characteristics of shocks in the solar corona, as inferred from radio, optical, and theoretical...

C H A R A C T E R I S T I C S OF S H O C K S IN T H E S O L A R C O R O N A ,

I N F E R R E D F R O M R A D I O , O P T I C A L , AND T H E O R E T I C A L

I N V E S T I G A T I O N S *

AS

A L A N M A X W E L L

Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, U.S.A.

and

M U R R A Y DRYER

NOAA Environmental Research Laboratories, Boulder, CO 80303, U.S.A.

Abstract. Solar radio bursts of spectral type II provide one of the chief diagnostics for the propagation of shocks through the solar corona. Radio data on the shocks are compared with computer models for propagation of fast-mode MHD shocks through the solar corona. Data on coronal shocks and high-velocity ejecta from solar flares are then discussed in terms of a general model consisting of three main velocity regimes.

1. Radio Data on Shock Waves Generated by Solar Flares

Solar flares of high intensity often generate shock waves, whose propagation through the solar corona can be tracked by their radio emission in the form of bursts of spectral type II. Examples are shown in Figures 1-3. The bursts are characterized by narrow bands of intense, randomly-polarized radiation that drift slowly toward lower frequencies: at 100 MHz the drift rate is about -0.3 MHz per sec. They typically have durations of about 20 min and generally comprise emission at a fundamental frequency and a second harmonic, indicating that the basic emission mechanism involves plasma oscillations. In many cases, the fundamental emission is first observed at frequencies of approximately 100 MHz, about 5 minutes after the explosive phase of a flare, which is generally indicated by emission of impulsive bursts in the microwave band, associated type III bursts in the meter band, and hard X-ray bursts.

If an appropriate model is adopted for the distribution of electron density above an active region, the radial velocity component of the shock may be derived from the drift rate of the type II burst. Shock velocities derived in this manner generally fall within the range 1000-2000 km s- i (Maxwell and Thompson, 1962; Weiss, 1963; and subsequent authors).

Data on the spatial distribution of type II emission regions have been obtained from the radioheliograph at Culgoora, Australia, which gives two-dimensional information, every second, on the brightness contours of solar radio bursts, in the two senses of circular polarization. At its original operating frequency of 80 MHz, the radioheliograph had an angular resolution of about 2 arc min. Wild and Smerd (1972), summarizing information on type II bursts gathered by the radioheliograph at 80 MHz up until 1972,

* An invited paper presented at STIP Workshop on Shock Waves in the Solar Corona and Interplanetary Space, 15-19 June, 1980, Smolenice, Czechoslovakia.

Space Science Reviews' 32 (I982) 11-25. 0038-6308/82/0321-0011502.25. Copyright �9 1982 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston, U.S.A.

Fo

Fig.

1.

Dyn

amic

spe

ctru

m o

f typ

e II

sol

ar ra

dio

burs

t rec

orde

d ov

er th

e fr

eque

ncy

rang

e 25

-580

MH

z at

the

Har

vard

Rad

io A

stro

nom

y S

tati

on. T

he ty

pe I

II b

urst

s is

suin

g fr

om t

he t

ype

II b

urst

are

ass

umed

to h

ave

been

gen

erat

ed b

y je

ts o

f su

pert

herm

al e

lect

rons

acc

eler

ated

in t

he o

utw

ard-

mov

ing s

hock

fro

nt.

Fig.

2.

Typ

e II

sol

ar r

adio

bur

st r

ecor

ded

over

the

freq

uenc

y ra

nge

10-2

000

MH

z at

the

Har

vard

Rad

io A

stro

nom

y S

tati

on. N

ote

the

impu

lsiv

e bu

rsts

in

the

ban

d

500-

1000

MH

z pr

eced

ing

the

type

II

burs

t.

U~

Fig.

3.

