implications of proton anisotropy development observed by the erne instrument during the 9 july 1996...

IMPLICATIONS OF PROTON ANISOTROPY DEVELOPMENTOBSERVED BY THE ERNE INSTRUMENT DURING THE 9 JULY 1996

SOLAR PARTICLE EVENT

L. G. KOCHAROV, J. TORSTI, T. LAITINEN and R. VAINIOSpace Research Laboratory, Department of Physics, FIN-20014 Turku University, Finland

(Received 4 March 1997; accepted 28 May 1997)

Abstract. We analysed the solar particle event following the 9 July 1996 solar flare. High-energyprotons were detected by the ERNE instrument on board SOHO. Anisotropy of arriving protonsrevealed very peculiar non-monotonic development. A short period of almost isotropic distributionwas imbedded into the prolonged period of beam-like distribution of 14–17 MeV protons. Thisimplies the existence of a narrow magnetic channel with a much smaller mean free path than in thesurrounding quiet solar wind plasma.

We used Monte Carlo simulations of interplanetary transport to fit the observed anisotropiesand intensity–time profiles. Proton injection and transport parameters are estimated. The injectionscenario is found to be very close to the scenario of the 24 May 1990 event, but the intensity and theinterplanetary transport parameters are different. The extreme anisotropy observed implies prolongedinjection of high-energy protons at the Sun and at the interplanetary shock front, and either a verylarge mean free path (� 5 AU) outside the slow transport channel, or alternatively, a somewhatsmaller mean free path (� 2 AU) and enhanced focusing between the Sun and the Earth.

1. Introduction

The 10 MeV protons, travelling in the interplanetary medium, are scattered byshort-scale fluctuations of the interplanetary magnetic field and focused by thelarge-scale component of the field (e.g., Toptyghin, 1983). These particles canbe used as probes of the magnetic fields that they traversed before they weredetected by a spacecraft (Wanner and Wibberenz, 1993). Being themselves a majorphenomenon of the interplanetary space, they also carry information about theirsources, i.e., the Sun and phenomena closely related to it such as interplanetaryshocks.

The fluctuation conditions are not stationary. For this reason, differences in theproton mean free path between one event and another can amount to 2 orders ofmagnitude (Kunow et al., 1991). The strong variation in the fluctuation level typ-ically occurs on the angular scale 3–7� in heliolongitude (Wanner and Wibberenz,1993). On the other hand, the large-scale component of the interplanetary field isalso not stationary, implying variability of magnetic focusing. The Parker (1958)theory is a steady-state prediction that avoids discussion of interplanetary dynamicprocesses such as overtaking high-speed streams or falling behind slow-speed sol-ar wind. However, such processes must change the magnetic field and affect thepropagation of energetic particles. The effect of a distorted interplanetary field on

Solar Physics 175: 785–795, 1997.c 1997 Kluwer Academic Publishers. Printed in Belgium.

786 L. G. KOCHAROV ET AL.

the transport of energetic particles has already been employed to explain spacecraftobservations (Tan et al., 1992, Anderson et al., 1995).

Analysis of the 9 July 1996 solar particle event observed by ERNE revealedcomplex behaviour depending on the proton energy channel selected (Torsti et al.,1997). At high energies, E > 12 MeV, the shape of the intensity-time profile ofthe event was rather close to the profile of the 24 May 1990 event that we recentlyanalysed (Torsti et al., 1996). Both events demonstrated a double-peaked structurebut the proton intensity in May 1990 was three orders of magnitude higher thanin July 1996. At low energies, E = 1:6–6 MeV, a huge drop, of 1–2 orders ofmagnitude, was observed in ERNE count rates at � 13:00 UT on 9 July 1996.This is a specific property of the event. Simultaneously, the extremely anisotropicflux of � 15 MeV protons was replaced by a much more isotropic distribution.The � 15 MeV proton beam reappeared at � 16:00 UT. Simultaneously with thedrop in the 1.6–6 MeV proton count rates and the vanishing of the � 15 MeVproton beam, the magnetic field observed on board WIND abruptly changed itsdirection by � 60� (Torsti et al., 1997). During the period 13:00–16:00 UT, themagnetic field direction changed repeatedly. It became stable after 16:30 UT on9 July 1996. These observations indicate that the interplanetary magnetic field andproton transport conditions changed at least twice during the event, at� 13:00 UTand at � 16:00 UT on 9 July 1996. For this reason, three periods in the protoncount rate were selected for further analysis: Period 1 covering 10:14–12:50 UT,Period 2 covering 12:50–16:00 UT, and Period 3 covering 16:00–24:00 UT on9 July 1996. Our study is aimed at the estimation of the injection and transportparameters. For this reason, it focuses on the 14–17 MeV proton anisotropy dataand does not attempt to cover comprehensively all the energy bands observed.

