References
1. Saito, K. 1972, Ann. Tokyo Astron. Obs. XII, 53, 120
2. Koutchmy, S., Picat, J.P., & Dantel, M. 1977, A&A, 59, 349
3. Allen, C.W. 1961, Solar Corona IAU Symp., 16, 1

Sp.-V/AQuan/1999/10/10:10:02 Page 359
14.8 C
ORONA
/ 359
ρ = r
/
R
1.003
1.005
1.01
1.03
1.06
1.10
1.2
1.4
1.6
2.0
2.5
3.0
4.0
5.0
10.0
20.0
Table 14.19. Smoothed coronal brightness and electron density in average models [1–5]. log
( surface brightness
) log
(ρ
−
2.5
−
2.3
−
2.0
−
1.5
−
1.2
−
1.0
−
0.7
−
0.4
−
0.2
0.0
+
0.2
+
0.3
+
0.5
+
0.6
1.0
1.3
−
1
)
Max.
4.9
4.65
4.45
4.3
3.9
3.34
2.92
2.23
1.63
1.23
0.70
0.3
−
0.5
K
Eq.
10
−
10
B
Min.
Pole
4.8
4.6
4.35
4.20
3.75
3.26
2.88
2.25
1.63
1.25
4.25
4.10
3.85
3.60
3.06
2.5
1.95
1.24
0.7
0.25
−
0.61
−
0.35
0.2
0.75
−
0.75
· · ·
F
Eq.
/
Pole
· · ·
· · ·
· · ·
3.10
2.90
2.50
2.25
1.91/1.82
1.66/1.56
1.48/1.33
1.23/1.03
1.0/0.80
Max.
Min.
9.0
8.8
8.7
8.6
9.0
8.8
8.7
8.6
8.4
8.4
8.25
8.25
Eq.
Pole
(cm
−
3 )
−
8.20
· · ·
8.0
· · ·
· · ·
7.50
7.90
7.8
7.44
7.35
7.05
6.52
6.00
5.60
5.1
4.8
log N e
7.05
6.50
5.95
5.50
5.05
4.75
0.31/0.06
4.10
4.05
−
0.33/
−
0.72
3.2
7.10
6.25
5.95
5.0
4.75
4.50
4.20
4.0
References
1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London), Secs. 73, 84, and 85
2. Newkirk, G., Dupree, R.G., & Schmahl, E.J. 1970, Solar Phys., 15, 15
3. Koutchmy, S., Zirker, J.B., Steinolfson, R.S., & Zhugzda, J.D. 1991, in Solar Interior and
Atmosphere, edited by A.N. Cox, W.C. Livingston, and M.S. Matthews (University of Arizona Press,
Tucson)
4. Blackwell, D.E., & Petford, A.D. 1966, MNRAS, 131, 383
5. Saito, K. 1972, Ann. Tokyo Astron. Obs. XII, 53, 120
eee
Assuming spherical symmetry, the distribution of coronal intensity I
0 radial distance
ρ may be used to determine the distribution of N e as a function of the projected as a function of radial distance r in
Table 14.20. The classical Baumbach expressions [92] are
10
6
I
0
/
I
=
0
.
0532
ρ −
2
.
5 +
1
.
425
ρ −
7 +
2
.
565
ρ −
17 , leading to
N e
( r
) =
10
8 (
0
.
036r
−
1
.
5 +
1
.
55r
−
6 +
2
.
99r
−
16 ) cm
−
3 .
The temperature in the inner corona is well described by the approximation of hydrostatic equilibrium [89] with T hyd
=
6
.
08
×
10
6
[d
( log N e
)/ d
( r
−
1 )
]
−
1 in K, assuming H
/
H e
=
10.

Sp.-V/AQuan/1999/10/10:10:02 Page 360
360 / 14 S
UN
Table 14.20.
Electron densities
( log N e coronal structures.
( cm
−
3 )) in
Coronal Coronal streamer hole (Void) Thread Loop r
/
R
2.0
2.5
3.0
4.0
5.0
1.0
1.1
1.3
1.5
10.0
8.75
8.25
7.90
7.30
7.0
6.75
6.3
6.1
5.45
7.0
6.6
6.2
5.25
4.80
10.0
9.5
9.0
8.25
10.0
9.0
Coronal line spectrum quantities are:
T m
= temperature (K) at which spectrum reaches greatest intensity
, f
= energy flux (10
−
6
W cm
−
2
) from the coronal line seen outside the Earth’s atmosphere
,
W
= equivalent width of coronal line in terms of K continuum
,
A
= transition probability (s
−
1
)
.
Tables 14.21, 14.22, 14.23, and 14.24 give some permitted, forbidden, and infrared coronal lines.
Table 14.21. Selected permitted lines, 1–61 nm [1–4].
λ
(nm) Ion Transition f log T m
1s
2
–1s2 p 0.92
1.21
1.36
1.51
1.69
Mg XI
Ne X , Fe XVII
Ne IX
Fe XVII
Fe XVII
1s
2
2 p
6
2 p
6
–1s2 p
–2 p
5
–2 p
5
3d
3s
2 6.4
1
2 6.20
8 6.58
9 6.58
1.90
2.16
5.06
6.97
17.10
17.48
17.72
18.04
18.83
19.50
20.20
21.13
28.41
30.34
33.54
O VIII
O VII
Si X
Fe XIV
Fe IX
Fe
Fe
Fe
Fe
Fe
Si
Fe
X
Fe X
Fe XI
Fe XI
XII
XIII
XIV
XV
XI
XVI
1s–2 p
1s
2
–1s2 p
2 p–3d
8 6.36
6 5.9
6 6.14
3 p–4s 4 6.27
3 p
6
–3 p
5
3d 85 5.85
3 p
5
–3 p
4
3d 90 6.00
3 p
5
3 p
4
–3 p
4
3d 33 6.00
–3 p
3
3d 75 6.11
3 p
4
3 p
3
–3 p
3
3d 40 6.11
–3 p
2
3d 60 6.16
3 p
2
–3 p3d
3 p–3d
3s
2
–3s3 p
2s
2
–2s2 p
3s–3 p
25
15
40
30
20
6.21
6.27
6.31
6.22
6.40

