Smithsonian

Contributions to Astrophysics

VOLUME 3, NUMBER 4

SOME SUNSPOT AND FLARE STATISTICS

by BARBARA BELL and HAROLD GLAZER

SMITHSONIAN INSTITUTION

Washington D. C.

1959
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Some Sunspot and Flare Statistics

By BARBARA BELL1 and HAROLD GLAZER2

Hale and Nicholson (1938) have studied the

distribution of the 1915-1924 sunspots among

the magnetic classes. Giovanelli (1939) has

investigated the relation of flare frequency to

sunspot area and to magnetic class, using 1935-

1937 data. For our recent study (Bell and

Glazer, 1958) of the relations between some

properties of sunspots and geomagnetic conditions, we accumulated on punch cards a substantial quantity of sunspot and flare data for

the years 1937—1953, which can be used to

bring up to date and supplement some aspects

of these earlier studies.

The present investigation employs information on 5,940 sunspots, observed from 1937

through 1953atthe Mount Wilson Observatory

and reported in the Publications of the Astronomical Society of the Pacific, and 8,403 flares

reported during the same period in the I. A. U.

Quarterly Bulletin of Solar Activity. For each

sunspot group listed by Mount Wilson in the

P. A. S. P., the following quantities relevant

to the present discussion were punched: magnetic classification, maximum magnetic field

strength, a duration factor, and the number of flares observed in the region. We

also used the area data on spot groups larger

than 500 millionths of the solar disc, published

by the Greenwich Royal Observatory (1955).

The Mount Wilson classification of sunspots

according to their magnetic properties provides

the basic data for our investigation. This

system, developed by Hale and Nicholson

(1938) from observation of hundreds of spot

fields and the distribution of their associated

calcium plages, recognizes unipolar (a), bipolar

(/3), and complex (7) groups, with the following

distinguishing properties:

Unipolar groups are single spots or groups of

1

 Harvard College Observatory, Cambridge, Mass.

1

 Formerly at Harvard College Observatory, Cambridge, Mass.; now

at Raytheon Maynard Laboratories, Maynard, Mass.

spots having the same magnetic polarity. They

are subdivided according to the position of the

group in its calcium plage into the following

classes:

a: Spots having a fairly symmetrical distribution of

calcium plages preceding and following the group.

ap: Spots situated in the preceding part of an

elongated plage.

af: Spots situated in the following part of an

elongated plage.

Bipolar groups in their simplest form consist

of two spots of opposite polarity. Often, however, the bipolar group is a stream of spots,

those in the preceding and following parts of

the group being of opposite polarity. Bipolar

groups are subdivided into the following classes:

0: Groups whose preceding and following members,

whether single or multiple, are approximately equal in

area.

/3p: Groups whose preceding member is the principal

component.

0f: Groups whose following member is the principal

component.

Semicomplex (fiy) groups have bipolar characteristics, but no clearly marked dividing line

between the spots of opposite polarity. This

class includes groups whose preceding or following members are accompanied by small

spots of the opposite polarity.

Complex (7) groups are those which have the

polarities so irregularly distributed that they

cannot be classified as bipolar; sharply bounded

regions of opposite polarity sometimes exist

within the same penumbra.

The Mount Wilson classification places the

symbols I or d before the magnetic class to indicate whether the spot rotated around the east

limb or was born on the disc; similarly, an / or d

after the magnetic class indicates whether the

spot rotated around the west limb or died on the

disc. From these data, plus the published dates

when the spot group was first and last observed,

we have constructed a "duration factor" which

25
26 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

divides sunspots into the following ten categories :

II: Groups that cross the disc, from east limb to

west limb.

Id,, lde, ldw: Groups that appear around the east

limb and die, respectively, on the disc east, within one

day either side of central meridian passage (CMP), or

west.

d.l, del, dj: Groups that are born on the disc east,

within one day either side of CMP, or west, respectively, and disappear around the west limb.

djLt, drd*, dJK: Groups that are born and die on

disc east, on disc west, and those that are born east

and die west.

Each spot group was placed in one of these ten

categories, usually without uncertainty. But

in some cases, where cloudy weather prevented

a definite classification, we inade assignments

more or less arbitrarily. We have no reason to

believe that these occasional arbitrary assignments have introduced any serious error in any

of the results.

Distribution of spot groups among magnetic

classes

Table 1 shows the frequency distribution of the

5,940 sunspot groups among the various magnetic classes. The spots are subdivided by

date, according to phase of the sunspot cycle.

While the exact dates of division are of course

arbitrary, the intervals do correspond roughly

to the maximum, declining (decl.), and rising

phases of the solar activity cycle.

Table 1 gives the percent of spot groups in

each magnetic class for the five periods. The

percents of the classified spot groups are taken

with reference to the total number of classified

groups, the quantity given in the next to last

column; but the frequency of unclassified spots

is taken relative to the total number of all

groups, given in the last column. The rows

labeled "North" and "South" give the average

distribution of spot groups in the respective

solar hemispheres, while the row labeled

"mean" gives the over-all average results for

the 17 years and 5,940 spot groups. In the

final row of the table we reproduce the frequencies obtained by Hale and Nicholson

(1938), to facilitate comparison.

The most striking difference between the last

two rows of table 1 is the great increase in the

frequency of unclassified spot groups in the

later period. In the earlier period the Mount

Wilson observers attempted to obtain daily

polarity measures for every group, whereas in

more recent years they have attempted to obtain polarities only once or twice during the

life of a group. This change in policy (see

Publ. Astron. Soc. Pacific, vol. 48. p. 124, 1936)

appears to explain fully the increase in unclassified groups which occur primarily among the

small and short-lived spots.

We see also for the more recent period a decline in the relative frequency of a and fip

groups with a corresponding increase in the frequency of ap and fi. If we consider merely the

unipolar and bipolar categories, without regard

to the p or / subdivisions, we find agreement

within one percent with the distribution obtained by Hale and Nicholson. Nicholson

states (private communication) that the differences can probably be adequately explained by

changes in the methods of classification.

