The heliospheric modulation of cosmic ray boron and carbon
Abstract. The observed boron to carbon ratio (B/C) at Earth provides a good measure of the overall secondary to primary ratio of galactic cosmic rays. This makes B/C an important constraint and test for the validity and general applicability of theoretical and numerical models of galactic propagation and heliospheric modulation. For this purpose, the modulation of boron and carbon in the heliosphere must be understood in greater detail. The latest approach to heliospheric modulation, using a numerical model containing a termination shock, a heliosheath and particle drifts, is used to the study the modulation of the two species. This model also includes a more comprehensive set of diffusion coefficients. From this and previous work follows that the model is compatible with a variety of observations, for seven species, i.e. protons, anti-protons, electrons, positrons, helium, boron, and carbon, with the same set of parameters for both solar magnetic polarity cycles. Despite the rather flat interstellar spectrum for carbon below 100MeV/nuc, the modulated spectra at 1AU look very similar for boron and carbon, caused by adiabatic energy losses, implying that the carbon modulation should have a much larger radial gradient in the outer heliosphere below ~200-500MeV/nuc than boron. Significant modulation can be caused by the heliosheath but it is strongly dependent on energy and on the field polarity, with almost no effect at high energies to the largest effect at low energies. The solar wind termination shock has an important effect on the B to C ratio in the heliosphere, although small at Earth, during the A<0 cycle, with E<~600MeV/nuc, but it seems less significant for the A>0 cycle and with increasing tilt angles. Drift models produce different spectra for consecutive solar minimum conditions which may account for the modulation level differences between observations around 100MeV/nuc compared to around 500MeV/nuc. All factors taken into account, heliospheric modeling indicates that the interstellar spectra for B and C need further refinement around 1GeV/nuc, in order to fit observations over a wide energy range at Earth and that this refinement probably has to take into account the proposed contribution of a local interstellar carbon component. These results confirm that this numerical model with a TS can reasonably reproduce the B and C modulation between the outer boundary and Earth, making it a reasonable approximation for both polarity cycles from solar minimum to moderate solar activity.