Sp.-V/AQuan/1999/10/10:10:02 Page 361
14.8 C
ORONA
/ 361
λ
(nm) Ion
Table 14.21. (Continued.)
Transition
36.81
49.9
61.0
Mg
Si
Mg
IX
XII
X
2s
2
–2s2 p
2s–2 p
2s–2 p f log T
15 5.97
10 6.27
12 6.04
m
References
1. Batstone, R.M., Evans, K., Parkinson, J.H., & Pounds,
K.A. 1970, Solar Phys., 13, 389
2. Walker, A.B.C., & Rugge, R.H. 1970, A&A, 5, 4
3. Jordan, C. 1965, Commun. Univ. London Obs., 68
4. Freeman, F.F., & Jones, B.B. 1970, Solar Phys., 15, 288
Table 14.22. Selected forbidden lines, 100–300 nm [1, 2].
λ nm Ion Transition log T m
124.22
134.96
144.60
146.70
212.60
214.95
216.97
Fe
Fe
Si
Fe
Ni
XII
XII
VIII
XI
XIII
Si IX
Fe XII p p
3 4
3 4
2 p
3 p
S
S
3 4
4 3
1
1
1
2
1
2
S
1
1
–
–
2
2
–
P
1
2
–
1
P
P
2
S
0
1
1
2
D
1
2
1
1
2
3 p
2 p
3 p
4 3
2 3
3 p
P
2
–
1
P
2
4
S
–
1
1
1
2
D
2
D
–
2
2
D
2
1
2
6.16
6.16
5.93
6.11
6.27
6.04
6.16
References
1. Jordan, C. 1971, Eclipse of 1970, COSPAR Symp.
2. Gabriel, A.H. et al. 1971, ApJ, 434, 807
Table 14.23. Selected forbidden lines, 300–700 nm [1–3].
λ
(nm) Ion Transition
332.9
338.82
360.09
423.20
Ca
Ni
XII
XII
2 p
Fe XIII 3 p
Ni XVI 3 p
3 p
5 2
P
1
2 3
2
P
P
2
1
2
–
–
2
1
2
1
P
1
P
1
1
2
2
5 2
P
1
1
2
–
2
D
2
530.281
Fe XIV 3 p
569.44
637.45
670.19
Ca
Fe
Ni
XV
X
XV
2 p
3 p
3 p
2
P
2 3
5 2
1
2
P
0
P
1
–
2
P
1
1
1
2
–
3
–
P
2
1
P
2 3
P
0
2
–
3
P
1
1
2
Upper
E.P. (eV) (s
3.72
5.96
3.44
2.93
2.34
2.18
1.94
1.85
A
−
1
488
87
193
237
60
95
69
57
) (10
−
10
W nm
0.07
1.0
0.13
0.11
2.0
0.03
0.5
0.12
× ¯
) log T
6.19
6.19
6.37
6.17
6.27
6.00
6.32
m
References
1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London),
Secs. 73, 84, and 85
2. Livingston, W., & Harvey, J. 1982, Proc. Ind. Natl. Sci. Acad., 48, Suppl. 3, 18
3. Jefferies, J.T., Orrall, F.Q., & Zirker, J.B. 1971, Solar Phys., 16, 103

Sp.-V/AQuan/1999/10/10:10:02 Page 362
362 / 14 S
UN
λ
Ion
789.19
[Fe XI ]
1074.617
[Fe XIII ]
1079.783
[Fe XIII ]
1083.0
He I
1252.0
[S IX ]
1283.0
1431.0
H I
[Si X ]
1523.0
1856.0
1876.0
1922.0
2167.0
2747.0
3019.0
Table 14.24. Near IR lines [1, 2]. a
[Cr XI ]
[Cr XI ]
H I
[Si XI ]
H I
[Al X ]
[Mg VIII ]
(
10
−
2 f
W m
−
2 sr
−
1 )
Transition
1.5
3 p
4 3
3 p
2 3
3 p
2 p
2 3
3
P
2
–
3
P
0
–
3
P
1
–
3
P–2s
P
P
1
1
3
P
2
S
1s
2
2s
2
2 p
4 3
P
1
–
3
P
2
3.00
1.55
0.47
0.4
13.0
<
0.7
<
0.5
<
1
<
1
Paschen (5–3)
1s
2
2s
2
2 p
2
P
3
2
3s
3s
2
2
3 p
3 p
2 3
2 3
P
2
–
3
P
1
–
3
Paschen (4–3)
–
2
P
1
P
0
P
1
2
1s
2
2s2 p
3
P
2
–
3
P
1
Brackett (7–4)
1s
1s
2
2
2s2 p
2s
2
2 p
3
P
2
2
P
–
3
3
2
–
P
2
1
P
1
2
Note a
Kuhn [3] points out that many of the IR lines in this table were not observed at the eclipse of 3 Nov. 1994 and questions their reality.
References
1. Olsen, K.H., Anderson, C.R., & Stewart, J.N. 1971, Solar Phys., 21, 360
2. Penn, M.J., & Kuhn, J.R. 1994, ApJ, 434, 807
3. Kuhn, J. 1995, private communication
The inclination of the solar equator to the ecliptic [93–96] is 7
◦
The longitude of the ascending node is 75
15 .
◦
46
+
84 T , where T is epoch in centuries from 2000.00.
The sidereal differential rotation coefficients from the formulas
ω =
A
+
B sin
2 φ deg
/ day
, where
φ is the latitude, and
ω =
A
+
B sin
2 φ +
C sin
4 φ deg
/ day
, are often used for features that extend to higher latitudes. These are given in Table 14.25. See also [97].