When the first classifications were made and

the laws of polarity distribution were not well

established, a group would be classified as a or

as ap solely by its position in the surrounding

calcium plage. Now, however, if a spot is

known to be the surviving leader-spot of a bipolar group, it will be classified as ap even

though its position in the plage on a majority

of days might be closer to that of a simple a.

Since many unipolar spots were formerly bipolar, this change in procedure clearly tends to

increase the percentage of ap and diminish that

of a. The absence of any increase in the aj

frequency results from the fact that the follower

spot usually disappears some time before the

leader spot.

In the early classifications of fi and fip, a very

slightly greater field strength in the leader

would yield a fip. More recently, however, a

group is likely to be called fi unless the difference between the spots is greater than the probable error of the field strength or area. Thus

fi's have become more common at the expense

of fip, and ap at the expense of a, although the

total percentages of unipolar and bipolar groups

remain unchanged.

Table 2 shows the percentage of sunspot

groups in each magnetic class when the spots

are subdivided according to their maximum

magnetic field intensity, H. The bottom row

repeats the mean frequencies to facilitate com-
SOME SUNSPOT AND FLARE STATISTICS 27

parisons. In subsequent discussion we shall

sometimes refer to these as the "expected" frequencies. Table 2 shows that sunspots of

strong and of weak magnetic field intensities

differ in their distribution among the magnetic

classes. Among the spots of large field

strength, the classes ap, fip, fiy, and 7 appear in

excess of the expected frequency, while among

the groups of small field strength the a, af, /3,

and /8/" are more numerous. The increase in

percent of fip and corresponding decrease in fi

is especially noteworthy as the field strength

increases. The results in table 2 suggest that

groups in which the follower spot is larger than

or equal to the leader are much less likely to

attain a large field strength and size than those

in which the leader spot is the larger. One

would infer that a more stable configuration

exists when the leader spot is the larger, or is

the only on« present.

Table 3 shows the percentage distribution

among magnetic classes for the spots of at least

2,000 gauss magnetic field intensity, subdivided

according to mean area of the spot group. It

has previously been found that the central

magnetic field intensity increases systematically

with the area of the individual spot up to an

area about 300 millionths and remains substantially constant for larger spots (Nicholson,

1933; Houtgast and van Sluiters, 1948). Group

areas are not closely related to the magnetic

field strength of any member spot. Previously

published figures on field intensities and areas

of large (^4>500) spot groups (Bell and Glazer,

1958, tables 1 and 2) indicate that any relation

between the two quantities is slight, particularly for the fi and a spots, and the scatter is

large. In general, however, one can certainly

say that the spots of HS900 gauss are small,

those of 1,000 to 1,900 gauss are small to

medium, and those of H> 2,000 gauss are

medium to large in area.

Table 3 shows a dearth of unipolar spots of

large area, as would be expected when group

areas are considered. Although there is a

dearth of fi and fij spots in all categories where

fi> 2,000 gauss, this deficiency is no more

conspicuous for groups of very large area than

for moderately large groups. If we consider

only the combined bipolar population with

H>2,000 gauss, the proportion of fi+fif groups

is greater for areas >750 than for areas <750

millionths.

The most noteworthy feature shown in

table 3, however, is the marked increase in

relative frequency of magnetically complex (7)

and semicomplex (fiy) sunspots with increase in

area of the group; this suggests that magnetic

complexity may be a form of instability tending

to occur when a spot group becomes unusually

large. Such an instability may be qualitatively

explained by a recent theory of active regions

(Krook and Menzel, 1957; Krook and Wild,

1957) which indicates that the inhibition of convection within a spot by its magnetic field

leads to a compensating enhanced convection

in the facular regions surrounding the spots.

The complex fields seen in so many of the largest

spot groups may arise from the conflict, over an

unusually large area, between the forces of convection and of magnetic inhibition. Menzel

(private communication) has suggested that the

forces of convection may churn up the magnetic

lines of force and associated electric currents,

redistributing them in the observed complex

and irregular patterns.

Table 4 presents a further subdivision, with

the duration factor added. This table gives the

ratio of frequencies, observed divided by expected, where the "expected" is the mean distribution, given in tables 1 and 2, and the

"observed" is the frequency percentage distribution for the specific magnetic field strength

and duration class. For convenience in discussion we may speak of the duration groups as

containing mature (U), dying (Id), young (dl),

and short-lived (dd) sunspots.

Inspection of table 4 reveals that mature sunspots show a marked preference for the classes

ap, fip, fiy, and 7, a preference which is more

marked for the larger mature spot groups but

which is still evident in those of middle size.

Very few small spots survive from limb to limb.

Dying spots, when large, appear in excess in the

unipolar categories ap and a and in a, ap, af,

when small. The excess of unipoles and dearth

of bipoles is greatest for the groups that die east

of CMP (Id,) and least for those dying west of

CMP; i. e., greatest in those groups where the

spots are nearest to extinction. Young spots,

on the other hand, tend to be bipolar and to

concentrate in ftp, fij, fiy if large, and in simple
28

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

/3 if small. Short-lived spots tend to be small

and to favor a, aj, and /3 in excess of the

expected frequencies.

These quantitative results are in accord with

the more general observations of Hale and

Nicholson (1938), who pointed out a conspicuous tendency for spots to begin life as bipolar

groups, with the follower spot tending to break

up first and leave the group as unipolar for its

last several days. They also emphasized the

predominance of the bipolar condition, and the

tendency of unipolar groups to hover on the

edge of bipolarity, as evidenced by the preponderance of ap (bipolar plages) and the occasional

detection of invisible magnetic spots in groups

that never attained a visibly bipolar condition.

Among the spot groups of area > 500 millionths, we find 78 percent II (2/8, 0y, and all

a, 7), 20 percent dl (2/3, ffy), and only 2 percent

Id (2/3, 0y). The frequencies of dl and Id appear

compatible with the Greenwich (1925) finding

that, in the case of large long-lived spot groups,

the size of individual spots tends to increase

rapidly at the start, reach a maximum around

the ninth day, and then slowly decline.

