Smithsonian

Contributions to Astrophysics

VOLUME 5, NUMBER 3

ON THE STRUCTURE OF

THE SUNSPOT ZONE

by BARBARA BELL

SMITHSONIAN INSTITUTION

Washington, D.C.

1960
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For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington 25, D.O. - Price 20 cents
On the Structure of the Sunspot Zone

By BARBARA BELL1

Just over a century ago Carrington discovered that the distribution of sunspots shifts

in latitude during the sunspot cycle. The

general features of this latitude shift are best

exhibited by Maunder's (1904, 1913) famous

butterfly diagram, recently brought up to date

(Greenwich, 1955). The first sunspots of a

cycle appear in latitudes 20-30° north and

south. The zone of maximum spottedness

moves toward the equator during the elevenyear sunspot cycle. The last spots occur

between 2° and 8° from the solar equator.

Waldmeier (1939) has determined the average

rate of this equatorward drift to be 2° per year.

While these general features of this shift in

latitude have long been among the best known

facts about sunspots, the cause of the displacement remains among the least understood of

solar phenomena. The process can be pictured

in several ways:

(1) A single zone, generating a single frequency

distribution of spots, exists in each solar hemisphere,

and drifts toward the equator at a rate of 2° per year.

(2) Two or more zones develop in each hemisphere,

each drifting equatorward.

(3) Several zones of activity develop in each hemisphere, and each remains stationary in latitude, but

they are just sufficiently out of phase to simulate a

latitude shift.

Lockyer (1904) argued that the law of spot

zones, discovered by Carrington aDd corroborated by Spoerer, represented only a very

general idea of a complicated pattern of sunspot

circulation and left many anomalies unexplained.

In an effort to obtain a more exact representation, he grouped the data in 3° intervals of

mean daily sunspot areas, formed yearly sums,

and found "several centers of spot action" each

year. He connected the peaks of activity in

successive years in such a way that each

center migrated toward the equator; he thereby

found three to four "spot activity tracks"

i Harvard College Observatory, Cambridge, Mass.

525613-60

along which move the centers of spot disturbance.

Maunder (1904) immediately criticized

Lockyer's peaks as a meaningless consequence

of assigning the areas of large spot groups to

a specific 3° interval of latitude, when in fact

the largest groups extend over as much as 6°

to 10°. Maunder argued for the concept that

a single frequency distribution occurs in each

hemisphere, and his picture has long been the

most generally accepted.

Recently, however, Becker (1954a) revived

the question whether the conventional butterfly

diagram is adequate for a quantitative analysis

of spot zones. He determined the number of

spot groups per 2° latitude interval per year for

sunspot cycles Nos. 12-18, covering the years

1880-1954. To take account of the latitude

drift and to determine the mean shape of the

distribution of spots with latitude, he introduced a shift of 2° from one year to the next and

summed the numbers of spots. The resulting

mean distribution gave evidence that the center

of the spot zone in each solar hemisphere coincides with a region of subnormal sunspot

activity. Becker pointed out further that the

position of this dip coincides with a division in

the direction of proper motions of sunspots—

a division between equatorward and poleward

proper motions (Becker, 1954b). Thus he concluded that each hemisphere's spot zone is

composed of two subzones, each drifting toward

the equator at 2° per year.

From sunspot data obtained at Mount

Wilson, and listed on IBM cards, Glazer and

I, in 1955, computed the annual sum of H (the

maximum magnetic field strength observed in

a. sunspot group) for each degree of latitude for

the years 1937-1953. An examination, some

time later, of the computations for the 1937

cycle (see figs, lc, 3) strikingly suggested the

hypothesis that several stationary nondrifting

17
18

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

zones occur in each hemisphere, as proposed in

the third concept listed above. The pattern for

the 1947 cycle (fig. 2a) however, was much less

clear.

Subsequently I extended the summations of

H back to 1917, the year when Mount Wilson

began systematic observations of sunspot field

strengths, and forward through 1958. Also I

determined the number of spot groups per year

at each degree of latitude, both from Mount

Wilson data and from the Greenwich Photoheliographic Results for 1912-1955. Greenwich

sunspots "seen on one day only" were not

included in the tabulations. While the original

tabulations were made for each degree, all

results shown here are based on either 2° sums

or 2° running means.

The resulting distributions of maximum

magnetic field strengths, H, for individual years

appear in figures 1, 2; for the individual sunspot

cycles in figure 3; and for all the years, from

1917 through 1958, in figure 4. Figures 5 and 6

show the distributions in numbers of spot

groups observed at Mount Wilson; figures 7

and 8 exhibit the numbers of groups observed

at Greenwich.