Sp.-V/AQuan/1999/10/10:10:02 Page 363
14.9 S
OLAR
R
OTATION
/ 363
Table 14.25. Empirical rotation coefficients.
A B
Individual sunspots [1]
Sunspot groups [1, 2]
Plages [3]
Magnetic field pattern [4]
Supergranular pattern [5, 6]
(Doppler features)
Filaments, prominences [7]
Coronal features [8, 9]
Small magnetic features [10]
From tracers
14.522
14.39
14.06
14.37
14.71
14.48
13.46
14.42
−
−
−
−
−
2.84
2.95
1.83
2.30
2.39
−
2.16
−
2.99
−
2.00
From the Doppler effect in solar lines
Surface plasma [11]
H
α line [12]
14.11
14.1
−
1.70
C
−
−
−
−
1.62
1.78
2.09
2.35
References
1. Howard, R., Gilman, P.A., & Gilman, P.I. 1984, ApJ, 283, 373
2. Balthasar, H., Vazquez, M., & Woehl, H. 1986, A&A, 155, 87
3. Howard, R.F. 1990, Solar Phys., 126, 299
4. Snodgrass, H.B. 1983, ApJ, 270, 288
5. Duvall, Jr., T.L. 1980, Solar Phys., 66, 213
6. Snodgrass, H.B., & Ulrich, R. 1990, ApJ, 351, 309
7. d’Azambuja, M., & d’Azambuja, L. 1948, Ann. Observ. Paris, 6, 1
8. Dupree, A.K., & Henze, Jr., W. 1972, Solar Phys., 27, 271
9. Henze, Jr., W., & Dupree, A.K. 1973, Solar Phys., 33, 425
10. Komm, R.W., Howard, R.F., & Harvey, J.W. 1993, Solar Phys., 145, 1
11. Snodgrass, H.B., Howard, R., & Webster, L. 1984, Solar Phys., 90, 199
12. Livingston, W.C. 1969a, Solar Phys., 7, 144; 1969b, 9, 448
Rotation of solar plasma as a function of depth from oscillation measurements increases from the surface rate by about 0.8 deg/day at a depth from 0.01R to 0.08R , then decreases slowly with depth [98, 99].
The period of sidereal rotation adopted for heliographic longitudes is 25.38 days. The corresponding synodic period is 27.275 3 days. Conversion factors between different units are given in
Table 14.26.
Table 14.26. Conversion factors.
To convert from Multiply by deg/day to
µ rad s
−
1 deg/day to m s
− 1 deg/day to nHz
0.202 01
140.596 cos
32.150
φ
Sidereal—synodic rotation
=
Earth’s orbital motion
=
0
.
985 6 deg/day (averaged over a year).

Sp.-V/AQuan/1999/10/10:10:02 Page 364
364 / 14 S
UN
The solar surface is covered by a hierarchy of patterns that are convective in origin: granulation, mesogranulation, and supergranulation [98–109]:
Granules
Diameter of granules
Range about 0
.
25 to 3
.
5
Intergranular distance 1
.
0
Number of granules on whole photospheric surface 5
×
10
Corresponding area occupied by a cell
1
.
4
=
1000 km
6
1
.
5
×
10
6 km
2
Granule intensity contrast
Brighter granule/intergranule 1.3
Corresponding temperature difference
Root-mean-square variations
300 K
Intensity at 550 nm observed
Corrected
Temperature
Mean lifetime of granules
Upward velocity of brighter granules
0.09
0.15
110 K
10 min
1 km s
−
1
Mesogranulation
Diameter
Lifetime
Vertical velocity
Proper motion
5000 km
3 h
0.06 km s
−
1
0.4 km s
−
1
Supergranulation
Diameter
Lifetime
Horizontal velocity to edge
32 000 km
20 h
0.4 km s
−
1
Buoyancy lofts magnetic fields from the solar interior into the photosphere where they emerge as active regions to be dispersed laterally under the influence of convection (various scales) and other largescale horizontal flows. White light tracers of magnetism are sunspots and faculae. Monochromatic tracers (line weakening) are plage, filigree, the network, internetwork, coronal holes, and prominences.
The network and plages are presumed to be composed of aggregates of flux tubes. Prominences are found along magnetic neutral lines or above active regions. Magnetic field details for various surface structures are given in Table 14.27.

Sp.-V/AQuan/1999/10/10:10:02 Page 365
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URFACE
M
AGNETISM AND ITS
T
RACERS
/ 365
Table 14.27. Magnetic fields. a
Field strength
Sunspot umbrae
Sunspot penumbrae
Pores
Plage or facular magnetic elements B
( z
=
0
)
Network magnetic elements B
( z
=
0
)
Internetwork
Flux [1]
Ephemeral region
Small active region
Moderate active region
Large active region
Giant active region
Magnetic elements
Diameter [2, 3]
Lifetime [4]
Global aspects [1]
Total flux at solar min
Total flux at solar max
2–4 kG
0.8–2 kG
1.7–2.5 kG
1.4–1.7 kG
1.3–1.5 kG
≤
600 G (probably)
3
×
10
19
3
×
10
20
Mx
Mx
3
×
10
21
≥
10
22
Mx
Mx
= (
20–50
) ×
10
22
Mx
200–300 km
18 min
= (
15–20
) ×
10
22
Mx
= (
100–120
) ×
10
22
Mx
Note a
The field strength is strongly height dependent.
See Sec. 14.12 on sunspots for more information on sunspot field gradients. For magnetic elements the field drops from the tabulated values at z
=
0 (i.e., the quiet Sun continuum forming layer) to roughly 200–500 G (in plage) near the temperature minimum (e.g., [6] and [7]). The magnetic element lifetime [5] is probably only a lower limit, being a lifetime measurement of the brightness structure that probably lives less long than the underlying magnetic structure. There is no permanent dipole field but one develops over solar cycle due to evolution of polar fields; at other times there is a dipole component to lower-latitude extended active-region fields [8, 9]. Mx means maxwell
(G cm
2
).
References
1. Harvey, K. 1992, in Proceedings of the Workshop on Solar Electromagnetic
Radiation Study for SOLAR CYCLE 22, edited by R.F. Donnelly (Natl. Info. Tech.
Service, Springfield, VA), p. 113
2. Keller, C.U. 1992, Nature, 359, 307
3. Grossmann-Doerth, U., Kn¨olker, M., Sch¨ussler, M., & Solanki, S.K. 1994, A&A,
285, 648
4. Muller, R. 1985, Solar Phys., 100, 237
5. Deming D., Boyle, R.J., Jennings D.E., & Wiedemann, G. 1988, ApJ, 333, 978
6. Zirin, H., & Popp, B. 1989, ApJ, 340, 571
7. Sheeley, Jr., N.R., & Boris, J.P. 1985, Solar Phys., 98, 219
8. Wang, Y.M., & Sheeley Jr., N.R. 1989, Solar Phys., 124, 81
Faculae are cospatial with photospheric magnetic fields. They become visible in white light near the limb (i.e., as
µ = cos
θ →
0
)
. While fragmented and irregular, they do tend to outline the circular boundaries of supergranular cells [112, 113].
The center-to-limb dependence of wide-band facular contrast (integrated over the spectral range
0.35–1.0
µ m) can be expressed as
C
(µ) −
1
=
0
.
115
(
1
− µ),

