Florinski, V

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29th International Cosmic Ray Conference Pune (2005) 2, 1922The interaction of solar wind structures with the termination shock andanomalous cosmic ray enhancements at low energiesV. Florinski, G.P. Zank and N.V. PogorelovInstitute of Geophysics and Planetary Physics, University of California, Riverside, CA 92521, USAPresenter: V. Florinski (vflorins@ucr.edu), usa-florinski-V-abs2-sh31-posterVoyager 1 anomalous cosmic ray measurements performed in close proximity to the termination shock during2002–2004 show a new low-energy particle population in addition to the modulated spectrum. While theprecise interpretation is still a subject of debate, several plausible explanations have been suggested, involvingthe excursion of the shock in response to changing conditions in the solar wind. Solar wind structures, such asshocks and merged interaction regions collide with the termination shock causing it to reform, become weakeror stronger and move inward or outward. We present an initial study of particle acceleration at a shock withincident perturbations in the form of simple waves (forward/reverse shock pairs or contact discontinuities)and discuss the effects of intermittent injection. It appears that motion of the TS alone cannot explain theobservations. However, it is possible to reproduce essential features of the observed double spectrum by makingseveral assumptions regarding the geometry of the system and the effectiveness of the injection process.1. IntroductionThe solar wind (SW) termination shock (TS) and the heliosheath are in a perpetually dynamic state owing tolarge scale structures in the solar wind such as global merged interaction regions (GMIRs), interacting withthe heliospheric boundaries. The collision of such a structure with the TS can be represented as a series ofelementary interactions between forward and reverse shocks and stream interfaces with a moderately strongstationary shock wave. The classical outcomes of such interactions are well known: the TS moves either towardor away from the Sun and a transmitted shock or rarefaction wave and a contact discontinuity (CD) appear inthe heliosheath and propagate toward the HP [1, 10]. Typically, a large number of waves are injected intothe heliosheath resulting in additional heating of the ambient plasma [11]. GMIRs also introduce propagating“barriers” in the heliosheath with magnetic field enhancement up to 4 times over the ambient field magnitudethat could have a significant effect on galactic cosmic ray propagation [9].Motion of the TS is undoubtedly an important factor affecting anomalous cosmic ray (ACR) acceleration.ACR spectra measured during the energetic particle increases in the second half of 2002 and in 2004 showtwo distinct populations of particles: a modulated spectrum at high energies (  MeV for protons) and apower law at low MeV energies with a rollover to a steeper spectrum at   MeV [2]. It has been suggestedthat the latter population originates at a local incursion of the TS [4] or at a location away from Voyager, butmagnetically connected to the spacecraft [6], while the former arrives my means of cross-field diffusion andis therefore heavily modulated. The second possibility can be realized if the TS curvature near the Voyager 1location is less than that of the Parker spiral and the field connects to a location on the shock surface downstreamof the spacecraft [5]. The latter is required to explain the observed anisotropy, which was directed away fromthe Sun during the events [7]. 3D MHD simulations of the heliosphere that take into account plasma-neutralinteractions show that this scenario is entirely plausible [8].In this communication we discuss a series of simple 1D demonstrative solutions to the ACR transport equationfor particles accelerated at a shock with incident perturbations in the form of simple waves. For simplicity weuse planar geometry instead of spherical because shocks and contact discontinuities (CD) propagate unchangedin the former, but evolve in the the expanding SW. To ensure the appearance of the high-energy cutoff in20 V. Florinski, G.P. Zank and N.V. Pogorelothe accelerated spectra we place a reflecting wall at