The Acceleration of Anomalous Cosmic Rays by the Heliospheric Termination ShockJ. A. le Roux, V. Florinski, N. V. Pogorelov, & G. P. ZankDept. of Physics & CSPARUniversity of Alabama in Huntsville, Huntsville, AL 35763SHINE Meeting, Nova ScotiaAugust 3-7, 2009

*1. The problem facing standard diffusive shock acceleration theoryNear-isotropic distributionsDistribution function continuous across the shockDistribution function forms a plateau downstreamPower law spectra with a single slopeSteady-state intensitiesStandard diffusive shock acceleration (DSA) theory:Large field-aligned beams upstream directed away from shock highly variable anisotropy peak in anisotropy at ~0.4 MeV Highly anisotropic intensity spikes at shockDistribution function deviates from plateau downstream Power law spectra harder than predicted by DSA theory multiple slopes- spectrum concave?Upstream intensities highly variable

Energetic particle observations by Voyager contradict standard DSA:A shock acceleration model that can handle large pitch-angle anistropies and includes the stochastic nature of the termination shocks shock obliquity, the focused transport model The solution:

*2. The Focused Transport EquationConvectionAdiabatic energy changesDiffusionFocused transportStandard CR transport 1st order Fermi accelerationShock driftacceleration due to grad-B driftShock driftenergy loss due to curvature driftFOCUSED TRANSPORT INCLUDE BOTH 1ST ORDER FERMI AND SHOCK DRIFT ACCELERATION BUT NO LIMITATION ON PITCH-ANGLE ANISOTROPY

*whereGrad-B driftCurvature driftElectric field driftConservation of magnetic moment3. Drifts in the Focused Transport EquationGrad-B and curvature drifts absent in convectionShock drift included with or without scatteringGuiding Center Kinetic Equation for f(xg, M,,t)

*No cross-field diffusion can be added or simulated by varying magnetic field angle

Gradient and curvature drift effect on spatial convection ignored might be negligible or can be added drift kinetic equation

Magnetic moment conservation at shocks reasonable assumption

Gyrotropic distributions reflection by shock potential at perpendicular shock not described

No polarization drifts can be added higher order drift kinetic equation only important at v~U 4. Possible Disadvantages of Focused TransportFocused transport equation suitable for modeling anisotropic shock acceleration

*5. Results of Shock Acceleration of core Pickup Ions with a Time- dependent Focused TransportInjection speed if 1 = BN = 89.4oVoyager 1 2004 1 hour averages Mimics anomalous perpendicular diffusion De Hoffman-Teller speed in SW frame is the injection speedWhen including time variations in spiral angle (stochastic injection speed), shock acceleration of core pickup ions works(i) Stochastic injection speed

*(ii) Multiple Power Law Slopes - ObservationsUpstream spectra are volatileDownstream spectra more stableMultiple power law slopesCummings et al., [2006] Decker et al. [2006]

*Both at V2 and V1, post-TS spectrum has multiple slopes

Exponential rollovers

Multiple power laws partly due to nonlinear shock acceleration?Decker et al., [2008] 78 day averages Breaking points at ~0.06 MeV & 0.3 MeV

Rollover at ~ 0.7 MeVBreaking points at ~0.07 & 0.2 MeV

Rollover at ~ 1-2 MeVBump at ~0.1 MeV

*(ii) Multiple Power Law Slopes - Simulationsupstreamdownstream101 AUBreaking points at ~0.01 & 0.4 MeVv-4.2v-3.3DSA predicts v-4.4 if s = 3.2Pickup proton core distributionSuccesses:Multiple power laws stochastic injection speedHigher energy breaking point at realistic and fixed energies downstreamBump feature - magnetic reflectionVolatility in upstream spectra damped out deeper in heliosheath3rd power law harder than predicted by DSA theory magnetic reflectionRollover at ~3.5 MeV

Bump at ~0.02-0.04 MeVle Roux & Webb [2009], ApJ123

*le Roux et & Fichtner [1997], JGRThe ACR spectrum calculated with a nonlinear DSA model TS modified self-consistently by ACR pressure gradient

Multiple power law slopesBreaking points at 0.01-0.02 MeV and at ~0.3-0.4 MeV

Exponential rollover

*(iii) Episodic Intensity Spikes - ObservationsDecker et al. [2005] V1 observations at TS intensity spike just upstream of TS along magnetic field

Factor of ~5-10 increase in counting rate

Anisotropy of ~ 92 % - highly anisotropic

No spikes seen at V2

*(iii) Episodic Intensity Spikes - Simulations10 MeV1 MeV1 MeVt2t1t3Spikes only occur when injection speed is low enough (BN is small enough) so that particles can magnetically be reflected upstream

Episodic nature of spikes controlled by time variations in BN

Spikes caused by magnetic reflectionle Roux & Webb [2009], ApJ

*(iv) Episodic Upstream Field-aligned Particle Beams - ObservationsUpstreamDownstreamTSUpstream: pitch-angle anisotropy is highly volatile, can reach ~ 100%, and field-aligned Downstream: anisotropy converge to zero with increasing distance and is very stable Decker et al., [2006] V1 observations from 2004 -2006.6 daily averages

*upstreamdownstream101 AUt1t2t3 = 72% = 50%Success:Large fluctuations in anisotropies upstreamdie out deeper in heliosheath (iv) Episodic Upstream Field-aligned Particle Beams - Simulationsle Roux & Webb [2009], ApJ1 MeV

*(v) Energy Dependence of Upstream Anisotropy - ObservationsDecker et al. [2006] V1 observations ~ 6 month averages Upstream 1st order pitch-angle anisotropy peaks at ~0.3 MeV - no continuing increase with decreasing particle energy

*(v) Energy Dependence of Upstream Anisotropy - Simulations1 MeV10 keV10 MeVVinj = U1/cos1Shock accelerationIf Einj = 1 MeV, 1= BN = 88oPeak in upstream anisotropy is signature of a nearly-perpendicular shockPeak indicates injection threshold energy shock obliquityFlorinski et al.,[2008]le Roux & Webb [2009], ApJ

*Summary and ConclusionsMultiple power law slopes stable break points downstream Strong fluctuations in upstream intensities die out in heliosheathStrong episodic intensity spikes at termination shock Strong fluctuations in upstream B-aligned pitch-angle anisotropy damped out in heliosheathPeak in upstream anisotropy at ~ 1 MeV peak is signature of nearly perpendicular shockThe role of nonlinear shock acceleration in contributing to multiple power law slopesExplanation of observed spectral slopes and TS compression ratio at V2 within shock acceleration context Inclusion of time variations in De Hoffman-Teller velocity determined by upstream time variations in BNJust as standard cosmic ray transport equation - Focused transport equation contains both 1st order Fermi and shock drift acceleration Advantage no restriction on pitch-angle anisotropy- Ideal for modeling injection close to the injection threshold velocity (de Hoffman-Teller velocity) Successes:Problems still to be addressed:Useful features of Focused Transport model:Key element in models success:

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