F O R E C A S T I N G THE I N T E N S I T Y OF S O L A R P R O T O N E V E N T S

F R O M THE TIME C H A R A C T E R I S T I C S OF

S O L A R M I C R O W A V E B U R S T S

DAVID L. CROOM*

Air Force Cambridge Research Laboratories Bedford, Mass., U.S.A.

(Received in final form 11 January, 1971)

Abstract. A survey of the main characteristics of solar microwave bursts in relation to their usefulness for indicating the intensity of associated solar proton emissions suggests that time parameters give much better results than intensity or spectrum parameters. In particular, best results are obtained by using the effective, or mean, burst duration defined by

~ , = 1/emax~ P(t) dt

where Tis the overall burst duration, P is the power density at time t, and Pm~ is the maximum power density. For proton energies > 10 MeV the proton flux N~ is given approximately by N~ = 0.034 T~s 3 particles ster -1 cm -2 s -~, where T~ is in minutes, with a correlation factor of 0.8. Corresponding coefficients have been derived for a number of energy ranges. Using this parameter solar proton warnings and intensity estimates can be made with observations at only one frequency, preferably in the range 5-20 GHz.

1. Introduction

The use of solar microwave bursts as indicators of the occurrence of solar proton events

has been discussed in earlier paper (Croom 1970a, 1971). In a further short paper

(1970b) it was suggested that the time characteristics of the bursts could be used to

estimate the intensity of these proton events. The purpose of the current paper is to

amplify thislatteridea and to compareits effectiveness with other solar burst parameters.

The solar microwave burst data used in this study have been obtained from published

and unpublished reports of the Air Force Cambridge Research Laboratories, Massa-

chusetts (Castelli), Manila Observatory (Hennessey), the Radio and Space Research

Station, Slough (Croom and Powell) and Tokyo Observatory (Takakura). The proton

data has been taken from the John Hopkins Universi ty- Goddard Space Flight

Center Explorer 34 and 41 satellite recorded hourly averaged particle count-rates as

published in the U.S. Environmental Science Services Administration monthly bulletin

of Solar-Geophysical Data (ESSA 1967-70). This data is available for proton energies

Ep of > 10 MeV, >30 MeV and >60 MeV.

The period of the study covers the 2�89 yr from the launching of Explorer 34 in May 1967 until the end of 1969.

2. The Main Parameters

The solar microwave burst characteristics likely to be of most use in connection with

predicting solar protons can be divided into SINGLE FREQUENCY and MULTI-

* On leave from the Radio and Space Research Station, Slough, England, as 1969-70 National Academy of Sciences/National Research Council Senior Post-Doctoral Research Associate at AFCRL.

Solar Physics 19 (1971) 171-185. All Rights Reserved Copyright �9 1971 by D. Reidel Publishblg Company, Dordrecht-Holland

172 DAVID L. CROOM

TABLE I

Solar microwave burst characteristics that possibly relate to the intensity of solar proton events

I. Single frequency

Intensity

(a) Peak power density (Peak flux density) Pmax W m -z Hz -1 (b) Mean power density P W m -2 Hz -1 (c) Energy E J m -2 Hz -1

Time

(d) Total duration T s (e) Rise time to Pmax TR s (f) Decay time to 1/e Pm~x T~ s (g) Mean duration Tz~ s (h) 3 dB duration T3 s (i) 10 dB duration T10 s (j) Harmonic content - s -1

Polarization

(k) Stokes parameters - -

II. Multi-frequency

(1) Frequency of maximum peak power f(Pmax)max HZ (m) Frequency of maximum mean power f(/5)max I-Iz (n) Frequency of maximum energy f(E)m~x Hz (o) Peak power density at f (Pm~x)m.~ (Pmax)max W m-2 Hz -1 (p) Mean power density a t f ( P ) ~ x P~a~ W m -2 Hz -1 (q) Energy density at f(E)raax Emax J m -2 Hz -1 (r) Total power density P~ W m -2 (s) Total energy density ET J m -2 (t) Spectral shape - - (u) Polarization as function o f f - -

FREQUENCY as listed in Table I. This list is not necessarily exhaustive and some of the characteristics listed require further Sub-division for a full description (e.g. Stokes polarization parameters, or the spectral shape). More specific descriptions of these parameters and their usefulness in forecasting solar proton event intensities are given below.