East-west asymmetry

The classification according to duration can be

used to investigate some aspects of the question

of an apparent east-west asymmetry in sunspot

distribution on the solar disc. An east-west

asymmetry was found originally by Maunder

(1907) from Greenwich sunspot data comprising 15,721 observations of 2,870 spot groups for

the years 1889-1901. She found that (1) the

eastern solar hemisphere contained about 51

percent of the total sunspot area and 52^ percent of the tot&l number of spot groups; (2) of

the total spots observed, 33 percent appeared

by rotation at the east limb while only 27 percent disappeared by rotation over the west

limb, or 6 percent more spots dissolved on the

visible disc than were born there; and (3) about

twice as many groups were seen to develop

east than west of the central meridian. Partial confirmation of these results was found by

Pocock (1918) for the years 1902-1917, and by

Rodes (1922) for 1910-1920 sunspots. The third

aspect of the asymmetry has been confirmed

by Waldmeier (1939) for 1925-1929, and by

Mme. d'Azambuja (1955) for 1919-1947 spots.

Mme. d'Azambuja finds not only that about

twice as many centers of activity appear to arise

east than west of the central meridian, but also

that the eastern-born centers are more durable.

(For other references see Kiepenheuer, 1953;

Waldmeier, 1955, p. 160; Link, 1954.)

Table 5 gives the percent of spot groups in

each of the ten duration classes and three

field-intensity groups, with the entire table,

rather than each row, totaling 100 percent.

In table 6 we have combined certain columns

of table 5 to better illuminate some aspects of

east-west asymmetry. The last two columns,

of spot groups visible east and west, give a

western excess of about 2 percent (E 75 and

W 77 percent). The first two columns reveal

that in the 1937-1953 period 2 percent more spot

groups by rotation departed at the west limb

(WL, 36 percent) than entered at the east limb

(EL, 34 percent), and 2 percent more spot

groups thus arose than dissolved on the visible

disc. These results indicate that parts 1 and 2

of the eastern excess found by Maunder do not

appear in the Mount Wilson data for 1937-1953.

On the other hand, from the central columns

of table 6, we see that 2.1 times more sunspots

appear to be born east than west of the central

meridian, while 2.3 times more spots appear to

die west than east of CM, in good agreement

with the third aspect of east-west asymmetry

found by Maunder, as well as the recent results

of Mme. d'Azambuja. For this eastern excess

in spot births, Schuster (1911) has given what

appears to be the most probable explanation,

that "the predominance of the eastern half

mainly points to an increased facility of detecting a sunspot when it is near the center of the

solar disc." From a discussion of a generalized

visibility function he concluded that "this

excess, therefore, only proves an increased

condition of visibility near the center, but, in

itself, no want of symmetry."

The probable correctness of Schuster's explanation is indicated, we believe, by the

individual columns of table 5. These columns

are separated by vertical lines into geometrically

similar groups. The first three columns have

no bearing on the east-west asymmetry in spot

birthplaces. The next two, comprising shortlived spots, give an excess of less than one

percent in favor of east (E 13.5 and W 12.8
SOME SUNSPOT AND FLARE STATISTICS 29

percent). This small eastern excess does not

appear significant, particularly in view of the

greater degree of uncertainty in the classification of short-lived (dd) groups. (In the case

of short-lived groups we have no dc category for

spots born or dying on the day of CMP, and

such spots have been arbitrarily assigned to

de or dw; spots seen only on the day of CMP

were classified as d,flw.)

The key to the asymmetry would appear to

lie in the last five duration classes. If, in fact,

independently of whether they are detected,

equal numbers of spots are born east and west

of central meridian, then the numbers N(didV!-\-

dJL) should equal N{dJ). Actually, among the

detected spot groups, we see that N{dJ) <CN(dJ,),

without even considering the large d^dw group.

However, since all spots in the ded^ and the dJL

groups must cross the central meridian, one

may assume that only an insignificant percent

would escape detection. Spots of the dJL group

never cross the central meridian and many

may escape observation. If we assume an

equality of births east and west, 214 spots

should exist undetected in the dj. group for

every 67 that are seen. Presumably most of

these would fall in the group with low field

strength. Applying similar reasoning to the

asymmetry of death place, we find that 239

spots should exist undetected in the ldt group

for every 47 that are seen. A greater percent

of ldt spots than of dj, spots appears to escape

detection.

The principal asymmetries manifested in

table 5 can be explained, at least qualitatively,

by two facts: sunspots are much more easily

detected near the center of the solar disc; and

spot groups tend to grow rapidly in their early

stages and to die out more slowly. Any quantitative discussion of the observed asymmetries

and of the adequacy of the suggested interpretations, as well as any analysis of the visibility

function, would require a finer subdivision of

spot lifetimes and birthplaces than is tabulated

on our IBM cards.

Flares and magnetic class of spot groups

Tables 7 and 8 present the distribution of the

8,403 solar flares observed in the years 1937-

1953 according to the magnetic class and field

intensity of the sunspot groups with which the

flares are associated. Table 7 gives total numbers of flares, and 8 gives the percent in each

category of sunspots. Tables 9 and 10 show

the average number of flares observed per sunspot group of the various types. Tables 7 to

10 show that for a given magnetic class the frequency of flare production increases markedly

with increasing field strength of the associated

spot group. This result is not unexpected, since

Giovanelli (1939) previously found a relation

between frequency of flares and area of the

spot group, and, as we discussed earlier, there

is at least a general relation between area of a

spot group and the maximum magnetic intensity of its largest component spot.