One can see immediately from figures 1—8

that the evidence for multizonality is stronger

in the Mount Wilson data than in the Greenwich numbers. Moreover, the evidence is

stronger in the magnetic field strengths than in

the numbers of spot groups. The 1937 cycle

(No. 17) shows the most striking impression of

multizonality, while the 1947 cycle gives the

smoothest distribution.

Although the first tabulations were made by

IBM machines, the remainder were carried out

by hand. During this manual tabulation I

obtained a strong impression that the latitude

of maximum activity does not move smoothly,

as might be expected from the slow drift of a

single zone or even of several zones. Rather,

the zone of maximum activity seems to jump

from one latitude to another several degrees

away, as though several narrow belts of activity

existed, waxing and waning in turn.

Various difficulties arise when one attempts

to test the statistical significance of the fluctuations in the latitude distribution curves. A

smooth curve was drawn through 5° running

means for each cycle and for the total period

covered by the observations, and the chi-square

method was used to test the significance of the

deviations from this smooth curve. Such tests

cannot be considered rigorous or exact, because

uncertainty exists as to the number of degrees

of freedom appropriate to such empirical, handa

FIGURE 1.—Distribution with latitude on the sun of total

magnetic field strength (H), plotted in 2° running means

and units of 100 gauss, of sunspots in cycles 15-17: a, No.

15 (1917-1924);b,No. 16(1923-1935) ;c,No. 17(1934-1945).
STRUCTURE OF

30 20 10 0 10 20 30 N

i i i I I I \};)A I i i

THE SUNSPOT ZONE

__S 30 20 10 0 10 20 30 N

H

50

100

50

0

100

50

0

200

150

100

50

0

100

50

0

100

50

0

100

50

0

5C

0

100

19

LAAJ VM

Ml nl

| | | /\J_i.l--!.-4—U

c

945
20 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

S 40 30 20

FIGURE 2.—Distribution with latitude on the sun of total

magnetic field strength (H), plotted in 2° running means

and units of 100 gauss, of sunspots in cycles 18 and 19:

a, No. 18 (1943-1954); *, No. 19 (1954-1958).

a
STRUCTURE OF THE SUNSPOT ZONE 21

S 40 30 20 10 0 10 20 30 4U N

H

4000

3000

2000

1000

0

S

-

-

-

-

40

1

30 20

1 ' 1 '

it

/

/

10 0

i • 1 -

\ r,

1

v

, Y

10

1 '

r

i •

20

1 '

I

\\

30

1 '

1 i

40 N

1

-

-

-

-

FIGURE 3.—Distribution with latitude on the sun of total

magnetic field strength (H), plotted in 2° running means

and units of 100 gauss, of sunspots in cycles Nos. 15-19

(1917-1958).

FIGURE 4.—Distribution with latitude on the sun of total

magnetic field strength (H), plotted in 2° running means

and units of 100 gauss, of sunspots for the period 1917-1958.

drawn smooth curves. For these tests, however, I set the number of degrees of freedom,

as a best guess, at three less than the number

of 2° sums entering the test; that is, at

2V-3.

When the test is applied to numbers of Greenwich sunspot groups (figs. 7, 8), the hypothesis

that the fluctuations are of a random nature is

not contradicted. Greenwich data provide no

statistically persuasive evidence for other than

random deviations from a smooth variation with

latitude.

For numbers of spot groups observed at

Mount Wilson, on the other hand, the chisquare test gives some probabilities so small

that one need not be disturbed by an uncertainty of one or two in the number of degrees of

freedom. Several tests were made. With the

combined data from the northern and southern

hemispheres, the probability that fluctuations

as large as the observed ones would arise by

chance was about 1 in 10* (or P~10~*) when

odd 2° sums (1+2°, 3+4°, etc.) were used.

With even sums (2+3°, 4+5°, etc.), however,

the fluctuations were barely significant, with

P~0.05. The reason for this difference appears

to be that the significance of the fluctuations

arises primarily from the subsidiary peaks at
22 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 5

S 40 30 20 10 0 10 20 30 40 N 40 N

FIGURE 5.—Distribution with latitude on the sun of numbers

(N) of sunspot groups, plotted in 2° running means, for

sunspot cycles Nos. 15-19; data obtained from observations

made at Mount Wilson in the years 1917-1958.

7-8° and 17-18°, which contribute more

effectively when combined in the odd manner

(i.e., not split into 6+7 and 8+9, etc.).