the left boundary of the simulation box. This producesmodulated spectra in front of the shock qualitatively similar to those in the spherical geometry with the cutoffproduced by cooling at the wall rather than in the expanding flow as would be the case for the SW [3].2. Termination shock evolutionThe gas-dynamic part of the problem consists of a moderately strong stationary shock (compression ratio	 ) in the initial conditions and a series of upstream perturbations. For the latter we use either a sequenceof four CDs (the MCD model) produced by changing the plasma density at the left boundary by  40%, or aforward-reverse shock pair (FRS model) produced by a single increase in the plasma velocity by 50%. In thesecond model the propagating shocks have a compression ratio of 1.85.0.05.0×10-41.0×10-31.5×10-32.0×10-32.5×10-3n, cm-38090100r sh, AU20 40 60 80 100 120r, AU0.05.0×10-41.0×10-31.5×10-32.0×10-30 100 200 300 400t-t0, days1234sFigure 1. Left panels: plasma density 50 days before the collision of the front stream interface with the TS (dashed)and 200 days after the collision (solid lines) for the MCD (top) and FRS (bottom) initial conditions. Right panels: shockposition (top) and compression ratio (bottom) for the MCD (solid) and FRS (dashed). Peaks are due to numerical errorsin calculating  at the moments of collisions between simple waves. A much more detailed discussion of the interactionprocess may be found in [10].Figure 1 shows the plasma density before and after the collision of the front structure with the stationary shock.The MCDs cause the shock front to move first in- and then outward by about 5 AU over a time scale of about 1year without changing its compression ratio appreciably. The FRS pair moves the TS steadily outward with itscompression ratio decreasing at first to 2.6 and then increasing to 3.35 (Fig.1, right). The heliosheath regionsbecomes filled with waves and discontinuities that are easy to identify. For example, the sequence of wavesin the MCD model from left to right is TS, CD, rarefaction, CD, shock. In our simulation the TS only attainsmoderate speeds relative to the solar frame — 55 km/s for the MCD and 75 km/s for the FRS perturbations.3. ACR acceleration at a moving shockIn solving the ACR transport equation we only inject particles at the TS. For ACR acceleration we consider firsta scenario where the entire population of particles is produced by a single source at the shock. Particle spectrathat would be observed by a spacecraft located at   AU, where  ﬀAU is the shock distancebefore the interaction, are shown in Fig. 2 (left panel) for the MCD case. Before the onset of interaction theTermination shock motion and ACR response 210.1 1 10 100 1000T, MeV10-210-1100101102103104105J, m-2s-1 ster-1MeV-1t0 + 15 dt0 + 75 dVoyager 1 (2002.5 - 2003)0.1 1 10 100 1000T, MeV10-210-1100101102103104105J, m-2s-1 ster-1MeV-1t0 - 50 dt0 + 150 d (single spectrum)t0 + 350 d (double spectrum)Figure 2. Left: accelerated particle spectra at ﬁﬃﬂ "!$#&%' ( AU for the time before the rst CD hit the shock (solid), 5 monthsafter the initiation of the collision for the single source scenario (dashed) and 1 year after the rst collision for the dualsource scenario (dot-dashed). Right: Shock spectra with intermittent injection during the injection phase (solid) and theacceleration phase (dashed).spectrum is modulated at low energies. As the shock moves closer, the spectrum gradually unfolds, approachingan unmodulated power law. Indeed, for plausible values of the diffusion mean free path, ACR accelerationproceeds significantly faster than the dynamical scale associated with the motion of the shock (  AU permonth), and the spectrum has time to adjust to the shock motion. Deviations from the steady-state distributionare only provided by modest changes in the strength of the TS. The situation is similar in the FRS case,although, of course, the amount of modulation only increases in time in this model as the shock moves fartheraway. It seems that motion of the TS by itself is not a valid explanation for the Voyager 1 measurements.Next, we consider the case where some of the particles observed upstream of the shock come from a limitedportion of the TS magnetically connected to