Sp.-V/AQuan/1999/10/10:10:02 Page 366
366 / 14 S
UN where
C
(µ) =
I facula
/
I photosphere
[114]. At the highest spatial resolution values of C
(µ
) increase by a factor of 3–4 [115].
The wavelength dependence of facular contrast is approximately given by
C λ
(µ) −
1
=
[C
5300
(µ) −
1]0
.
5
λ −
1 , where C
5300
(µ) is the intensity of the faculae relative to the photosphere at 5300 ˚
Life of average faculae 15 days
Life of large faculae (dominating solar variations) 2.7 months
The excess temperature of magnetic elements [117, 118] is given in Table 14.28.
Table 14.28. Excess temperatures. log
τ
5000
−
5
−
4
−
3
−
2
−
1 0
Plage: T
Magel
Network: T
−
T phot
Magel
(K)
−
T phot
1400 1500 650 500 560
(K) 1400 1500 700 700 770
−
130
460
Plages or bright flocculi are readily visible in H
α and in the H and K lines of Ca II . The locations agree well with faculae but plages are visible over the whole disk. Measurements of area and eye estimates of intensity (scale 1
→
5) are made regularly [119].
Table 14.29 shows the approximate relation between plage area and sunspot area (both in 10
−
6 hemisphere).
Plage area
Sunspot area
Table 14.29. Plage and sunspot areas.
500 1000 2000 3000 4000 6000 8000 10 000
0 30 100 180 280 500 900 2000
Since the duration of the plage is longer than that of the spot, the spot area may be much less than the value given. Normally sunspots are present when the plage intensity is
≥
3.
The exponential decay time of a plage observed area is 1.6 rotations (43 days). The actual area of a plage expands continuously but the fainter parts are below measurement threshold.
Values for a typical large active region [115] are:
Sunspot area
Plage area
Plage diameter
600
×
6000
10
×
−
6
10
Plage area at disk center 12 000
×
10
3
.
5 arcmin.
−
6 hemisphere.
hemisphere.
−
6 disk.

Sp.-V/AQuan/1999/10/10:10:02 Page 367
Table 14.30 shows the physical conditions in quiescent prominences.
14.12 S
UNSPOTS
/ 367
Table 14.30. Quiescent prominences. log [electron density
( cm
−
3 )
] Temperature (K)
10.48–11.02 [1]
9–10
5000–7000
20 000–600 000 [2]
References
1. Hirayama, T. 1986, Coronal and Prominence Plasmas, edited by A.I. Poland (NASA, Washington, DC), p. 2442
2. Orrall, F.Q., & Schmahl, E.J. 1980, ApJ, 240, 908
The temperature varies considerably within a prominence.
The proton-to-hydrogen density ratio is 0
.
05
<
N p
/
N
H
<
1 [120].
Sizes
Threads [121]
Height
300–1800 km (diameter).
2000 km (active),
10 000–50 000 km (quiescent).
Length
Thickness
50 000–200 000 km.
3000–5000 km.
Magnetic field (horizontal) 2–20 G (quiescent) [122],
Velocity
10–40 G (active).
15–35 km s
1–3 km s
−
1
−
1
(threads, apparent) [123],
2–10 km s
−
1
(Doppler, horizontal) [124],
(turbulent).
The angle of the field with the axis of the prominence
∼
20
◦
[122].
Lifetimes are approximately 1 week to 3 months; the average is 2 months.
The formula for the center-to-limb variation of umbral brightness (1
≥ µ >
0
.
3) is i u
(µ, λ) = i u
(µ =
1
, λ) − b u
(λ)(
1
− cos
θ), i u
=
I u
/
I q
, where I q is the quiet Sun brightness, and i p
=
I p
/
I q given in Table 14.31.
. Brightness data for sunspots are