Typ

e II

sol

ar r

adio

bur

st r

ecor

ded

over

the

fre

quen

cy r

ange

25-

580

MH

z at

the

Har

vard

Rad

io A

stro

nom

y St

atio

n. N

ote

the

type

II1

-V b

urst

s pr

eced

ing

the

type

II

burs

t, t

he f

unda

men

tal

and

seco

nd h

arm

onic

com

pone

nts

in t

he t

ype

II b

urst

, an

d th

e sp

litti

ng o

f th

e fu

ndam

enta

l an

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cond

har

mon

ic

com

pone

nts.

> >

CHARACTERISTICS OF S H O C K S IN THE SOLAR CORONA 15

A

"~--4

Fig. 4. Radio emission from the solar limb event of 1969 March 30, recorded with the radioheliograph at Culgoora at 80 MHz. A flare was presumed to have occurred behind the limb at position X, starting at 02 : 45 UT. The radioheliograms were taken at 02 : 50 (left) and 03 : 03-06 (right). Type II bursts occurred

in sources A, C, and D. Source B was a flare continuum source. (After Smerd, 1970.)

noted that the areas of type II emission were often of very large dimensions, sometimes extending over 180 arc deg around the solar disk (Figure 4) and that the emission regions were often characterized by rapid variations of brightness distribution. In recent years, additional information on type II bursts has been obtained with the radioheliograph while it has been operating at frequencies of 43, 80, and 160 MHz (Nelson and Robinson, 1975; Nelson, 1977). Existing evidence also indicates that type II emission regions coincide with open field lines (Newkirk, 1971; Dulk et al., 1971).

The first convincing instance in which a shock was tracked, by means of its radio emission as it travelled from the sun through the interplanetary plasma right to the earth, occurred with the intense flare of 1972 August 7, 15:00 UT. The passage of the shock through the corona was detected by ground-based radio equipment, covering the frequency range 10 to 2000 MHz, at the Harvard Station (Maxwell and Rinehart, 1974); its subsequent passage through the interplanetary plasma was tracked with radio equipment covering the band 0.04 to 2.6 MHz on board the IMP-6 satellite (Malitson et al.,

1973). More recently, investigators with radio equipment covering the band 0.02 to 1.2 MHz on board the Voyager I and II satellites have also recorded radio emission from flare-generated shocks as they traversed the interplanetary plasma (Boischot et al., 1980; Riddle et al., 1980). Radio emission from shocks traversing the interplanetary plasma

has also been recorded with receivers covering the band 0.03-2.0 MHz on board the ISEE-3 satellite (Stone, private communication).

About 30~o of type II solar radio bursts are associated with bursts of spectral type IV in the meter and dekameter bands, and these bursts may be either moving or stationary. Of the moving type IV bursts, Smerd and Dulk (1971) distinguished three categories, the properties of which have been further discussed by Schmahl (1972), Robinson (1978),

16 ALAN MAXWELL AND MURRAY DRYER

and Kai (1979). The categories are as follows:

(i) Advancing front: a wide irregular arc of emission is seen on radioheliograph records a few minutes after the passage of a type II source; the delay in the appearance of the type IV radiation is interpreted in terms of Razin-Tystovich suppression; the outward velocity of the arc is of the order of 1000 km s - l ; the radio emission shows little or no polarization. Figure 5 shows data on one of these bursts recorded at Culgoora.

RO 2'5

2-0 1400km/s ~ / "

~ " 1I / $ ~ ///

/ ! /

! # / /

�9 I d I I I l - -

Fro= Onset 00 Time(UT) 0010 0020

Fig. 5. Development of a moving type IV burst of the 'advancing front' variety recorded at Culgoora at 80 MHz on 1968 October 23-24. The diagram shows derived height-time plots of the type II burst (using

radio spectral data), and the moving type IV burst, which is shown by dots (using radioheliograph data at 80 MHz). (After Kai, 1970.)

