Interplanetary energy flux associated with magnetospheric substorms

Planet. .SpaccSci.. Vol. 27. pp. 425-43 I

0032-0633/79/0401-O425SO2.00/0

0 Pewamon PressLtd.. 1979. Printed in Northern Ireland

INTERPLANETARY ENERGY MAGNETOSPHERIC

FLUX ASSOCIATED SUBSTORMS

WITH

S.-I.AKASOFU Geophysical

Institute, University (Received

of Alaska,

Fairbanks,

1 August

AL 99701.

U.S.A.

1978)

Abalraet-It is shown that the interplanetary quantity .s(t), obtained by Perreault and Akasofu (1978), for intense geomagnetic storms, also correlates well with individual magnetospheric substorms. This quantity is given by e(t) = VB’ sin4 (0/2)l,‘, where V and B denote the solar wind speed and the magnitude of the interplanetary magnetic field (IMF), respectively, and 0 denotes the polar angle of the IMF; I,, is a constant -7 Earth radii. The AE index is used in this correlation study. The correlation is good enough to predict both the occurrence and intensity of magnetospheric substorms observed in the aurora1 zone. by monitoring the quantity ~(0 upstream of the solar wind. 1. INTRODUCIION

A number of studies have been made in the past in an attempt to find interplanetary quantities which are related to magnetospheric substorm activity. Snyder, Neugebauer and Rao (1963) and Olbert (1968) found a good correlation between the daily sum of the K,,index (denoted by CK,,) and the solar wind speed. It is given by V&m s -‘) = 6.3ZK,

values of the B, component. They found also that the magnitude of the B, component alone cannot predict quantitatively the intensity of magnetospheric substorms and storms. In their search for interplanetary quantities which can provide a better, quantitative correlation with substorm activity, they found the quantity e(t) given by

8

+ 262.

e(t) = VB’ sin4 2 I,,’

Ballif, Jones and Coleman (1969) showed that the variance of the interplanetary magnetic field is correlated with the K,,index. Fairfield and Cahill (1966) and Rostoker and Filthammar (1967) were the first to recognize the importance of the B, component of the interplanetary magnetic field (IMF) on the occurrence of magnetospheric substorms. Since then a large number of papers have been published, reporting a good correlation between the southward component of B, (or B, (0) and the magnetospheric substorm index AE (cf. Arnoldy, 1971; Burton ef al, 1975; for reviews, see Burch, J. L., 1974; Akasofu, 1977). Most recently, however, Perreault (1974), Burlaga and Lepping (1977) and Perreault and Akasofu (1978) have examined closely this correlation and have found that the dependence of substorm activity on the B, component is far from satisfactory. Burlaga and Lepping (1977) pointed out the importance of the solar wind speed in the correlation, in particular in a later period of recurrent geomagnetic storms. Perreault (1974) and Perreault and Akasofu (1978) noted that a significant substorm activity can occur even when the B, component is positive and thus that the magnetosphere cannot be a rectifier which passes only negative

where V = the solar wind speed B= the magnitude of the IMF 8 = the polar angle of the IMF vector in the y - z plane in solar-magnetospheric coordinates = tan ’ (I B, 1)/B, for B,> 0 =T- tan '(IB,I)/B, for B,
426

S.-I. AKAsoFu

weak storms during which individual substorms can reasonably be resolved. Fortunately, the necessary interplanetary quantities in estimating I are available for some of the recurrent geomagnetic storms in the interval 1973-1975. All quantities dealt with in this paper are hourly average values.

by Burlaga and tipping (1977), a good correlation breaks down after the second day of the recurrent storm. In Fig. lb, I and the AE index are plotted by a solid line and a dotted iine, respectively. One can see immediately considerably higher correlation between I and the AE index and between B, and the AE index. Note in particular that s(t) traces out reasonably well AE index variations. In fact, the correlation coefficient for the s(t)-AE relation is 0.665, while it is -0.477 for the B,-AE relation for this particular storm. For reference, the correlation coefficient for the VB,-AE correlation is 0.459. Since the AE index is only a rough index for substorm activity (Akasofu, 1977), the coefficient value of 0.665 shouid be considered to be quite significant.

2. RF.suLTs

(a) The November 3-10,

1973 storm

This particular storm was examined by Burlaga and L,epping who noted that a good quantitative correlation between the B, component and the AE index holds only during an initial period of recurrent storms and that the solar wind speed plays an important role in a later period. In Fig. la, the relationship between the AE index and the B, component is shown for this particular storm. The B, component was plotted in reverse; a negative period is hatched and a positive period is plotted by a dotted line. Further, the two quantities are normalized in such a way that peaks of both quanitit~ have similar “heights” during an initial period of the storm. As recognized correctly

c -10 t

(b) The June 7-14,

1974 storm

In Fig. 2a, one can see an example similar to (a). Fig. 2a also illustrates that the reasonably good correlation between B, and the AE index breaks down after the middle of June 12 and there is little quantitative relationship during a later period of

AE .../. Bz

-cy 1000

In

h

800 soo:

400 200 0

7 THE FIG. la. COR_RELATIONBEIWFEN INTERPLANETARY The

AURORAL

MAGNEZIC

8

ELECTROJEI

J?IELD (Ih@)

FOR THE

9

INDEX

m

10 AND THE B,

COhPONJZNT

NOVEMBER 3-10,1973

OF THE

STORM.