2. Basic Model

Taking into account the similarity of the 24 May 1990 and the 9 July 1996 sol-ar particle events, we attempted to fit observational data with two (prompt anddelayed) injections of particles. In the same way as Torsti et al. (1996), we con-sider (i) solar injection of particles at the root of the magnetic line connected tothe spacecraft and (ii) interplanetary shock wave injection of particles in the shockarea that is magnetically connected to the observer for the prompt and delayedcomponents, respectively. The intensity near the detector, I(E;�; t), was obtainedas a convolution of the injection profile, q(t; E), and the interplanetary transportGreen’s function, G(z0; t� t0; �):

I(E;�; t) =

tZ�1

q(t0; E)G(z0; t� t0; �)V

r2�

cos (r�)

dt0 ; (1)

where q(t0; E) is the production of accelerated particles per unit of heliocentricsolid angle at time t0 at spiral distance z0 in the interplanetary medium; (r

�) is the

IMPLICATION OF PROTON ANISOTROPY DEVELOPMENT 787

tilt angle of the interplanetary magnetic field at the site of observations, r = r�

;E,V , and � = cos(�) are proton energy, velocity and pitch angle cosine, respectively.

To calculate interplanetary transport functions,G(z0; t� t0; �), and fit the data,some spatial dependence of the mean free path must be adopted. Kallenrode (1993)discussed a number of possibilities for the spatial dependence of the radial meanfree path �r, and decided to use �r = constant. In such a case the dependence ofthe parallel mean free path on distance along the magnetic line is almost linear:� � z at z > 0:7 AU. For this reason, we fitted the data under the propositionthat the parallel mean free path is linear in z at z > 0:7 AU and constant atz < 0:7 AU. This assumption on �(z) allows us to obtain reasonably good fits ofthe event. However, somewhat steeper spatial dependence could also be acceptable.The rigidity dependence of � is not essential because protons in a single narrowenergy band, 14–17 MeV, are studied. The Monte Carlo simulations of focusedtransport were used to obtain interplanetary transport functions (see Appendix). Itis convenient to describe the pitch-angle scattering in terms of a parallel mean freepath, �, given by

� =3V8

1Z�1

1� �2

�(�)d� ; (2)

where �(�) is the scattering frequency (e.g., Toptyghin, 1983). When defined inthis way, the parallel mean free path may take any value, even exceeding 1 AU.The parallel mean free path at the Earth orbit, �

�, and the source function, q(t; E),

were adjusted to fit the anisotropies and intensity-time profiles observed. We useParker’s (1958, 1963) model of the interplanetary magnetic field at solar windvelocity 400 km s�1. Throughout the paper, this standard model is designated asModel 1.

In order to perform fitting in a limited energy and temporal range, we useda simplified injection model. The source of the prompt component injection waspositioned at the spiral distance of two solar radii from the centre of the Sun,z0 = 2RS. For the interplanetary shock injection, the source was fixed at z0 = 20RS

because we mainly consider the first 8 hours of the event when the shock wastravelling not very far from this point. For both components, the injection timeprofiles are fitted by exponents:

q(t; E) = A exp(�(t)) ; (3)

where �(t) is a piecewise linear function of time, A is a normalization constant.We used

�(t) = (D � 1=�) (t� tm) at 0 < t < tm ;

and �(t) = �(t� tm)=� at t > tm ; (4)


Table IInjection and transport parameters for Model 1

Component Periods 1 and 3 Period 2�� D � tm

AU AU min�1 min min

Prompt 5.2 0.35 0.095 50 37Delayed 5.2 0.35 0.05 230 132

where tm, D, and � are fitting parameters,D� > 1. These parameters are differentfor different injection components (see Table I). The ‘zero’ time is 09:04 UT on9 July 1996.

