A study of the global heliospheric modulation of galactic Carbon

1. A study of the global heliospheric modulation of galactic Carbon M. D. Ngobeni, M. S. Potgieter Centre for Space Research, North-West University, 2520 Potchefstroom, South Africa CHPC-Cape town

2. Introduction: Observations from V1, V2 and ACE [1997-2010] Webber, Private Communication 2011 • Carbon spectra measured at different spatial positions and times in the heliosphere are compared in the figure. • ACE Carbon intensities were ~20% higher in 2009 (A < 0 cycle) than in 1997 (A > 0 cycle).Never seen before!! • We use a north-south asymmetrical numerical model of Ngobeni & Potgieter (2011, 2012, 2013) based on the Parker's transport equation (TPE) to fit selected spectra. • We show that: • (1) the level of drift effects are not necessarily the same every 11-year cycle; • (2) the latitude diffusive term in the TPE becomes increasingly important in the inner heliosphere; • (3) further advances in the effects of diffusive scattering on drift coefficient are needed. • The results of this presentation are extracted from Ngobeni& Potgieter, Submitted, 2013 • . Ngobeni & Potgieter, 2008 CHPC-Cape town

3. Numerical TS-Drift model Parker’s (1965) Transport Equation (TPE): (1) DiffusionConvectionsourcesParticle drifts Adiabatic energy changes f(r,p,t) is the cosmic ray distribution function. Kis the diffusion tensor: V(r, θ) = V(r, θ)er is the solar wind velocity vector: νDis the averaged gradient and curvature drift velocity If we assume azimuthal symmetry (∂/∂ = 0) the Equation (1) becomes: where CHPC-Cape town

4. In a geometry other than a sphere, the TPE is transformed in this way: f(r, θ, p) g(u, v, w) Where See: Haasbroek & Potgieter (1998); Langner & Potgieter (2005); Ngobeni & Potgieter (2011, 12) Transformation of the TPE CHPC-Cape town

5. Elements of the diffusion tensor Parallel mean free path of Burger et al. (2008): Perpendicular diffusion coefficients extracted from Burger et al. (2000): and , with , , and Drift coefficient from Burger et al. (2000): where CHPC-Cape town

6. Modulation at Earth with the new heliopause spectrum (HPS) New galactic carbon HPS • A reasonably good fit to ACE observations in the previous solar minimum (1997; A > 0) is obtained for the entire energy range. CHPC-Cape town

7. Modulation at Earth towards increasing solar activity • Modulation parameters between 1997 and 2009 are different at 1 AU: the level of drifts doubled and the parallel mean free path has increased by ~ 50% • !Modulation between moderate solar maximum and the recent solar minimum exceeds the level of total modulation between the HP and Earth. CHPC-Cape town

8. Outer heliosphere modulation: Are drifts necessary in the heliosheath? • Black lines: No drifts in the heliosheath • Blue lines: 50% level of drifts in the whole heliosphere • Observations of galactic cosmic ray Carbon from both V1&2 seem to suggest that drifts are not necessary in the heliosheath. • drifts in the heliosheath • WHAT ABOUT THE EQUATORIAL PLANE??? CHPC-Cape town

9. Modulation in the heliosheath along V1 heliolatitude • The latitudinal diffusive term in the TPE becomes larger in the inner heliosphere hence the enhancement of polar perpendicular diffusion has smaller effects in the outer heliosphere. CHPC-Cape town

10. Modulation in the heliosheath in the equatorial plane drifts in the heliosheath: YES! • Drifts are necessary to transport particles away from the shock in the equatorial plane in the A < 0 cycle. CHPC-Cape town

11. Summary and Conclusions • 100% drift level and 50% increase in λ׀׀ [λ׀׀ (A<0)=1.5 λ׀׀ (A > 0)] is necessary to obtain a reasonable fit to ACE observations in the recent solar minimum (2009; A < 0 cycle) relative to the previous solar minimum (1997; A > 0 cycle). • Our understanding of the evolution of modulation at Earth from solar minimum to solar maximum is an important diagnostic tool towards understanding modulation of GCRs in the whole heliosphere. • The contribution of the enhancement of the polar perpendicular diffusion in the heliosheath to the total modulation seems insignificant. • Drifts in the heliosheath play a less important role at the Voyager heliolatitudes, but this is not to say that drifts do not occur at all in the heliosheath. • Further advances in the effects of diffusive scattering on the drift coefficient are needed to derive a self-consistent drift reduction function suitable for modulation in the outer heliosphere. CHPC-Cape town