A. PEAK POWER DENSITY, Pmax ( = PEAK ENERGY FLUX DENSITY = PEAK FLUX DENSITY)

I n the mic rowave reg ion this is genera l ly a n u n a m b i g u o u s m easu re of the in tens i ty of

a r ad io event , t h o u g h occas iona l ly the presence of very sharp spikes supe r imposed on

the m a i n event can give rise to the p r o b l e m o f wha t shou ld be t a k e n as the peak va lue

- the t ip o f the shor t - l ived spike or the b r o a d top of the less in tense , b u t m o r e durab le ,

m a i n pa r t o f the burs t . U s u a l l y this p r o b l e m on ly arises in the reg ion be low a b o u t

3 G H z , tha t is in the reg ion where there is over lap wi th wha t are bas ica l ly dec imet r ic

ra the r t h a n mic rowave bursts . I n this over lap r eg ion m o s t p r o t o n associa ted micro-

wave burs t s t e n d to have a m i n i m u m of emiss ion (Croom, 1971).

FORECASTING THE INTENSITY OF SOLAR PROTON EVENTS 173

There is a general relation between microwave burst peak power density and solar

proton particle flux density, in that if a certain intensity threshold value, which is a

function of frequency, is exceeded then the probability of a proton event is very high. However, there is no direct relation between the peak power density (sometimes simply called the peak flux) and the intensity of the proton events. This has been illustrated in Croom (1970b) for a frequency of 19 GHz, though a similar scatter of points would be obtained for any other microwave frequency. Thus peak intensity is not a very useful indicator of proton flux intensity, other than as a threshold value which must be exceeded.

B. MEAN POWER DENSITY (/~ AND TOTAL DURATION (T)

These two parameters are taken together since calculation of the first involves meas- urement of the second. Both (together with the peak power density) are recommended

by the International Astronomical Union (IA U) for use in describing the main features of solar radio bursts.

However, the mean power density is often difficult to measure accurately since it

(a)

(b)

_

�9 T = L I I

T ,,,

(c)

Fig. i. Illustrating the difficulties in measuring the overall duration and mean power of a burst.

174 DAVID L. CROOM

involves the use of a somewhat crude second parameter, namely the total duration. The mean power density is defined as:

T

T (1) 0

where P(t) is the instantaneous burst intensity at time t, and E is the burst energy density.

Thus burst (a) in Figure 1 has a P of nearly twice that of the otherwise almost identical burst (b) though it has the same P as the very dissimilar burst (c).

The overall duration T is in practice often difficult or impossible to measure ac- curately, since it involves deciding at what point the slowly decaying tail of the burst (often with fluctuations superimposed on it) meets the level representing the solar out- put in the absence of the burst (also often fluctuating). This difficulty is particularly apparent in the case of bursts relating to proton events since these frequently have very long durations of the order of one to four or more hours. Thus at the lower end of the microwave band the output of the non-flaring Sun can have changed appreciably during the course of a long burst through variations in the slowly-varying component, while at the high frequency end the attenuation due to the lower terrestrial atmosphere can likewise have varied noticeably (Figure ld). Moreover, at all frequencies the chances of the burst continuing into the sunset period and beyond are high.

Even under the ideal conditions of a burst decaying smoothly towards a flat base, the value of Twill tend to depend on the gain of the recording channel, since the value of T will appear to be much greater with a high gain than with a low one.

C. ENERGY DENSITY ( E )

This is defined as

T

E = I" P (t) dt (2)

0

i.e. is proportional to the area enclosed under the burst, and is thus a more meaningful parameter than the mean power, since it is not sensitive to errors in T. However, in general bursts with small peak powers have small energies and those with large peak powers have large energies and so the relation between burst energy density and proton flux is again similar to that for peak power (Croom, 1970b).

D.-J. TIME PARAMETERS

Although these come next in Table I, in view of their importance they will be discussed separately, in Sections 3 and 4.

K. A N D U. P O L A R I Z A T I O N

The study of burst polarization characteristics gives considerable information on the

FORECASTING THE INTENSITY OF SOLAR PROTON EVENTS ] 75

nature of the burst generating mechanism and hence is potentially capable of leading to a means of distinguishing between proton and non-proton events, and possibly estimations of the intensity of the proton event. However, polarization measurements made at Slough since late 1967 at a frequency of 2.8 GHz show that at this frequency proton-associated bursts are often completely unpolarized, though a few exhibit a very weak degree of polarization (~< 15 ~). This does not however necessarily apply at other frequencies, as the sense of polarization is known to reverse within the 2-4 GHz band.