Sp.-V/AQuan/1999/10/10:10:02 Page 368
368 / 14 S
UN
Table 14.31. Center-to-limb variation and
λ
dependence of umbral and penumbral brightness [1–4].
λ (µ m) i u
(µ =
1
, λ) early i u
(µ =
1
, λ) middle i u
(µ =
1
, λ) late b u
(λ) i p
(µ =
1
, λ)
−
0.387
0.010
0.64
0.579
0.022
0.061
0.191
0.327
0.451
0.507
0.543
0.567
0.565
0.008
0.066
0.090
0.215
0.345
0.495
0.548
0.577
0.589
0.581
0.110
0.119
0.239
0.358
0.534
0.590
0.612
0.611
0.597
0.012
0.768
0.669
0.009
0.794
0.876
0.019
0.827
1.215
0.031
0.876
1.54
0.087
1.67
0.087
0.914
1.73
0.094
2.09
0.090
0.928
2.35
0.058
References
1. Albregtsen, F., & Matby, P. 1978, Mat., 274, 41
2. Albregtsen, F., Jor˚as, P.B., & Matby, P. 1984, Solar Phys., 90, 17
3. Maltby, P. 1972, Solar Phys., 26, 76
4. Matby, P., Avrett, E.H., Carlsson, M., Kjeldseth-Moe, O., Kurucz, R.L., & Loeser, R. 1986, ApJ, 306, 284
3.8
0.936
A model for the sunspot umbral core is given in Table 14.32.
log
τ
1
Table 14.32. Model of the dark umbral core [1–4].
0
−
1
−
2
−
3
−
4
−
5
−
6
T (K) log P log P g e
z (km)
(cgs)
(cgs)
6140
5.78
2.01
−
94
4040
5.43
0.52
0
3540
4.91
−
0.28
−
0.80
−
1.28
−
1.75
−
1.96
−
1.04
95
3420
4.28
220
3400
3.64
380
3450
2.95
600
6400
0.99
1115
8700
−
0.61
1850
References
1. Maltby, P., Avrett, E.A., Carlsson, M., Kjeldseth-Moe, O., Kurucz, R.L., & Loeser, R.
1986, ApJ, 306, 284
2. Avrett, E.H. 1981, in The Physics of Sunspots, edited by L.E. Cram and J.H. Thomas
(Sacramento Peak Obs., Sunspot, NM), p.235
3. Van Ballegooijen 1984, A&A, 91, 195
4. Obridko, V.N., & Staude, J. 1988, A&A, 189, 232
Magnetic field data for sunspots are given in Tables 14.33 and 14.34.
Table 14.33. Maximum magnetic field B
0 as a function of umbral radius r u
[1, 2]. r u
(km)
B
0
(G)
500
2000
1000
2000
2000
2000
4000
2300
6000
2700
8000
3100
10000
3500
References
1. Brants, J.J., & Zwaan, C. 1982, Solar Phys., 80, 251
2. Kopp, G., & Rabin, D. 1992, Solar Phys., 81, 231

Sp.-V/AQuan/1999/10/10:10:02 Page 369
14.12 S
UNSPOTS
/ 369
Table 14.34. Relative magnetic field B
/
B
0 and its inclination
γ relative to the vertical versus
position in spot r for a large symmetric sunspot [1–5]. r
/ r p
0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
B
/
B
0
1 0.99
0.96
0.92
0.84
0.74
0.62
0.50
0.41
0.35
0.30
γ
(deg) 0 7 15 24 35 48 58 66 73 77 80
References
1. Solanki, S.K., R¨uedi, I., & Livingston, W. 1992, A&A, 263, 339
2. McPherson, M.R., Lin, H., & Kuhn, J.R. 1992, Solar Phys., 139, 255
3. Lites, B.W., & Skumanich, A. 1990, ApJ, 348, 747
4. Kawakami, H. 1983, PASJ, 35, 459
5. Adam, M.G. 1990, Solar Phys., 125, 37
The azimuthal angle of the field is
φ ≤
20
◦ for symmetric sunspots. In the penumbra
γ is an average value, with bright and dark filaments inclined relative to each other by 20
◦
–40
◦
[125–127].
In the outer penumbra the inclination depends on the size of the sunspot, with smaller sunspots having more vertical fields [128].
Table 14.35 gives structure details of the outer parts of sunspots.
Table 14.35. Superpenumbral canopy: Base height z c as a function of distance from center of spot r
/ r p normalized by the spot radius r p
[1, 2]. r
/ r p
1.0
1.2
1.4
1.6
Base height z c
(km)
B
/
B
0
γ
(deg)
0
0.30
80
200
0.21
86
300
0.15
89–90
350
0.11
89–90
References
1. Giovanelli, R.G. 1980, Solar Phys., 68, 49
2. Giovanelli, R.G., & Jones, H.P. 1982, Solar Phys., 79, 267
Table 14.36 gives the magnetic field gradients in sunspots.
Table 14.36. Vertical gradient of the field [1–7]. r
/ r p d B
/
d z in photosphere (G/km) d B
/
d z in photosphere and chromosphere (G/km)
0.0
2
0.5
0.6
2
0.4
1.0
1
0.2
References
1. Bruls, J.H.M.J., Solanki, S.K., Carlsson, M., & Rutten, R.J. 1993, A&A, 293, 225
2. Abdussamator, H.J. 1971, Solar Phys., 16, 384
3. Henze, N., Jr., Tandberg-Hanssen, E., Hagyard, M.J., Woodgate, B.E., Shine, R.A.,
Beckers, J.M., Bruner, M., Gurman, J.B., Hyder, L.L., & West, E.A. 1982, Solar
Phys., 81, 231
4. Lee, J.W., Gary, E.E., & Hurford, G.J. 1993, Solar Phys., 144, 45 and 349
5. R¨uedi, I., Solanki, S.K., & Livingston, W. 1994, A&A, 293, 252
6. Whittman, A.D. 1974, Solar Phys., 36, 29
7. Pahlke, K.-D. 1988, Ph.D. thesis, University of G¨ottingen, G¨ottingen, Germany

Sp.-V/AQuan/1999/10/10:10:02 Page 370
370 / 14 S
UN
Wilson depression. The apparent depression of
τ =
1 of the umbra seen near the limb [129–132] and derived from MHS equilibrium [133, 134] is z
W
=
600
±
200 km
.
u
The relative magnetic flux in umbra and penumbra [135], with t the magnetic flux of the umbra, and p the total magnetic flux of spot, the magnetic flux of the penumbra, is u
/ t p
/ t
=
1
/
3
−
1
/
2
,
=
1
/
2
−
2
/
3
.
The variation of the umbral-to-photosphere intensity ratio
φ with solar cycle (at
λ =
1
.
67
µ m) is
φ =
0
.
44
+
0
.
15t
/ t
0
, where t is the time elapsed from the starting epoch and t
0 is the length of the solar half-cycle [136].
The average East–West inclination of field lines in spots is all spots leading
−
−
3
2 following spots
−
3
.
.
.
◦
◦
◦
4,
8,
8.
The negative angle indicates that the field lines trail the rotation [137].
Sunspot axial tilt angles (individual sunspots) are the angles between the line joining the leading and following spots of a group and the local parallel of latitude. The leading spots on average are closer to the equator than the following spots as a function of latitude with the value of about 2
◦ at the equator to about 12
◦ at
±
35
◦ latitude [138–141].
The area distribution of individual sunspots can be described as a two-parameter log-normal distribution [142]: ln d N d A
= −
( ln A
− ln A
) 2
2 ln
σ a
+ ln d N d A max in terms of sunspot umbral area A (in units of 10
−
6
2
π
R
2
). Values of the three other quantities in the above equation (Table 14.37) depend somewhat on the range of umbral areas used to derive them:
Table 14.37. Sunspot area distribution.
Range A
σ a
( d N
/ d A
) max
1.5–141
5.5–116
0.62
0.34
3.8
4.8
9.2
16.4
The sunspot number is defined as
R
= k
(
10g
+ s
), where k is an observatory reduction constant of order unity, g is the number of sunspot groups, and s is the total number of individual spots [143–145]. Prior to January 1981, R was referred to as the Zurich sunspot number. From January 1981 on, R has been referred to as the International sunspot number.

