Smithsonian

Contributions to Astrophysics

VOLUME 5, NUMBER 12

NORTH-SOUTH ASYMMETRY IN SOLAR SPOTTEDNESS

AND IN GREAT-STORM SOURCES

SMITHSONIAN INSTITUTION

Washington, D.C.

1962
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Contents

Page

A Long-Term North-South Asymmetry in the Location of Solar Sources of

Great Geomagnetic Storms: Barbara Bell 187

On the Unequal Spottedness of the Two Solar Hemispheres: John G.

Wolbach 195

On Short-Period Relations between North-South Asymmetry in Spottedness

and in Great-Storm Sources: Barbara Bell and John G. Wolbach . . 203

iii

A Long-Term North-South Asymmetry in the Location

of Solar Sources of Great Geomagnetic Storms

By Barbara Bell

In a previous paper (Bell, 1961), I presented

evidence of a striking north-south asymmetry

in the number of major solar flares, and an

even greater asymmetry in the number of such

flares followed by a great geomagnetic storm.

During the years 1937 through 1959, about 62

percent of the 580 observed major solar flares

occurred in the northern solar hemisphere;

about 86 percent of the 74 major flares that were

followed within three days by a great geomagnetic storm occurred north of the solar equator.

The probability of such large asymmetries occurring by chance is, according to the normal

distribution law, about 10~8 for the major

flares in general, and less than 10 ~

9

 for the greatstorm flares. These surprising asymmetries

appeared in each of the three sunspot cycles

within the interval studied. These asymmetries thus have no apparent relation either to the

11-year cycle in sunspot numbers or to the 22-

year cycle in the magnetic polarities of sunspots.

In this paper we shall examine evidence on the

preferred location of great-storm sources in

earlier sunspot cycles.

Systematic observation of solar flares has

been carried out only since about 1936. Although a few bright flares were observed in

earlier years, the number of these is much too

small for use in any study of the location of

great-storm sources. For earlier years one

must rely on sunspot data. For the years subsequent to 1874, I obtained such data from

Sunspot and Geomagnetic-Storm Data, 1874-

1954, compiled at the Royal Greenwich Observatory (1955) under the supervision of

1

 Harvard College Observatory, Cambridge, Mass.

H. W. Newton. These data include: (1) the

annual average spotted area for north and south

separately for each year, which I summed to

obtain a measure of the "total spotted area"

for each cycle; (2) a list of great sunspot groups

(area>500X10~6 of the visible disk), which

includes the heliographic latitude and average

area for each spot group; and (3) lists of great

and of small geomagnetic storms recorded at

Greenwich and/or Abinger from 1874. The

last tables include the position and average

area of the largest sunspot group in the region

—3 to + 5 days of the solar central meridian

at the time of storm onset. If we assume that

the listed spot group is the source of the storm,

we can readily determine the number of great

and of small storms arising from spots in each

solar hemisphere in each cycle. In the few

cases where the accompanying notes indicated

some other spot as the more probable source,

the spot listed in the "notes" was used instead

of the one in the table.

Figure 1 shows the percentage of spotted area,

of great spots, and of great and small storms

appearing to arise from northern active centers

in each cycle. The Greenwich data cover

cycles 12 through 18. Table 1 gives additional

information, including the year of sunspot maximum corresponding to each cycle number.

Three sources provide data on four earlier

cycles, 8 through 11. A paper by Newcomb

(1901) provides data, based on observations by

Sporer, whereby the spotted-area curve of figure

la can be extended back for two cycles, 10 and

11. Sporer (1874) published spot frequencies

according to hemisphere for 1853 to 1871.

187
188 SMITHSONIAN CONTRIBUTION TO ASTROPHYSICS VOL. 5

Newton and Milsom (1955) determined the

annual numbers of spot groups in each hemisphere for the years 1832 to 1866 from

Schwab e's drawings; these unpublished numbers, which they generously made available to

me, provide the points representing cycles 8

and 9 and, together with Sporer's and Newcomb's data, cycle 10.

An estimate for cycle 19 has been added as a

broken line to figure la. Based on the numbers

of groups observed at Mount Wilson through

1960, the northern hemisphere has contributed

about 56 percent of the spottedness in cycle 19.

Although the remaining years of the cycle may

alter this percentage, it seems safe to say that

cycle 19 will be north-dominant in spottedness.

Figure la shows that the northern solar

hemisphere contributed over 50 percent of the

spottedness in cycles 8 and 9 (1833 to 1856) and

in cycles 14 through 19 (1901 to 196-); the

southern hemisphere contributed over 50 percent of the spottedness in cycles 10 through 13

(1856 to 1901). As a guide to the statistical

significance of the deviation of the individual

cycles from 50 percent, the expected fluctuation (standard deviation a) for a random distribution of spottedness is about ± 1.0 percent,

ranging from ±0.9 percent for a strongly

spotted cycle like 18 to ±1.2 percent for a

weakly spotted cycle like 12. Cycles 8, 9, 11,

12,13,15,16, and 19 deviate from a symmetrical

distribution by more than 3<r. The remaining

4 cycles deviate by less than 2 a (see Wolbach,

following paper). The number of large deviations suggests that the relative spottedness of

the two hemispheres is a nonrandom phenomenon.

For great spots, because of the smaller sample

sizes, only cycles 12 and 13 deviate by as much

as 2a, while cycles 15 and 17 deviate by more

than a. The persistence of the direction of the

deviation for several successive cycles is perhaps

more impressive than the actual magnitude of

the individual deviations.

Great storms recorded at Greenwich from

1840 to 1874 are listed in a supplementary table

of the Greenwich (1955) publication. Here the

date of central meridian passage and the area

of notable relevant sunspots are included, but

not the latitude of the spots. Information on

the latitude of these spots was obtained from

Carrington's (1863) drawings covering the

period from November 1853 to March 1861,

and Sporer's (1874, 1876) solar maps covering

January 1861 to October 1871. Additional

data were kindly supplied by A. S. Milsom from

his inspection of Kew photographs for 1868

through 1872, and of Schwabe's drawings for

1840 through 1852.

The curve representing the location of greatstorm sources (fig. 16) has a larger amplitude,

or more pronounced north-south asymmetry,

than does the curve of total spottedness or the

curve representing total numbers of great

spots. This agrees with the earlier finding

(see fig. 2) that location of great-storm flares

showed a greater hemisphere asymmetry than

did that of major flares in general. While the

spot and storm-source curves differ in amplitude, a majority of the great storms apparently

arose from the more-spotted hemisphere in all

but two (nos. 12 and 14) of the 11 cycles available for study.

Because of the small numbers of great storms

per cycle, only the points for cycles 9,11,13,17,

and 18 represent deviations greater than 2 a

from the 50-percent line in figure 16. Here

particularly, however, the persistence of the

sense of the asymmetry for several cycles

appears more significant than the magnitude of

the individual deviations. If we consider

cycles 10 through 14 as a unit, we find 77 great

storms, of which 49 appeared to arise from

southern spot groups; for cycles 15 through

18, we find 66 great storms, 45 of them apparently arising from northern spots. According to the normal distribution law, the probability of so large a difference between north and

south occurring by change is 0.02 for the first,

and 0.003 for the second of these intervals.

The addition of cycle 19 would further diminish

the second value.

The asymmetry in location of small-storm

sources is less systematic and less in amplitude

(fig. 16) than that for great-storm sources.

While in agreement with the results of Bell

(1961) (see also fig. 2), the small-storm curve

cannot be considered particularly significant.