L. FREQUENCY OF MAXIMUM PEAK POWER, f (Pmax)m,x

This is obtained by using observations at a number of fixed frequencies to estimate the frequency at which the burst is most intense. Recent work by Castelli (private com- munication) has emphasized the importance of observations in the frequently neglected region between 4 and 10 GHz in this respect, since the overwhelming majority of microwave bursts have their peak outputs in this region. It is also apparent (Croom, 1971) that many bursts associated with proton flares have their peaks at still higher frequencies, the most notable example of this being the burst of 6 July 1968, which had its maximum emission at 71 GHz or higher. The median value of this parameter for bursts associated with proton events is about 10-12 GHz, and the mean about 17 GHz. However, despite this tendency of the peak power spectra of proton events to

TM

(a)

Fig. 2.

"TM

(b)

(c)

.~-TM-~ TIME, f

Illustrating the mean, or effective duration of a burst.

176 D A V I D L . C R O O M

Fig. 3.

i

rY Lu

~) 10 2

bJ (.9

, ~ I O :

to-Z

x

X~K

�9 9 JUNE 196B �9 I0 APRI i i i i i i i i i L I I J l l l

X

x

1969 �9 2 NOVEMBER 1969 i i i i i i i i t i i i i i i i 1 i 1[111[

x X

�9 ~ :

i 1 i i I X l l

10 4

X x ;~ X X ~ X X X,

X )0(

I i i _ l i i i 1 1 i i i i i i i i i i [ ~ 1 1 1 1 i T I I F I I I I I I [ 1 1 1 1

I 0 - I I I 0 1 0 2 103 PROTON FLUX FOR Ep > I 0 Mev, PARTICLES ster -I c m -2 sec - I

The frequency at which the peak power is a max imum, f(PmaX)m~x as a funct ion of proton flux for Ep > 10 MeV.

have their maximum emission at higher frequencies than ordinary bursts, there ap- pears to be no relation between this frequency of maximum emission and the intensity of the proton event (Figure 3). This is in any case a difficult parameter to measure accurately as it has a small dynamic range and in many cases insufficient frequencies are monitored to allow it to be well defined.

M.-Q. OTHER PARAMETERS INVOLVING THE PEAK OF THE SPECTRUM

The frequency at which the mean power is maximum, f(-P)m.x, and the mean power density at this frequency, F . . . . suffer from the same disadvantages as (b).

The maximum peak power density (Pm.x)m~ performs no better than any other parameters characteristic of the size of the burst (Figure 4).

Because of the general similarity in shape of microwave bursts recorded at different frequencies, the frequency at which the energy is maximum, f(E)m.x , and the energy

2

G.

~v io 4

I . - O

N - i0 ~

o

Fig. 4.

�9 9 J U N E 1968 �9 I O A P R I L 1969 I I 2 NOVEMBER 1969 i i i i T i r l i f i . q l l ~ l

X

x 'G'--X X

t~ ( x x

.~-•

I I I I I I I i 1 0 2 n I q l I I IL I l lL I I I [ 1 1 1 1 td ~ Io "t I to IO z io ~

i x �9

[

q

,o 4 PROTON FLUX FOR Ep ~" I0 Mev, PARTICLES ster - I crn -2 sec - I

The peak power density at f(Prn~x)~ax as a f u n c t i o n o f proton flux for Eao > 10 MeV.

i t i i l l l l i i r l l l l

X

X

X X X X

X X

•

- - - - X . - -

I I B JILl

FORECASTING THE INTENSITY OF SOLAR PROTON EVENTS 177

Em.x at this frequency give essentially the same results as the corresponding peak power

parameters.

R. AND S. TOTAL POWER DENSITY, PT, AND TOTAL ENERGY DENSITY, E T

These are defined as:

PT= r Pmaxdf (3) i t /

t = eonst

and:

Er= f f P(t,f)dtdf (4)

Pr is the instantaneous power emitted at a fixed time t, which in practice would need to be at or near the time of peak emission for purposes of inter-comparison between different events.

E r is a measure of the total energy output of the solar radio event. However for many proton events it would be necessary to have data at frequencies up to 70 GHz or more in order to measure these parameters (Croom, 1971), and at present there is a great scarcity of such information.

