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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
Introduction: Observations from V1, V2 and ACE [1997-2010]
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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.
Webber, Private Communication 2011
Ngobeni & Potgieter, 2008
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Numerical TS-Drift model
Parker’s (1965) Transport Equation (TPE):
(1)
Diffusion Convection sources Particle drifts Adiabatic energy changes
f(r,p,t) is the cosmic ray distribution function. K is the diffusion tensor:
V(r, θ) = V(r, θ)er is the solar wind velocity vector: νD is the averaged gradient and curvature drift velocity
If we assume azimuthal symmetry (∂/∂ = 0) the Equation (1) becomes:
where
13 ln Df f Q( r, p,ff t
t p)f K VV v
2 20 0 0 0 02 2 2 2 2
1 1 1 1 1; ; (sin ) ; (sin ) ( ); sin sin 3
rr rr r rKa K b c r K K V d K rK e r Vr r r r r r r r r
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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
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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
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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.
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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.
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Outer heliosphere modulation: Are drifts necessary in the heliosheath?
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???
Black lines: No drifts in the heliosheath
Blue lines: 50% level of drifts in the whole heliosphere
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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.
Modulation in the heliosheath along V1 heliolatitude
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drifts in the heliosheath: YES!
Modulation in the heliosheath in the equatorial plane
Drifts are necessary to transport particles away from the shock in the equatorial plane in the A < 0 cycle.
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.
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