If the spot numbers for the northern and the

southern hemispheres are tested separately, by

comparison with a single mean smoothed curve,

the probabilities for chance occurrence of the

observed fluctuations become 1 in 10s for the

northern and 1 in 500 for the southern hemisphere (P~10"5

 and 0.005); and P~10~7 for

300 _

200 _

FIGURE 6.—Distribution with latitude on the sun of total

numbers (AT) of sunspot groups, plotted in 2° running

means; data obtained from observations at Mount Wilson

in the years 1917-1958.

north plus south. If the numbers for north and

south are tested separately and each compared

to its own smooth curve, one obtains P~10~6

for the north, P~0.5 for the south, and P~10~8

for north plus south. Thus the evidence for nonrandomness is impressive only for the northern

solar hemisphere.

Tests of the Mount Wilson numbers for

individual sunspot cycles (fig. 5) indicate that

the fluctuations in cycles 15 and 18 are not

statistically significant. Cycle 16 gives

P~0.02, and cycle 17 gives P~0.001.

Properly, chi-square tests are of course not

applicable to measures of intensities, such as

magnetic field strengths. However, to obtain

some approximate idea of the significance of

the variations in the field-strength curves

(figs. 3, 4), I normalized H to H' so that the

total number of spots, N, equaled total H',

thus making the units in Hf comparable to

those in spot numbers. Chi-square tests on

H' gave P<10~10 with north and south combined throughout the test; odd sums were

used. When the solar hemispheres were tested

separately, and each compared with its own

smooth curve, the north gave a probability

P<10~8, the south gave P~0.08, and north

plus south gave P<10~7, that the fluctuations

are of a random character.

Thus, statistically, the field-strength data

provide more persuasive evidence for multizonality than do numbers of spot groups.

The evidence from Mount Wilson numbers is
NO. 8

S 40 30 20 10 0

T

STRUCTURE OF THE SUNSPOT ZONE

10 20 30 40 N S 40 30 20

23

10 20 30 40 N

FIGURE 7.—Distribution with latitude on the sun of numbers

(N) of sunspot groups, plotted in 2° running means, for

sunspot cycles Nos. 15-18; data obtained from Greenwich

observations for the years 1912-1954.

better than that from Greenwich numbers.

In Mount Wilson data the evidence is stronger

by far in the northern than in the southern

solar hemisphere. Most of the statistical

significance arises from the major secondary

peaks at 7-8° N and 17-18° N.

These results make it impossible to distinguish conclusively among the three pictures

of the sunspot zone and its latitude shift, from

presently available observations alone. We

shall need further and different observations,

and/or a theory based on one of the hypotheses which will satisfactorily explain the

apparent shift of the zone(s) over the cycle.

On the other hand, the probability that the

northern hemisphere distributions could arise

100 _

FIGURE 8.—Distribution with latitude on the sun of total

number (N) of sunspot groups, plotted in 2° running means;

data obtained from observations at Greenwich in the years

1912-1954.

N

10

0

0

0

0

0

S 30 20 1

-

A A/

AA

i

V

w

V

A/

0 0

1 • i

A

v

\ y v

AM AA

A,

Vi

•/

0 20 30 N

1

AVA

1

A A

V \

v y • >

V V

A ,

V

 V

-

a

c

FIGURE 9.—Number (N) of local maxima in 2° sums, at various

solar latitudes, derived from: a, Greenwich numbers of

sunspot groups for the years 1912-1954; b, Mount Wilson

numbers of sunspot groups, 1917-1955; c, sunspot magnetic

field intensities, 1917-1955.

by chance is so small that theoreticians would

seem justified in seriously exploring the multizonal concept of sunspot activity. The low

probability may justify also some further

discussion of the data here compiled, in the

light of such a concept.

If we are to accept a multizonal picture

even tentatively, we should be able to say with

some confidence where the maxima and minima

of the subzones lie. I have already referred

to the subsidiary maxima at 7-8° and 17-18°,

which contribute the largest chi-square deviations found in the Mount Wilson data. From

the location of these peaks and from the curves

shown in figures 3-6, one can conclude that
24

N

40 L_

30

20

30

1920

I I l I I l i l i I I I I l I I I I

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

1930 1940 1950 I960

1 i I

- ^

the apparent maxima of spot activity lie at

latitudes between the multiples of 5°, with

local minima approximately at the multiples

of 5°. In the north the principal maximum

lies at 12-13°, with a third secondary peak

clearly visible at 21-22°.

The subzones can be located also by study

of the 2° nonrunning sums. On a graph of

time against solar latitude, I plotted the latitudes of peaks and subpeaks for each year,

for both Greenwich and Mount Wilson data.

The number of peaks in each latitude interval

was counted, with the results shown in figure 9.