N. SPECTRAL SHAPE

Castelli et al. (1967), Castelli (1968) and Castelli and Aarons (1970) have used several years of fixed frequency observations up to 8.8 GHz to show that bursts with high peak intensities at a few hundred MHz and at 8-10 GHz, and low peak intensity at 2-3 GHz

are closely enough related to proton events to be used for forecasting purposes. The general shape of such spectra when plotted on a log-log scale has led to the term 'U-shaped spectrum' being applied to these criteria, to distinguish the events from the majority of microwave bursts. The latter have maximum emission at less than 10 GHz

Fig. 5.

l a J i - -

Z O

b I -

DA

�9 9 JUNE 1968

Io ] . . . . . ; - - ~ . . ~ . _ ~ _..

0"11( I0 -I IO

�9 I0 APRIL 1969 �9 2 NOVEMBER 1969

(TM)3 Np = 0.034

I I I I r l l l l r i ~ r i i I I

i0 z i03 F i i l l l l

jo ~ PROTON FLUX FOR Ep> I0 Mev, PARTICLES ster -[ crn-Zsec "l

Effective burst duration as a function of proton flux for Ep > 10 MeV. (The horizontal bars indicate the possible error in the pro ton measurements.)

178 D A V I D L . C R O O M

1 0 0 B

I---

Z 0

F -

C~ I

O

0 " ~ - 2 I

Fig. 6.

�9 9 JUNE 1968 i i i i ~ l r l

x X

x x

i I I f r l l i I I I I I I i i I I I I I I I I

I0 I0 PROTON FLUX FOR Ep > [0 Mev, PARTICLES ster -I cm'2sec "1

�9 IOAPRIL I969 �9 2 NOVEMBER 1969 i i i i i I H I i i i i i i 1 1 i [ [ i i i i i i i i i i i i i

x f " ~

fXx X

Np : 0.013 (1"1o) 27

i i I I I t l l I r I I I I I I I i i i t { 1 1

IO 2 i0 3 i0 4

Burst 10 dB duration as a function of proton flux for Ep > 10 MeV.

Fig. 7.

hA

W r r O Z

O3

Y

hA

WAVELENGTH, mm I 0 0 30 20 I 0 9 8 7 6 5 4

I i I t I i I ; I ]

5000 5 JUNE 1969 1002 UT

T ~. 4000

3000 ( ' 4

o 2000 "- -...,.

1 0 0 0 v -DECIMETER BURST

I ; J 4JO I I I I 910 0 0 I 0 2 30 50 60 70 .80

FREQUENCY, GHz FIGURE 7 ILLUSTRATION OF THE IMPORTANCE OF MILLIMETER

SOLAR BURSTS

Peak power density spectrum of the large burst of 5 June 1969, showing the importance of the contributions from frequencies > 10 GHz.

and cut-off relatively rapidly at both the low and high frequency ends, and thus have

an'inverted U spectrum' which may or may not be accompanied by a further increase

at a few hundred MHz. It should be noted that the term U-shaped spectrum refers to the combined microwave-decimeter region and is used for its convenience in relating

to proton events. The true microwave burst, which is usually quite distinct from the decimeter event characteristically has the inverted U spectrum. More recent extensions of observations to the region above 10 GHz at AFCRL (15.4 and 35 GHz) and at Slough (19, 37 and 71 GHz) have shown that even the microwave portion of the hybrid

FORECASTING THE INTENSITY OF SOLAR PROTON EVENTS 179

U spectra has this typical inverted-U shape when the complete radio spectrum is recorded (Croom, 1971), the only fundamental difference between these and the bulk of microwave bursts being that the peak occurs at much higher frequencies. An example of a peak power spectrum (for the large burst of 5 June 1969) is shown in Figure 7. It has been plotted on linear scales to emphasize the importance of the contributions from millimeter wavelengths.

Parameters describing the shape of the spectrum (peak power, mean power or energy), such as the 3 dB width (relative to the peak value), or the high and low fre- quency cut-off spectral indices x given by:

Pmax(Or /~ or E) oc f -~' (5)

are still difficult to determine in many cases because of insufficient frequency coverage, particularly at the high frequency end (the use of peak frequencies and intensities at peak frequencies has already been discussed).

3. The Elementary Time Characteristics of Solar Microwave Bursts (d, e, f)

These are the more obvious time parameters which can be read directly from the burst records (the sections have been labelled to correspond with Table I).

