Stochastic Variations of Cosmic Rays in the Solar System

Abstract

view Abstract Citations (11) References (15) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Stochastic Variations of Cosmic Rays in the Solar System Jokipii, J. R. Abstract The response of the cosmic-ray intensity in the solar system to turbulent fluctuations in the solar wind is calculated. The cosmic-ray diffusion coefficient K and the wind velocity V vary stochastically about their mean values, and the variations are assumed to be frozen into the solar plasma. The resulting fluc- tuations in the cosmic-ray intensity I are determined to first order in the fluctuations of K and V by solving the full time-dependent Fokker-Planck equation and regarding all three fluctuations as stationary random functions of time. The results, expressed in terms of autospectra and cross-spectra of I, V, and ,c (at a given heliocentric radius r) depend on distant as well as local features of the solar-wind turbulence and may therefore serve as a sensitive probe of the struc'ture of plasma turbulence in the solar wind. This technique may permit an estimate of the distance to the boundary of the modulating region (that helio- centric radius beyond which there is little turbulence). Power spectra which were computed from counting rates obtained by the Climax neutron monitor in 1965 show some evidence of enhanced fluctuations at a frequency of 0 15 cycles per day. The theory would predict a peak at this frequency if the boundary of the modulating region were at 2.7 ± 0.5 a u. This tentative estimate of the size of the modulating region is consistent with, and independent of, previous estimates. I. INTRODUCTION The intensity of galactic cosmic rays observed in the inner solar system changes with the time because of varying modulation by the solar wind. The well-known eleven-year cyclic variation, for example, is due to the eleven-year cycle of solar activity. Shorter- term, irregular fluctuations in the intensity also occur due to a variety of causes, such as blast waves from solar flares (Forbush decreases). The interpretation of these phenomena in terms of Parker's (1958, 1965) diffusion-convection theory and in terms of the Fourier spectrum of the magnetic field (Jokipii 1966, 1967) has considerably deepened our insight into the turbulent structure of the solar wind. For example, analysis of the phase lag between the solar-cycle variations of the cosmic-ray intensity and appropriate solar ac- tivity indices (Forbush 1954) permits an estimate of the size of the modulating region (that heliocentric distance beyond which turbulence in the wind becomes too weak to exclude cosmic rays effectively; e.g., Simpson and Wang 1967). This paper concerns the theory of irregular, short-term variations in the cosmic-ray intensity which are produced by the day-to-day variations in the turbulent solar wind. It has been demonstrated observationally that the fluctuating cosmic-ray intensity dur- ing quiet times shows a significant correlation with the measured particle-diffusion co- efficient (Jokipii and Coleman 1968). Using measurements carried out on board Mariner 4 in 1965, Jokipii and Coleman found that periods when the diffusion coefficient was smaller than normal (high magnetic-field variance) tended statistically to be followed by decreased counting rates, as the region of high magnetic variance was carried out beyond the point of observation so that it shielded Mariner 4 from incoming galactic particles. It is shown in the present paper that variations in the cosmic-ray intensity and in the solar wind may be related statistically by using Parker's modulation theory. The obser- vations may then be used to analyze the structure of solar-wind turbulence. The plan of this paper is as follows: In the next section Parker's diffusion-convection theory with adiabatic deceleration is discussed, and appropriate time-dependent solu- tions are presented for small variations in solar-wind parameters. In § III these results are used to obtain the statistical properties (power spectra) of the cosmic-ray intensity 110 Publication: The Astrophysical Journal Pub Date: June 1969 DOI: 10.1086/150038 Bibcode: 1969ApJ...156.1107J full text sources ADS |