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S
TATISTICS
/ 371
Monthly values of R are combined to yield the 12-month moving average of R (denoted R
0
), which is also known as the smoothed sunspot number [146]. For a cycle, the minimum value of R
0 denotes the sunspot minimum (R m
), while the maximum value denotes the sunspot maximum (R
M
).
Conventionally, the length of a sunspot cycle is determined from minimum to minimum (m
↔ m
) and is comprised of two parts: the ascent interval, the time from minimum to maximum
( m
↔
M
)
, and the descent interval, the time from maximum to succeeding cycle minimum
(
M
↔ m
)
. Occasionally, the time between maxima is also of interest
(
M
↔
M
)
. Each sunspot cycle is numbered with the most recent sunspot cycle being cycle 22
(
R m occurred in September 1986 and R
M occurred in July 1989).
The sunspot record is of uneven quality [144]. The most reliable sunspot data extend from the present back to about 1850 and 1818 (covering cycles 7–9), while data of poor quality occur for earlier times (cycles before cycle 7). Some evidence exists suggesting that there was an extensive period of time when sunspots were few in number [147]. This interval of time (ca. 1645–1715; cycles
−
9 to
−
4) is often referred to as the Maunder minimum.
Other information from the sunspot record follows:
Waldmeier effect. The sunspot amplitude (R
M
) varies inversely with the ascent duration (m
↔
M
)
.
Hale cycle. The magnetic polarity changes in alternate cycles (even-numbered cycles have leading spots of southern polarity in the northern hemisphere, and vice versa).
Sp¨orer law. The latitude of sunspots progresses equatorward with the phase of the solar cycle
(yielding the so-called butterfly diagram).
Odd–even effect. The odd-following cycle tends to be of larger amplitude than the even-preceding cycle.
Gleissberg effect. Sunspot cycles vary according to an 8-cycle variation (the so-called 80–100 year variation).
Tables 14.38 and 14.39 list the sunspot number variations over the solar cycle.
Table 14.38. Variation of the annual sunspot number over the solar cycle (based on the reliable data of cycles [10–21]). a
Parameter
Mean
Standard deviation
High
Low
0 1 2
Elapsed time (yr) from sunspot minimum occurrence year
3 4 5 6 7 8 9 10
6.2
18.9
5.9
16.7
60.2
38.6
99.4
50.0
107.0
41.1
98.5
36.6
79.1
27.6
52.4
19.7
36.5
19.6
21.2
13.4
12.0
10.4
28.4
89.2
201.3
253.8
202.5
217.4
153.8
108.5
88.4
60.7
55.8
0.0
0.0
10.4
24.5
39.3
17.8
34.4
14.8
0.3
1.6
0.2
Note a
Values listed are monthly mean values based on cycles 10–21 only.
Table 14.39. Variation of the smoothed sunspot number over the solar cycle (based on the reliable data of cycles [10–21]). a
Parameter
Mean
Standard deviation
High
Low
0 12 24 36
Elapsed time (month) from R m
48 60 72 84 96 108 120 132
5.1
18.6
3.2
6.1
61.6
23.9
98.0
109.2
41.2
41.3
99.3
33.9
79.9
52.4
34.7
20.4
11.7
11.7
25.9
14.9
13.9
9.8
8.3
7.4
12.2
26.3
118.7
181.0
196.8
169.2
119.6
70.5
60.6
41.3
30.3
15.4
1.5
9.3
35.5
52.5
54.5
56.9
48.0
31.2
13.8
11.5
3.2
2.6
Note a
Values listed are smoothed sunspot number values based on cycles 10–21 only.
Characteristics of all the known sunspot cycles are listed in Table 14.40. Mean values are listed in
Table 14.41.