Tables 7 to 10 also show that the frequency of

flare production depends on the*magnetic class

of the associated sunspot. Bipolar spot groups

produce more flares than unipolar groups of

comparable field intensity, while magnetically

complex groups produce the largest average

number of observed flares.* This result is in

accord with that of Giovanelli (1939) although

no detailed comparison is possible because he

studied only those spot groups that produced at

least one observed flare, and counted each group

anew each day it appeared on the disc. However, the results in table 8 suggest a stronger dependence of flare productivity on sunspot magnetic class than Giovanelli found. This difference may be partially explained by area considerations (to be discussed in the next section^

and partially by Giovanelli's omission of groups

possessing no observed flares. Flareless spots

are relatively rare among complex groups, and

most numerous among unipolar groups. If,

therefore, we considered only those groups with

one or more observed flares, the average number

of flares per spot group would be increased sub-

•XOTE ADDED IN PROOF: At the Moscow (1958) meeting of the International Astronomical Union. A. B. Severny reported that, according

to observations with the solar magnetograph at the Crimean Astrophysical Observatory, flares originate at "neutral points of sunspot

magnetic fields, when the gradient of field strength is sufficiently high in

the vicinity of such points."

The greater flare productivity of 7 and 0y spots can be readily understood, at least qualitatively, in the light of Seventy's observations, because the required neutral points should be most numerous in magnetically complex spot groups where the positive and negative polarities

are more or less intermingled.

At the same meeting Hoyle and Gold presented a theoretical paper

outlining a method of storage and sudden release of flare energy in the

chromosphere. Also according to their theory, neutral lines should be

the seat of flares; and the energy storage would require uncommon field

configurations, which should occur more often in complicated spot regions

than in simple ones.
30 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

stantially for unipolar spots, moderately for

bipolar, and scarcely at all for complex groups;

the dependence on magnetic class would thus

be minimized.

This point may be further illuminated by

table 11, which shows the percent of spot groups

in each magnetic class that produced no observed flares, and by table 12, which shows the

percent of groups that produced ten or more

observed flares. A large (Jy or y group (H>

2,000 gauss) appears almost certain to produce

a few flares and likely to produce a large number; 60 percent of these complex spots produced

ten or more observed flares, in contrast to 17

percent of the bipolar and a mere 3 percent of

the large unipolar spot groups. An essentially

similar result was obtained bj7 Richardson

(1951). Newton (1943) has pointed out that

the majority of very large (3+) flares are also

associated with magnetically complex spot

groups.

In this connection it is interesting that Behr

and Siedentopf (1952) found that, in the years

around the 1947 sunspot maximum, the ratio

between the number of flares and the sunspot

relative number was some 25 percent less than

around the 1937 maximum. The data in table

1 show that complex spot groups were relatively

less frequent around the 1947 maximum than

around the previous maximum, and this deficiency in 1947 (or excess in 1937) may be related

to the findings of Behr and Siedentopf.

The duration classes have been used to investigate in a preliminary way whether a significant difference in flare productivity exists

between recently born, mature, and dying spot

groups. Table 13 shows the average number

of observed flares per spot group for the three

basic magnetic types, various duration classes,

and the two categories of larger field intensity.

Since the data on our IBM cards provide no

means of obtaining exact mean lifetimes for each

group, it seemed advisable to present the table

in this form rather than to attempt an approximate and possibly misleading tabulation of

flares per spot group per day. Thus, in table 13

one may meaningfully compare the group Id*

with dJL but neither of these with any other

duration group unless one keeps in mind the

difference in number of observing days for the

group.

It has commonly been said that young spot

groups produce more flares than do dying

groups. When all classes are taken together,

the data in table 13 support this opinion: dl

groups produce more flares than corresponding

Id groups. However, if we compare spot groups

of a given magnetic class, we see that this apparent advantage for young spot groups all but

disappears. The data in table 13 seem to indicate that magnetic class rather than phase in

the life cycle of a spot is the more important

factor in the rate of flare production. The

greater flare productivity of young spot groups

may well be connected with the tendency of

young groups to be bipolar and dying spots to

be unipolar, rather than with the phase of the

life cycle in itself.

Flare frequency in groups of large area

While Giovanelli found a general over-all relation between field strength of a spot and its flare

productivity, he also found the latter property

to be more closely related to area of the spot

group. For spot groups in a particular area

interval, 300 to 400 millionths, he found very

little relation between maximum field intensity

and flare productivity.

We have investigated the relation between

area and flare productivity in spot groups of

mean area greater than 500 millionths. For the

years 1937-1953, Greenwich (1955) lists 271

spot groups of this size, of which 248 had a maximum field strength greater than 2,000 gauss,

while 23*fell in the range 1,000 to 1,900 gauss.

In table 3 we gave the distribution of the spot

groups of large area among the various magnetic

types. Table 14 lists the average number of

flares observed in spot groups of maximum field

strength greater than 2,000 gauss, subdivided

according to the area of the group. In each

magnetic class flare frequency increases in a

conspicuous and systematic way with increase in

area of the group. Within a given area interval

complex spot groups produce more flares than

do bipolar groups, but, because of the tendency

of complex groups to be large in area, the contrast between magnetic types is less striking

than when area is not considered, and the relation is closer to that found by Giovanelli.

Table 15 presents the average number of

flares observed per unit (10~s of solar disc) of
SOME SUNSPOT AND FLARE STATISTICS 31

spot group area (or, 10F/A) based on the 271

spot groups with mean area greater than 500

millionths.

Figure 1 shows the mean number of observed

flares plotted against mean spot-group area and

FIGURE 1.—Relation between the average number of observed

flares (F) and the average area of the sunspot group (A),

for sunspot groups larger than 500 millionths of the solar disc.

The spot groups are divided into four magnetic classes, which

are distinguished by the following symbols: dots (•),

a spots; crosses (X), 0 spots; filled circles ( • ), fiy spots;

and open circles (o), y spots.

various intervals of area. Each magnetic class

is plotted separately. The lines were determined from the plotted points by the method of

least squares to fit the relation Ft—C+B At.

