Cosmic-ray density distributional normal to the solar equatorial plane and the semi-diurnal anisotropy

Abstract

Distributions of galactic cosmic-ray density normal to the solar equatorial plane are derived by two different methods and the resulting semi-diurnal anisotropy is studied in detail. In the first method, it is assumed that cosmic-ray intensity at any heliolatitude θ is inversely proportional to the solar coronal intensity (λ 5303) at the same heliolatitude. The second method is based on Parker's model of the anisotropic diffusion of cosmic rays, in which the size of the modulating region ( R) and the parallel diffusion coefficient ( K ∥) are assumed to be independent of heliolatitude while the solar wind velocity ( V) is assumed to be a function of heliolatitude through an empirical relationship connecting λ 5303 intensity and solar wind velocity observed on Mariner-2 and IMP-1 spacecrafts. Following the method suggested by Subramanian and Sarabhai (1967), the semi-diurnal anisotropy arising from these distributions is estimated for neutron monitors situated at Deep River and Huancayo. It is found that both methods give semi-diurnal amplitude with a rigidity dependence given by P β where P is the rigidity and β is positive in agreement with the observations. The phase of the semidiurnal anisotropy obtained by the first method is found to be generally along the direction of the interplanetary magnetic field while that obtained by the second method is nearly perpendicular to the direction of the interplanetary magnetic field in agreement with the experimental observations. The implications of the above results are discussed and the various assumptions tested. In view of the recent observations regarding the absence of long-term variations in V and K ∥ (Mathews et al., 1971), it is shown that a small change in R (~2 AU) over a solar cycle can produce the required long-term modulation of galactic cosmic-ray intensity when V and K ∥ are constant.