Many of the small storms must be of the recurrent or M-region type, and Allen (1944) has

shown that this type of storm source tends to

avoid large sunspots. Thus the procedure of
ASSYMETRY IN SOLAR SPOTTEDNESS 189

70

%

30

8

I

1 a

1

9

1

— \

1

10

1

1

II

1

— \

1

12

1

13

I

14

1

15

l

16

1

i

17

i

—

Cycle

18

I

19

t

-

Cycle

18 19

90

c

/

/o

70

30

10

8

1

- b

-

-

i

9

1

\

\

I

10

1

\

V

II

1

V

12

i

A

13 14

I i

I i

15

l

i

16

I

^

17

l

^

I

18

i

19

I

-

-

-

1

FIGURE 1.—Percentage of spot activity occurring in the northern solar hemisphere

in each sunspot cycle from 8 to 19. a, Heavy line indicates great {A > 500) sunspot

groups; thin line, total spottedness. b, Percentage of great (• •) and

small ( ) geomagnetic storms attributed to northern spot groups.

90

Of

70

30

10

8

l

-

-

-

i

9

I

•

\

I

10

1

\

V

1

II

1

i

12

i

A

i

13

l

V

i

14

i

/

i

15

l

/

/

i

16

i

/

17

i

^ * — •

i

18

i

—•+

i

19

i

-

-

-

i

- 30-

- 10-

FIGURE 2.—Percentage of

observed major flares occurring in the northern

solar hemisphere in cycles

17-19. Top, Heavy line

indicates major flares;

thin line, all flares. Bottom, flares followed by a

great (• •) , moderate (O O), and

small ( ) geomagnetic

storm. (From Bell, 1961.)

FIGURE 3.—Percentage of extra-great geomagnetic storms attributed to northern

spot groups in each cycle, 9 through 18.
190

SMITHSONIAN CONTRIBUTION TO ASTROPHYSICS

ascribing the storm source to the largest centrally located sunspot probably has little consistent validity for small storms, and the curve

is included only for completeness.

Figure 1 should be compared with figure 2,

reproduced from Bell (1961). The hemispheric

inequality in production of major flares appears

greater than that in spots, and both are smaller

than the inequality in numbers of great-storm

flares. Figure 2 shows also that in cycles 17

and 18, when major flares are used to identify

the storm-producing region, 91 percent of the

great storms appear to arise from northern

active centers. This percentage drops to about

70 when spots are used, as in figure 16.

At least two factors contribute to this difference. There is little doubt that observation

of a major flare permits a more reliable identification of the storm-producing solar center,

which is not always the largest spot group near

the central meridian. Thus major flares should

be considered to give the more accurate picture

of the actual north-south asymmetry in location of great-storm sources. In addition, the

criterion of figure 2 for identification of a

"great" storm (Ap> 100 and/or a 3-hr Kp>9~)

excludes the lower range of storms listed by

Greenwich (1955) as "great"; figure 2 indicates

that the asymmetry is more pronounced for

great than for moderate-storm sources.

To explore the importance of this second

factor, I subdivided the Greenwich "great

storms" into greater and lesser great-storms.

The Greenwich (1955) criterion for a "great

storm" is a deflection of the H or Z component

of the earth's field >300y and/or a deflection

of at least 60' in the D component. To select

a list of greater great-storms, I raised these

limits to H or Z>400y and/or D>70'. As

figure 3 shows, the greater great-storms have,

in most cycles, the larger north-south asymmetry in location of source, particularly from

cycle 12 onward. Cycles 17 and 18 are now

in better agreement with the flare data. Also

cycle 12 becomes south-dominant, as one might

expect from the greater spottedness of the south

in this cycle. Cycles 14 and 15, however, show

a less satisfactory accord with spot asymmetry.

What can we say about a long-period cycle

in either aspect of north-south asymmetry?

Newcomb (1901) drew attention to a general

excess of southern spots from 1856 to 1898.

Brunner-Hagger and Liepert (1941) subsequently presented evidence for a long-period

variation in relative spottedness of the two

hemispheres over the years 1853 to 1938, and

inferred a period of about 80 years. The later

years of cycle 17, however, did not confirm

their inference that this would be a southdominant cycle; cycle 18 was again slightly

north-dominant in total spottedness; and,

through 1960, cycle 19 produced 56 percent

of its spot groups in the north. Hence if a

true cycle does exist, its period appears to be

greater than 80 years. Since the available

data, from 1832 through 1960, do not appear

to define even one possible complete cycle, we

cannot draw any conclusions as to whether

figure 1 illustrates some long-period cycle of

solar behavior, or merely irregular long-period

variations in the relative activity of the two

hemispheres. We can, however, conclude that

the frequency of substantial inequalities is

greater than would be expected to occur by

chance (see Wolbach, following paper, especially fig. 3), and that the direction of the inequality does not vary in a random manner

from cycle to cycle.

Another difference between northern and

southern solar hemispheres was pointed out by

Bell (1960), who presented evidence suggesting

a more systematic structure of the northern

than the southern sunspot zone in the years

since 1917.

Newton and Milsom (1955) examined the

annual values of the spotted areas in the form

of the ratio (N—S)I(N+S), where N and S

are the annual mean values of the spotted area

in the north and in the south. They found that

in cycles 12 through 14 this ratio diminished

during each cycle; in cycles 17 and 18 the ratio

increased, while in cycles 10 and 11, and 15

and 16 it lacked any systematic trend. Waldmeier (1957) suggested that the behavior of the

ratio reflects a phase difference in the activity

of the two hemispheres, a phase difference that

changes slowly with a period of the order of 80

years. The hemisphere that is the more spotted

later in the cycle tends to produce a majority

of the great storms in that cycle, but from so

few cycles we can draw no definite conclusions.
A

60

40 -

20 -

12

ASSYMETRY IN SOLAR SPOTTEDNESS

13 14 15 16 17

191

18 19

1 1 1

a

-

1 1 1

1 1 1

1

N

^

 S

I

-

1

N

80

60

4 0

20

0

b

-

-

-

-

12

1

I

13

I

14

1

I

15

1

y

1

16

1

•

y

1

17

1

y y

y

18

1

1

N

S

19

1

-

-

-

-

1

FIGURE 4.—Plot of spottedness of each hemisphere for cycles 12 through 18.

a, Sum of annual spotted areas per cycle (unit of 10~* of visible disk), b, Number of

great spot groups. Solid lines indicate southern spots, broken lines, northern.

Wolf, and later Sporer, demonstrated (see

Maunder, 1922) that in the latter part of the

17th century and the beginning of the 18th,

the northern hemisphere of the sun failed for

many years to produce a single recorded spot.

The south had some spots, but not many, and

for nearly 70 years the sun showed a prolonged

sunspot minimum. The failure in spot activity

in the north was not compensated by an increase in the south. No aurorae were reported

during these years, and from this Maunder

reasonably inferred that there were also no

great geomagnetic disturbances occurring then

on earth.

In connection with the prolonged dearth of

spots in both solar hemispheres in the period

around 1700, it is interesting to note that for

632056—62 2

several recent cycles the total spotted area and

the numbers of great spot groups have been

steadily rising in both hemispheres. The recent dominance of the northern hemisphere

does not arise from any particular weakness in

the southern. Figure 4 shows, for example,

that the south was more spotted in cycle 17

than the north in any previous cycle since 1874;

again in cycle 18 the south was more spotted

than the north in any previous cycle. Indeed,

after the cross-over from south to north

dominance between cycles 13 and 14, the spottedness of the two hemispheres increases roughly

in parallel, as figure 4 shows.