The top section of table 16 gives the parameters

of these least squares solutions, where each mean

point was weighted according to the number of

spot groups contributing to it. The table also

gives sF, the standard error3 of Ft predicted

from the equation, and r2 where r is the coefficient of correlation. As we previously noted, the

complex spot groups produce the most flares per

unit area and the unipolar spots the fewest.

For the large spots in our sample this difference

between magnetic classes appears in the intercepts rather than in the slopes of the lines,

which do not show any systematic variation

with magnetic class.

The intercepts for the /3 and the a spots pass

satisfactorily close to the origin, so that these

relations may be assumed to apply also to spots

1

 These standard errors are underestimates because they do not take

account of the uncertainty in B and C; furthermore, they can be only

approximate because F does not actually have a normal distribution

about the line.

473209 O-59 2

of smaller area. For the fiy and the y spots,

however, the intercepts are large. The slope

and the intercept for the fiy spots are strongly

influenced by the five spots of area >2000

millionths. If these are omitted, we obtain

£=1.55X10"2 and (7=2.20; but the improvement in sF and r2

 is negligible. If the fiy and y

lines were forced to pass through the origin,

the correlations would be lower but the slopes

would then show a systematic increase with

magnetic complexity, of the sort found by

Giovanelli (1939). For example, if the lines

were drawn arbitrarily through the origin and

the mean, we should obtain Z?(7) = 1.90X10~2,

£(j87) = 1.55X10-2, B(fi) = 1.20 Xl0~\ and

i?(a) =0.8X10~2. If we ignore the two points

corresponding to the largest areas and pass the

lines through the origin, we obtain B(y)»2.7

X10~2 and £(07)«1.8X1O-2. This situation

clearly suggests that the relation between flare

productivity and area of the spot group is not

linear over the entire range of areas, particularly

for the y and the fiy spots. Even from figure 1

there is an indication that spots of intermediate

area, around 1,000 millionths, may be more

efficient flare producers per unit area than are

the very largest spot groups.

We accordingly also plotted the mean numbers of observed flares against the logarithms

of the mean areas, with the result shown in

figure 2. The middle section of table 16 gives

the least squares parameters for the relation

Ft= C-\~BlogAt. If we compare the corresponding values of r

2

, we see that the linear relation

gives the better fit for the a and the 7 spots,

while the log relation fits the fi spots slightly

better and the fiy spots markedly better. Except for the fiy's the differences are slight, however, and the linear and the log relations fit the

data about equally well. From an inspection

of the intercepts, C, we infer that the log relations would not apply to small spots. If we

take account both of the above results for large

spot groups and of the results of Giovanelli, it

appears very probable that there is a gradual

transition from a linear relation for small spots

to a logarithmic relation for very large spots.

The spot size around which the transition occurs

appears to be smaller for complex spots (500-

1000 millionths) than for bipolar spots (>2000

millionths).
32 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 1

*• LOG A

FIGURE 2.—Relation between the average number of observed

flares (F) and the logarithm of the average spot-group area

(log A), for spot groups larger than 500 millionths of the

solar disc. The spot groups are divided into four magnetic

classes, which are distinguished by the following symbols:

dots (•), a spots; crosses (x), fi spots; filled circles ( • ),

fiy spots; and open circles (o), y spots.

On the average there is a good relation between the mean area and the flare productivity

of a spot group. But for individual spot groups

in a given area range and a single magnetic class,

there is a wide variation in the number of observed flares, as shown, for example, by the fiy

spots plotted in figure 3. The least squares

parameters for the linear relation, Ft=C+BA{,

for individual spot groups is given in the bottom section of table 16. While the slopes and

intercepts are close to those shown in the top

section of the table, r2 has decreased and s? has

FIGURE 3.—Relation between the number of observed flares

(F) and mean area (A) of individual fiy sunspot groups

larger than 500 millionths of the solar disc. The symbols

distinguish the season of the year in which the spot group

occurred: dots (•), November through February; crosses (x),

May through August; and circles (o), March, April,

September, and October.

increased to a point where the relations can

hardly be considered good.

Since most flare observations have been made

at observatories located in the Northern Hemisphere, there will tend to be more observing

hours in summer than in winter; thus a seasonal

factor probably contributes to the scatter in the

number of observed flares per unit spot area.

To estimate the importance of this factor, we

divided each class of spots into three groups

according to the date of central meridian passage. These three groups are distinguished by

separate symbols in figure 3. Table 17 gives

the average flare productivity, 10F/A, for the

three seasonal groupings of each magnetic type

of sunspots. The influence of seasonal observational selection in observed flares per unit

area, 10F/A, seems apparent in the case of the

07 and the y spot groups, and negligible in the

0 samples, which, it should be noted, are the

largest and thus presumably the most reliable.

A further test for a seasonal factor in the

frequency of flares observed in /3 spots is given

in table 16. In the last two rows of each section, the (8 spots were divided into two seasonal

groups, /9( April-September) and ^(OctoberMarch), which gave values of 10F/A of 0.129

and 0.105 respectively. This division by season

produces no improvement in the parameters s?

and r2, and the scatter appears to be greater in

summer, when the observations are more complete. The summer and winter slopes are in

better agreement for the log than for the linear

relation.

While the scatter can certainly be attributed

in part to variation in completeness of the

observations, it also seems clear that the relation between area and flare productivity of a

sunspot group is only a general tendency, subject to wide and real variation for individual

spot groups.

Acknowledgments

The work reported in this paper has been

supported by the Air Force Cambridge Research Center, Geophysics Research Directorate, through contracts AF19(6O4)-146 and

AF19(6O4)-1394 with Harvard University.

