A Predictive Analytic Model for the Solar Modulation of Cosmic Rays

An important factor limiting our ability to understand the production and propagation of cosmic rays pertains to the effects of heliospheric forces, commonly known as solar modulation. The solar wind is capable of generating time and charge-dependent effects on the spectrum and intensity of low energy ($\lsim$ 10 GeV) cosmic rays reaching Earth. Previous analytic treatments of solar modulation have utilized the force-field approximation, in which a simple potential is adopted whose amplitude is selected to best fit the cosmic-ray data taken over a given period of time. Making use of recently available cosmic-ray data from the Voyager 1 spacecraft, along with measurements of the heliospheric magnetic field and solar wind, we construct a time, charge and rigidity-dependent model of solar modulation that can be directly compared to data from a variety of cosmic-ray experiments. We provide a simple analytic formula that can be easily utilized in a variety of applications, allowing us to better predict the effects of solar modulation and reduce the number of free parameters involved in cosmic ray propagation models.