The relation, if any, of the various solar

asymmetries cited above to the asymmetry in

the location of major geoactive sources is far
192 SMITHSONIAN CONTRIBUTION TO ASTROPHYSICS

20 30 40 50 60 70 80

VOL. 5

6 0 -

% •

spots J

-

-

-

-

-

1

1 •

13

1 ,

1

11

|

1

 1

14

K)

12

1

15

|

1

 1

16

18

17

1

 1 ' .

storms _

9 —

-

-

-

-

-

, 1 , '

50

45

4 0 -

FIGURE 5.—Percentage of total spotted area in the solar north plotted against percentage of great storms attributed to northern spot groups, for cycles 9 through 18.

from clear. In figure 5 the spot distribution is

plotted against storm-source distribution, in

terms of percent north of the equator, for each

sunspot cycle. In 9 out of 11 cycles (including

cycle 19) the more-spotted hemisphere produced more of the great storms. The northsouth asymmetry in the location of great-storm

sources, however, far exceeds the asymmetry

in either the total spotted area or in the frequency of large spot groups. The degree of

asymmetry in numbers of major flares appears

to be intermediate between the degree of asymmetry in spottedness and that in great-storm

sources.

From table 1 we see that some cycles are

more effective in producing great storms, not

only in the total number of storms produced—

as one might expect from the differing heights

of the spot maxima—but also in the numbers

of storms relative to the various measures of

spottedness. For example, the number of

great storms per great spot group varies by a

factor of two, the minimum value being 0.10

for cycles 14 and 15, and the maximum 0.22

for cycle 13.

The cause of these long-term inequalities in

the activity of the two solar hemispheres is

completely unknown. The existence of such

inequalities would, as Maunder (1922) pointed

out, seem to imply a lack of symmetry in the

internal structure of the sun, at least with

respect to the forces producing sunspots, flares,

and corpuscular emission. If, however, sunspots and their associated activity arise from

the general dipole field in a manner similar to

that proposed by Babcock (1961), the persistence of the direction of the asymmetry for

several cycles can perhaps be qualitatively

understood. According to Babcock's hypothesis, the residual fields from the follower components of spot groups tend to drift poleward,

first neutralizing and then reversing the dipole

field. This new dipole field, gradually amplified in lower latitudes by differential rotation,

in due course generates the next cycle of spots.

The significant point here is that each hemisphere apparently generates its own half of the

dipole field, which in turn gives rise to its spots

in the next cycle. If such a picture is correct,

one might expect that any asymmetry that

developed between the hemispheres would tend

to persist for several cycles.

In the second following paper evidence for

a relation between the asymmetry in spottedness and the asymmetry in location of greatstorm sources will be explored on a yearly basis,

and compared with the relation on a cycle

basis.
ASSTMETRT IN SOLAR SPOTTEDNESS

TABLE 1.—Some properties of the sunspot cycles 8 through 19

193

Cycle no.

8

9

10

11

12

13

14

15

16

17

18

19

Year of

maximum

1837

1848

1860

1870

1883

1893

1905

1917

1928

1937

1947

1957

Maximum

smoothed

monthly

sunspot

number

147

132

98

140

75

84

64

105

78

119

152

201

Sum of

annual

sunspot

numbers

649

692

545

626

383

459

375

456

410

606

754

827*

Sum of

annual

spotted

areas

5845

7300

5739

6577

7176

9947

12029

Total numbers of

Great

spot

groups

80

95

80

83

111

137

164

Great

storms

18

14

24

15

21

8

8

12

22

24

29*

Extragreat

storms

11

12

15

6

14

7

4

5

13

18

Small

storms

46

68

68

76

82

128

122

•Through 1960. The great storms of cycle 19 are defined by Ap> 100; cycles 17 and 18 had 18 and 19 great storms, respectively, by this criterion.

Acknowledgments

The work reported in this paper was supported

by the Geophysics Research Directorate of the

Air Force Cambridge Research Laboratories,

Office of Aerospace Research, under Contract

AF19 (604)^962.

I wish to thank A. S. Milsom and H. W.

Newton of the Royal Greenwich Observatory

for generously making available to me their

unpublished data on the spottedness of the two

hemispheres from 1832 through 1866. I am

indebted to Milsom also for consulting the

original sunspot records and determining for

me the latitudes of the sunspots most probably

associated with the great storms recorded during

cycles 9 and 11.

References

ALLEN, C. W.

1944. Relation between magnetic storms and

solar activity. Monthly Notices Roy.

Astron. Soc, vol. 104, pp. 13-21.

BABCOCK, H. W.

1961. The topology of the sun's magnetic field

and the 22-year cycle. Astrophys.

Journ., vol. 133, pp. 572-587.

BELL, B.

1960. On the structure of the sunspot zone.

Smithsonian Contr. Astrophys., vol. 5,

no. 3, pp. 17-28.

1961. Major flares and geomagnetic activity.

Smithsonian Contr. Astrophys., vol. 5,

no. 7, pp. 69-83.

BBUNNER-HAGGER, W., AND LIEPERT, A.

1941. Vergleichung der Sonnenfleckenkurven fur

die Jahre 1853-1939 fur die Nord- und

Sudhalbkugel. Astron. Mitt., Zurich,

vol. 14, pp. 556-574.

CABBINGTON, R. C.

1863. Observations of the spots on the sun.

Williams and Norgate, London, 248 pp.

GREENWICH, ROTAL OBSEBVATOBY

1955. Sunspot and geomagnetic-storm data, 1874-

1954. Her Majesty's Stationery Office,

London, 107 pp.

MATJNDEB, E. W.

1922. The sun and sunspots, 1820-1920. Monthly

Notices Roy. Astron. Soc, vol. 82, pp.

534-543.

NEWCOMB, S.

1901. On the period of the solar spots. Astrophys

Journ., vol. 13, pp. 1-14.

NEWTON, H. W., AND MILSOM, A. S.

1955. Note on the observed differences in spottedness of the sun's northern and

southern hemispheres. Monthly Notices

Roy. Astron. Soc, vol. 115, pp. 398-404.

SPOBEB, G.

1874. Beobachtungen der Sonnenflecken. Publ.

Astron. Ges., Leipzig, vol. 13, 161 pp.

1876. Beobachtungen der Sonnenflecken II.

Publ. Astron. Ges., Leipzig, vol. 13,

142 pp.

WALDMEIEB, M.

1957. Der lange Sonnenzyklus. Zeitschr. Astrophys., vol. 43, pp. 149-160.
194 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. B

Abstract

Inequalities in the relative sppttedness of the two solar hemispheres and in the location of solar sources of great

geomagnetic storms have been investigated for the years 1833 through 1960, with the sunspot cycle as the basic unit

of time. It was found that the northern solar hemisphere contributed over 50 percent of the spottedness in cycles

8 and 9 (1833 to 1856) and in cycles 14 through 19 (1901 to 196-); the southern hemisphere contributed over 50

percent of the spottedness in cycles 10 through 13 (1856 to 1901). With eight cycles deviating by more than 3<r

from a symmetrical distribution, the frequency of substantial inequalities is much greater than would be expected to

occur by chance. The direction of the inequality does not vary in a random manner from cycle to cycle, but the

available data are not sufficient to establish whether the variation is periodic.

A majority of great geomagnetic storms appeared to arise from sunspot groups in the more-spotted hemisphere

in all but two of the cycles from 9 onward. In most cycles the asymmetry in location of great-storm sources far

exceeds the asymmetry in total spottedness, and tends to increase when the lower limit for defining a great storm

is raised.
On the Unequal Spottedness of the

Two Solar Hemispheres

B Y JOHN G. WOLBACH *

The findings of Bell in the preceding paper

led me to investigate in more detail the asymmetry in spottedness about the sun's equator

for periods of time less than a complete sunspot

cycle.