We wish to thank Dr. Seth B. Nicholson for

his interest and helpful suggestions during the

course of our work, and for reading the manuscript in advance of publication.
SOME SUNSPOT AND FLARE STATISTICS

TABLE 1.—Percent of sunspot groups in each magnetic class

33

Interval

Jan. 1937-Nov. 1940

Dec. 1940-May 1944

June 1944-Nov. 1946

Dec. 1946-May 1950

June 1950-Dec. 1953

1937-1953 (north)

1937-1953 (south)

1937-1953 (mean)

•1915-24

Phase

of spot

cycle

max.

decl.

rise

max.

decl.

all

all

all

all

Magnetic class

a ap af 0 0p 0f 0y y

9.9 22.0 2.9 26.8 25.8 8.3 3.4 0.7

5.6 24.2 4.9 23.3 26.2 10.5 3.8 1.3

11.5 19.7 4.8 29.0 23.7 8.6 2.5 0.3

7.5 27.5 3.9 30.8 21.2 6.1 2.5 0.5

13.3 28.0 4.4 20.8 21.6 9.7 0.9 1.1

9.4 25.2 4.4 27.1 21.8 8.3 3.0 0.8

9.2 24.3 3.3 27.5 25.2 7.6 2.3 0.6

9.3 24.7 3.9 27.3 23.5 8.0 2.7 0.7

14.0 20.4 4.0 20.9 29.2 7.9 3.0 0.8

Unclassified

23.0

22.2

22.0

20.4

19.2

21.4

6.9

Total

groups

classified

1434

446

524

1626

638

2350

2318

4668

2025

Total

of all

groups

1863

573

672

2043

789

5940

2174

•Frequencies obtained by Hale and Nicholson (1938)

TABLE 2.—Percent of spot groups in each magnetic class, subdivided by maximum magnetic field intensity

Field strength

(gauss)

ooo

1000-1900

2000-2900

>3000

Total

Magnetic class

a ap af 0 fip 0f $y y

13.2 22.9 7.4 35.1 12.9 7.9 0.6 0.1

5. 7 22. 5 1. 2 27. 7 29. 9 9. 8 2. 7 0. 5

6. 5 32. 9 0. 7 12. 4 32. 9 6. 1 6. 6 2. 0

7. 1 28. 7 0. 3 7. 1 41. 4 4. 3 7. 7 3. 4

9. 3 24. 7 3. 9 27. 3 23. 5 8. 0 2. 7 0. 7

Unclassified

35.5

1.5

0. 7

21.4

Total

groups

classified

2107

1528

709

324

4668

Total

of all

groups

3351

1551

714

324

5940

TABLE 3.—Percent of spot groups in each magnetic class, vrith field strength >2000 gauss, and subdivided by area of

spot group

Area (10-" of

solar disk)

>2000

>1500

>1000

750-1000

500-750

<500

Mean

a

1.

a

6.

5

6

8

ap

3.

5.

5.

14.

38.

31.

4

1

5

1

3

4

a

0.

0.

0.

/

7

6

6

Magnetic class

0

13. 3

13. 8

13.6

16.7

8.9

10. 4

10.7

0P

6. 7

13. 8

23.7

38.9

53. 3

33. 2

35. 6

0/

6. 7

3.4

6. 8

7.4

5.9

5. 2

5.5

07

33.

34.

35.

22.

11.

2.

7.

3

6

6

2

9

9

0

7

40.0

31.0

15. 2

9.3

3. 7

0.8

2.4

Combined classes

Za

3.

5.

5.

16.

47.

3a

4

1

5

3

5

8

20

26.7

31.0

44. 1

63.0

6a i

4a 8

51. 8

7 + 07

73.3

65.6

50.8

31.5

15. 6

3.7

9. 4

Total

No.

15

29

59

54

135

787

1035
34 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 4. Ratios of observed to expected frequencies of sunspots, subdivided by magnetic class, magnetic field strength,

and duration factor

Field strength

(gauss)

>2000

1000-1900

<1000

Duration

class

11

Id

dl

dd

11

ldt,c

Mw

del

de,J

did.

d,dw

11

Id.

ldc

ldw

d,l

dcl

dj

ded.

d*dw

dcd*

a

. 71

. 86

1.27

. 10

.52

. 61

1. 02

1.68

.98

0

. 18

.68

. 17

1.42

. 70

1. 89

1. 05

1. 67

. 20

. 10

. 74

2. 14

1. 88

1. 10

ap

1.28

1. 51

2. 36

. 15

.77

.91

1.26

1. 79

1.75

. 15

.25

. 58

. 53

.92

.60

2.08

1.70

1.06

. 2 6

. 3 6

. 4 8

. 9 8

. 84

. 79

« /

. 15

. 18

0

0

. 61

. 3 1

. 33

. 41

. 43

0

. 30

. 4 0

. 40

1.90

0

2.25

1. 40

1.20

0

. 60

1.00

2. 82

2.20

1. 82

Magnetic class

0

. 39

. 22

. 16

. 91

1. 14

1.05

. 65

. 42

. 51

1.42

1. 62

1. 45

1. 26

1.20

1. 80

. 70

. 79

1. 31

2. 42

1.96

1. 69

1.09

1.29

1. 34

0P

1. 51

1. 42

.73

2. 22

1. 11

1. 27

1.23

. 87

.91

1. 79

1. 33

. 81

1. 49

. 55

. 60

. 10

. 42

. 51

. 81

. 81

1.06

. 34

. 43

. 68

0/

. 69

. 44

. 81

1. 29

1.49

1. 22

. 66

. 71

. 83

1. 21

1. 67

2. 38

1. 75

.99

1. 70

0

1. 14

. 60

. 80

. 95

. 70

. 87

.95

1. 24

2. 60

2.82

. 78

2. 74

1. 78

1. 00

1. 81

. 30

1. 17

1. 70

. 80

0

. 10

. 22

0

. 30

. 80

0

0

. 40

. 20

. 10

. 10

. 20

y

3. 43

5.00

0

.70

0

.72

1.40

0

1. 00

1. 30

0

0

0

. 14

0

0

0

1. 70

0

0

0

0

0

0

Unclassified

—

—

—

—

—

—— •

—

—

—

—

—

— .

