Time‐dependent modulation of galactic cosmic rays by merged interaction regions

Abstract

Models that solve the one‐dimensional, solar modulation equation have reproduced the 11‐year galactic cosmic ray cycle using functional representations of global merged interaction regions (MIRs). This study extends those results to the solution of the modulation equation with explicit time dependence. The magnetometers on Voyagers 1 and 2 provide local magnetic field intensities at regular intervals, from which one calculates the ratio of the field intensity to the average local field. These ratios in turn are inverted to form diffusion coefficients. Strung together in radius and time, these coefficients then fall and rise with the strength of the interplanetary magnetic field, becoming representations of MIRs. These diffusion coefficients, calculated locally, propagate unchanged from ∼10 AU to the outer boundary (120 AU). Inside 10 AU, all parameters, including the diffusion coefficient are assumed constant in time and space. The model reproduces the time‐intensity profiles of Voyager 2 and Pioneer 10. Radial gradient data from 1982‐1990 between Pioneer 10 and Voyager 2 are about the same magnitude as those calculated in the model. It also shows agreement in rough magnitude with the radial gradient between Pioneer 10 and 1 AU. When coupled with enhanced, time‐dependent solar wind speed at the probe's high latitude, as measured by independent observers, the model also follows Voyager 1's time‐intensity profile reasonably well, providing a natural source for the observed negative latitudinal gradients. The model exhibits the 11‐year cyclical cosmic ray intensity behavior at all radii, including 1 AU, not just at the location of the spacecraft where the magnetic fields are measured. In addition, the model's point of cosmic ray maximum correctly travels at the solar wind speed, illustrating the well‐known propagation of modulation. Finally, at least in the inner heliosphere this model accounts for the delay experienced by lower‐rigidity protons in reaching their time‐intensity peak. The actual delays in this model, however, are somewhat smaller than the data. In the outer heliosphere the model sees no delays, and the data are ambiguous as to their existence. It appears that strong magnetic field compression regions (merged interaction regions) that are 3‐4 times the average field strength can, at least in a helioequatorial band, disrupt effects, such as drifts, that could dominate in quieter magnetic fields. The question remains: Is the heliosphere ever quiet enough to allow such effects to be unambiguously measured, at least in the midlatitudes?

The cosmic radiation in the heliosphere at successive solar minima: 3. Steady state drift solutions of the transport equation

“…It is probable that neutral sheet drift, especially, is overemphasized in our models. Previously, Perko [1993] used the Voyager i and 2 magnetic field data to define a diffusion coefficient mrr that is proportional to the inverse of the measured IMF intensity. These values of mr• form a time series that propagate out to a modulation boundary at 120 AU.…”

Cosmic ray modulation during solar cycle 22: Solar maximum loops at earth and global transients in the heliosphere

“…Loops may close, e.g., due to the relaxation of a mechanism causing an additional reduction of lower-energy cosmic rays and/or a relatively more effective recovery at higher energies (e.g., GMIRs leave the heliosphere [Webber and Lockwood, 1993b]) or when acceleration effects disappear [Stoker and Moraal, 1986] predicts that GMIRs begin to dominate over drifts in modulation at higher levels of solar activity. A simple comparison ofLe Roux and Potgieter [1992] and Perko [1993] theoretical results on rigidity-dependent phase lags in the MIR-dominated and drift-dominated modulation allows us to suggest as a conclusion that the rigidity-dependent recovery from a step decrease at neutron monitor energies may be a manifestation of a GMIR being present in the heliosphere.…”

“…It seems that rigidity-dependent effects in cosmic ray modulation may be crucial in the identification of the modulation mechanism prevailing in a given phase of the solar magnetic and solar activity cycle. For example, Perko [1993] noted that his model of 11 (1992,1993). So now it is possible to continue the previous long-term analyses of cosmic ray modulation into the present solar cycle 22.…”

“…So the specific character of this transient modulation apparently does not depend on the polarity of the IMF. hysteresis may be interpreted in terms of a rigidity-dependent phase lag in the frame of timedependent modulation theory[O'Gallagher, 1975;Perko and Fisk, 1983; Chih and Lee, 1986;Perko, 1993]. The amount of phase lag of low-rigidity particles relative to high-rigidity ones was found in paper 1 to increase with the global modulation level at which the corresponding large FD started.…”

On the heliolatitudinal variation of the galactic cosmic-ray intensity. Comparison with Ulysses measurements

“…The cosmic-ray variations for various heliodistances was well studied from the measurements of the deep space probes Voyager 1, 2 and Pioneer 10, 11 (Venkatesan et al, 1984(Venkatesan et al, , 1985Lockwood and Webber, 1981;Perko, 1995;Webber and Lockwood, 1995;Fujii and McDonald, 1997;McDonald et al, 2001;Potgieter and Ferreira, 2001). …”