As a working hypothesis, the periods of time

in which one hemisphere tends to be more

spotted than the other can be divided into

three categories: A-periods of several consecutive months; B-periods of several consecutive

years; and C-periods of several consecutive

sunspot cycles.

During any one of these periods, the prevailing greater spottedness of one solar hemisphere

may be reversed for some small fractions of the

time. The C-period is the one discussed by

Bell in the preceding paper, and elsewhere by

Waldmeier (1957).

Study of Greenwich (1955) data on the

average spotted area in each hemisphere per

rotation, from 1874 to 1954, shows that the

A-period may persist for eight to ten rotations.

These periods do not appear to be cyclic, and

may be largely explained by long-lived centers

of spot formation at a particular latitude and

longitude (see Kiepenheuer, 1953).

This paper will deal mainly with two questions: First, do B-periods recur in a cyclic

manner and with any characteristic cycle

length? Second, are the asymmetries in spottedness significantly greater than one might

expect them to be by chance when intervals of

a year, a hah* sunspot cycle, and a complete

sunspot cycle are considered, and, if so, to

what extent?

Newton and Milsom (1955) first studied the

regularity in sequences of what I here call

' Harvard College Observatory, Cambridge, Mass.

B-periods. They examined the annual values

of the spotted areas in the form of the ratio

q=(N—S)/(N+S), where N and S represent

the average yearly spotted areas in the northern

and in the southern solar hemispheres. They

found that in cycles 12 through 14 this ratio

diminished in the course of each cycle; in

cycles 17 and 18 the ratio rose toward the end

of the cycle; in cycles 15 and 16 the ratio

showed no systematic trend. From investigations of cycles 8 through 18 they concluded

that the behavior of the ratio showed "changes

from cycle to cycle which, although not random,

appear to have no definite period. There is

the suggestion of a dependence of the pattern

of the excess of spottedness, north or south,

upon the degree of activity of any particular

cycle. The results indicate no dependence

upon a 22-year cycle."

Xanthakis (1959a, 1959b, 1959c) attempted

to relate the behavior of q to the steepness of

rise of the sunspot activity in a number of

cycles. Waldmeier (1957) suggested that the

behavior of the ratio reflects a phase difference

in the activity of the two hemispheres, a

phase difference that changes slowly with a

period of the order of 80 years.

From an inspection of plots of the data used

by Newton and Milsom, I proposed, as a

working hypothesis, to attribute the appearance

of the curve (see fig. lb) to the alternation of

B-periods from one hemisphere to the other,

forming a cycle about one year shorter than

the sunspot cycle. From cycles 12 through 18,

the maximum value of q moved from the waxing

part of the cycle to the waning part of the preceding cycle. The critical parts of cycles 15

and 16 would then be around minimum, where

195
196 SMITHSONIAN CONTRIBUTION TO ASTROPHYSICS

1830 IMO

SPOT CYCLE 8

M«S

ZOOO1000- / \

0 •

aa-

-««

-Off

-at

1 1

MM 1840

r

9

o

A

/ \

b

1

i

T

10

A

V

1

I860

T

ii

/

J \

^>-1

1870

1880

12

A

i

$L

i

1880

r

IS

A

1

1900

\ /

k

4\ •• /

V

1900

T

14

K

y

i

i'

1910

1920

19

i

A' V

i

M

1

1

1920

1930

16

W

1

J

1

1930

1940

f\A

i

1*40

1990 I960

/-J0C>0

18 IS

\

/ V

-tooo

'1000

-a*

1 i

1950 I960

FIGURE 1.—Variation of solar spottedness with time, a, Annual average spotted area, N-\-S, of the

whole sun. b, Relative spotted area of the northern and southern hemispheres, expressed by the

ratio q=(N—S)/(N+S). Dark shaded areas indicate the north was more spotted; light areas,

the south. The standard deviation of q is shown by the scalloped lines.

the small number of spots precludes a meaningful determination of q. Hence the behavior

of the ratio in these cycles would not show

any trend.

The observational data available to test this

hypothesis are the yearly average areas of

spottedness in each hemisphere from 1874

(Greenwich, 1955), the same data employed by

previous workers. Data for earlier years consist of numbers of individual spots (not groups)

published by Sporer (1874) for 1853 through

1871, and Newton and Milsom's (1955) data

on annual group numbers for each hemisphere

for the years 1832 through 1866, derived from

Schwabe's drawings.

Figure la shows the total annual average

spotted area against time from 1874 onward,

and numbers of spot groups from 1832 through

1871 on an arbitrary scale. Figure 16 shows

the observed annual values of q, from 1832,

based on Greenwich areas and the Sporer and

Schwabe data. To obtain data as homogeneous

as possible, I graphically converted the annual

Schwabe-Newton-Milsom group numbers to

the Sporer scale, because the latter, which is a

count of individual sunspots rather than groups,

seemed more closely proportional to the area.

The sunspot cycle, shown in figure la, gives

a rough guide to the significance of the various

values of q.

To obtain a more precise measure of the

significance of each value of q, I determined

the standard deviation for each year (the

scallop-like curve in figure 16) from the number

of spot groups observed each year. These

were obtained from the Greenwich Photoheliographic Results.

If we denote the number of spot groups in a

year in the northern and southern hemispheres

by Nr and <S", then the standard deviation of

the number of groups to be expected in the

northern or southern hemisphere is

(1)
ASSYMETRY IN SOLAR SPOTTEDNESS 197

The expected magnitude of fluctuations for

N'KN'+S'),

( N' \_ a _ 1

For q', the value of q for spot numbers,

N'—S'\ 1

r

wr"~w§r

The scalloped lines in figure 16 were computed

from equation (2).

The standard deviation of q', being inversely

proportional to the square root of the number

of spot groups, is greatest around spot minima,

as figure 16 shows. The southern B-periods of

cycles 12, 13, and 14, although containing a

number of individual years that deviate less

than 2<r, gain statistical significance from their

duration of five to eight years. The adjoining

halves of cycles 8 and 9, and all of cycles 15

and 16, consist of almost unbroken B-periods

in the north, with only one year of greater

southern spottedness in each interval. While

the ratio of observed deviation to standard deviation is not very significant for many individual years, the run of consecutive years and

the succession of several B-periods are striking.

The frequency of large deviations will be discussed quantitatively in the final section of this

paper.

To investigate whether B-periods show a cyclic periodicity, I computed the autocorrelation

coefficient for periods of 1 to 26 years. Let qt

be the value of q for a given year, r (=1, 2,

3, . . .) the length of cycle in years, and n

the number of years of observation available.

Then the autocorrelation coefficient of r may

be expressed by

(3)

»=1

Figure 2a shows/(r) for r=\ to r=26. If q

varies at random, j(r) should fall to a value

close to zero. In figure 2a, except for a small

rise around r=10, f(r) shows no pronounced

cyclic tendency.

A further test for any cyclic tendency in the

data can be made by using the Fourier transformation, F}

, of <r or power spectrum of the

time series qt. The values of/(r) in equation (3)

may be represented as j(U), where t is time in

years. Then

(4)

when

W('o ) cos cos

forl<w<26.

Figure 26 shows the variation of Ft for t and

r = l to 26. The rise in F} at t=8 through 14

years is the only statistically significant deviation in the diagram. Bisecting the area under

this positive deviation yields a period of 11.16

years, a value not differing significantly from

the average length of 10.77 years for the 7

sunspot cycles from 1878.9 to 1954.3.