3. Results and Discussion

We calculated 14–17 MeV proton intensity at the Earth–Sun L1 point as a functionof pitch angle and time, I(�; t) � d2N=d dt. This intensity was integratedover Periods 1, 2, and 3 to obtain angular distributions, dN /d, for the periods.Then the angular distributions and the intensity-time profiles were compared withobservations (see Figures 1 and 2). The choice of the integration periods wasgoverned by two circumstances: (i) the limited count statistics available, and (ii) thepreliminary analysis of magnetic field data which revealed the disturbed magneticregion observed during Period 2 (Torsti et al., 1997). It is also important that thecharacter of anisotropy is kept constant during each time period, so that the choiceof the integration time does not affect our principal conclusions. To estimate thepredicted count rate, the following procedure was applied. The angular distributionwas extremely anisotropic during Periods 1 and 3, so that almost all protons werearriving inside the ERNE/HED view cone and contributing to the count rate. Forthese periods, the calculated intensity was simply integrated over pitch angles,and the intensity-time profile obtained, dN /dt, was superimposed on the observedcount rate (see solid line in Figure 2). During Period 2, the proton distribution wasalmost isotropic, so that the fraction of protons contributing to the count rate wasabout 1

4 , and this fraction is only weakly dependent on model parameters. For thisreason, to estimate the model count rate, it is sufficient to divide the angle integratedintensity by a factor� 4. The corresponding curve is shown with the mainly dottedline in Figure 2. It is seen that, with the statistics available, the obtained fits arereasonably good at least as a first approximation. Thus, we can conclude that themean free path was extremely high during Period 1, at least �

�= 5 AU, after

which it abruptly dropped by more than factor 10 (Period 2), and finally, at thebeginning of Period 3, the mean free path returned to its original extremely largevalue.


Figure 1. Illustration of fitting to the ERNE anisotropy measurements. The ERNE data are shownas points (see also Torsti et al., 1997). Dashed lines correspond to 14–17 MeV proton distributioncalculated in the framework of the standard transport model (Model 1). Solid lines correspond to theoff-standard focusing model (Model 2). Period 1 covers 10:14–12:50 UT, Period 2 covers 12:50–16:00 UT, and Period 3 covers 16:00–24:00 UT on 9 July 1996.


Figure 2. The 10-min-average count rates in the proton 14–17 MeV channel during the 9 July 1996solar particle event as observed by ERNE (points) and the parameter fit according to Model 1 (curves).Solid line illustrates the intensity-time profile outside the slow transport channel. Mainly dotted lineillustrates the intensity-time profile inside the slow transport channel. Periods observed by ERNE areshown with heavy solid portions of the curves and two heavy arrows (the double-headed arrow isdiscussed in the text).

In addition to the traditional transport model, we considered the possible effectof deviation of the interplanetary magnetic field from the standard Parker (1958,1963) model (Model 1). Our alternative model (Model 2) does not attempt toreproduce the real interplanetary magnetic field but is aimed only at answeringthe question of whether or not a deviation of the real field from the standardParker model can affect proton anisotropies observed by ERNE. In this attempt,the injection scenario and the parallel mean free path �(z) are proposed to be thesame at all magnetic flux tubes traversed. To estimate the possible effect of off-standard focusing, we propose that the standard magnetic field, BP, be distortedwith the factor

� = 1 + �0 + �1 sin��(z � zs)

2zm

�

at

z < zc � 4zm �2zm�

arcsin(�0=�1) + zs ;

and

� = 1 at z � zc ; (5)

so that the magnetic field at point z is B(z) = �(z)BP(z). To limit the choice ofthe new transport parameters (�

