Interplanetary cosmic ray radial gradients with steady state modulation models

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Abstract
We have used steady state modulation models of increasing complexity, with emphasis on drift models, to establish to what extent these models can simulate the observed cosmic ray integral radial gradient (energy ≥60–70 MeV/nucleon) in the heliosphere from 1977 to 1986. Special attention has been given to the apparent asymmetric behavior of the radial gradient with respect to the recent interplanetary magnetic field polarity reversal, and the remarkable constant radial gradient for the years 1977–1982. Instead of using differential intensities at specific energies, we presented integral radial gradients calculated from the computed integral intensities which made comparison with observations more realistic. We found that nondrift models had difficulties producing constant radial gradients over several years of increasing solar activity, because these models depend primarily on changes of the radial diffusion coefficient Krr to simulate an 11‐year cycle and therefore produce, in general, radial gradients symmetric with respect to solar maximum activity. Making these models independent of changes in Krr needs, in our opinion, unrealistic changes in the conventional modulation parameters. Drift models, on the other hand, could produce a constant radial gradient for the period 1977‐1982 and account for the asymmetric behavior of the radial gradient. But because of the inherent insensitivity of these models to changes in modulation parameters during this period, the radial gradient remained less than 1% per AU, even with the effects of a wavy neutral sheet incorporated. In an attempt to increase it, we scaled drift effects down by a factor of 10 over the entire heliosphere and found a radial gradient remarkably compatible with observations. This reduction of drift has the advantage that the models produce drift effects closer to what has actually been observed, and it retains effects which apparently need drift as an explanation, for example, charge‐dependent modulation. With diminished drift effects a polarity reversal (as in 1981) produced an increase in the radial gradient in the inner heliosphere but a decrease in the outer heliosphere (r ≥ 25 AU). For the period after the polarity reversal, drift models accounted remarkably well for the behavior of the integral radial gradient; the magnitude and change in the radial dependence could be obtained, even without scaling drift down. With the effects of a wavy neutral sheet incorporated, the gradient responded, at first, slowly to changes in the waviness of the neutral sheet with the tilt angle α ≥ 45°, but significantly and nonlinearly when α dropped below this value.