In summary, examination of figures 16 and

2 reveals a tendency toward the existence of a

cycle of alternation of B-periods of varying

length. The evidence for a 10-year cycle,

although striking for limited time spans and

of some limited statistical significance, is not

particularly convincing. With the addition

of data prior to 1874 it becomes clear that the

statistical significance would be diminished

rather than increased. Thus my computations

lead to agreement with the conclusion of Newton and Milsom (1955) that the behavior of q

shows "changes from cycle to cycle, which,

although not random, appear to have no definite

period."

I next investigated to what extent the asymmetries in spottedness are significantly greater

than one might expect to occur by chance when

intervals of a year, a half sunspot cycle, and a

complete cycle are considered.

Figure 3 compares the observed and the

random distributions of q/aq for intervals of

(a) a year, (b) a half cycle, and (c) a full cycle.

In each section of figure 3, the values are

normalized to make equal the areas encom-
198 SMITHSONIAN CONTRIBUTION TO ASTROPHYSICS

5 10 15 20 Years 25

-0.4-

FIGURE 2.—Determination of cyclic tendencies in the unequal spottedness of the hemispheres, a,

The autocorrelation coefficient, /(r), for 1 to 26 years, b, Fourier transformation Ff of <r for 1 to 26

years.

passed by the normal curve and the histogram.

Table 1 shows that, for each of the three time

intervals, less than 50 percent of the area of

the observed histogramic distribution falls

within the normal curve. The percentages

within the normal curve for the year are, however, somewhat higher than those for the^half

cycle and for the full cycle. Each of these two

longer intervals has about one-third of its area

within the normal curve. Thus figure 3 and

table 1 show that large inequalities in the

spottedness of the two hemispheres are much
ASSYMETRY IN SOLAR SPOTTEDNESS 199

TABLE 1.—Proportion of observed distribution of asymmetry in spoltedness falling within the normal curve

Interval

Year

Half cycle

Full cycle

North

0.467

0. 334

0.349

South

0.439

0.354

0.296

Total

0.454

0.343

0.330

more frequent than could be expected if these

inequalities arose from random fluctuations.

They indicate also that the most significant

inequalities between the hemispheres are obtained when intervals longer than one year are

studied. While the actual deviations tend to

be larger for the half than for the whole cycle,

in terms of statistical significance the deviations

for the two intervals are about equal. The

larger deviations for full cycles result when

both their halves deviate in the same sense.

To compare further the characteristics of

B-periods with other intervals of time, I determined the value of N/(N-\-S) for each solar

rotation from 1880, using the average daily spot

areas for each hemisphere published by Greenwich (1955). Let us imagine a histogramic

representation in which N/(N-\-S) is plotted

against rotation number. For a given time

interval, the area encompassed by the histogram

above the 0.5 line may be denoted by N",

and the area below this line by S". The percent of histogram areas above the 0.5 line is

then N"/(N"+S"). The uninterrupted persistence of greater spottedness in a single

hemisphere over a given time interval gives

N"!(N"+S")=0 or 1, even though the actual

difference between the hemispheres may be

FIGURE 3.—Comparison of the observed distribution of q in units of <ra, with the normal distribution to

be expected under an assumption of random fluctuation of the relative spottedness of the two hemispheres, for intervals of: a, the year; b, the half cycle; c, the full spot-cycle. The areas encompassed

by the normal curve and the histogram are equal in each section. Negative values, to the left of

the zero line, indicate the south is the more-spotted hemisphere.
200

SMITHSONIAN CONTRIBUTION TO ASTROPHYSICS VOL. 5

slight. Thus N"/(N"-{-S") measures consistency as well as magnitude of asymmetry.

I excluded all rotations for which the average

daily spotted area for the entire sun is less than

300 X 10~6 of the disk. No yearly determination of N"!(N"+S") was made unless at least

eight usable rotations were available. All

sufficiently spotted rotations, however, entered

into calculations of N"/(N"+S") for longer

periods.

If we let k represent the average number of

spot groups per rotation, and No the number of

rotations in a given time interval, then the

standard deviation of Y2\q'\ is given by

(5)

'" 2V&Fo

or in the logarithmic form,

log <rlfl|=—0.5 (Iog4£+log JVo). (6)

These equations involve the dubious assumption that all rotations are equally spotted.

However, examination of average N/{N-\-S)

and N"/(N"-±-S") for each of several years

showed no systematic variation with phase of

the spot cycle, and seemed to justify the use

of equation (6) as a first approximation.

TABLE 2.—Absolute values of the average deviation of

N/(N+S) and N"/(N"+S") from 0.5 for various

time intervals

Interval

Rotation

Year

Half cycle

Full cycle

Cycles 15-18

N/(N+S)

0. 198

.099

.054

.038

.024

N"/(N"+S")

0.239

. 166

.094

.083

Table 2 shows the absolute values of the average deviation of N/(N+S) and N"/(N"+S")

from 0.5 for different intervals of time. The

southern C-period of cycles 10 through 13

cannot be included because data by rotation

are not available prior to cycle 12. The two

measures of asymmetry differed in sign for

cycle 14, which was accordingly omitted from

either C-period. As one would expect, the

values of the ratios in table 2 become smaller

with longer time intervals, as the short term

asymmetries in opposite hemispheres tend to

cancel each other out. The rate of the decrease,

however, is worth further attention.

The observed rate of decrease for both ratios

is shown (broken lines) in figure 4, and compared with the rate to be expected from a random distribution in asymmetry (solid lines) as

given by equation (6). The value of k was

arbitrarily chosen to make the yearly observed

and computed values equal.

The observed quantities decrease less rapidly

than the computed ones, with increase of No

up to the half cycle. From the half cycle to the

full cycle q decreases randomly; q" decreases

faster than random and approaches the computed value. From the full cycle to the

C-period both quantities again fail to decrease

as rapidly as predicted.

Figure 4 thus illustrates that the yearly

asymmetry is greater than one would predict

-0.6

-1.0

-1.4

-1.8

0.0

1 1

\

-

•

-

1.0

1 1 1 1 1 1

1

2.0

\

• , 1 ,

l o q N o

-

-

FIGURE 4.—Plot of the log of the observed values

(broken lines) of the asymmetry in spottedness

from table 2, against log Ne, where No is the

number of solar rotations in the time interval.

The solid lines, from eq. (6), indicate the slope

to be expected from a random variation in the

sense of the asymmetry. Observed and computed lines are arbitrarily set equal for the

interval of a year. The upper pair of lines

refer to N"/(N" + S"), the lower to N/(N+S).
ASSYMETRY IN SOLAR SPOTTEDNESS 201

if the short-term (rotation) asymmetries cancelled out in a random way over a year. A

given hemisphere is favored in more rotations

than "expected," and this trend continues out

to the points representing the half cycle.

From the half cycle to the whole cycle the

decrease is random. In the case of q", where

both the persistence in direction and the magnitude of the asymmetry are important, the value

of the ratio is more nearly random for the full

than for the half cycle. This would imply that

the direction of the asymmetry tends to change

around spot maximum and minimum, a finding

which lends support to Waldmeier's (1957)

suggestion that Newton and Milsom's (1955)

trends, and B-periods, arise from the two

hemispheres being slightly out of phase.

From the whole cycles to the C-period of

cycles 15 through 18, the observed ratios again

decrease more slowly than at random. If cycle

19 and earlier spot data could be added to give

two C-periods, I do not doubt that the slope

of the last segment would deviate still more

strongly from the random curve. This result

gives additional statistical support to the

reality of the C-periods found by Bell in the

preceding paper.