2. 35

. 60

. 16

. 19

.43

2. 17

2. 24

2. 20

1. 23

Total No.

classified

1035

687

93

213

42

1530

304

122

286

216

231

63

308

2103

14

125

143

84

47

89

160

401

382

679

TABLE 5.—Percent of sunspols in various duration and field intensity classes

Field strength

(gauss)

<900

1000-1900

>2000

Total

>'

0.

5.

11.

16.

2

1

6

9

lde

2. 8

1. 6

0. 1

4. 5

del

1. 6

2. 6

0. 8

5. 0

Duration classes

dede

13. 0

0. 4

<0. 1

13. 5

dKdw

12. 1

0. 6

<0. 1

12. 8

(see

15. 1

5. 3

0. 6

20. 9

p. 26)

Id,

4. 2

0. 5

<0. 1

4. 7

d

5.

1.

0.

6.

J

0

5

2

7

Id

1.

4.

1.

7.

-

5

8

4

7

0. 8

3. 7

2. 7

7. 2

Total No.

sunspots

3347

1553

1040

5940

TABLE 6.—Percent sunspots in various categories, illustrating east-west asymmetry

Field strength

(gauss)

<900

1000-1900

>2000

Total

Spots rotating

over

EL

8. 7

12. 0

13. 2

33. 8

WL

7. 6

12. 9

15. 3

35. 8

Spots first seen

East

28. 9

9. 4

3. 3

41. 6

West

17. 1

2. 1

0. 2

19. 5

Spots last seen

East

17. 2

0. 9

0. 1

18. 2

West

28. 7

10. 7

2. 0

41. 4

Spots

East

37. 6

21. 4

16. 4

75.4

visible

West

36. 3

23. 6

17. 3

77. 2
SOME SUNSPOT AND FLARE STATISTICS

TABLE 7.—Total number of flares observed in 1987-1953 in various magnetic classes

35

Field strength

(gauss)

OOO

1000-1900

>2000

Total

a

34

80

87

201

ap

90

273

577

940

«/

33

8

17

58

Magnetic class

0

234

762

630

1626

0P

116

844

1881

2841

Pf

60

228

321

609

07

16

257

1127

1400

y

0

61

568

629

Unclassified

77

14

8

99

Combined classes

la

157

361

681

1199

410

1834

2832

5076

7 + 07

16

318

1695

2029

Total

660

2527

5216

8403

TABLE 8.—Percent of flares occurring in spot groups of various magnetic classes

Field strength

(gauss)

OOO

1000-1900

>2000

Total

c

0.

1.

1.

2.

c

4

0

0

4

ap

1. 1

3.2

6.9

11.2

0.

0.

0.

0.

/

4

1

2

7

Magnetic class

0

2.8

9. 1

7. 5

19. 4

0P

1.4

10. 1

22.4

33.9

0/

0.7

2. 7

3.8

7.2

07

0.2

3. 1

13.4

16. 7

7

0

0.7

6.8

7.5

Unclassified

0.9

0.2

0. 1

1. 2

Combined classes

2 a

1.9

4.3

8. 1

14.3

20

4. 9

21.8

33.7

60.4

7 + 07

0.2

3.8

20.2

24.2

All classes

7.9

30. 1

62.0

100.0

TABLE 9.—Average number of flares observed per spot group in each magnetic class

Field

strength

(gauss)

OOO

1000-1900

>20O0

Mean

a

. 12

.92

1.24

. 46

ap

. 19

.80

1.77

.81

«/

.21

. 40

2.83

.32

Magnetic class

0

. 32

1.79

5. 67

1. 28

0P

.43

1.85

5. 11

2.60

0/

.36

1. 53

5.63

1. 64

07

1.33

6.37

15.65

11.20

8.

22.

19.

7

0

7

70

1

Unclassified

.06

.6

1.6

.08

Combined classes

2 a

. 17

. 80

1. 70

.68

20

.35

1. 79

5.28

1.85

7+07

1. 23

6. 62

17. 48

12.82

All

classes

. 20

1.63

5.02

1. 42

TABLE 10.—Average number of flares observed in limb-to-limb (II) spot groups of each magnetic class

Field

strength

(gauss)

1000-1900

>2000

1

1

a

. 94

.34

ap

1.03

2.04

.50

3.40

Magnetic class

0 0P

3. 13 2. 86

8. 95 5. 80

0/

4.25

8.63

07

5.53

16.80

7

13.7

23.60

Unclassified

i.T

Combined classes

2 a

1. 23

1.95

20

3.09

6. 46

7 + 07

6.90

19. 00

All

classes

2. 53

5.70
36 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 11.—Percent of spot groups in each magnetic class producing no observed flares

VOL. a

Field strength

(gauss)

<9O0

1000-1900

>2000

a

93

72

60

ap

92

70

56

Magnetic class

"f

94

70

50

0

85

49

22

0P

79

41

22

80

52

19

07

58

15

4

7

0

0

4

Unclassified

97

83

40

Combined classes

2 a

93

71

56

20

83

46

22

7 + 07

54

12

4

TABLE 12.—Percent of spot groups in each magnetic class producing ten or more observed flares

Field strength

(gauss)

<900

1000-1900

>2000

a

0

2

0

ap

0

1

4

Magnetic

«/

1

0

17

0

1

4

19

0P

0

3

16

class

0/

0

1

21

07

8

27

57

7

0

43

68

Unclassified

1

0

0

Combined classes

2 a

1

1

3

1

3

17

7+07

8

29

60

TABLE 13.—Average number of observed flares in spot groups of different magnetic classes

Field strength

(gauss)

>20O0

1000-1900

Duration

class

11

ldK

dd

lde

del

d4-

11

ldw

del

lde

del

lde

dj

dedvc

Combined magnetic

2a

1. 95

. 82

. 72

. 14

0

1. 3

1. 23

.99

.38

. 21

.58

. 29

.33

.38

classes

20

6. 46

3.35

4.87

—

3.37

. 83

3. 09

2. 24

2. 35

. 84

1. 78

1. 22

1. 45

.80

7 + 07

19. 00

12. 0

14. 1

—

1. 0

1.5

6.90

7.54

6. 42

1.0

10. 5

—

1.33

8.0

All classes

5. 70

1. 88

5. 61

. 14

3. 07

1. 0

2. 53

1. 78

2. 51

. 46

1. 80

. 62

1. 33

. 75

Total

flares

3964

158

897

1

135

36

770

508

541

44

275

16

104

231

Total

spots

688

84

160

7

44

36

304

286

216

96

153

26

78

308

TABLE 14.—Average number of flares observed per large spot group with magnetic strength >_2000 gauss

Area (10-»

of solar

disk)

>1000

750-1000

500-750

<500

Mean

4.