(ii) Isolated source (ejected plasmoid) : the velocities of these sources generally fall within the range 200-800 km s- 1 ; the radiation is highly circularly polarized; the sources are usually not associated with a type II burst or, if they are, the type IV source may propagate in a different direction from the type II burst.

(iii) Expanding magnetic arch: the expansion velocity of the order of 300 km s- 1; radio emission is unpolarized at the top of the arch and circularly polarized at its footpoints; these bursts are observed only rarely.

Theoretical work on the nature of the processes that give rise to the radio emission from outward travelling shocks has been summarized by Wild and Smerd (1972), Krall (1974), McLean (1974), and by Svestka (1976). Most theories find common ground in terms of an exciter that consists of a collisionless, fast-mode MH D shock, as first suggested by Uchida (1960); but agreement has not been reached on the mechanisms in the shock front that actually give rise to the radio emission of spectral type II. The processes by which particles can be accelerated to high energies in an outward-travelling shock which is carrying magnetic field with it has been examined by a number of

CHARACTERISTICS OF SHOCKS IN THE SOLAR CORONA 17

investigators (see Svestka, 1976, and references therein). The shocks have repeatedly been identified as a possible source of many of the high-energy particles that pervade the interplanetary plasma after major solar flares.

Uchida (1974), in considering the case of type II bursts generated by blast waves, showed by linear, three-dimensional computer simulations that fast-mode MHD waves tend to refract into regions of low Alfv6n velocity in the corona, where the waves implicitly strengthen into shocks and thus give rise to localized type II emission sources of the sort recorded by the Culgoora radioheliograph. In the case of large flares, however, radio, optical, and interplanetary evidence suggest that the shocks may be driven by pistons. Nagakawa et al. (1978), Steinolfson et al. (1978), and Wu et al. (1978), have developed non-linear, two-dimensional computer codes for the propagation of fast mode MHD shocks through the solar corona and interplanetary plasma; and these models explicitly examine the development of the shocks and associated global response of the corona.

2. Radio Data and Computer Models for Coronal Shocks

Dryer and Maxwell (1979) have compared radio data on the velocity of shock waves generated by solar flares with computer models for the outward passage of fast-mode MHD shocks through the solar corona. The radio data were taken from the records of the Harvard Station, and the computer simulations were carried out at NOAA. The models were derived for the case of blast- or piston-driven shocks.

From the data on the type II radio burst generated by a given flare, and with the assumption of an appropriate model for the electron density above the flare region, Dryer and Maxwell estimated the radial velocity component of the outward-travelling shock that excited the type I! burst to be about 1100 km s - 1. The radio data on this shock were then compared on a minute-by-minute basis with a non-linear, two-dimensional, time- dependent computer simulation for the outward passage of a fast-mode MHD shock through the solar corona from the codes developed by Nakagawa eta[. (1978), Steinolf- son etal . (1978), and Wu etal . (1978).

The assumed magnetic topology was that ofa hexapole embedded in the solar corona. An input pulse was then applied at a region where the magnetic field lines appeared to open into the interplanetary plasma. The pulse was applied at the base of the corona over 5 degrees in heliographic latitude. The ambient temperature was assumed to be 2 x 106 K, the magnetic field 2 G, and the plasmabeta was assumed to be 1. The density in the solar atmosphere was assumed to decrease outwards in a quasi-exponential manner. (The density model for the computer simulation approximated the density model used for the interpretation of the radio data at heights of about 2 to 3Re). The model was applied in the meridional plane, and the simulation was terminated at 6R o.

The computer simulation provides information on the global response of the corona to the input pulse, in terms of density, temperature, particle velocity, and the redistri- bution of magnetic field. Various forms of input pulses could be applied; for example, a series of rapid pressure pulses, a square-wave pressure pulse, a magnetic pulse, etc.

