Solar Energetic Particle Events

Home , Helios (spacecraft)

A TOOL TO MODEL SOLAR ENERGETIC PARTICLE EVENTS.

1 2;3 1

D. Lario , B. Sanahuja , A.M. Heras

Space Science Department, ESTEC/ESA, 2200AG No ordwijk, The Netherlands

Dept. Astronomia i Meteorologia, Universitat de Barcelona, Barcelona, Spain

Institut d'Estudis Espacials de Catalunya, Barcelona, Spain

ABSTRACT may also expand through the heliosphere driving a

sho ckwave across the interplanetary medium. The

b ehavior of the sho cks close to the Sun and through

interplanetary space is quite di erent Cane, 1997.

Gradual solar energetic particle events p ose a serious

While strong sho cks may extend up to 300 in longi-

risk to spacecraft comp onents. The origin of these

tude near the corona, they extend at most 180 at 1

particle events is closely asso ciated with the devel-

AU Cliver et al., 1995.

opment of coronal mass ejections and sho ck waves

driven by them. Prediction of uences observed at

As the sho ckgoesaway from the Sun, it crosses many

di erent heliospheric p ositions during these events re-

IMF lines and may be resp onsible for accelerating

quires to know the physical pro cesses o ccurring dur-

particles to energies much higher than the thermal

ing their development. We outline the main ingre-

solar wind background Sanahuja & Domingo [1987]

dients of a mo del that repro duces particle ux and

and references therein. These energetic particles

anisotropy pro les of these events. This mo del in-

propagate along the IMF lines owing outward from

cludes a simulation of the propagation of the asso ci-

the sho ck and arriving at the spacecraft p ositions.

ated CME-driven sho cks and a simulation of the in-

These space prob es detect particle intensity increases

jection and transp ort of sho ck-accelerated particles.

which constitute the SEP events. The particle in-

We present an application of this mo del to pro duce

tensity pro les observed by spacecraft take di er-

several \typical" synthetic ux and anisotropy pro-

ent forms dep ending on 1 the heliolongitude of the

les which allows us to delimit the particle e ects

source region with resp ect to the observer lo cation,

under di erent conditions and situations.

2 the strength of the sho ck and its eciency accel-

erating particles, 3 the presence of a seed particle

p opulation sub ject of b eing accelerated, 4 the evo-

Key words: solar proton events; CME; Interplanetary

lution of the sho ck its sp eed, size and shap e, 5 the

Sho cks.

conditions for the propagation of sho ck-accelerated

particles, and 6 the energy considered Cane et al.,

1988; Lario et al., 1998. Particle ux pro les range

1. INTRODUCTION

from a prompt increase shortly after the CME with a

p osterior gradual decay, to a sudden increase shortly

a few hours b efore the arrival of the interplane-

Large solar energetic particle SEP events, charac-

tary sho ck at the spacecraft, passing through gradual

terized by gradual intensity timescales, are generated

and progressing enhancement of the particle intensity

at the sho ck fronts asso ciated with coronal mass ejec-

from the moment of the CME up to the arrival of the

tions CMEs Cane et al., 1988; Kahler et al., 1998.

sho ck see Figure 15 of Cane et al., 1988.

These gradual particle events p ose a serious threat

The simulation of these particle events requires a

to spacecraft comp onents, materials and op erations

knowledge of how particles and sho cks propagate

Turner, 1996. They are characterized by high SEP

through the interplanetary medium, and how sho cks

intensities, rich proton abundances, long time dura-

accelerate and inject particles into interplanetary

tions of the order of several days, and may b e simul-

space. The mo deling of particle uxes and uences

taneously observed over a broad range of heliospheric

asso ciated with SEP events has to consider 1 the

lo cations Reames et al., 1996.

changes in sho ckcharacteristics as it travels through

The injection of energetic particles during gradual

the interplanetary medium, 2 the di erent p oints

events starts when a p erturbation, originated as a

of the sho ck where the observer is connected to, and

consequence of a CME, generates a sho ckwave which

3 the conditions under which particles propagate.