Sp.-V/AQuan/1999/10/10:10:02 Page 372
372 / 14 S
UN
Table 14.40. Characteristics of sunspot cycles [1]. a
Data quality Cycle
P
Maximum M epoch R
M
Minimum m epoch R
M m
↔ m m
↔
M M
↔ m M
↔
M
−
12 1615.5
−
11 1626.0
−
10 1639.5
−
9 1649.0
−
8 1660.0
−
7 1675.0
−
6 1685.0
−
5 1693.0
−
4 1705.5
−
3 1718.2
−
2 1727.5
−
1 1738.7
0 1750.3
1610.8
1619.0
1634.0
1645.0
1655.0
1666.0
1679.5
1689.5
1698.0
1712.0
1723.5
1734.0
92.6
1745.0
14.0
11.5
10.5
11.0
10.3
1 1761.5
86.5
1755.3
8.4
11.2
2 1769.8
115.8
1766.5
11.2
9.0
3 1778.4
158.5
1775.5
4 1788.2
141.2
1784.8
5 1805.2
49.2
1798.4
7.2
9.5
3.2
9.3
13.6
12.3
6 1816.3
48.7
1810.7
0.0
12.7
8.2
15.0
11.0
10.0
11.0
13.5
10.0
8.5
6.2
3.3
2.9
3.4
6.8
7.5
6.2
4.0
4.7
5.3
5.6
4.7
7.0
5.5
4.0
5.0
9.0
5.5
3.5
Intervals (yr)
3.5
8.0
5.5
6.0
6.0
4.5
4.5
5.0
6.5
5.3
6.5
6.3
4.9
5.0
5.7
6.4
10.2
5.5
7.1
12.5
12.7
9.3
11.2
11.6
11.1
8.3
8.6
9.8
17.0
11.1
10.5
13.5
9.5
11.0
15.0
10.0
8.0
F
R
7 1829.9
71.7
1823.4
8 1837.3
146.9
1833.9
0.1
7.3
10.5
9.7
9 1848.2
131.6
1843.6
10.5
12.4
10 1860.2
97.9
1856.0
11 1870.7
140.5
1867.3
12 1840.0
13 1894.1
74.6
1879.0
87.9
1990.3
14 1906.2
64.2
1902.1
15 1917.7
105.4
1913.7
16 1928.3
78.1
1923.7
3.2
11.3
5.2
11.7
2.2
10.7
5.0
11.8
2.6
11.6
1.5
10.0
5.6
10.1
17 1937.3
119.2
1933.8
18 1947.4
151.8
1944.2
19 1958.3
201.3
1954.3
20 1968.9
110.6
1964.8
3.4
7.7
3.4
9.6
10.4
10.1
10.5
11.7
21 1980.0
164.5
1976.5
12.2
10.3
22 1989.6
158.5
1986.8
12.3
6.5
3.4
4.6
3.5
3.2
4.0
4.1
3.5
2.8
4.2
3.4
5.0
3.8
4.1
4.0
4.6
4.0
6.3
7.8
7.1
8.3
6.3
8.0
7.5
6.0
5.5
6.9
6.9
6.5
7.6
6.8
13.6
7.4
10.9
9.0
10.1
10.9
10.6
11.1
9.6
12.0
10.5
13.3
10.1
12.1
11.5
10.6
Note a
R denotes a “reliable” data interval, F denotes a “fair” interval, and P denotes a “poor” interval.
Reference
1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London), Sec. 87
Table 14.41. Mean values for selected sunspot cycle parameters.
Parameter m
↔
m period (yr)
M
↔
M period (yr) m
↔
M ascent interval (yr)
M
↔
m descent interval (yr)
R
M
R m
R
Mean value
R
+
F All
(
R
+
F
+
P
)
10.9
10.9
3.9
7.0
10.9
10.8
4.0
6.8
119.6
119.0
5.7
5.7
11.0
11.0
4.7
6.3
112.9
6.0

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Table 14.42 shows how certain solar activity characteristics vary throughout the sunspot cycle.
0
Minimum
1 2
Table 14.42. Solar activity.
3 4 5
Maximum
6 Year
Sunspot regions
R new cycle 68 237 488 547 561 510 360 269 168 99 38 13
R old cycle 9 7 3
Spot latitude 24 22 19 17 14 13 12 10 9 8 7 6
Low
To high
16
42
7
39
3
40
1
42
Latitude range
0
38
0
37
0
33
7
0
28
8
0
24
9 10 11
0
20
1
16
1
9
Characteristics of an average size sunspot group:
Sunspot number R
=
12
.
Number of individual spots 10.
Spot area (umbra
+ penumbra) 200 millionths of hemisphere,
260 millionths of disk.
Spot radius (if a single spot)
Ca II plage area
0.020R .
1800 millionths of hemisphere.
[148, 149]
The H
α line importance classes are detailed in Table 14.43.
S
1
2
3
4
Table 14.43. Classes of optical importance in the H
α line.
H
α importance Area (10
−
6 hemisphere) Mean duration
A
<
200
200
<
A
<
500
500
<
A
<
1200
1200
<
A
<
2400
A
>
2400 few minutes
25 min
55 min
2 hr
2 hr
H
α brilliance: f
= faint, n
= normal, b
= bright
Temperature
∼
15 000 K
Density
∼
3
×
10
13 cm
−
3

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Frequency of observed importance
≥
1 flares:
Frequency near solar maximum 1000–2000 flares per year.
Frequency near solar minimum 20–60 flares per year.
White-light flares [150, 151]:
Frequency near solar maximum
∼
15 per year.
Luminosity 10
27
–10
28 erg s
−
1
.
[152]
Bn
= n
×
10
−
7
Mn
= n
×
10
−
5
W m
W m
−
2
−
2
,
,
Cn
= n
×
10
−
6
X n
= n
×
10
−
4
W m
W m
−
2
−
2
,
.
Frequency of
≥
M1 flares near solar maximum
∼
500 per year.
Frequency of
≥
M1 flares near solar minimum
∼
15 per year.
Peak temperatures
Peak emission measures
( n
2 e
Density
(8–22)
×
10
6
V
)
10
48
–10
50
10
10
–10
12 cm
K.
−
3 cm
−
3
.
.
The duration is from
<
1 min to
>
30 min; the median duration
∼
100 s. The
γ
-ray fluence [154] from
<
10 to 10
4 γ cm
−
2 at
>
300 keV; from
<
0
.
3 to 3
×
10
2 γ cm
−
2 for 4–8 MeV lines. For hard
X-rays [155, 156]:
Peak flux at E
>
20 keV from
<
10
−
6
Spectra: 3
< γ <
9, where N
(
E
) =
AE
Thermal fits yield T
≥
10
8
K.
to
>
10
− γ
−
3 erg cm
−
2 photons cm
−
2 s
−
1
.
s
−
1 keV
−
1
.
Peak fluxes from
<
3
×
10
−
2 to 10 erg cm
−
2 s
−
1
.
Temporal profiles match those of E
>
10 keV X-rays.
For microwaves (1000–35 000 MHz) [156]:
Peak fluxes from
<
10 to
≥
10
4
Hz
−
1
).
Temporal profiles match those of E
>
20 keV X-rays, and flux
(
E
>
20 keV) (erg cm
−
2
∼
10
−
7 × flux (3 cm) (s.f.u.).
solar flux units (s.f.u.) (10
−
22
W m
−
2 s
−
1
)
Most coronal mass ejection (CME) quantities range over about two orders of magnitude. Average values follow [158–161]:
Mass
Kinetic energy
3
×
10
15
2
×
10
30 g.
erg.