18 A L A N M A X W E L L A N D M U R R A Y D R Y E R

In the investigation by Dryer and Maxwell, the best simulation for the radio data was give n by a thermodynamic pulse which had the form of a square-wave of duration 10 rain, containing a temperature (or pressure) increase of 40 times the ambient value. The energy in the applied pulse was of the order of 2 x 1032 erg. The ejected mass, as indicated by the computer simulation, was 6.4 x 1016 g. (It may be noted that Gosling et al. (1975) estimated the energy content and mass of matter ejected by a selected class 2B flare as 1.1 x 1032 erg and 2 x 1016 g, respectively.)

~5 (3

rr"

0 03

. E

"S

( . )

o E &

~o g

~5

g

5! i

4 -

Simulated Fast-Mode MHD Shock

Shock Position Inferred from Type ][ Burst

ConlQcl Surface

m o Moving Emission Front

I Eruptive Filamenl

2 ~

~ . ~ , , f , , , , I , , , , I . . . . I . . . . I . . . . Omin 5 10 I5 20 25 30

18 =26 UI 18:51 18:56 18:41 18 46 18:51 18:56

1973 September 5

Fig. 6. Position of shock wave in solar corona determined from data on radio burst of spectral type II, compared with positions inferred from the computer simulation of a fast-mode MHD shock (Dryer and

Maxwell, 1979).

A comparison of the shock velocities derived from the computer model with shock velocities derived from radio data is shown in Figure 6. Velocity magnitudes and vectors for the movement of coronal plasma, determined from the computer simulation for times corresponding to 2, 4, 6, and 15 min after the input pulse was first applied, are shown in Figure 7.

Potential deficiencies of the present models lie in the inability to simulate three- dimensional responses within complex magnetic topologies. Non-planar, two- dimensional (that is, quasi-three-dimensional) models are, however, now being developed by Nakagawa et al. (1980).

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3. Velocity Regimes for Shocks and Flare Ejeeta

Over the past 20 years, many authors have discussed the 'association' of coronal shocks

and type II solar radio bursts with optical coronal phenomena such as H e surges, sprays,

eruptive prominences, green-line (2 5303/~) transients, white-light transients, and so on.

In most cases, however, the suggested association between the type II bursts and the

exciter shocks on the one hand, and the optical phenomena on the other, is very tenuous.

Thus the velocities of the shocks and of the optical phenomena generally fall into separate

velocity regimes, the shocks moving with velocities of the order 1000-2000 km s-1 and

the optical ejecta moving with velocites in the range100-1000 km s -~.

Maxwell and Dryer (1981) have recently examined 10 specific cases in which investi-

gators have related fast-moving optical ejecta from flares with type II radio bursts and

coronal shocks. The optical data were mainly fast H e sprays, which have velocities up

to 1000 km s -1 and which may be tracked out to about 2R o and the leading edges of

Fig. 8. White-light coronal transient photographed on 1973, October 27, 16:59 UT with equipment on Skylab (Gosling et al., 1976). The flare that generated the transient commenced at 15 : 43 and was located at N 20 E 55. In the photograph, north is at the top and east to the left; the field of view is six solar diameters; the occulting disc is 1.5 solar diameters. The location of a shock wave, estimated to be moving at 1200 km s - 1, that originated in the flare at the time of the explosive phase, is indicated by the dashed line at 6,5R o (Maxwell

and Dryer, 198t).

1.4

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Fig.

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white-light coronal transients, which may have velocities of the order of 1000 km s- 1 and which may be observed from about 2 to 10R o (Figure 8).

Maxwell and Dryer suggested that there exist three main velocity regimes for shocks and ejecta originating in intense solar flares. The regimes are diagramatically illustrated in Figure 9, which shows the relative locations of shocks and ejecta in the solar atmosphere, for assumed open field configuration, about 6 rain after the explosive phase. The explosive phase (t = 0) is assumed to be signified by the commencement of impulsive bursts in the centimeter band, associated bursts of hard X-rays, and bursts of spectral type III in the decimeter and meter bands and is assumed to last for approximately 30-300 s. This phase is also presumed to be associated with the large-scale heating in the chromosphere and lower corona that ultimately give rise to an outward-travelling shock. For intense flares, the total energy of the ejected matter is believed to be of the order of 1032 erg and the mass of the order 1016 g.