propagates across the solar corona. If the condi-

tions are appropriate this sho ck is able to acceler-

ate particles from the ambient plasma and to inject

2. THE MODEL

them at the base of the interplanetary magnetic eld

IMF lines. These energetic particles stream out

along these lines en route to earth and to the space-

Wehave develop ed a numerical mo del Heras et al.,

craft lo cated in the interplanetary medium. The p er-

1992, 1995; Lario et al., 1998 that repro duces SEP

turbation that generated the sho ck into the corona

events by simulating the propagation of the asso- usually detected through in situ observations of so-

ciated interplanetary sho cks and the injection and lar wind plasma and magnetic eld. These measure-

transp ort of sho ck-accelerated particles. In order to ments, made at the lo cation of space prob es, can only

derive the injection rate of sho ck-accelerated parti- give us a few insights ab out the global shap e of the

cles, it is necessary to deconvolve the e ects of the sho ck top ology, but nothing ab out the evolution of

journey of particles from the p oint of the sho ck where its large-scale structure during its journey from the

they are accelerated to the observer's p osition. Dur-

-D MHD, self- Sun to the spacecraft. We use the 2

ing this propagation, energetic particles su er the

consistent, time-dep endent co de develop ed byWuet

e ects of the IMF and solar wind, that is, fo cus-

al. 1983 as a suitable to ol for studying the evo-

ing, pitch-angle scattering, solar wind convection and

lution of sho cks in the ecliptic plane Dryer, 1994.

adiabatic deceleration e ects. A complete transp ort

This co de gives a dynamical description of the prop-

equation to rst order in v =c, where v is the

sw sw

agation of an interplanetary sho ck between 18 R

constant solar wind velo city which takes into ac-

and 220 R from the Sun. An initial input sho ck

count these e ects is the following Ru olo, 1995:

is considered at 18 R which represents the inter-

planetary sho ck at this distance, and which allows us

to repro duce the arrival times, plasma and magnetic

@F t; ; r;p @

= cos vF

eld data, as well as the sho ck parameters supplied

@t @r

by several spacecraft lo cated at di erent p ositions in

the heliosphere. A mo del describing quantitatively

v @

the formation of a sho ckwave in the corona from rea-

1 v sec F cos

@r c

sonable physical parameters related to observations,

and its evolution to the interplanetary medium, do es

not exist yet. That is b ecause, at present, it is not

v v v @ v

sw sw

sec sec 1 F + 1+

p ossible to infer quantitative information concerning

@ 2Lr v c

the initial conditions of a sho ck at the corona and

its transition to interplanetary space from the obser-

d @

vations made at the onset of CMEs Cane, 1997.

sec 1 F + v cos +

@ dr

Then, what happ ens b elow 18 R remains masked

to our simulation. Injection of particles from the so-

@ @ v v

lar corona or b elow18R accelerated by a di erent

+ ' 1 sec F +

evolving coronal sho ck is represented by the mo del

@ @ c

by a Reid-Axford pro le from the ro ot of the IMF

line connecting the observer with the Sun. Once the

sec d @

2 2

sho ck describ ed by the MHD mo del establishes mag-

pv 1 + cos sec F + +

@p 2Lr dr

netic connection with the observer, the injection of

particles is considered from the cobp oint see discus-

+ Qt; ; r;pAr

sion in Lario et al., 1998.