Two to three times more maxima occur at

some latitudes than at others, and most of

these peaks fall clearly between the multiples

of 5°. In this respect the patterns from

Greenwich and Mount Wilson data agree fairly

well. Again, the northern solar hemisphere

shows a more orderly pattern than the southern

hemisphere.

Figure 10 shows the location of peaks derived from the 2° running means of total H;

that is, from the data of figures 1,2. Because

running means permit more wobbling in the

position of the local peaks, they do not locate

the zones as clearly as do the 2° nonrunning sums employed in figure 9. To illustrate

more vividly the multizonal concept, on figure

FIGURE 10.—Caterpillar diagram, illustrating the multizonal concept

of sunspot activity. The dots and

crosses represent the peaks in the

curves of figures 1, 2, plotted at the

appropriate year and solar latitude.

The crosses locate the highest peaks

of the year; the dots represent the

secondary peaks and vary in size

roughly according to their importance. The caterpillars enclose

peaks postulated to belong to a

single narrow activity zone. (A second graph of local minima was

used to help locate the boundaries,

and accounts for many of the seemingly arbitrary wiggles.)

10 I have drawn curves enclosing maxima

which might reasonably be considered as

springing from a single belt of activity. In

contrast to the famous butterfly diagram, figure 10 might be termed a "caterpillar diagram."

A second graph, of the local minima, was used

as a guide in determining which belt a given

point seemed to belong to; thus the outlines

of the individual caterpillars are somewhat less

arbitrary than they might at first appear to be.

Figure 11 shows the number of spot groups,

and figure 12 the amount of magnetic field

strength (in percentage of total H in the hemisphere for the given sunspot cycle), per 5°

zone of latitude per year. The principal reason for plotting H in percentages is that the

average value of H appears to have changed

during the years under study (see Bell, 1959).

The average magnetic field strength is larger

for cycles 15 and 16 than for subsequent cycles,

as may be seen from the composite N and H

curves in figures 13 and 14. Figure 15, showing the mean annual spotted area (Greenwich,

1955), indicates a similar decrease in the ratio

of field strength to area. Nicholson (personal

communication) advises that this decrease may

possibly result from changes in observing

procedure at Mount Wilson.

Differences between the Mount Wilson and
STRUCTURE OF THE SUNSPOT ZONE 25

1910 1920 1930 1940 1950 i960

>35°

" 31-35°. .. .

-26-30° . '•

-21-25° "

-16-20° *

- 11-15°

- 6-10° •

-0-5 °

1910 1920 1930 1940 1950 I96 0

I I I I I I I I I I I I I I I I I I I I I I I I

a

FIGURE 11.—Number (N) of spot groups per year in each 5° zone of heliograpbic latitude. Solid line, Mount Wilson data; open

circles, Greenwich data. <J, In the northern solar hemisphere; b, in southern hemisphere.

Greenwich numbers of spot groups (figs. 11,

13) can be accounted for by the fact that

Greenwich sunspots "seen on one day only"

and Mount Wilson spots without published

field strengths were omitted from this study.

Completeness of the H data for small spots, of

100-200 gauss or so, varies from year to year.

In figures 11 and 12, note the great enhancement of spot activity in the higher latitudes,

which appears more or less simultaneously in

the northern and southern hemispheres during

the present sunspot cycle (No. 19). Since

cycles characterized by high sunspot numbers

tend also to show a rapid rise to maximum

(Waldmeier, 1935), perhaps unusually vigorous

activity in the higher latitude subzones may

be necessary for the occurrence of an unusually

high sunspot maximum.

From figures 1, 2, and 12 one can see that

the subzones have a retardation in phase of

about one year per 5°, or one year per zone.

This fact suggests the interesting speculation

that the reversal of the general magnetic field

of the sun, recently found by Babcock (1959),
2 6 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 5

1920 1930 1940 1950 I960 1920 1930 1940 1950 I960

1—1—1 1 1 i—1—1—I—1—r—1—i—r—1—1 1 1 1 1 1 1

a

FIGURE 12.—Percentage of magnetic field intensity (H) of sunspots in each 5° zone per year. Percents are taken relative to the

total H observed at Mount Wilson in the particular cycle and hemisphere. (Total H for cycle No. IS was estimated from

Greenwich spot numbers, for cycle No. 19, arbitrarily taken as 20,000 for each hemisphere, about 12 percent above that observed

in cycle No. 18; the points of cycle No. 19 are shown as larger open circles with broken lines.) a, In the northern solar hemisphere; b, in southern hemisphere.

might be considered as a manifestation of the

phase lag at high latitudes. In 1953, late in

cycle No. 18, the sun's general magnetic field

had a polarity opposite to that of the lead

spots in the respective hemispheres. At the

start of the new cycle the lead spots and the

general field had the same polarity. After the

reversal of the general field in 1957-58, the

polarities of the general field and the lead spots

were again opposite, as if cycle No. 20 had

already begun at the poles. The polar faculae

appear also to have their maximum frequency

around the time of the general sunspot minimum, being thus perhaps in phase with the

general field.

