Physics
Scientific paper
Aug 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001icrc....9.3653f&link_type=abstract
Proceedings of the 27th International Cosmic Ray Conference. 07-15 August, 2001. Hamburg, Germany. Under the auspices of the Int
Physics
1
Scientific paper
The local interstellar spectrum (LIS) for galactic electrons is an important parameter in heliospheric modulation studies, and is still basically unknown at energies of interest to modulation. In this work the effects of different published LIS scenarios on model computations are shown, and in particular compared to the ˜16 MeV Pioneer 10 observations. The modulation of galactic and Jovian electrons is studied using a fully three-dimensional, steady-state model based on Parker's transport equation including the Jovian source. Compatibility between the model computations and observations gives an indication as to the magnitude of the diffusion coefficients because electron modulation responds directly to the energy dependence of the diffusion coefficients below ˜500 MeV. Comparing the different parallel mean free paths needed to compute compatible solutions with observations an upper and lower limit to the electron LIS are proposed. 1. Introduction The local interstellar spectrum (LIS) for galactic electrons is important for the study of the heliospheric modulation of cosmic ray electrons. Because of solar modulation it is impossible to determine a realistic LIS from observed modulated electron spectra at Earth because of the lack of knowledge of the transport coefficients (e.g., Potgieter, 1996; Langner et al., 2001). The LIS is therefore still basically unknown at energies of interest (e.g., Langner et al., 2001). Fortunately, ~16 MeV electron measurements had been made by the Pioneer 10 spacecraft up to ~70 AU (Lopate, 1991). The measurements include an encounter with the Jovian magnetosphere which is a relatively strong source of electrons with energies up to at least ~30 MeV (e.g., Simpson et al., 1974; Teegarden et al., 1974). The modulation of cosmic rays in the heliosphere is generally simulated by numerical models where the LIS is introduced as an initial condition. Ferreira et al. (2001b) compared model calculations with ~7 MeV observations from Ulysses, which covered a wide variety of latitudes in the inner heliosphere. This was followed by Ferreira et al. (2001c) who compared model solutions with ~16 MeV electrons observations from Pioneer 10 that stayed close to the equatorial regions up to ~70 AU. These studies provided new insights of model parameters (especially the transport coefficients) necessary to compute solutions compatible to observations. Strong et al. (1994) produced a LIS by using a sophisticated galactic propagation model in combination with gamma ray and radio synchrotron data. This spectrum has been used extensively as the LIS in modulation studies (e.g., Potgieter, 1996; Ferreira et al., 2000). Strong et al. (2000) argued that this LIS was too high for energies < ~200 MeV and proposed new, much lower spectra. Recently, Langner et al. (2001) also determined a new electron LIS, using a phenomenological approach. In this paper, the effects of these proposed LIS on modulation model computations are shown as different scenarios, comparing the computed results with the observed Pioneer 10 intensities. 2. Modulation model and parameters The model is based on the numerical solution of Parker's [1965] transport equation (TPE) : ∂ ∂ ∂ ∂ f f f t f R = - + < > ṡ∇ + ∇ṡ ṡ∇ + ∇ ṡ +( ) ( ) ( ) ln V v VD Ks Q 1 3 , (1) where f (r,P,t) is the cosmic ray distribution function; P is rigidity, r is position, and t is time. Terms on the right-hand side represent convection, gradient and curvature drifts, diffusion, adiabatic energy changes and a source function, respectively, with V the solar wind velocity. The symmetric tensor Ks consists of a parallel diffusion coefficient K|| and two perpendicular diffusion coefficients, namely K⊥r the perpendicular diffusion coefficient in the radial/azimuthal direction, and K⊥θ the perpendicular diffusion coefficient in the polar direction. The parallel mean free path is given by
de Jager Ocker C.
Ferreira Stefan E. S.
Langner U. W.
Potgieter Marius S.
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