Rudolf Wolf and the
Sunspot Number
Leif Svalgaard
Stanford University
Sept. 2011
1st SSN Workshop, Sunspot, NM
1
The Sunspot Number ~1856
•
•
•
•
Wolf Number = kW (10*G + S)
G = number of groups
S = number of spots
kw = scale factor + site +
personal factor
Rudolf Wolf (1816-1893)
Observed 1849-1893
2
The Sunspot Number
• Wolf Number = kW (10*G + S)
• G = number of groups
• S = number of spots
Rudolf Wolf (1816-1893)
Observed 1849-1893
3
The Sunspot Number
• Wolf Number = kW (10*G + S)
• G = number of groups
• S = number of spots
Rudolf Wolf (1816-1893)
Observed 1849-1893
4
The Sunspot Number
• Wolf Number = kW (10*G + S)
• G = number of groups
• S = number of spots
Rudolf Wolf (1816-1893)
Observed 1849-1893
5
Wolf used 4’ Fraunhofer telescopes
with aperture 80 mm [Magn. X64]
Still in use today [by T. Friedli] continuing
the Swiss tradition [under the auspices of
the Rudolf Wolf Gesellshaft]
This is the ‘Norm’ Telescope
6
Wolf occasionally [and eventually – from 1870s on exclusively] used much smaller handheld, portable
telescopes [due to frequent travel], leaving the
80mm for his assistants or when he was home
These telescopes also still exist and are still in use today to
safeguard the stability of the series
Wolf estimated that to scale the count using the small telescopes to the 80mm
Standard telescope, the count should be multiplied by 1.5
7
Recording Variations of the
Geomagnetic Field
8
Wolf’s Discovery: rD = a + b RW
.
North X
rY
Morning
H
rD
Evening
D
East Y
Y = H sin(D)
dY = H cos(D) dD For small dD
A current system in the ionosphere is created
and maintained by solar FUV radiation
9
10 Days of geomagnetic variations
rY
10
The clear solar cycle variation of rY
Yearly Average Range rY
80
nT
PSM - VLJ - CLF
70
60
50
40
30
20
All mid-latitude stations show the same variation,
responding to the same current system
10
0
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
This was Wolf’s justification for his calibration of the SSN
11
Solar Activity: Radio Flux at
2.8 GHz [or 10.7 cm]
Solar Flux Units
F10.7 Flux Penticton
400
350
300
250
200
150
100
18
19
20
21
22
23
50
0
1945
1950
300
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
1990
1995
2000
2005
2010
Composite F10.7 Solar Flux
sfu
Monthly Averages
250
200
150
100
50
0
1950
1955
1960
1965
1970
1975
1980
1985
100
Very
stable and well-determined from Canadian and Japanese stations
95
90
12
Using rY from nine
‘chains’ of stations
we find that the
300
F10.7
250
y = 5.4187x - 129.93
R2 = 0.9815
200
correlation
150
100
y = 0.043085x 2.060402
R2 = 0.975948
50
rY
0
30
35
40
45
50
55
60
65
70
between F10.7 and
rY is extremely
good (more than
98% of the
variation is
accounted for)
Solar Activity From Diurnal Variation of Geomagnetic East Component
250
200
Nine Station Chains
F10.7 sfu
F10.7 calc = 5.42 rY - 130
150
100
12
13
14
15
16
17
18
19
20
21
22
23
1980
1990
2000
50
25+Residuals
0
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
2010
2020
This establishes that Wolf’s procedure and calibration are physically sound
13
Helsinki-Nurmijärvi Diurnal Variation
Scaling to 9-station chain
70
rY '9-station Chain'
65
60
Helsinki and its replacement station Numijärvi
scales the same way towards our composite
of nine long-running observatories and can
therefore be used to check the calibration of
the sunspot number
(or more correctly to
reconstruct the F10.7
radio flux)
y = 1.1254x + 4.5545
2
R = 0.9669
55
50
45
40
1884-1908 1953-2008
35
Helsinki, Nurmijärvi
30
25
30
35
40
45
50
55
Range of Diurnal Variation of East Component
70
65
60
55
50
45
40
35
30
rY nT
1840
9-station Chain
Helsinki
1850
1860
1870
Nurmijä rvi
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
14
2010
Rudolf Wolf’s 1861 List
SIDC 2009
1837 138.3
25% higher
15
Wolf got Declination Ranges for Milan from Schiaparelli
and it became clear that the pre-1849 SSNs were too low
Justification for Adjustment to 1874 List
160
R Wolf
140
'1874 List' 1836-1873
120
Wolf = 1.23 Schwabe
100
'1861 List' 1849-1860
Wolf
80
60
'1861 List' 1836-1848
Schwabe
40
20
rD' Milan
0
4
5
6
7
8
9
10
11
12
13
The ‘1874’ list included the 25% [Wolf said 1/4] increase of the pre-1849 SSN
16
Wolf increased all pre-1849
numbers by 25%
Wolf started his own
observations in 1849
SIDC 2009
1837 138.3
25% higher
17
The Wholesale Update of SSNs before 1849 is
Clearly Seen in the Distribution of Daily SSNs
The smallest
non-zero SSN
is 11, but there
are no 11s
before 1849
11 * 5/4 = 14
18
Wolfer’s Change to Wolf’s Counting Method
• Wolf only counted spots that were ‘black’ and
would have been clearly visible even with
moderate seeing
• Wolfer disagreed, and pointed out that the above
criterion was much too vague and advocating
counting every spot that could be seen
• This, of course, introduces a discontinuity in the
sunspot number, which was corrected by using a
much smaller k value [~0.6 instead of Wolf’s 1]
19
The Impact on the SSN after 1893 is Clearly Seen
in the Distribution of Daily SSNs
The smallest
non-zero SSN
is 11, but there
are lots of 7s
after 1893
11 * 0.6 = 7
20