This paper may have raised more questions

than it has answered. However, the observations now available apparently do not permit

any decisive choice among the available concepts of the sunspot zones. Perhaps a more

detailed study of local magnetic fields would

be useful.

Menzel (personal communication) has pointed

out that if the fluctuations in spottedness with

latitude are real and meaningful, the significant

aspect may be the minima rather than the

maxima. Instead of belts of greater activity,

the sun may have regions of suppression in a

single zone—in the manner of zonal harmonics.

Only intensive theoretical work can resolve

these questions.

Acknowledgments

The work reported in this paper has been

supported by the Air Force Cambridge Research Center, Geophysics Research Directorate, through contracts AFl9(604)-1394 and

AFl9(604)-4962 with Harvard University.
1910 1920

STRUCTURE OF THE SUNSPOT ZONE

1930 1940 19 50 I960

27

N

400

200

1910

400

200

I \ I T i [ r i T

i i i i i i i i i i i i i i i I I i i i

i i i i i i i i i i i i i i

I I I l I il l il l i i i _ I i

FIGURE 13.—Total number (N)

of sunspot groups per year

in the northern (top) and

southern hemispheres. Solid

195 0 l96 9 line, Mount Wilson data;

open circles.Greenwich data.

FIGURE 14.—Total sunspot magnetic field

intensity in the northern (top) and 0

southern hemispheres observed at

Mount Wilson per year, plotted in units

of 100 gauss.

H

3200

240 0

1600

8 0 0

0

1920 1930

II l i I I 1 l

: \

: \

: \ rvA

: \ / \

I I i i i i i i

1940

i l l 1

KK

\

/ \

1950

i l l II

J\ A

I960

-

I \ -—

i 1

1920 1930 1940 1950 I960
28

1910

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

1920 1930 1940 1950

VOL. f

I I I I

•A

1200

800

400

0

1910 1920

I / 1 1 "

•

1 1 1 1 1 1

9 3 0

1 l 1

V

1 1 1

i 1

/

J

1 1

1940

1 1

A

\

1 1

1950

1 I i

n

1

k

\

/ \ J \

1 1 1 1

1 I 1

—

-

-

1 1 1

FIGURE IS.—Mean annual spotted

area (A) (Greenwich, 1955) in

the northern (top) and southern

hemispheres.

References

BABCOCK, H. D.

1959. The sun's polar magnetic field. Astrophys.

Journ., vol. 130, pp. 364-365.

BECKBB, U.

1954a. Die Struktur der Fleckenzone. Zeitschr.

Astrophys., vol. 35, pp. 137-144.

1954b. Die Eigenbewegung der Sonnenflecken in

Breite. Zeitschr. Astrophys., vol. 34, pp.

129-136.

BELL, B.

1959. On the magnetic field strengths of sunspots.

Publ. Astron. Soc. Pacific, vol. 71, pp.

165-167.

GREENWICH, ROYAL OBSERVATORY

1955. Sunspots and geomagnetic storm data,

1874-1954. 106 pp.

LOCKYER, W. S. J.

1904. Sunspot variation in latitude, 1861-1902.

Monthly Notices Roy. Astron. Soc, vol.

64, pp. [5H15].

MAUNDER, E. W.

1904. Note on the distribution of sunspots in heliographic latitude, 1874-1902. Monthly

Notices Roy. Astron. Soc, vol. 64, pp.

747-761.

1913. Distribution of sunspots in heliographic

latitude, 1874-1913. Monthly Notices

Roy. Astron. Soc, vol. 74, pp. 112-116.

WALDMEIER, M.

1935. Neue Eigenschaften der Sonnenfleckenkurve. Astron. Mitt. Zurich, vol. 14,

pp. 105-130.

1939. Die Zonenwanderung der Sonnenflecken.

Astron. Mitt. Zurich, vol. 14, pp. 470-481.

Abstract

Published data on the magnetic field strengths and numbers of sunspots for the years 1917-1958 are used to

study the structure of the sunspot zone as a function of heliographic latitude. Some evidence is presented in favor

of the hypothesis that several zones of activity develop in each solar hemisphere, and that these zones remain stationary in latitude and are just sufficiently out of phase to simulate the latitude shift over the solar cycle described by

Spoerer's law. A caterpillar diagram is proposed to supplement the well known butterfly diagram.