Cosmic-Ray Radial Density Gradient and its Rigidity Dependence Observed at Solar Minimum on Mariner IV
Abstract
The radial intensity gradients for both protons and helium nuclei have been measured from the orbit of Earth out to a heliocentric range of 1.56 a.u. on the Mariner IV interplanetary probe in 1965 In the diffusion convection model for solar modulation the inward transport of particles resulting from these gradients is balanced by the outward convection of particles in magnetic irregularities carried by the solar wind so that the diffusion coefficient K, can be determined by these measurements of the gradients and the solar-wind velocity. In this paper the observations of the gradient have been extended another decade in magnetic rigidity below the preliminary results already reported, so that the dependence of the diffusion coefficient on particle parameters (magnetic rigidity R and velocity cp) can be studied over a large range of energies (from 20 MeV to 10 GeV) which are appreciably affected by solar modulation We find that the observations are well described by K R for R > 0 6 GV and Ka for R <0 6 GV. Furthermore, the dependence of the gradient on R and p is found to be the same as that observed for intensity variations with time in 1965. This suggests that, at least at solar minimum, the dependence of the modulation on magnetic rigidity and velocity is roughly the same throughout the modulating region. The mean gradient for protons in the energy range 20-100 MeV is 215 l 40 per cent (a u )-1 and for helium nuclei with energies 10(F420 MeV/nucleon it is 66 1 9 per cent (a u.)-1. The gradient for charged particles of mean magnetic rigidity 6 GV is 9 0 1 1 5 per cent (a u )-1. The diffusion coefficient along the spiral magnetic lines of force derived from these observed gradients is found to be 3 2 X 1021 cm2/sec for a particle with Rfl = 1 GV. In the diffusion convection model the ratio of the modulated cosmic-ray spectrum u(R,p,r,t) to the unmodulated spectrum u(R,P,'x') can be written as exp 77(r,t)/ftR, )], where fiR, p) has the same form as K(R,p) described above. The observed gradient corresponds to a change in the modulating parameter of A = 0.2 1 005 GV for a mean change in heliocentric radius Ar = 0.4 a u Comparison of this value of A with estimates of during 1965 suggests strongly that at solar minimum the galactic spectrum is not significantly modulated beyond 5 a.u The measurements were made using a three-element solid state detector telescope which separately identifies protons and helium nuclei by a simultaneous measurement of their energy loss and range.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- November 1967
- DOI:
- 10.1086/149367
- Bibcode:
- 1967ApJ...150..675O