Table 3 lists the average values of the ratio

g/o-j of the observed deviation to the standard

TABLE 3.—Average value of ratio q/<r Q of observed to standard deviation for various time intervals

Interval

Year

Half cycle

Full cycle

Cycles 10-13

Cycles 15-18

«/«•«

2.7

3.4

3.5

8. 1

4.7*

*If cycle 19 through 1960 were Included, this value would become 8.1.

deviation for intervals of a year, a half cycle,

and a full cycle. The values of g/<rf for the

southern C-period of cycles 10 through 13 and

the northern C-period of cycles 15 through 18

are included. Cycle. 19 also evidently belongs

to this northern C-period, for 56 percent of its

spot groups observed at Mount Wilson through

1960 have occurred in the north. If this trend

continues through the remainder of cycle 19,

the ratio qja^ for the C-period of cycles 14

through 19 will be about 8; in any case, the

ratio appears unlikely to fall below 7.

Summary

Although B-periods may alternate between the

two hemispheres, perhaps for a few spot cycles,

no convincing evidence has been found for a

10-year or any other cycle of B-periods. The

alternation of greater spottedness from one

hemisphere to the other in a period roughly

equal to one sunspot cycle occurs only occasionally, when g shows a trend during the spot cycle.

The variation in asymmetry is far less regular

than the variation in spot numbers.

However, persistence of unequal spottedness

of the two solar hemispheres, as seen in Greenwich spot areas, seems clearly to be a nonrandom phenomenon. The results presented

here show that short intervals (a solar rotation)

of asymmetry do not alternate in a random

manner, but tend to recur in the same hemisphere for as long as a year and, even more

strikingly, for as long as a B-period or half

cycle. A full spot-cycle is likely to contain two

B-periods, often in opposite hemispheres, and

the persistence of greater spottedness in one

hemisphere appears to end around spot minima

and maxima more frequently than one would

expect to occur by chance, suggesting that

B-periods arise at least in part from a tendency

of the two hemispheres to be slightly out of

phase.

Finally, the very long-term asymmetries,

persisting for several spot cycles, and found by

Bell in the preceding paper, are shown to be

statistically significant.

Acknowledgments

The work reported in this paper was supported

by the Geophysics Research Directorate, of the

Air Force Cambridge Research Laboratories,

Office of Aerospace Research, under Contract

AF19 (604)-4962.

I am grateful to Dr. David R. Layzer for

valuable discussions and advice on the statistical

procedures used in this paper. I join with Dr.

Bell in thanking A. S. Milsom and H. W.

Newton for making available sunspot data for

the years 1832 through 1866 derived from the

drawings of Schwabe.
202 SMITHSONIAN CONTRIBUTION TO ASTROPHYSICS

References

GREENWICH, ROYAL OBSEBVATORY

1955. Sunspot and geomagnetic-storm data, 1874-

1954. Her Majesty's Stationery Office,

London, 107 pp.

KlEPENHETTER, K. O.

1953. Solar activity. In The sun, ed. G. P.

Kuiper, pp. 322-465. University of

Chicago Press, Chicago.

NEWTON, H. W., AND MILSOM, A. S.

1955. Note on the observed differences in spottedness of the sun's northern and

southern hemispheres. Monthly Notices

Roy. Astron. Soc, vol. 115, pp. 398-404.

SPOREB, G.

1874. Beobachtungen der Sonnenflecken. Publ.

Astron. Ges., Leipzig, vol. 13, 166 pp.

WALDMEIER, M.

1957. Der lange Sonnenzyklus. Zeitschr. Astrophys., vol. 43, pp. 149-160.

XANTHAKIS, J.

1959a. Les aires des taches solaires vers le nord et

vers le sud de l'^quateur du soleil en

fonctions du temps d'ascension. Comptes

Rendus, vol. 249, pp. 1315-1317.

1959b. L'expression de l'activite' solaire en fonction

du temps d'ascension. Ann. Astrophys.,

vol. 22, Fasc. 6, pp. 855-876.

1959c. L'asym6trie N-S dans l'activite" solaire.

Comptes Rendus, vol. 249, pp. 1458-

1459.

Abstract

The unequal spottedness of the two solar hemispheres has been investigated from 1833 through 1954, for time

intervals of a year, a half spot-cycle, and whole cycle. For each of these three intervals, large deviations from

equality were found to occur much more frequently than a hypothesis of random fluctuations would predict. Large

deviations were particularly numerous for the half- and the whole-cycle intervals, where only about one-third of the

cases fell within the random curve.

Statistical tests were made for the existence of a periodicity in the alternation of greater spottedness from one

hemisphere to the other. Some evidence was found for a period of 8 to 14 years; because of the wide spread, however, this result cannot be considered very meaningful. Evidence is presented which suggests that the sense of the

asymmetry tends to change around spot maximum and minimum more often than might be expected by chance.
On Short-Period Relations Between North-South

Asymmetry in Spottedness and in Great-Storm Sources

By BARBARA BELL AND JOHN G. WOLBACH

The results presented in the two preceding

papers led us to examine in more detail relations

between the asymmetry in location of greatstorm sources and inequalities in spottedness of

the two solar hemispheres. Bell, in the first of

these papers, found that one hemisphere tends

to be more spotted than the other for several

consecutive sunspot cycles (the C-period as defined in Wolbach's paper); and that the activity

in the more-spotted hemisphere is disproportionately more effective in producing great geomagnetic storms. Wolbach, in the second paper,

found that large inequalities in the spottedness

of the two hemispheres, for periods of a

year, a half cycle, and a whole cycle, were more

frequent than a random distribution law would

predict. The frequency and persistence of

these large inequalities were greater for the half

cycle (B-period) than for the year (A-period),

and greatest of all for the geomagnetically significant C-period. (For definitions of the A-,

B-, and C-periods, see Wolbach's paper, p. 195.)

In this paper we investigate the following

questions. Does a great geomagnetic storm

usually arise from the hemisphere that is more

spotted at the time (i.e., month or year) of the

storm? Or does the hemisphere enjoying a

long-term or C-period of spot dominance produce most of the great storms even when a

shorter-term B- or A-period of spot dominance

is present in the opposite hemisphere?

Here, as in the two preceding papers, we used

the storm and sunspot data compiled at the

Royal Greenwich Observatory for the years

1874 through 1954 (Greenwich, 1955). Some of

these data are shown in figure 1, with northern

and southern data plotted separately. According to Newton (1949), spot groups with an

average area exceeding 1500 X10"8 of the visible

disk (shown in black) are the most likely to be

sources of major geomagnetic disturbance, primarily, as Bell and Glazer (1958) showed, because these very large groups contain the highest

proportion of sunspots with complex magnetic

fields.

Of the 113 great storms plotted in figure 1,

24 appear to arise from spot groups with mean

areas exceeding 1500X10"8 of the disk; 33 from

spots with area exceeding 1000; 35 from spots

with areas between 500 and 1000; and 45 from

spots smaller than 500 X10"8.

The storms were first grouped into four

classes: (1) storms from north spots when (a)

the northern hemisphere, or (b) the southern

hemisphere is the more spotted; and (2) storms

from south spots when (a) the northern, or (b)

the southern hemisphere is the more spotted.

This division provided a two-by-two array

whose observed deviation from a random distribution of population could be evaluated by

the c^i-square test.

We studied three intervals of unequal spottedness—the year (A-period), the half cycle (Bperiod), and the full spot cycle or C-period.

(Since neither of the two C-periods observed to

date contains any full sunspot cycle at variance

with the long-term trend of unequal spottedness, the full cycle and the C-period distributions are identical.) Table 1 gives the values

of P, the probability that the observed stormsource distribution occurs by chance, for each

of these three intervals of unequal spottedness.