1.

1.

a

5

15

24

ap

10.3

9.0

4.05

1.47

1.77

«/

4.0

2. 6

2.83

Magnetic class

0

21. 1

11.3

5. 78

3.62

5.67

0P

20.2

12.0

6.80

3.28

5. 11

0/

16.2

11.5

5.87

3.98

5.63

07

2a 7

15.3

12.0

6. 95

15.65

7

35.8

21. 6

21.2

5. 34

22. 70

Combined classes

2 a

10. 3

9.0

4. 10

1.42

1. 70

20

19.9

11.8

6.53

3.42

5.28

7 + 07

30.8

17.2

13.6

6.63

17.48

All classes

25. 0

13. 3

7. 22

2. 59

5.02
38 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 17.—Seasonal effects on the frequency of observed flares

VOL. I

Magnetic class

hi

Ifiyl

Ifiyl

lal

101

w

Area

>400

>1OOO

500-999

>500

>800

500-799

Season No.

Nov.-Feb. 5

Equinox 10

May-Aug. 9

Nov.-Feb. 5

Equinox 8

May-A>ug. 5

Nov.-Feb. 10

Equinox 7

May-Aug. 11

Nov.-Feb. 3

Equinox 10

May-Aug. 16

Nov.-Feb. 11

Equinox 14

May-Aug. 16

Nov.-Feb. 21

Equinox 20

May-Aug. 33

Mean area

(A)

1280

1420

1180

1730

2070

1960

680

650

800

670

800

600

1660

1180

1150

610

690

630

No. flares

(F)

14.8

28.8

26.0

15.8

29.5

38.4

7.4

15.3

15.4

4.3

5.6

5.6

18.5

16.8

16.5

6.1

6.8

6.4

10F/A

.116

.202

.220

.092

.143

.196

.108

.236

.192

.064

.070

.093

.112

.142

.143

.100

.109

.102

References

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1958. Smithsonian Contr. Astrophys., vol. 2,

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Abstract

This paper presents some statistics on 5,940 sunspot groups observed at the Mount Wilson Observatory during

the years 1937 through 1953. The principal topics studied are: the frequency of spot groups occurring in the various

Mount Wilson magnetic classes, and the dependence of this frequency on the size and age of the spot groups; some

aspects of the apparent east-west asymmetry in spot distribution on the solar disc; and the distribution of 8,403

observed solar flares among spot groups of various magnetic classes, sizes, and ages.
SOME SUNSPOT AND FLARE STATISTICS

TABLE 15.—Flares observed per unit (1O~S of solar disk) of spot group area

37

Area (10-"

of solar disk)

>1500

1000-1500

750-1000

600-750

500-600

Mean

a

.06

.06

op

. 11

.06

. 106

.056

.084

.083

Magnetic class

af 0

— . Ill

— . 160

— . 118

— .078

. 07 . 123

.07 .113

*

. 171 .

. 132 .

. 139 .

. 109 .

. 107 .

. 124 .

0f

075

074

115

141

073

090

*

. Ill

.230

. 178

. 180

. 177

. 167

y

. 145

.24

.256

.373

. 12

. 184

Combined

Za

. 11

.06

. 106

.058

.083

.081

20

. 125

. 127

. 129

. 104

. 106

. 117

classes

y+0r

. 126

.232

. 199

.222

. 162

. 173

All classes

. 125

. 165

. 150

. 129

. 106

. 135

TABLE 16.—Least squares parameters relating flare production and mean area for large spot groups (see p. 31)

Equation

F^C+BA,

Ft=C+BAt

Mag. class

lyl

101

Ictl

0 (summer)

0 (winter)

lyl

I0yl

101

Ictl

0 (summer)

/3(winter)

lyl

I0yl

101

Id

^(summer)

0 (winter)

No.

5

6

6

5

6

6

5

6

6

5

6

6

24

47

115

29

69

46

Mean No.

flares

(F)

24.88

18. 55

10. 27

5.48

10.38

10. 11

24. 88

18. 55

10. 27

5.48

10.38

10. 11

24.88

18.55

10.27

5. 48

10.38

10. 11

Mean

area

(A)

1302

1196

868

677

806

961

3. 0103

3.0081

2. 8958

2 8104

2 8812

2 9175

1302

1196

868

677

806

961

Least squares parameters

(C)

10. 95

a 72

- 0 . 73

- 1 . 49

- 4 . 13

- 1 . 44

-76. 94

-77. 42

-97. 27

-49. 53

-101.56

-97.91

11. 72

a 8i

0.49

- 1 . 47

-2.5 7

+ 0. 36

(B)

1. 07X10-'

0. 82X 10-'

1. 27X10-*

1. 03X10"*

1. 80X 10-*

1. 20X 10-*

33.82

31.90

37. 13

19. 57

3a 85

37.02

1. 01X10-'

0. 83X10-'

1. 13X10-'

1. 03X10-'

1. 61X10-*

1. 02X10-*

Standard

error

(sr)

1. 60

4. 23

1. 61

1. 46

1. 57

0.98

2 35

3. 41

1. 62

1. 59

2 14

2 15

12 4

11.5

7.85

3.86

a 28

6. 84

Coef. of

correlation (r»)

.977

. 667

. 940

. 769

. 927

.986

.951

.827

. 968

. 658

. 873

.933

. 421

.310

.378

.326

.300

.554