d N

where F t; ; r;p = is the density of parti-

dr ddp

cles in a given magnetic ux tub e as a function of

3. APPLICATION OF THE MODEL TO THE

four indep endent variables: t time, pitch-angle

SPACE WEATHER

cosine in the solar wind frame, r helio centric ra-

dial distance, and p momentum in the solar wind

frame. Also v is the particle sp eed, r is the angle

Prediction of particle uxes at di erent heliospheric

between the IMF and the radial direction, Lr is the

lo cations during gradual SEP events requires to know

fo cusing length B=dB =dz , z is the distance along

the characteristics of the evolving sho cks and their ef-

the magnetic eld line dr = dz cos , and ' is

fects on particle p opulation. There is a wide variety

the pitch-angle di usion co ecient. Ar represents

of SEP events and asso ciated sho cks Cane et al.,

the area of the ux tub e at a distance r , and Q the

1988. The contribution of a sho ck to the energetic

injection rate of particles accelerated at the sho ckat

particle p opulation evolves as it moves from the Sun

a given energy. In the upstream region of the sho ck,

to 1 AU and b eyond. In principle, its eciency as an

the IMF can be describ ed by a Parker spiral in a

accelerator of particles is di erent at di erent parts

solar wind steady regime. Pitch-angle di usion co-

of its front and for di erent energies. The strongest

ecient is parameterized following the quasi-linear

parts of a sho ck near its central region are pre-

theory Jokipii, 1971.

sumably more ecient accelerating particles than its

weak anks. When sho cks are close to the Sun, they

The injection of particles is considered to take place

are able to accelerate particles to high energies up to

at the cobp oint Heras et al., 1995, that is the fo ot

energies as high as 1 GeV; Kahler, 1994 but only to

p oint at the sho ck front of the IMF line connecting

lower energies when they are arriving at 1 AU. That

with the observer. All particles injected from the cob-

leads to a softening of the sho ck-accelerated particle

p oint are considered to ll the same ux tub e where

energy sp ectrum while the sho ck propagates b etween

they propagate. As the sho ck expands, the cobp oint

the Sun to farther in the interplanetary medium.

moves along the sho ck front. The instantaneous p o-

sition of the cobp ointisgiven by the intersection b e-

In order to discern the e ect of the di erent factors tween the instantaneous p osition of the sho ck and the

that determine the particle ux of SEP events, the ux tub e where the observer is lo cated.

simulation of a large numb er of particle events is re-

quired. The present state-of-the-art of SEP-event In order to describ e the evolution of sho cks through

simulation is rather reduced see Sanahuja & Lario the interplanetary medium a magnetohydro dynamic

[1998] for a review. In Lario et al. 1998, we MHD mo del is required. Interplanetary sho cks are

Figure2. Dependence of the injection rate Q on VR at

di erent energies for the SEP event on 24 April 1979

after a simulation of ISEE-3 observations.

Figure1. Two bottom panels: Evolution of the cobpoint

coordinates heliocentric radial distance and angle with

respect to the Sun-spacecraft line for Helios-2 and ISEE-

3. Top panel: Evolution of VR at both cobpoints. The

origin of time is set at the occurrence of the solar event.

Each line extends from the moment where the simulated

shock and spacecraft establish magnetic connection up to

the arrival of the shock vertical lines at both spacecraft.

have repro duced the 50 kev-10 MeV proton ux

and anisotropy pro le of four SEP events asso ciated

with interplanetary sho cks observed by the ISEE-3

Figure3. Low-energy ux pro le derived for Helios-2 as-

spacecraft. These simulations allow us to relate the

suming log Q /VR. Thin lines show the ux pro les mea-

temp oral evolution of the MHD prop erties of sho cks

sured by ISEE-3 and Helios-2. Thick dashed line shows

to the injection rate of sho ck-accelerated particles.

the t for ISEE-3. The thin dashed line shows the ux

From the MHD simulation of the sho ck propagation,

pro le predicted by the model for Helios-2, under the as-

it is p ossible to estimate the MHD strength at each

sumptions commented on in the text. Vertical lines repre-

p oint of its front, and particularly at the cobp oint.

sent the shock passage, and the arrow indicates the time

The strength of the sho ck is characterized by the

of the solar activity.

downstream to upstream normalized velo city ratio,

VR=[V d V u]=V u, where V is the radial

r r r r

plasma velo city and u and d stand for the values up-

stream and downstream of the front, resp ectively,as

considered Q as a free parameter of the simulation.

measured from a xed frame at the Sun. We have

After the simulation, wehave compared the evolution

found a functional dep endence of the injection rate

of Q to the evolution of VR at the cobp oint. Figure

Q with VR for the di erentevents wehave simulated

2 displays logQ versus VR at di erent energies. Each

Lario et al., 1998. Once the prop erties of a sho ck

dot gives a value of VR and Q used for the simulation

in particular VR are known, this dep endence al-

at each temp oral step. Dashed lines are the result

lows us to infer the contribution of the sho cktothe

of linear regressions to each set of p oints. We have

particle p opulation as it travels to 1 AU.

