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Astron. Astrophys. 360, 729-741 (2000)

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Appendix A: interplanetary transport model

A comprehensive description of fitting proton anisotropy data for the SEP event and corresponding description of the interplanetary transport model are given in a separate paper (Kocharov et al. 1999b). In what follows we mainly explain definitions and parameter values for the model.

To deduce electron injection scenario, interplanetary mean free path should be determined in the electron rigidity range. However, electron anisotropy data are not available. For this reason, the following method has been employed. The late phase of the relativistic electron event (Fig. 3) looks like a diffusion decay tail. The observed decay rate corresponds to the near-Earth radial mean free path parameter [FORMULA] for [FORMULA] electrons. This interpretation implies a rather isotropic electron distribution after the intensity maximum. An abrupt change of the interplanetary magnetic field direction gave us an opportunity to verify this point. Interplanetary magnetic field direction abruptly changed at 12:50 UT by more than [FORMULA] (Torsti et al. 1997), so that electron sampling into the narrow view cone of COSTEP could be strongly affected if electron flux was as anisotropic as the proton flux was. However, only a minor change in the electron count rate was observed (marked with vertical line B in Fig. 3), being consistent with our estimate [FORMULA].

While the simplest model with exactly constant radial mean free path fits the electron event decay, the expected shape of the rising portion of the intensity curve is more rounded than the observed one. For this reason, we have adjusted the interplanetary transport model by choosing a constant parallel mean free path between Sun and Earth, whereas the constant radial mean free path is still employed beyond the Earth's orbit.

To obtain a precise fit to the observed proton angular distribution (Torsti et al. 1997), we introduced a composite scattering model where conventional pitch angle diffusion is supplemented with a large angle scattering. The large angle scattering is modeled as Small time-Step Isotropizations (similar to the SSI model by Kocharov et al., 1998). The scattering frequency correspondingly comprises two terms: [FORMULA], where two scattering processes are suggested: (i) pitch angle diffusion with corresponding partial mean free path [FORMULA], and (ii) small-chance isotropizations with partial mean free path [FORMULA],


We have adopted the following parametrization for the partial mean free paths:


where f designates the fraction of the large-angle scattering, [FORMULA] is the radial mean free path parameter, [FORMULA] is the interplanetary magnetic field tilt angle. Available proton anisotropy data allow us to select the best-fit parameters: [FORMULA] and [FORMULA].

Notes added in proof:

1). The steep rise of proton intensities observed at 11:50 UT (Fig. 5), with no change in the pitch-angle distribution, allows also a spatial-type interpretation. That is the magnetic connection of the spacecraft was abruptly changed-over from hard to soft spectrum source. However we do not observe a similar discontinuity in electrons (Fig. 2).

2). The electron spectrum of the 9 July 1996 event reveals hardening above 2 MeV (Sierks H., Elendt I., Dröge W., et al., 1997, Proc. 25th Internat. Cosmic Ray Conf., Durban, South Africa, 1, 297). This behaviour is commonly observed for events with impulsive X-ray emission (Dröge W., 1996, in: Ramaty R., Mandzhavidze N., Hua X.-M. (eds.), AIP Conf. Proc. 374, High Energy Solar Physica, Woodbury, New York, p. 78).

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© European Southern Observatory (ESO) 2000

Online publication: August 17, 2000