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Speeds (of leading edges) at solar maximum at solar minimum
450 km s
160 km s
Angular width (plane of sky, subtended to solar disk) 47
◦
.
−
1
−
1
.
.
Frequency [162] at solar maximum at solar minimum
2–3 CMEs per day.
0.1–0.3 CMEs per day.
Solar radio emission is expressed quantitatively in terms of the flux density S units (s.f.u.), where 1 s.f.u.
=
10
−
22
W m
−
2
Hz
−
1
ν , usually in solar flux
. For observations that spatially resolve the source of radio emission, the intensity of the radiation is often expressed in terms of its brightness temperature
T
B
, where S ν
=
7
.
22
×
10
−
51
T
B
ν 2
W m
−
2 arcsec
−
2
Hz
−
1
. T at the center of the solar disk. The degree of polarization,
ρ
C
C refers to the brightness temperature
, is defined by the ratio of the Stokes polarization parameters V and I . Expressed in terms of brightness temperature in the orthogonal
(right- and left-hand) senses of circular polarization,
ρ
C
= (
T
RCP
−
T
LCP
)/(
T
RCP
+
T
LCP
)
, where the
RCP sense corresponds to a counterclockwise rotation for radiation propagating toward the observer.
The brightness temperature of the quiet Sun at disk center may be calculated approximately from the following expressions for millimeter and centimeter wavelengths (T
C in K, u
= log
10
λ
,
λ in cm): log T
C
=
3
.
9609
+
0
.
1856u
+
0
.
0523u
2 +
0
.
13415u
3 +
0
.
0834u
4 , valid between 0.1 and 20 cm; log T
C
=
0
.
7392
+
4
.
3185u
−
0
.
9049u
2 , valid for
λ =
20–2000 cm. The fits are based on [163–165].
Storm continua and type I bursts (see below and [166]) are often associated with solar active regions.
Type I storm durations range from hours to days and are distinguished by high values of
ρ
C of a few times 10 MHz, and apparent brightness temperatures
<
10
10
K.
, bandwidths
Decimetric and microwave emission associated with active regions is characterized by [167, 168] a diffuse morphology for
λ
10 cm and a low to moderate degree of circular polarization
ρ
C
Its brightness is typical of coronal temperatures [T
B
∼ (
1–2
) ×
10
6
K]. For
λ
15%.
10 cm, the diffuse morphology gives way to one or more compact components associated with sunspot umbrae

Sp.-V/AQuan/1999/10/10:10:02 Page 376
376 / 14 S
UN and penumbrae that possess a degree of polarization that ranges from low (
ρ
C
(
ρ
C
∼ few %) to high
90%) values. The brightness of compact components is again near coronal values. Radio emission associated with solar active regions typically possesses a spectral maximum in flux density between 8 and 10 cm [169].
(i) Type I [166, 170]:
Frequency range
Bandwidth
Duration
Brightness
Polarization
Fine structure
(iv) Type IV [173, 174]:
Frequency range
Bandwidth
Duration
Brightness
Polarization
Variants
150–350 MHz.
2.5–7 MHz (
∼
0
.
025
ν
MHz;
ν in MHz).
0.2–0.7 s (
∼
80
/ν s).
As high as 10
7
–10
10
K.
Up to 100% circularly polarized.
Chains, periodic variations.
(ii) Type II [171]:
Frequency range
Bandwidth
<
20–150 MHz; harmonic structure in 60%.
∼
100 MHz.
Frequency drift rate
∼
1 MHz s
−
1
.
Duration
Brightness
5–15 min.
10
7
–10
13
K.
Polarization
Fine structures
Unpolarized or weakly circularly polarized; herringbone structure sometimes displays
∼
50% circular polarization.
Band splitting, multiple lanes, herringbone structure.
(iii) Type III [172]:
Frequency range
Variants
Full range; harmonic structure common,
Frequency drift rate
Duration
−
∼
0
1–100 MHz.
.
01
220
ν
ν
1
.
84
−
1 s.
MHz s
−
1
.
Brightness
Polarization
10
8
–10
ρ
C
12
K.
15% (harmonic);
ρ
C
(fundamental).
Type J and type U bursts.
50%
20–200 MHz.
Broadband continuum.
3–45 min.
<
10
8
–10
10
ρ
C
K.
20% (early), often increasing to high values for events with durations longer than
20 min.
Moving type IV, slow-drift continuum, type II–associated, pulsations.

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(v) Type V [172]:
Frequency range
Bandwidth
Duration
Brightness
Polarization
<
10–120 MHz.
Broadband continuum.
∼
500
ν
10
7
–10
−
1
/
2
12
K.
s.
ρ
C
10%, decreasing from disk center-tolimb, sense of polarization usually opposite to that of preceding type III bursts.
[175]
(i) Type III–like or fast-drift bursts:
Bandwidth
Duration
Drift rate
Variants
Variable.
0.5–1.0 s.
>
100 MHz s
−
1
.
Classical type III and type U bursts, dm extensions to type IIIm bursts, narrowband type III bursts (blips), long duration type III bursts.
(ii) Pulsations:
Bandwidth
Periods
Duration
Variants
Few
×
100 MHz.
Pulses recur periodically or quasiperiodically with separations of 0.1–1.0 s.
Groups of pulses (10–100 s) last from seconds to minutes.
Quasiperiodic pulsations (regular, long period), dm pulsations (irregular, short period).
(iii) Diffuse continua or type IV–like bursts:
Bandwidth Few
×
100 MHz.
Duration 10 s of seconds to minutes.
Variants Smooth continua, modulated continua, ridges.
(iv) Spikes:
Bandwidth
Duration
Variants
Few MHz.
<
0
.
1 s individually, with groups (10–10
4 occurring in broadband clusters during some seconds to minutes.
Type III–associated spikes, type IV–associated spikes.
)
Solar bursts at centimeter and millimeter wavelengths tend to be broadband continua, moderately polarized, with a brightness of a few
×
10
6
K to a few
×
10
9
K. The spectral peak is generally near 8 GHz [176]; roughly 80% of solar radio burst display more than one spectral component [177].

Sp.-V/AQuan/1999/10/10:10:02 Page 378
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