D. TOTAL DURATION~ T

The disadvantages of this parameter have already been discussed in connection with the mean power density (Section 2b).

E. RISE TIME TO PEAK, r R

This has been used in conjunction with peak power density to demonstrate that single frequency observations can be used to distinguish between proton and non-proton solar flares (Croom, 1971). The probability that bursts exceeding a certain intensity threshold level will be accompanied by proton emission is increased if the rise from start to peak is equal to or greater than 3 min (at 19 GHz) i.e. impulsive type bursts are not accompanied by protons whatever their peak intensity. However, this is not in general recommended as a useful parameter, since in many important bursts either the start time or peak time is difficult to define meaningfully. For an example of an ill- defined start see the 19 GHz burst of 1 November 1968 (Croom and Powell, 1970) and for an ill-defined peak see the 2.7 GHz burst of 28 August 1966 (Castelli et al., 1967).

F. DECAY TIME~ T D

The use of burst decay time back to the pre-burst solar level has the same disadvan- tages as the total duration, T. The exponential decay time, that is the time taken for the level to decrease to 1/e of the peak value is a possible alternative though again not perhaps a very good one since not all bursts exhibit an exponential-like decay (see the 2.7 GHz burst mentioned in previous section).

180 DAVID L. CROOM

4. The Mean or Effective Burst Duration, Tu, (g)

The concept of mean or effective burst duration (Croom, 1970b) is one that does not appear to have received much attention in connection with solar radio bursts though it is commonly used in Fourier transform applications (e.g. the equivalent width of a spectral line, the effective beamwidth of an antenna), although its converse, the mean power flux density (Section 2b), is a widely quoted burst parameter. Mathematically, it is:

T

T~t = P (t) at = Pma-~ (6)

0

(compare this with Equation (1)). Thus it is the duration of an equivalent burst having the same energy density but for

which the emission is at a constant level corresponding to Pmax" Figure 2 shows the effective duration of the same examples as in Figure 1. However, unlike the mean power P the new parameter correctly represents the differences between the burst waveforms, since (a) and (b) have nearly the same T u, with that for (b) being slightly greater than that for (a) to reflect the contribution from the long, low-intensity tail, whereas (c), the stronger but more impulsive event, has a much shorter T u. Moreover, it has eliminated from consideration the actual intensity of the burst, which as we have seen earlier is a very unreliable indicator of the proton intensity.

Alternative ways of considering Tu are as the area enclosed by the burst, normalized with respect to the peak intensity, or as the dc component of the Fourier transform of the burst waveform P ( t ) , also normalized with respect to Pr, ax"

Its significance is that it is a reliable measure of the overall 'shape' of the burst, independent of the burst intensity and not subject to the uncertainties of the time parameters discussed in the previous section. Within the microwave-millimeter range it is nearly independent of frequency.

Further, as Figure 5 shows, unlike the other parameters it shows distinct signs of a relationship with the intensity of the protons, and so provides a means of predicting the actual intensity of proton events from their radio signatures, as opposed to the inverted U spectra of Castelli et al. (1967) or the single frequency criteria of Croom (1970a, 1971) both of which predict the onset of protons but say nothing of the im- portance of the event.

In particular it should be noted that the vast majority of microwave bursts have very small values of T M (of the order of 1 min or less) and are not associated directly with proton emission. This includes such intense events as those listed in Table II. Note particularly the event of 0716 UT on 6 July 1968, which although of moderate in- tensity compared with the other events listed is still large in comparison with the major- ity of microwave bursts. Nevertheless it has the extremely short T u of only 0.07 min. This burst is an extreme example of an impulsive microwave burst, and is of the type referred to by Kundu and Haddock (1961) as a 'rare short outburst'. The 6 July 1968

F O R E C A S T I N G T H E I N T E N S I T Y O F S O L A R P R O T O N E V E N T S

TABLE II

Some intense bursts that do not appear to have had protons associated directly with them

181

Date Time (UT) Frequency of maximum Maximum peak power T,~ emission (GHz) (10 2~ W m -2 Hz -1) (min)

2 Jan. 1968 0522 19 4700 3.2 6Ju ly 1968 0716 3 480 0.07 8Aug. 1968 1817 17 2300 1.8

18Nov. 1969 1652 8 6200 5.0 19Nov. 1969 0537 5 1600 3.5 23 Nov. 1969 1017 20 1100 3.2

I00

I0

z I

0.1

0.01 0.1

. . I i I f | I I I

?

