On the importance of the local interstellar spectrum for the solar modulation parameter

Cosmogenic Isotopes are produced in the Earth's atmosphere due to the interaction of galactic cosmic rays with nuclei of atmospheric atoms. Among others, the Be-10 concentration in ice cores depends on the galactic cosmic ray flux outside of the Earth's magnetosphere and provides therefore a unique tool to investigate the solar modulation over very long time periods. In this study we investigate the importance of different local interstellar proton spectra often used in literature obtained outside of the Earth's magnetosphere. In order to parameterize the heliospheric modulation we apply the force-ield solution using individual local interstellar proton spectrum (LIS) model dependent phi values. Thus among atmospheric and magnetospheric processes, the Be-10 concentration depends on an interplay of the different LIS and their modulation parameters. Since Be-10 measurements do not provide any spectral resolution, PAMELA data have been used for a comparison with the calculated spectra and to provide the model dependent modulation parameters during the solar minimum in July 2006. Within the limitation of the force-field solution and the freedom in parameter space, all LIS lead to a reasonable agreement with the data. Taking the LIS dependency of the modulation parameter into account, we derive linear equations to convert the individual phi between the different LIS. The conversions used here are then applied to a long-term reconstruction of phi derived from a record of the cosmogenic radionuclide Be-10. By using the derived LIS conversions, we show that the occasionally observed negative phi values in the reconstruction of Steinhilber et al. (2008) vanish if another LIS model is used. In order to estimate other processes which alter this conclusion, the influence of the palaeo-magnetic field has been included. Thus, if all inner-heliospheric effects on the Be-10 flux would be known, this investigation would have the potential to rule out certain LIS.