the spacecraft, while the rest of the particles arrive from a broadrange of longitudes by, e.g., cross-field diffusion. The spectrum shown at     AU is essentially a sumof the modulated spectrum at this location and a portion (10% here) of the spectrum at a location 3 AU furtherdownstream. Figure 2 (dot-dashed line) shows that it is possible to obtain a double population spectrum thatqualitatively resembles Voyager 1 observations. However, the latter exhibit a change in the slope to a softerpower law (which can also be interpreted as a cutoff) at about   3 MeV. As mentioned earlier, accelerationat the TS is sufficiently fast compared to the timescale of the shock motion, certainly enough to establish thepower law to energies in excess of 10 MeV . The limited size of the acceleration region may be an importantfactor here; however, it is not possible to include it in the 1D model.4. Intermittent injectionDisturbances in the solar wind also affect the direction of the interplanetary magnetic field. Even slight changesin the direction of ) relative to the shock normal could have a dramatic effect on the rate of injection of lowenergy particles into the diffusive shock acceleration process. Figure 3 shows the effective injection energy atthe TS, defined as the energy where the particle anisotropy upstream of the shock is  . More details aboutthis calculation may be found in [12]. Injection is inefficient at quasi-perpendicular shocks. However, because22 V. Florinski, G.P. Zank and N.V. Pogorelo0 10 20 30 40 50 60 70 80 90Θbn , deg100101102103T inj, keVFigure 3. Injection threshold as a function of the shock-normal angle *+-, ..0/213.54 at all energies of interest, the injection threshold decreases sharply when the angle between ) andthe shock normal, 6798 approaches 90 : because there is not field-aligned anisotropy in this case.For the final scenario we assume that the entire population of particles originates at a location magneticallyconnected to the spacecraft, i.e., the spectra observed are essentially spectra at ; . In addition we assume a130-day cyclical injection pattern where injection operates for 15 days when the shock is either quasi-parallelor strictly perpendicular, followed by 115 days of acceleration without injection. Because the TS is expected tobe quasi-perpendicular most of the time, our assumptions regarding the injection cycle are not unreasonable.Figure 2 (right panel) shows the resulting particle distributions at two different moments in time. Duringthe injection part of the cycle a power law is quickly established at low energies. Once the injection ceases,particles continue to be accelerated to higher energies by the shock. At those times the distribution resemblesa modulated spectrum, although it is more of a consequence of limited acceleration time rather than particleescape from the shock region upstream. Comparing the model spectra with the Voyager 1 observations showsa good qualitative agreement. It appears that intermittent injection might be the mechanism that could explainthe properties of the double spectrum.This research was supported by NSF grant ATM-0428880 and by NASA grant NAG5-12903.References[1] A. Barnes, J. Geophys. Res. 98, 15,137 (1993).[2] A.C Cummings and E.C. Stone, in Physics of Collisionless Shocks, AIP Conf. Proc., in press (2005).[3] V. Florinski and J.R. Jokipii, Astrophys. J. 591, 454 (2003).[4] J.R. Jokipii and J. Giacalone, 28th ICRC, Tsukuba, 3753 (2003).[5] J.R. Jokipii et al., Astrophys. J. 611, L141 (2004).[6] J. Kota and J.R. Jokipii, in Physics of the Outer Heliosphere, AIP Conf. Proc. 719, 272 (2004).[7] S.M. Krimigis et al., in Physics of the Outer Heliosphere, AIP Conf. Proc. 719, 133 (2004).[8] N.V. Pogorelov and G.P. Zank, Adv. Space Res. 35, doi:10.1016/j.asr.2005.03.124 (2005).[9] N.V. Pogorelov and G.P. Zank, in Solar Wind Eleven, in press (2005).[10] T.R. Story and G.P. Zank, J. Geophys. Res. 102, 17,381 (1997).[11] G.P. Zank and H.-R. Mu¨ller, J. Geophys. Res. 108, 1240 (2003).[12] G.P. Zank et al., in Solar Wind Eleven, in press (2005).

The interaction of solar wind structures with the termination shock and anomalous cosmic ray enhancements at low energies

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