I 1 I 1 l l i l

I I I I I I l l J

1

! I 1 I I I 1 '

X X X

I r I l l l l I I I 1 1 l [ l

IO IOO

TIO, MINUTES

Fig. 8. The relation between the effective duration TM and the 10 dB duration T10,

182 DAVID L. CROOM

burst has been described by Cribbens and Matthews (1969). It was followed by a major burst at 0950 UT on the same day.

The largest T u among the events studied was 30 min for the bursts of 1 November 1968 (0912 UT) and of 2 November 1969 (1041 UT) and thus this parameter has a dynamic range of at least 25 dB.

5. The 3 dB and 10 dB Burst Durations

Although the mean duration of a burst has the advantages of being both well defined mathematically and of being closely related to the intensity of proton events, it involves measurement of both the area enclosed by the burst and the intensity of the burst before it can be evaluated. For practical purposes (involving rapid decisions regarding proton events) it would be more convenient if some more arbitrary time parameter approximating to TM, but capable of being read directly from the burst record, could be found. The immediately obvious one is the half-power duration of the burst, or 3 dB duration (relative to Pmax), T3. However, in practice this does not turn out to be a very good parameter for this purpose.

A more effective relation (Figure 7) is obtained by taking the tenth-power duration (relative to Pm,,), Tlo which comes closer to the overall duration T but without the same difficulties of measurement. Figure 8 shows the relation between the mathemati- cally defined T u and the arbitrary 7"10. Included in the diagram is a point for the ex- tremely short duration event mentioned in Section 4. At least squares power curve fit to these points gives:

o r

Z M = 0.56 (710) 0.93 (7)

T~ ~ ~ T~0 (8)

with a correlation factor of 0.98.

T A B L E I I I

Coefficients re la t ing var ious solar microwave burst parameters and the p ro ton part icle flux N~ for Ev > 10 MeV (r = corre la t ion coefficient, N~ = Ax B)

x Uni t s r A B

Peak power densi ty 10 -z2 W m -z Hz -1 - -0 .17 - Energy densi ty 10 -18 J m -2 Hz -1 + 0.14 -

f ( P ..... )ma~ G H z - -0 .16 - Peak power at f (Pm~)m~x 10 2"2 W m -z Hz -1 -- 0.11 - T~r min + 0.78 0.034 /"8 min § 0.66 1.19 Tlo min + 0.74 0.013

3.2 2.0 2.7

FORECASTING THE INTENSITY OF SOLAR PROTON EVENTS 183

6. Comparison of the Effectiveness of the Various Parameters

Table I I i shows the results of a least squares fit power curve of the form:

Np = A x B (9)

with respect to plots of various burst parameters x against the proton flux, Np. It

illustrates numerically that TM is the best mathematically definable parameter to use for predicting the intensity of proton events, and that 7"10 provides a useful alternative

for 'quick-look' purposes.

7. The Apparent False Alarms

The points enclosed by the broken triangle in Figure 6 constitute a group of bursts which according to their values of Tu should have resulted in medium to large proton

TABLE IV Some apparent false alarms

False alarm UT T~ Source Subsequent proton event Same region Date Date UT

2 Jan. 1968 0522 3.2 $24 E90 11 Jan. 1968 1700 Yes 24 Feb. 1969 2314 6.2 N12 W33 25 Feb. 1969 0911 Yes 27 Mar. 1969 1327 5.9 N20 W70 30 Mar. 1969 0249 Yes 26 Apr. 1969 2307 4.6 N08 E39 In tail of 10/11 April event No. 18 Nov. 1969 1652 5.0 N14 E40 24 Nov. 1969 0919 Yes 19 Nov. 1969 0537 3.5 N05 E28 24 Nov. 1969 0919 Yes 23 Nov. 1969 1017 3.2 N15 W18 24 Nov. 1969 0919 Yes

events, but which with one exception produced no observed protons according to the Explorer 34/41 data. The single exception (1327 UT on 27 March 1969) resulted in

only 0.2protons ster -1 cm -z s -1 in the Ep>10 MeV range, despite its large TM.