B, component is plotted in reverse and negative periods are hatched; positive periods are plotted by a dotted line. (x 10”ergs /set ) 8 u^ 6 G

800

4

600 2 400

2

200

0

0 NOVEMBER

FIG.

1 b. COFMELATION

BEXWEEN QUANTITY

THE s(t&h

AURORAL

1973

ELECXROJET

FORTHENoVEWB?XR

INDEX 3-10,1973

AE

AND STORM.

THE

INTERPLANEWLRY

421

Interplanetary energy flux associated with magnetospheric substorms

FIG.

INDEXANDTHEB,COMPONENTOFTHEI~FORTHEJuNE 2a. Co RRELATIONBETWEENTHE~ 7-14,1974 STORM;FORDETATLSSEETHECAPITONFORFIG. la.

( X d’ergshec

i0 t

f

C(t)

”

..

AE

Y 1000

800 600~ a 400 200 0 JUNE FIG.

2B.

CORRELATIONBETWEENTHEAJZWD

the storm. On the other hand, the correlation between s(t) and the AE index remains remarkably high throughout the period (Fig. 2b). The only serious discrepancy between I and the AE index occurred near the end of June 10 and the beginning of June 11. The correlation coefficients between e(t) and AE, B, and AE, and VB, and AE are 0.639, -0.580 and -0.609, respectively.

(c) The April 16-23,

1974 storm

This is another good example to show the breakdown of a good correlation between B, and Al? during a later period of a storm (Fig. 3a). The correlation coefficient between B, and AE is only -0.352. On the other hand, the correlation between s(t) and AE is 0.565, much higher than the former value. For reference, the correlation coefficient between VB, and AE is -0.447 for this particular Strom. One should note also that in this particular storm the correlation between I and

4974 c(t)/477FOR-JUNE

7-14, 1974 STORM.

AE become less than satisfactory period of the storm. (d) The January

22-29,

during a later

1974 storm

This particular example provides an additional feature which is not apparent in the earlier ones. Again, one can easily recognize that the good correlation between B, and AE lasted for less than one day and there is little quantitative relation during the rest of the storm (Fig. 4a). The correlation coefficient between B, and AE is only -0.367. The correlation between s(t) and AE is significantly higher, 0.562, than the former value. However, in spite of a generally good correlation, one serious breakdown occurred on January 25 during which I was considerably greater than what is predicted by the correlation with AE. This storm is quite unique, compared with the earlier examples, in that a significant main phase (-657) developed on this day. It appears that the excess

S.-I. AKASOFU

428

2yoo -

t

AE

-.

I

1800 1600

A

I

I

I

I

16 ' 17 ' 18Ad,:'

I

' 20 ' 21 1974

I

' 22 '23

B, COh4F'ONENTOFTHEIh@FORTHEhRlL la.

FIG.3a. CORRELA~ONBET~BENTHE~INDEXANDTHE

16-23,1974STORM:FORDETAILS,SEETHECAPT~ONFORFIG.

(x 10”ergs

/sac )

42

Y (200 1000 BOOW 4 600 400 200 0 APRIL FIG. 3b. Co RRELATION

BETWEENTHE

AE

I974

INDEX

AND

I

I

22

16-23,

~(C)/47rFORTHEkRIL

L

1974

STORM.

I

' 23 ' 24 ' 25 ' 26 ' 27 ' 28 ' 29 JANUARY

FIG.4a.CORRELATIONBETWEENTHE JANUARY 22-29, 1974

!974

AE INDEX ANDTHE B, COMPONENTOFTHE STORM: FORDETA~SEE~ECA~ONFORFIG.

Ih@ la.

FORTHE

Interplanetary energy flux associated with magnetospheric substorms

429

(X 10” ergs /see 1

r&o iooo 800 600 2 400 200 0 JANUARY

Fro. 4b.

coRREL.4TION

B ETWEEN

THE AE

INDEX

energy flux was deposited in the ring current belt. We shall discuss this feature later. (e) The July 3-10,

1974 storm

This storm is similar to the previous example in that a large excess of I over AJZ occurred during the storm. Again, the correlation between B, and AE ispoor except for the first three days (Fig. 5a), while the correlation between e(f) and AE is reasonably good for the entire period. The only exception is a large excess of I during an early part of June 6. In fact, an intense main phase of -198~ developed during the same period.

AND

4974 ~(t)/4~r

FOR THE JANUARY

3. DISCUsSION

Perreault (1974) and Perreault and Akasofu (1978) have already shown that e(t) correlates well with the total energy dissipation U which includes the ring current injection and the kinetic energy flux of aurora1 particles, as well as the joule heat production by the aurora1 electrojet. In this paper, it is shown that I correlates well also with the AEZ index for recurrent storms which are much weaker than those examined by Perreault and Akasofu (1978). In fact, individual substorms observed at aurora1 zone stations are well correlated with peaks of I.

