1. M. D Ngobeni*,1, M. S. Potgieter1
Modelling of galactic carbon in an asymmetrical heliosphere: Effects of asymmetrical modulation
M. D Ngobeni*,1, M. S. Potgieter1
1Centre for Space Research, North-West University, 2520 Potchefstroom, South Africa
*Dept of Physics and NDT, Vaal University of Technology, 1900 Vanderbijlpark, South Africa
11-18 AUG 2011
ICRC-Beijing-CHINA

2. Introduction
It is now established that the geometry of the heliosphere deviates significantly from a sphere.
We study the effects of an asymmetrical geometry of the heliosphere on the modulation of galactic cosmic rays (GCRs) from solar minimum to moderate maximum conditions.
We extend the study to include different modulation conditions between the north and south heliospheric hemispheres.
Conclusions about the effects of the heliospheric geometry and asymmetrical modulation conditions on GCR carbon is made.
11-18 AUG 2011
ICRC-Beijing-CHINA

3. Heliospheric asymmetries
Opher et al.(2008)
Snyman (2007)
The TS in the V1 direction in 2007 was closer to the Sun than in Dec 2004.
The crossings of the TS by V2 at 84 AU compared to 94 AU observed by V1 show that the TS position changes dynamically and also suggest that the heliosphere is asymmetrically shape (at least the width of the heliosheath differs with heliolatitude).
MHD modeling supports this so that we have a well defined and large nose-tail asymmetry together with a north-south asymmetry
11-18 AUG 2011
ICRC-Beijing-CHINA

4. Numerical TS-Drift model
Parker’s (1965) Transport Equation (TPE):
(1)
Diffusion Local sources
Convection
Particle drifts
Adiabatic energy changes
f(r,p,t) is the cosmic ray distribution function.
K is the diffusion tensor [k|| from Burger et al. (2008) and kr and k from Burger et al. (2000)]
V(r, θ) = V(r, θ)er is the solar wind velocity vector:
νD is the averaged gradient and curvature drift velocity
11-18 AUG 2011
ICRC-Beijing-CHINA

5. TS and HP positions (~ 8 & ~ 22 AU asymmetry)
In a geometry other than a sphere, the TPE is transformed (Haasbroek and Potgieter, 1997):
f(r, θ, p) g(u, v, w)
e.g.
TS and HP positions (~ 8 & ~ 22 AU asymmetry)
Eq. (1) in 2D (spatial) can now be written as:
, (2)
where the primed variables are the transformed coefficients.
See: Haasbroek & Potgieter (1998); Langner & Potgieter (2005); Ngobeni & Potgieter (2011)
55°
94 AU
131 AU
125°
86 AU
109 AU
11-18 AUG 2011
ICRC-Beijing-CHINA

6. Modeling Results
Testing the transport coefficients and verifying of model: Observational and computed spectra during solar minimum
Ngobeni & Potgieter, ASR, 2011
Red: Webber & Higbie (2009)
Black: Moskalenko et al. (2002)
The model reproduces reasonably well modulation of GCR carbon at Earth and in the outer heliosphere simultaneously.
The assumed transport coefficients are reasonable; observable features are produced
11-18 AUG 2011
ICRC-Beijing-CHINA

7. Radial Intensities: Geometrical effects towards increasing solar activity
Red: 55°
Black:125°
11-18 AUG 2011
ICRC-Beijing-CHINA

8. Asymmetrical modulation condition
Sample solutions: contours of 200 MeV during solar minimum in an A > 0 cycle
11-18 AUG 2011
ICRC-Beijing-CHINA

9. Radial Intensities: Asymmetric modulation combined with geometric effects during solar minimum
Red: 55°
Black:125°
11-18 AUG 2011
ICRC-Beijing-CHINA

10. Radial Intensities: Asymmetric modulation combined with geometric effects during solar maximum conditions
Red: 55°
Black:125°
11-18 AUG 2011
ICRC-Beijing-CHINA

11. Summary and Conclusions
Geometric asymmetric effects (~8 AU in TS and ~ 22 AU in the HP positions) between polar angles of 55° (northern hemisphere) and 125° (southern hemisphere) only become significant deep inside the heliosheath and at energies < ~ 1.0 GeV in A > 0 cycles for both solar minimum and maximum conditions. This feature is however enhanced with increasing solar activity in A < 0 cycles.
The enhancement of k over the poles that is different between the two hemispheres can produce modulation differences between 55° and 125° that cancel or enhance geometric effects depending on the drift cycle. This feature also becomes strong during moderate solar maximum conditions in both polarity effects.
11-18 AUG 2011
ICRC-Beijing-CHINA