These events are listed in Table IV, together with the times of the next subsequent proton event and an indication of the relation between the active regions involved. I t turns out that of these 7 'false' alarms, only two appear to be not closely associated

with proton events, these being the events of 2 January 1968, which was followed by a nine day gap, and of 26 April 1969, which was followed by a two weeks gap (and

where in any case different regions were involved). The source of the 2 January event was on the east limb and therefore the probability of protons being detected in the vicinity of the earth was relatively low. Of the remaining five, the events of 24 February 1969, 27 March 1969, and 23 November 1969 were all close enough to the subsequent events for there to be some ambiguity as to which in fact resulted in the emission of protons. The other two bursts, on 18 and 19 November 1969, form part of the same sequence of events that resulted in the proton flare of 24 November. In view of the

184 DAVID L. CROOM

anisotropy of solar proton streams it is to be expected that there will be a few instances in which protons are emitted from the Sun but are not observed in the general vicinity of the Earth.

8. The Relation of T+vl to Higher Energy Protons

Table V lists the coefficients relating the effective burst duration TM to the proton particle flux for various energy ranges. In particular, it shows that the correlation is

TABLE V

Coefficients relating the effective burst duration T~ and the proton particle flux for various proton energy ranges

Proton energy range r A B

10-30 MeV + 0.79 0.022 3.3 > 10 MeV + 0.78 0.034 3.2

30-60 MeV + 0.73 0.036 2.4 > 30 MeV +0.69 0.070 2.3 > 60 MeV + 0.42 0.385 1.0

highest for the 10-30 MeV range and lowest for the very high energy protons, > 60 MeV. The power law changes from approximately cubic for the lowest energies, through square for the middle ranges to linear for the very high energies.

9. Harmonic Content of the Burst Waveform

The waveforms of a number of bursts were Fourier analyzed to see if one of the har- monic components could be used. The results suggested that although the longer

period components (30-40 min period) might be useful they did not give as good results as T u (which corresponds to the dc term in the analysis for a fixed fundamental period), and in view of difficulties associated with making this analysis it was not carried any further. However a more detailed analysis could conceivably lead to a means of distinguishing between various sub-groups of events.

10. Conclusions

It has been shown that the solar proton flux in the energy range 10-30 MeV is approxi- mately proportional to the cube of the mean duration of the associated microwave burst, with a correlation of nearly 0.8. In particular, although intensity parameters are necessary for eliminating the many minor bursts from consideration, once this has been done time parameters give a much better indication of whether or not a proton event will occur, and if so what its likely intensity will be. However, the use of parameters involving the overall burst duration is not recommended.

FORECASTING THE INTENSITY OF SOLAR PROTON EVENTS 185

Acknowledgements

This work was carr ied out as pa r t o f the p r o g r a m of the Ai r Force Cambr idge Re-

search Labora to r i e s while the au thor was on leave f rom the Rad io and Space Research

Stat ion, Slough, as 1969-70 Na t iona l A c a d e m y of Sciences - Na t iona l Research Coun-

cil Senior Pos t -Doc to ra l Research Associa te suppor ted by the former Office of Aero-

space Research. The au thor is grateful to J. P. Castel l i o f A F C R L , Rev. J. J. Hennessey

o f M a n i l a Observa tory , R. J. Powell of RSRS and Professor T. T a k a k u r a o f T o k y o

Observa to ry for access to unpubl i shed solar rad io burs t data .

References

Castelli, J. P.: 1968, 'Air Force Surveys in Geophys. No. 203', Air Force Cambridge Research Labora- tories. Massachusetts, March, 1968.

Castelli, J. P and Aarons, J.: 1970, 'Proc. XV Electromagnetic Wave Propagation Meeting of AGARD', CP No. 49.

Castelli, J. P., Aarons, J., and Michael, G. A.: 1967, J. Geophys. Res. 72, 5491. Cribbens, A. H. and Matthews, P. A. : 1969, Astrophys. Letters 3, 215. Croom, D. L. : 1970a, J. Geophys. Res. 75, 6940. Croom, D. L. : 1970b, Astrophys. Letters 7, 133. Croom, D. L. : 1971, this volume, p. 152. Croom, D. L. and Powell, R. J. : 1970, Solar Phys. 14, 221. ESSA: 1967-70, Solar Geophysical Data, ESSA Research Laboratories, Boulder, Colorado. Kundu, M. R. and Haddock, F. T.: 1961, IRE Trans. Antennas and Propagation AP-9, 82.