AE BZ

FIG.

5a.

CORRELATION

B?iiTWZN

3-lo,1974

Y i600 1400 1200 1000 800 ‘$ 600 4GO 200 0

I

JULY

(974

~AEINDEXAND’I1IEB,CO~~OFTHEIMFFOR~JULY

srom:

FoR

D~~~AIIS,

22-29, 1974 STORM.

sEi53-H~ C-ON

FOR Fxo.

la.

430

S.-I. AKASOFIJ

FIG.

5b.

CORRELATION

B FIWEEN

THE /&

INDEX

As a first approximation, the AE index is proportional to the rate of joule heat energy production by the aurora1 electrojet, since the variability of the conductivity of the ionosphere is much greater than that of the electric field. The “normalization” employed in constructing the e(t)-AE correlation figures suggests that an AE value of lOOOr corresponds to an input value I of the order of 8.0 x lOI ergs s-l. In their paper, Perreault and Akasofu (1978) obtained the joule heat production of 5.5 x 1O1’ ergs s-l for a lOOOr value of the AE index. The quantity VB’ is approximately the interplanetary energy flux per unit area and (In sin2 (e/2))* may be considered to be the cross-section through which the energy flux flows into the magnetosphere. It is interesting to note that V and II31vary much more smoothly than sin” (O/2). Thus, the term sin4 (e/2) tends to construct individual substorms. However, all the three parameters, V, (BI and sin4 (O/2), contribute significantly in determining the intensity of substorms observed at the standard aurora1 zone stations. It is also important to recognize that the correlation with the AE index is higher with E(t) = VB2sin4 (e/2)&’ than with B, or VB,. Recognizing that the AE index is only a rough index for magnetospheric substorm activity, the correlation coefficient between I and AE of order 0.6 can be considered to be satisfactory. Indeed, it may be worthwhile to re-examine the AE index in some instances. In particular, since the AE index cannot properly reflect substorm activity along a contracted oval, the correlation refers only

AND

E(T) FOR THE JULY

3-10, 1974

STORM.

to substorms observed at the standard auroral zone stations. It is also shown that when I “exceeds” greatly the energy dissipated in terms of the joule heat production in the ionosphere, a significant ring current develops in the magnetosphere. Indeed, it has been shown by a number of workers that the rate of energy injection in building up an appreciable ring current exceeds the rate of joule heai energy production (cf. Akasofu, 1977, p. 274). 4. CONCLUSION

With this success of obtaining a reasonable correlation between I and AE, we should be able to predict both the occurrence and intensity of magnetospheric substorms, as well as the growth of the ring current, if the interplanetary quantities V, (BI, and 8 can be monitored on a real time basis. Acknowledgements-I would like to thank Dr. P. Perreault for his discussion on the results reported in this paper. The project was supported in part by a grant from the National Science Foundation, Atmospheric Sciences Section ATM74-23832 and in part by AF Contract F1962876-C-0074. REFERENCXS

Akasofu, S.-I. (1977). Physics of Magnetospheric Substorms. Reidel, Dordrecht, Holland. Ballif, J. R., Jones, D. E. and Coleman, P. J., Jr. (1969). Further evidence on the correlation between transverse fluctuation in the interolanetaw magnetic field and K.Y J. geophys. Res. 74, 2289. _ Burch, J. L. (1974). Observations of interactions between interplanetary and geomagnetic fields, Rev. geophys. Space Phys. 12, 1969.

Interplanetary

energy flux associated with magnetospheric

Burlaga, L. F. and Lepping, R. P. (1977). The causes of recurrent geomagnetic storms. Planet. Space Sci., 25, 1151. Burton, R. K., McPherson, R. L. and Russell, C. T. (1975). An empirical relationship between interplanetary conditions and Dst. J. geophys. Res. 80, 4204. Fairfield, D. H. and Cahill, L. J. Jr. (1969). Transition region magnetic field and polar magnetic disturbances. J. geophys. Res. 71, 155. Olbert, S. (1968). Summary of experimental results from M.1.T. detector on IMP-l, in Physics of the Magnetosphere (Ed. R. L. Carovillano, J. F. McClay and H. R. Radoski), p. 641. Reidel, Dordrecht, Holland.

substorms

431

Perreault, P. (1974). On the relationship between interplanetary magnetic fields and magnetospheric storms and substorms. Ph. D. Thesis, Univ. Alaska, August. Perreault, P. and Akasofu, S.-I. (1978). A study of geomagnetic storms. Geophys. J. R. astr. Sot. 54, 547. Rostoker, G. and Falthammar, C.-G. (1967). Relationship between changes in the interplanetary magnetic field and variations in the magnetic field at the Earth’s surface. J. geophys. 72, 5853. Snyder, C. W., Neugebauer, M. and Rao, U. R. (1968). The solar wind velocity and its correlation with cosmicray variations and with solar and geomagnetic activity. J. geophys. Rex 68, 6361.