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Acceleration of Anomalous Cosmic Rays at a Non Spherical Termination Shock Abstract ID: SH21B-1919 Udara K Senanayake 1 ([email protected] ) , Vladimir A Florinski 1 ([email protected]) 1 Physics/CSPAR, University of Alabama in Huntsville, Huntsville, AL 1. Introduction ● Anomalous Cosmic Rays (ACRs) are assumed to be accelerated at the Termination Shock (TS) . Shape of the TS is not yet known exactly. Most of the current simulations on ACRS are done using a spherical TS. Here we use a blunt TS to study the ACR acceleration. ● Voyager I and Voyager II are the two major spacecrafts collecting ACR data. Most theories made by scientist using a spherical shock didn't match up with the observation when Voyager I (V1) and Voyager II (V2) crossed TS in 2004 and 2007 respectively. 2. Background ● The blunt shock and the plasma velocities used in this model are similar to Fahr (1993). The radius of the shock is given by, where is the spherical polar angle, b = 140 and k = 1.53 2 - 1 ● The plasma velocities are given by the following equations, ● Inside the TS Magnetic Field behave as Parker Field, so the field outside of the TS is calculated by integrating along streamlines. u r =a ( b 2 r 2 −cos θ ) 3. Numerical Model ● Same code used for Galactic Cosmic Rays (GCRs) in Florinski & Pogorelov (2009) was adapted to the ACR acceleration. Difference is that trajectory exit points are in momentum space (T min ) rather than in real space (heliopause). Shock strength of 3 was used. ● Transport is modeled using the Parker's equation (Parker 1965; Gleeson & Axford 1967), ● Drift velocity ● Diffusion (Czechowski et al. 2001) where; w-particle velocity, P-rigidity in GeV, B 0 -magnetic field at 1AU ● Here the stochastic particle trajectories are integrated backward in time similar to works of Zhang (1999), Ball (2005) and Florinski & Pogorelov (2009). References ● (1) From Browse Data Plots link at http://sd-www.jhuapl.edu/VOYAGER/ ● Ball, B., Zhang, M., Rassoul, H., & Linde, T. 2005, ApJ, 634, 1116 ● Czechowski, A., Fitchner, H., Grzedzielski, S., Hilchenbach, M., Hsieh, K. C., Jokipii, J. R., Kausch, T., Kota, J., Shaw, A., 2001 A&A 368, 622 ● Fahr H. J., Fitchtner H., Scherer K., 1993, A&A 277, 249 ● Florinksi, V., & Pogorelov, N. V., 2009, ApJ, 701, 642 ● Gardiner, C. W. 1985, Handbook of Stochastic Differential Methods for Physics, Chemistry and the Natural Sciences (Berlin: Springer) ● Gleeson, L. J., & Axford, W. I., 1967, ApJ, 149, L115 ● McComas, D. J. and N. A. Schwadron, 2006, Geophys. Res. Lett. 33, 25437 ● Parker, E. N., 1965, Planet. Space Sci., 13, 9 ● Zhang, M. 1999, ApJ, 513, 409 where a = 100 Fig.1 Shape of the TS used Fig.3 3D cutout view of the calculated magnetic field magnitude Fig.4 Magnetic Field Lines (Parker Spiral) Fig.9 Parker spiral in the ecliptic plane 6. Acknowledgments I would like to thank my adviser Dr. V. Florinski for providing me with the code for the spherical TS model and also for all the guidance and support. 4. Results contd ... Fig.7 Trajectories of 2 particles - spherical TS u θ =a sin θ u ϕ =0 r = b √ k √ √ k cos 2 θ+1− cos θ ∂ f ∂ t +( u i + v d,i ) ∂ f ∂ x i − ∂ ∂ x i ( κ ij ∂ f ∂ x j ) − ∇ . u 3 ∂ f ∂ ln p = 0 v d,i = pcw 3 e ϵ ijk ∂ ∂ x j ( B k B 2 ) Fig.2 Velocity magnitude plot with streamlines in the ecliptic plane Fig.5 Energy spectra - spherical TS 4. Results Fig.6 Energy spectra at the nose – blunt TS Fig.11 Energy spectra at the blunt TS Fig.12 Voyager 1 observations (1) Fig.13 Voyager 2 observations (1) 5. Conclusions ● It is clear from above results that the TS is blunt and ACR acceleration is happening at the flanks of the TS which is similar to results of McComas & Schwadron (2006). ● Currently V1 ACR intensities decreasing may be due to leaking of particles through the heliopause ● V2 intensities increasing may be because it may be going towards flanks so as shown above ACR intensities should increase. Fig.8 Trajectories of 2 particles - blunt TS Fig.10 Average intensities at the TS for 30MeV ACR particles κ ∥ = κ ⊥ = 0.01 κ ∥ w c P B 0 B