found, as a go o d approximation, a linear dep endence

logQ /VR. This dep endence is di erent at di erent

Let us study an application of such a dep endence.

energies. That is a re ection of the multitude of fac-

The two b ottom panels of Figure 1 show the evolution

tors that may in uence the values of Q at di erent

of the cobp oint p osition as given by the MHD sim-

energies: the presence of a seed particle p opulation to

ulation of the sho ck asso ciated with the SEP event

b e accelerated, the presence of a turbulent foresho ck

on 24 April 1979 see Lario et al., 1998. This sho ck

region whichmay act as a reservoir of particles, the

was observed by the ISEE-3 and Helios-2 spacecraft

dep endence of the mechanism of acceleration on the

Sanahuja et al., 1983. The lo cation of b oth space-

angle which at the present state of the mo del

craft with resp ect to the parent solar activityisin-

is dicult to compute without large error bars, etc.

dicated by the inset on the top panel of Figure 1.

All these factors mayhave a signi cant e ect on the

Each spacecraft has di erent cobp oints. In the lowest

result shown in Figure 2. In spite of these uncertain-

panel we show the angle between the Sun-cobp oint

ties the dep endence logQ /VR provides us a wayto

and Sun-spacecraft lines, and in the top panel the

relate the MHD prop erties of the sho ck to the injec-

evolution of VR at the cobp oint for b oth spacecraft.

tion rate of sho ck-accelerated particles, and to infer

As the cobp oint moves toward the central part of

once the sho ckisknown the ux pro les at di erent

the sho ck, VR increases indicating a higher velo city

heliospheric p ositions. Lario et al. 1998 apply this

jump across this part of the sho ck front. As the sho ck

idea to predict the proton ux observed by Helios-2

moves away from the Sun it weakens.

after the simulation p erformed for ISEE-3 observa-

tions. Figure 3 shows the observed and simulated

In Lario et al. 1998 wehave pro ceeded to simulate

ux pro les at low energy in two similar energetic

the proton ux and anisotropy pro les observed by

channels of Helios-2 and ISEE-3 for this SEP event.

ISEE-3 for this event at di erent energies. Wehave

As can b e seen, the observed and synthesized pro les

also 100 MeV and 70 MeV for two particular events

for Helios-2 t closely well.

In Lario et al. 1995 we have pro ceeded in the

same way to pro duce \typical" synthetic ux and

anisotropy pro les characteristic of di erent SEP

events. After the analysis of the most intense

SEP events asso ciated with interplanetary sho cks ob-

served by ISEE-3 between August 1978 and April

1980 Sanahuja & Domingo, 1987 we have con-

sidered an averaged sho ck whose propagation from

the Sun to 1 AU lasts between 45 and 50 hours.

The MHD simulation of such sho ck see Lario et

al. 1995 for details allows us to know VR along

its front and throughout its journey and to deduce

the injection rate Q of sho ck-accelerated particles

through a dep endence logQ /VR. Assuming aver-

age prop erties for particle transp ort see Lario et al.,

1995 we have pro duced di erent synthetic 1-MeV

proton ux and anisotropy pro les at di erent helio-

spheric p ositions. Figure 4 shows those pro les over-

plotted on observations for three SEP events. The

tting of the pro les are surprisingly go o d in spite of

the simplicity of the assumptions made.

4. CONCLUSIONS

Assuming very simple and average conditions we in-

fer a relation that allows us to determine the in-

jection rate of sho ck-accelerated particles from the

MHD conditions at the frontofinterplanetary sho cks

driven by CMEs. The \synthetic" particle ux and

anisotropy pro les built up using this simple relation

can b e used as a to ol to describ e the uence of parti-

cles and its temp oral evolution at a particular helio-

spheric lo cation b efore the o ccurrence of SEP events.

A study of a larger numberofevents is required b e-

fore drawing de nite conclusions.

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