�, �0, �1, zs, and zm), we imposed the following


Table IIInjection and transport parameters for Model 2

Component D � tm

min�1 min min

Prompt 0.11 35 32Delayed 0.05 180 122

Period �� 0 �1 zm zs

AU AU AU

1 and 3 2.0 1.5 1.5 0.3 0.32 2.0 0.15 �0.75 0.6 0

limitations: (i) along the length of a magnetic tube, the ratio of maximum tominimum values of factor � is not more than 4, which is a typical value of variationof magnetic field strength as observed near the Earth orbit, (ii) the scale of thedistortion, zm, is about 0.5 AU, and the size of the distorted region, zc, is 1–3 AU,and (iii) the large-scale magnetic field is not distorted near the Sun. We also tookinto account the fact that the expansion of a tube is likely to go on concurrentlywith the compression of some neighbouring tubes to keep the total magnetic fluxroughly constant.

Table II presents a possible set of parameters fitting the 14–17 MeV protonobservations. We have enhanced focusing between the Sun and the spacecraft atmagnetic lines traversed during Periods 1 and 3. For Period 2, the magnetic fieldis decreased at � 0:6 AU but increased at � 1:8 AU from the Sun. The protonangular distributions obtained for Periods 1, 2, and 3 are depicted by solid linesin Figure 1. The intensity-time profiles are shown in Figure 3. It turns out thatthe 14–17 MeV proton observations can be fitted equally well in both transportmodels. In particular, almost the same angular distribution can be obtained in thestandard model at �

�� 5 AU or in the off-standard focusing model at�

�� 2 AU.

Employing only the 14–17 MeV energy band, we cannot select the most plausiblemodel, because only a small portion of the intensity-time profile near the secondpeak was actually observed during Period 2. However, a very big difference betweenthe model predictions really exists at the rise phase of the event (marked withdouble-headed arrows in Figures 2 and 3).

Around 12:00 UT, the rise phase of the event was observed at lower energies,E � 4 MeV. At about 12:50 UT, low energy channels revealed a huge drop ofmore than one order of magnitude (see Torsti et al., 1997). This lends support forModel 1. In fact, in the 1.6–6 MeV proton energy band, the onset of the 9 July 1996event was observed twice. On the first occasion, the onset was observed inside thefast propagation region during Period 1. Then SOHO entered the slow transport


Figure 3. The same as in Figure 2 but for Model 2.

channel where the onset of the event in the 1.6–6 MeV band was observed again(see Figure 5 by Torsti et al., 1997). In the 14–17 MeV band, reconstruction ofthe event according to Model 1 is shown in Figure 4. For these energies, the slowtransport channel (STC) was traversed near the time of the maximum intensityof the delayed component (marked with STC in Figure 4). It can, of course, notbe ruled out that some extra focusing further contributed to the sharpening ofthe proton angular distribution outside STC because, even at an unusually lowscattering level (�

�� 5 AU) and standard focusing, the calculated distribution

is still not sharp enough to reproduce precisely the extreme beam-like anisotropyobserved by ERNE during Period 1.

4. Conclusions

(1) During the 9 July 1996 solar particle event, ERNE observations revealed that anarrow (� 2� in heliolongitude) magnetic channel with special transport parameters(slow transport channel, STC) was imbedded in a wide region of fast propagationof high-energy protons.

(2) Inside STC, the magnetic field was disturbed, the proton angular distributionwas almost isotropic, and the proton propagation was slow.

(3) Outside STC, the 14–17 MeV proton mean free path was extremely large,�� 5 AU, if focusing corresponded to the standard model of the interplanetary

magnetic field. In contrast, the mean free path was less or about 0.35 AU insideSTC.

(4) The same proton angular distribution may come from extremely weakscattering (�

�� 5 AU) in the standard interplanetary magnetic field or from a


Figure 4. Reconstruction of the observed 14–17 MeV proton event in the pitch-angle cosine andtime plane according to Model 1.

stronger scattering (�� 2 AU) at magnetic lines additionally compressed at

� 0:6 AU from the Sun. Proton anisotropies measured by ERNE are sensitive tothe actual shape of the interplanetary magnetic field lines. A narrow beam-likeproton distribution may be a signature of extra focusing and exceptionally weakscattering between the Sun and the spacecraft.