No attempt is made to specify the nature of the primary energy release in flares. (A recent review of these matters has been given by Kahler et al. (1980).) The model is concerned only with the secondary phase (fluid response) of the corona. The type of secondary phase discussed in the model is, however, consistent with the description of Syrovatskii and Somov (1980) of a primary, explosive phase which involves current- sheet disruption triggered by tearing-mode instabilities, which are then followed by intense local chromospheric and coronal heating, etc. Mass in the chromosphere is thus heated, and then ejected, by the conversion of magnetic energy within the original force-free fields into thermal and kinetic forms. The latter are manifested as a 'pressure pulse' at the base of the corona. Magnetic control dominates the initial phase. Sub- sequent motion in the secondary, coronal phase, is modulated by local magnetic topologies and plasma betas, as discussed by Nakagawa et al. (1978), and Wu et al. (1978). Given sufficient energy conversion and release in the flare process, local dynamic pressures can exceed the magnetic pressure, as indicated by attainment of Alfvtn Mach numbers that exceed unity. Thus temporal and spatial distribution of plasma betas and Alfvtn Mach numbers must be examined in order to assess the degree of magnetic control.

The fastest velocity regime that develops after the explosive phase of a flare then corresponds to that of a quasi-hemispherical shock wave moving outward from the flare with a velocity of the order 1000 to 2000 km s- ~ and with an Alfvtn Mach number of approximately 1.5. When the shock is fully developed it gives rise to type II radio bursts. The fast-moving type IV emission that is sometimes seen immediately behind the shock front is presumed to originate in the region of high compression between the contact surface and the shock front. In the compression region the plasma beta may be of the order of unity or higher. In fact, if the original pulse is taken to be caused only by emerging magnetic flux instead of by a pressure (temperature and/or density enhancement) pulse, it has been shown by Steinolfson et al. (1981) that/3 < 1 behind the contact surface and /3 > 1 in front of it. Thus the degree of magnetic control can be explicitly shown to be extremely strong in some portions of the disturbed plasma volume and weak in Others. The magnitude and duration of the pulse, whether it be a magnetic or pressure pulse,


will determine whether matter will in fact be ejected and, if so, its ultimate mass and associated energy.

The second velocity regime corresponds essentially to the velocity of the piston driving the shock. The velocity of the contact surface, that is, the front edge of the piston, is of the order of 0.8 that of the shock itself (see Dryer, 1975, and references therein). In this regime we might identify the leading edge of the fastest white-light transients; behind the leading edge of these transients we have white-light loops expanding outward at some- what lower velocities. Plasma betas in this region may be < 0.1. This regime might also cover higher-velocity flare sprays.

In the third regime, we place slower moving Ha ejecta, with velocities of the order of 300-500 km s-1. This regime covers the slower flare sprays, eruptive prominences, surges, moving type IV bursts of the ejected plasmoid or expanding arch varieties, and SO on.

Acknowledgements

Work described in this paper was supported in part by NSF Grant ATM 77-21453 and NASA Grant NSG7648 to A. Maxwell, and by NASA Contract S-59811 with M. Dryer.

References

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Discussion

Sarris: How common is it to observe type III bursts following the onset of a type I[ burst which might indicate the acceleration of energetic electrons at the shock front during the early stages of its evolution?

Maxwell: Type II bursts that generate type III bursts or herringbone bursts seem to be fairly rare: about 10 to 20~o of the cases.

