Properties of the Sunspot
Number and 10.7cm Solar Radio
Flux Indices, Their InterRelationship and Unusual
Behaviour Since the Year 2000
(How things changed during Cycle 23
and continue to change in Cycle 24)
Ken Tapping
ken.tapping@nrc-cnrc.gc.ca
F10.7 Flux Monthly Means
300
Adjusted Flux in sfu
250
200
150
100
18
50
1945
1950
19
1955
1960
20
1965
1970
21
1975
1980
Year
22
1985
1990
23
1995
2000
24
2005
2010
What Is F10.7?
F10.7
F10.7 = 10 22
2k ⎛
⎛
⎞ ⎞
⎜ T Ω + ⎜ Ω 0 − ∑ Ω 0 ⎟T0 ⎟⎟
2 ⎜∑ i i
λ ⎝ i
i
⎝
⎠ ⎠
F10.7 = 10 22
2k ⎛
⎞
⎜ (Ti − T0 )Ω i + Ω 0T0 ⎟
2 ∑
λ ⎝ i
⎠
2k ⎛
⎞
= 10
⎜ (Ti − T0 )Ω i + Ω 0T0 ⎟
2 ∑
λ ⎝ i
⎠
22
T = αTchrom + (1 − α )Tcor
Running Mean and Running Standard Deviation
1 i +182
µi =
xj
∑
365 j =i −182
⎛ 1
σ i = ⎜⎜
⎝ 364
Index of longer-term activity
1/ 2
2⎞
( x j − µi ) ⎟⎟
∑
j =i −182
⎠
i +182
Index of shorter-term activity
The same filtering processes are applied to the F10.7 and
sunspot number time-series
One-Year Running Mean for F10.7 and Sunspot Number
300
250
F10.7
M ean
200
150
100
50
Ns
0
1945
1950
1955
1960
1965
1970
1975
1980
Year
1985
1990
1995
2000
2005
2010
Running Standard Deviation
70
Standard Deviation
60
F10.7
50
40
30
20
10
Ns
0
1945
1950
1955
1960
1965
1970
1975
1980
Year
1985
1990
1995
2000
2005
2010
Mean F107 v Mean Sunspot Number
300
250
F10.7 in sfu
Cycle 23
200
150
F10.7 = 0.448 N S (2 − exp(− 0.027 N S )) + 66
100
50
0
50
100
Sunspot Number
150
200
F10.7 and Sunspot Number Standard Deviations
F107 (sfu) Standard Deviation
60
50
Cycle 23
40
30
20
σ F 10.7 = (0.23)σ
10
1.33
Ns
0
0
10
20
30
40
Sunspot Number Standard Deviation
50
60
70
F10.7 Observed versus Proxy
µ F′ 10.7 = 0.448µ Ns (2 − exp(− 0.027 µ Ns )) + 66
σ F′ 10.7 = (0.23)σ 1Ns.33
Where x´ = proxy for x, and
define
x − x′
ξx =
x
ξ: Means
0.2
Excess of F10.7
0.15
0.1
ξ
0.05
Excess of Sunspot Number
0
-0.05
-0.1
-0.15
1945
1950
1955
1960
1965
1970
1975
1980
Year
1985
1990
1995
2000
2005
2010
ξ: Standard Deviation
0.6
0.4
0.2
ξ(σ )
0
-0.21945
1950
1955
1960
1965
1970
1975
1980
-0.4
-0.6
-0.8
Year
1985
1990
1995
2000
2005
2010
Means
0.2
ξ=
Excess of F10.7
0.15
F10.7 (observed ) − F10.7 ( proxy )
F10.7 (observed )
Cycle 24
Cycle 18
Cycle 19
Cycle 20
Cycle 21
Cycle 22
0.1
Cycle 23
Cycle 24
0.05
ξ
Cycle 23
Excess of Ns
0
-0.05
-0.1
-0.15
0
50
100
Sunspot Number
150
200
Standard Deviations
0.6
Cycle 24
Cycle 18
0.4
Cycle 19
Cycle 20
Cycle 21
Cycle 22
0.2
Cycle 23
Cycle 24
ξ
0
-0.2 0
50
100
-0.4
-0.6
-0.8
Sunspot Number
150
200
Proxies Based Upon Sunspot
Number
85
25
80
23
y = 0.092x + 6.1055
21
R = 0.8775
17
Bav
R2 = 0.9263
70
He10830
19
y = -0.001x2 + 0.3941x + 40.501
75
2
15
13
65
60
55
11
50
9
45
7
40
5
0
50
100
0
150
50
100
150
Sunspot Number
Sunspot No
250
1366.6
230
210
10.7 solar radio flux (sfu)
Irradia nc e
1366.4
1366.2
1366.0
1365.8
y = 0.0066x + 1365.5
R2 = 0.9312
1365.6
190
170
150
Data
130
"Model"
110
90
70
1365.4
0
50
100
Sunspot Number
150
50
0
20
40
60
80
100
120
Sunspot Number
140
160
180
200
Other Indices
observed − proxy
ξ=
observed
0.15
xi(F10.7) x 1
0.1
xi(He10830) x 1
xi(Bav) x 0.25
xi(Irrad) x 600
aξ
0.05
0
-0.05
-0.1
-0.15
1945
1950
1955
1960
1965
1970
1975
1980
Year
1985
1990
1995
2000
2005
2010
2015
How Homogeneous is Solar Activity?
Julio Valdes
xn = Ψ (xn −1 , xn − 2 , xn −3 , xn − 4 .....)
NRC-IIT
xn = Ψ ( xn −1 , xn − 2 , xn −3 , xn − 4 .....)
Conclusions
•
•
•
•
•
•
During late Cycle 23, the relationship between photospheric activity
changed, with more coronal activity than one might expect on the
basis of the level of photospheric activity. Since photospheric activity
drives coronal activity, there is an issue here that needs some
serious consideration.
Indications are that in Cycle 24 so far the deviation from “standard
behaviour” is continuing or perhaps increasing.
There are indications in earlier cycles of a trend towards changing
solar behaviour.
Single indices are of limited use. Multiple indices are needed.
Use of one index (usually sunspot number or F10.7) as a proxy for
another, as is frequently done, is possibly not reliable, because the
relationships between different manifestations of solar activity can
change. However, changing relationships between proxies may
provide a very high resolution detector of deviations from “standard
behaviour”.
The 60+ years we have had multiple activity indices is a negligible
amount of time compared with solar evolutionary timescales, so we
are a long way from knowing the true context of solar behaviour.
Next Generation Solar Flux Monitor
Multiple operating wavelengths
provides indices for different
levels in the solar atmosphere
and separation of emission
components.
Antenna under test,
March, 2010