Data for the epoch 1840-1874 were obtained

from various sources (see Bell's preceding paper). Several years had values of N/(N+S) =

0.500; these were omitted from the yearly de203
204

1880

SMITHSONIAN CONTRIBUTION TO ASTROPHYSICS

1900 1920 1940 Year

2 0 -

great sunspots

_ b

FIGURE 1.—Plot against time of: a, Annual numbers of great sunspots, of A > 500 and (in black) A

> 1500 X 10~8 of the visible disk, b, Individual great storms, with lengths of the individual vertical

lines indicating the intensity of the storm as measured by A(H-\-Z), the sum of the deflections in

the H and Z components of the earth's field, in units of 100 y; two or more storms from a single spot

are placed one above the other; the large and small dots indicate storms arising from spots of A >

1500 and A > 500, respectively, c, Annual numbers of great storms, with greater storms (see Bell,

p. 190) in black. In each section northern spots, or storms arising from northern spots, are plotted

above the zero line, and southern ones below the zero line.

termination, which accounts for its smaller number of storms.

We also considered various periods in combination. For example, when the direction of

the inequality in spottedness for the year agrees

with that of the long-term C-period, we have an

A- and a C-period in the same hemisphere. The

bottom lines of table 1 give the values of P for

the A,C and the B,C combinations.

Of the three intervals of unequal spottedness

in table 1, the full cycle or C-period gives the

smallest probability that the observed distribution in the four-celled array might occur by

chance, while the B-period gives the largest

probability. Also the A,C combination gives

a probability that is smaller by an order of

TABLE 1.—Values of P, the probability that the observed

storm-source distribution arises by chance, for various

intervals of unequal spottedness of the solar hemispheres,

1840-1954

Interval (s) of unequal

spottedness

Year, A

Half-cycle, B

Long-term, C

A,C

B,C

Number of

great storms

152

166

166

104

126

P

.00007

.00011

. 000003

. 000001

. 000026

magnitude than that obtained from the B,C

combination. None of these probability values

is independent of the others, because all of the
ASSYMETRY IN SOLAR SPOTTEDNESS 205

0.7

N_

0.6

0.5

0.4

0.3

0.1

X

—2—"——'

r-

• <

0 3

•

&>

X

0.5

•

•

—x~~

•

0.7 n+s

X

X

"

* ®

®

i . i

0 9

j

!

>

.

-

FIGURE 2.—Yearly average values of the ratio

N/(N+ S) of spotted area plotted against«/(» +/)

of great storms; s and n are the total values of

A(H-\-Z) for great storms attributed to the

northern and to the southern hemispheres during

the interval. Symbols indicate the weight of the

points, according to the number of storms:•,

2 storms; X, 3 or 4 storms; and &, 5 to 9 storms.

Years having only one great storm are omitted.

full cycles, 80 percent of the half cycles, and 70

percent of the year intervals have greater

spottedness in the C-period hemisphere. However, table 1 shows for each of the three time

intervals a highly significant tendency for the

more-spotted hemisphere to produce a majority

of the great geomagnetic storms.

We examine the possibility of linear correlations from the scatter diagrams of figures 2-4,

and from table 2. Figure 2 is based on yearly

data. For each year having two or more great

storms, the ratio N/(N-\-S) of spot distribution

was plotted against the ratio n/(n-\-s), where

n and s are the total values of A(H-{-Z), the

sum of the deflections in the H and Z components of the earth's field, for the northern

and the southern storms in the year. Figure

3 shows the average values of these ratios for

each half cycle, while figure 4 shows the values

for the whole spot cycles. Table 2 gives the

parameters of the least-squares lines fitted to

the points in figures 2-4, the coefficient of

N

N+S

0.6

0.5

0.4

0.1

•

O3

X*

x

x

05

•

—•—— '

X

0.7 rus

5

09

X

!T " *

-

FIGURE 3.—Half-cycle average values of N/

(N+S) plotted against n/(n+s) (see legend for

fig. 2). Symbols: •, 2 to S storms; X, 6 to 9

storms; and ®, 11 to 19 storms.

correlation (r), and the standard deviations in

the storm (ax) and spot (av) directions. In

these determinations each point was weighted

by the number of storms contributing to it.

The value of the intercept was computed for

nf(n-\-s) = l.

Figures 2-A and table 2 show that no significant linear correlation exists between inequalities of spottedness and of storm-source location.

The scatter is reduced as longer periods of time

are used. Most of this reduction in scatter is

in the y or spot direction, and the correlations,

though increased, never become large, even for

the full spot cycle. The large values of <rx and

<rv indicate that knowledge of one of the ratios,

NJ(N-{-S) or n/(n-\-s), does not suffice for

a meaningful prediction of the other ratio for

any of the three time intervals.

Thus while we find strong evidence of a nonrandom distribution in storm-source location,

there is only a negligible linear relation between

the magnitude of the inequality in spottedness

and the magnitude of the inequality in location

of storm sources. Tables 1 and 2 both suggest

that the C-period is of greater geomagnetic

significance than the A- or B-period.

Tables 3 and 4 represent an attempt to

evaluate the relative efficiency of the two

TABLE 2.—Least-squares parameters of relations between unequal spottedness of the solar

hemispheres and location of great-storm sources

Interval, "Period"

Year, A

Half cycle, B

Spot cycle, (C)

r

0. 479

.505

.555

r*

0. 229

.255

.308

Slope

+ 0. 148

. 119

. 103

Intercept

0.552

.545

.540

<r*

0.362

.282

.255

a,

0.094

.059

.043
206 SMITHSONIAN CONTRIBUTION TO ASTROPHYSICS VOL. 6

0.6

h

0.4

0.1

-

0.3

•

0 5

—X

•

X

X

0.7

-i

TT.-5

&

0.9

X

-

FIGURE 4.—Average values of N/(N-\-S) for the

full sunspot cycle plotted against n/(«+j) of

the cycle (see legend for fig. 2). Symbols: • ,

8 storms; X, 10 to 19 storms; and ®, > 20

storms.

hemispheres in producing great storms for the

various periods of time. Table 3 gives the

percent of great spot groups and the percent

of great-storm sources occurring in the morespotted hemisphere for various intervals and

combinations of intervals of unequal spottedness. We here consider the solar rotation (27

days) as a fourth interval of unequal spottedness. In terms of the four-celled array, the

quantity tabulated is the percent occurring on

the Nn-Ss diagonal. We took the distribution

of all great spots (>500X10~6) between the

two hemispheres as defining the "expected"

distribution of great-storm sources, and computed the probability (P) of obtaining by

chance a distribution of storm sources deviating

as much as observed from the expected.

S^The values of P in table 3 indicate that for

the three shorter periods, the rotation, the year,

and the half cycle, the storm-source distribution

does not differ significantly from that of great

spots. Only in the C-period does the morespotted hemisphere produce a significantly

higher percentage of great storms than of great

spots.

The top section of table 3 shows that the

concentration of great spots in the more-spotted

hemisphere diminishes as the time interval increases. This is not unexpected, because the

shorter the time interval the greater is the contribution that a single large spot group can

make toward the inequality of spottedness.

The spots with areas exceeding 1000 X10~8 of

the disk have a higher percentage in the morespotted hemisphere than do the spots with

areas of 500 to lOOOXlO"8.

In striking contrast to this behavior of great

spots, the concentration of great-storm sources

in the more-spotted hemisphere increases from

the year to the C-period.

In the lower section of table 3 another comparison can be made between the behavior of

great spots and storm sources. The rotation

intervals are divided into those in which the

direction of the asymmetry in spottedness

agrees with that of the C-period (R,C) and that

in which it is opposite (R,-C). Between these

two cases the difference in percentage of great

spots in the more-spotted hemisphere is minor.

