The Evolution of the Heliospheric Current Sheet and its Effects on

Cosmic Ray Modulation

József Kóta and J.R. Jokipii

The University of Arizona

Tucson, AZ 85721-0092 USA

kota@lpl.arizona.edu

29th ICRC, Pune, India, August 6, 2005 SH-34

Global structure of Heliosphere

GCR

ACR SEP

Magnetic wall

Based on 2-D Flow Simulation(Florinski, Izmodenov)

Wall

Pile-up of field lines near the Heliopause builds magnetic wall

Cosmic rays find hard to penetrate into the Heliosheath through the magnetic wall (?)

“Polar line” does not connect to Helio- pause

Motivation

• A large part of cosmic ray modulation occurs in the heliosheath

• Particle drifts are important in the cosmic-ray transport, but their role in the heliosheath has not been investigated thoroughly

• To explore the role of drift in the heliosheath we consider otherwise simplified models (test particle etc.)

Parker Equation

Diffusive transport equation of energetic charged particles:

- assumes near isotropic distribution

Diffusion(anisotropic)

Drift Convection Cooling/ Acceleration

Source

Related to regular gyro- motion

Polarity/charge dependent

ACR drift for A< 0 (1980-1990) (Cummings – Jokipii)

Model simplified – major simplification in topology

Re-acceleration of GCR at the TS

Re-acceleration

Spiral Field beyond the Termination Shock – contn’d

Solar wind & field lines are deflected toward the heliotail

Sun

TS

Sun

IS Wind

Sun

IS Wind

Schematic Heliosphere

outw

ard

inward

bi[polar

bipol

ar

HCS may mitigate the effect of magnetic wall ?

Mapping the heliosphere: fold around poles

Θ,Φ footpoints - ψ=cosθ

inward

outw

ard

Θ=0

Θ=π

Mapping the heliosphere into T,θ,(Φ)

unipolar out

unipolar in

bip

ol

arSW

T=

0

equatorSP

T: transit timeΘ-Φ: footpoints

SW: uniform in T-direction

B in Φ-direction

Magnetic field

• General Formulation of Heliospheric Field:

Bi = B(θ,T)o εijk sinθ θ,j T,k

Θ,Φ: Footpoints of StreamlinesT: transit time from footpoint

● No θ component in B (+)● θ,Φ no longer orthogonal (-)● Boundary conditions change● Test particles only !

θ,j = ∂θ/∂xj

+ deal with singularities

Parker’s equation rewritten in general coordinates:

ii x /

}/)(}{{}{/ pFpVgFVFgtFg jjijij

i

g

2fpF

gbgbb kijkA

ijjiij /

Identical equation for

notations: volume element

Diffusion convection cooling/acceleration & drift

Diffusion tensor:

Metric tensor non-diagonal - can be ugly

i,j=1,2,3

How to condense into 2-D ?

o Heliosphere is inherently 3-d even for a flat current sheet. One way to proceed is

o Assume F=F(T,θ) – these are magnetically connected . Then average the 3-D equation

}/{// FVgxFgxtFg ijiji

}/)(}{/{ pFpxVg jj

+

i,j=1,2

“average” κ

“average” V

Summary/Conclusions

o Topology of field lines: polar lines never connect to heliopause – important difference for A>0

o HCS connects from the equator to the heliopause, which might(?) reduce the effect of the magnetic wall

o Quantitative work still to come

Thank you

Motto:

● “Make everything as simple as possible, but not simpler “

Cosmic-ray gradients for A>0 and A<0: Flat HCS vs Wavy HCS

Reacceleration

Flat HCS: large θ gradient

Wavy HCS: small θ gradient

Reacceleration at TS