Anderson: The Earth's bow shock is a strong shock (M ~ 8) which continuously accelerates electrons in a small 'hot spot' located where the shock is in the perpendicular condition. The highest energy electron coming from the shock and moving upstream is ~ 100 keV. Often, however, the maximum energy is closer to 10 keV. Coming to the question of why interplanetary shocks do not accelerate electrons into the 10-100 keV range, we may say first of all that interplanetary shocks are usually weaker. Also, the bow shock has a much smaller radius of curvature which insures that somewhere on the shock surface the perpendicular condition, evidently essential for acceleration, is met.

Sehwenn: The Culgoora observations as well as the computer simulations shown here showed significant expansions of flare produced shocks over solar longitude and latitude. What is the time history of this 'lateral' coronal shock propagation? The background of this question is the still unknown mechanism that allows flare produced high energy particles to be observed, although rernarkedly delayed, at locations which are not all magnetically connected to the flare site. There is a recent hypothesis (for example, Wibberenz, G.: 1979, Proc. 16th lnternat. Cosmic Ray Conference (Kyoto), Conference Papers (Publ. Univ. of Tokyo) 14, 234) that these particles might be accelerated by shocks propagating laterally in the Sun's vicinity.

Maxwell: Data from Culgoora show,that type II emission can be spread over more than 180 ~ around the solar disk. I believe that considerable tangential velocities are also recorded sometimes.

Dryer: The latitudinal-longitudinal extent of the shock would depend on several parameters, such as the duration of energy release, size of emitting region, and, probably most important, the topology of the magnetic field before and during the shock propagation through it. Thus, some flares may produce highly-collimated shocks in latitude and longitude. Others (such as the 'Steve Smerd' shock of March 30, 1969) would produce latitudinal extents greater than 180 ~ It should easily be possible for a shock to expand laterally over > 45 ~ in longitude-latitude in, say, 15 min.

Krivsky: Have you found that the 'radio' shock front precedes, in all cases, the position of the leading edge of white light coronal transients?

Maxwell: As far as we can determine, the shock front is usually ahead of the 'leading edge' of white-light transients, and probably travelling at least 20% faster. The MHD model, together with some limited observational data, has been used as a guide in this determination.

Ivanov: Is there any connection between the distance from the shock front to the boundary &ejection? Is there a typical length of flare ejection? Does the shock front break away from the boundary of ejection?


Maxwell: The shock front would be expected to 'stand-off" ahead of ejected matter by about 20~o of the distance covered. The shock would always be expected to break away from the ejected matter. The time scale for matter to be ejected from the chromosphere or lower corona may be as short as 5-10 rain and possibly as long as an hour, thereby determining the 'initial length' of the always-expanding flare ejecta.

Wu: We all believe that type II bursts are produced by shock waves. But do we really understand the physical mechanism of the radio emission process?

Maxwell: Although a number of theories have been advanced over the past 20 years, there is, to my knowledge, no agreement about the microscopic processes in shock fronts that actually give rise to radio emission.

Kruger: It should be taken into mind that evidently shock waves are not always accompanied by type II burst emissions since special conditions of the conversion into radio waves must be fulfilled. Also, different source regions are contributing to the dynamic radio spectrum as the Culgoora heliograms show.

Shea: Do you have any intuitive feeling about the time of high energy (i.e., relativistic) particle acceleration and/or emission from the flare with respect to the time of the explosive radio emission?

Maxwell: The work of Frost and others indicates that second-stage acceleration (in an outward travelling shock front) usually commences about 5-10 min after the explosive phase of a flare.

Sarris: It is well known that the onset time for the arrival of relativistic (i.e., GeV) solar protons at the earth is often 15-20 rain after the flare is 'seen' at the Earth or a total of 23-38 rain if one considers that it takes 8 min for light to travel the Sun-Earth distance). Since these relativistic protons are travelling at essentially the speed of light, they should travel between the Sun and the Earth in a total time of about 8-16 rain, allowing some time for the curvature of their orbits. It would appear that these relativistic particles are not accelerated and/or released with the onset of the actual flare but at some later time during the flare process.

characteristics of shocks in the solar corona, as inferred from radio, optical, and theoretical...

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