In the case of great-storm sources, however, we

TABLE 3.—Percent of great sunspot groups, and of great-storm sources, occurring in the morespotted hemisphere; and the probability (P) of obtaining by chance a distribution of storm

sources deviating by as much as observed from the spot distribution.

Interval (a) of

unequal spottedness

Rotation, R

Year, A

Half-cycle, B

Long-term, C

A,C

A-C

R,C

R,-C

Great sunspot groups,

1874-1954

>l>1000

No.

141

138

141

141

93

45

83

58

Percent

88.0

69.0

61.0

59.6

71.0

64 5

90.4

84.6

1000>/1>

500

No.

621

611

610

621

381

230

357

264

Percent

76.3

61.4

57.7

54. 6

63.0

58.7

77.0

75.4

Great-storm sources

1874-1954

No.

112

103

112

112

61

42

67

45

Percent

72.3

61.2

64.3

67.9

73.8

42.9

83.6

55. 6

1840-1954

No.

152

166

166

104

48

Percent

64.5

65. 1

68.7

74.0

43.8

1

P

0. 11

.7

.2

.01

.13

.03

.4

.0007
NO. 12 ASSYMETRY EN SOLAR SPOTTEDNESS 207

TABLE 4.—Number of great geomagnetic storms per great spot group (A>500) in the more-spotted solar hemisphere and

in the less-spotted solar hemisphere, 1878-1954, and the probability of obtaining by chance two values deviating from

the mean by as much as observed

Interval(s)

of unequal

spottedness

C

B

A, year

R, rotation

A,C

A,-C

R,C

R,-C

B,C

B,-C

The

Spots

of

^4>500

424

438

470

598

306

164

350

248

361

77

more-spotted hemisphere

1aroduced

Great magnetic storms*

No.

76

72

63

81

45

18

56

25

65

7

N'o.

45

41

36

54

26

10

37

17

36

5

No.

per

spot

0. 179

. 164

. 134

. 135

. 147

. 110

. 160

. 101

. 180

. 091

N'o.

per

spot

0. 106

.094

.077

.090

.085

.061

. 106

.069

. 100

.065

The

Spots

of

A>500

338

313

279

164

168

111

90

74

256

57

less-spotted hemisphere

]>roduced

Great magnetic storms*

No.

36

40

40

31

16

24

11

20

29

11

N'o.

22

26

28

13

11

17

5

8

17

9

No.

per

spot

0. 107

. 128

.143

.190

.095

.216

. 122

.270

. 113

. 193

N'o.

per

spot

0.065

.083

. 100

.079

.065

. 153

.056

. 108

.066

. 158

P

0.002

. 10

. 6

.05

.066

.008

.28

.0001

.012

. 0 5

P'

0.024

. 5

. 2

. 6

. 4

.006

. 10

.20

.09

.05

•"No." - the total number of storms attributed to this hemisphere; "N'o." - the number of storms attributed to great spots in this hemisphere. P and

P" are the probabilities corresponding to No. and N'o. respectively.

find a difference of 28 percent. The values of

P indicate that in the R,C case each hemisphere

produces storms in proportion to the number of

great spots it has, but in the R,-C case the

C-period hemisphere produces a significantly

larger proportion of great storms than of great

spots. The great spots in the temporarily morespotted, non-C-period hemisphere are relatively

ineffective storm producers. A similar contrast

can be seen in the A,C combination although

the statistical significance is less striking. Here

however more than 50 percent of the storm

sources lie in the C-period hemisphere even

when the other is more spotted during the year

(A,-C).

Table 4 gives the average number of great

geomagnetic storms per great spot group in

the more-spotted and in the less-spotted hemispheres, and thus provides a measure of the

ability of great spots in each hemisphere to

produce great storms. The number of storms

per great spot is tabulated for all great storms

(No.) and for those (N'o.) specifically attributable to spots with areas exceeding 500X10"6

 in

that hemisphere. The average values of these

two ratios are 0.147 and 0.089 respectively.

In the intervals involving a combination of two

periods, the "more-spotted hemisphere" refers

to the one designated by the first symbol. For

example, in the case A,-C the "more-spotted

hemisphere" was more spotted for the year in

direction opposite to the C-period asymmetry;

while the "less-spotted hemisphere" (right-hand

section of the table) was less spotted for the

years in question but more spotted for the

C-period.

Of particular interest is the comparison of

corresponding columns for the more- and for

the less-spotted hemispheres. To evaluate the

statistical significance of the differences we

determined the mean number of storms per

great spot for a given row and computed the

probability P (and P' corresponding to N'o.)

of obtaining by chance two values deviating

from the mean by as much as observed. The

values of P and P' are given in table 4. In

every line of the table that involves the Cperiod, the C-period hemisphere produces more

great storms per great spot than the non-C

hemisphere, regardless of which hemisphere

may be temporarily more spotted for a year or

a rotation. The values of P show that most of

these differences are statistically significant at

the 5 percent level or better. Because of the
208 SMITHSONIAN CONTRIBUTION TO ASTROPHYSICS VOL. s

smaller samples only a few of the differences

measured by P' attain the 5 percent level of

significance.

If we consider the probability that, in the

absence of flare data, some of the storms are

attributed to a spot that is not the actual

source, it seems likely that the A,-C and the

R,-C values for storms in tables 3 and 4 are

too high rather than too low. Bell's paper has

pointed out that for cycles 17 and 18 a higher

percentage of great-storm sources was found

in the C-period hemisphere when flare data

were used to identify the probable storm source.

In conclusion, the data discussed in this

paper clearly indicate that short-term inequalities contributes nothing beyond what is

obvious from the previously known tendency

of great storms to arise from great spot groups.

Only the long-term or C-period inequality in

the spottedness of the hemispheres appears more

fundamentally related to the relative efficiency

of a solar hemisphere in producing corpuscular

emission sufficient to cause a great geomagnetic

storm.

Acknowledgments

The work reported in this paper was supported

by the Geophysics Research Directorate, of the

Air Force Cambridge Research Laboratories,

Office of Aerospace Research, under Contract

AF19 (604)-4962.

We are indebted to A. S. Milsom and

H. W. Newton for data on the spottedness

of the two hemispheres from 1832 through

1866, and to Milsom also for information on

the latitudes of the sunspots most probably

associated with the great storms recorded

during cycles 9 and 11.

References

BELL, B., AND GLAZER, H.

1958. Sunspots and geomagnetism. Smithsonian

Contr. Astrophys., vol. 2, no. 8, pp. 161-179.

GREENWICH, ROYAL OBSERVATORY

1955. Sunspot and geomagnetic-storm data, 1874-

1954. Her Majesty's Stationery Office,

London, 107 pp.

NEWTON, H. W.

1949. Observational aspects of the sunspot-geomagnetic storm relationships. Geophys. Suppl.,

Monthly Notices Roy. Astron. Soc, vol. 5,

pp. 321-335.

Abstract

Data for the years 1840 through 1954 were studied in an attempt to evaluate the relative importance of longterm (one and several spot-cycles) and short-term (27-day and 1 year) inequalities in the spottedness of the two

solar hemispheres as factors in the location of sources of great geomagnetic storms. There is a significant tendency

for the more-spotted hemisphere to produce a majority of the great storms, but no significant linear relation for any

of these intervals of time was found between the magnitude of the inequality in spottedness and the magnitude of

the inequality in number of storms arising from the two hemispheres. The short-term inequalities were shown to

be unimportant. Only the long-term inequality in the spottedness of the hemispheres appears to be related in any

fundamental way to the relative efficiency of the two solar hemispheres in generating corpuscular emission sufficient

to cause a great geomagnetic storm.