Acknowledgements

The Academy of Finland is thanked for financial support. SOHO is a mission ofinternational co-operation between ESA and NASA.

Appendix. Monte Carlo Simulations of Interplanetary Transport

Calculations of the particle propagation are based on the model of focused transport(e.g., Toptyghin, 1983). The code employed is basically similar to that describedby Torsti et al. (1996) but the scattering is dependent on particle pitch angle, i.e.,we take into consideration the anisotropic scattering model. Thus, the transportequation for high-energy particles is in the form (Roelof, 1969; Earl, 1976):

@f

@t+

@

@z�V f +

@

@�

V

2L(1� �2)f �

@

@�(1� �2)�

@f

@�= Q(z; �; t) ; (A1)


where f = f(z; �; t) is the number of particles per unit of magnetic tube length andper unit of solid angle in velocity space; z is the coordinate of the observer (alongthe magnetic field line); � is the cosine of pitch angle; V is the particle velocity;L(z) is the focusing length, 1=L(z) = �(dB=dz)=B; B(z) is the magnetic fieldstrength, � = �(z;R) is the scattering frequency which determines the parallelmean free path, �;R is the particle rigidity;Q(z; �; t) is the source function. In thecase of anisotropic scattering we adopt � = �(�) as

�(�) =3V

2(2� q) (4� q)�0(�2

0 + (1� �20)�

2)(q�1)=2 ; (A2)

where q is the spectral index of MHD turbulence, the parameter �0 coincides withthe mean free path if �0 = 0. We adopted the values q = 1:5 and �0 = 0:04.

In order to calculate numerical Green’s functions, G(z0; t� t0; �), we performMonte Carlo simulations of particle transport. We consider an impulsive and iso-tropic injection of particles with energyE at time t0 at the distance z0 from the Sun.We calculate, per one Monte Carlo temporal step, �t, the change of the particlepitch angle cosine as �� = (1��2)V�t=(2L)+ �, and the change of the particlecoordinate as �z = V ��t. The value of �, which is the change of the particlepitch angle cosine due to scattering, is calculated by means of the following meth-od. The particle scattering can be considered with respect to the direction of theparticle movement at the moment. In the isotropic scattering case, by means ofsuch a ‘turnable’ axis, under the small-angle approximation, the scattering term ofthe Fokker–Planck equation can be written in the form

�

#

@

@##@f

@#: (A3)

Hence, after each Monte Carlo step, the angular distribution (with respect to the‘turnable’ axis) is

f(#; �;�t) d =1

4��texp

(�

#2

4��t

)# d# d� ; (A4)

where # is the angle of the particle scattering during a given Monte Carlo step;# 2 [0; �]; � is the azimuth angle of the particle turn about the axis, � 2 [0; 2�].Hence, the values of #2 and � are determined from an exponential distribution andthe uniform distribution, respectively. The new value of the pitch angle, �, can becalculated by means of spherical geometry. In the case of anisotropic scattering, anadditional streaming term in the phase space causes additional regular change in �so that � = �0 + �A, where �0 can be obtained in the same way as in the case ofisotropic scattering and �A = (d�=d�) (1 � �2)�t. The actual Monte Carlo timestep �t depends on the current value of scattering frequency �(�; z) to keep thescattering angle small in comparison with characteristic scales of the problem. The


total number of traced particles was 105 for each Green’s function calculated. Thevelocity of the solar wind is taken to be 400 km s�1.

We have performed a number of simulations to verify the technique. In par-ticular, the case of the constant mean free path has been considered. In this case,the focused transport equation was solved earlier by Ruffolo (1995) using thefinite difference method. A good agreement between our intensity-time profile andthe profile reported by Ruffolo has been obtained when no adiabatic decelerationis taken into account. On the other hand, provided that the ratio �=L does notchange with distance, an exact analytical expression may be obtained for the timeintegrated (steady-state) angular distribution of particles (for the steady-state dis-tributions see, Roelof, 1969; Kunstmann, 1979; Earl, 1981). The comparison ofsuch a distribution with the distribution obtained in Monte Carlo simulations alsorevealed a good agreement.

References

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implications of proton anisotropy development observed by the erne instrument during the 9 july 1996...

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