5 A TOOL TO MODEL SOLAR ENERGETIC PARTICLE EVENTS. 1 2;3 1 D. Lario , B. Sanahuja , A.M. Heras 1 Space Science Department, ESTEC/ESA, 2200AG No ordwijk, The Netherlands 2 Dept. Astronomia i Meteorologia, Universitat de Barcelona, Barcelona, Spain 3 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 6 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 1 they are accelerated to the observer's p osition. Dur- -D MHD, self- Sun to the spacecraft. We use the 2 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 2 v @ 2 the formation of a sho ckwave in the corona from rea- 1 v sec F cos sw 2 @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 2 sec sec 1 F + 1+ p ossible to infer quantitative information concerning 2 @ 2Lr v c the initial conditions of a sho ck at the corona and its transition to interplanetary space from the obser- d @ 2 vations made at the onset of CMEs Cane, 1997. sec 1 F + v cos + sw @ 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 sw + ' 1 sec F + 2 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 + + sw @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. 3 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.