energetic particle anisotropies at the heliospheric boundary - IOPscience

The Astrophysical Journal Letters, 776:L37 (5pp), 2013 October 20  C 2013.

doi:10.1088/2041-8205/776/2/L37

The American Astronomical Society. All rights reserved. Printed in the U.S.A.

ENERGETIC PARTICLE ANISOTROPIES AT THE HELIOSPHERIC BOUNDARY 1

V. Florinski1,2 , J. R. Jokipii3 , F. Alouani-Bibi2 , and J. A. le Roux1,2

Department of Space Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USA 2 Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, Huntsville, AL 35899, USA 3 Department of Planetary Sciences and Lunar and Planetary Lab, University of Arizona, Tucson, AZ 85721, USA Received 2013 June 27; accepted 2013 September 19; published 2013 October 7

ABSTRACT In 2012 August the Voyager 1 space probe entered a distinctly new region of space characterized by a virtual absence of heliospheric energetic ions and magnetic fluctuations, now interpreted as a part of the local interstellar cloud. Prior to their disappearance, the ion distributions strongly peaked at a 90◦ pitch angle, implying rapid escape of streaming particles along the magnetic field lines. Here we investigate the process of particle crossing from the heliosheath into the interstellar space, using a kinetic approach that resolves scales of the particle’s cyclotron radius and smaller. It is demonstrated that a “pancake” pitch-angle distribution naturally arises at a tangential discontinuity separating a weakly turbulent plasma from a laminar region with a very low pitch-angle scattering rate. The relatively long persistence of gyrating ions is interpreted in terms of field line meandering facilitating their cross-field diffusion within the depletion region. Key words: cosmic rays – magnetic fields – solar wind – turbulence Online-only material: color figures

interstellar medium. We propose an explanation for the puzzling observational result that the intensity of particles streaming along the magnetic field decreased faster than those gyrating at nearly 90◦ angles resulting in a “pancake,” or double loss cone pitch-angle distribution (Stone et al. 2013; Krimigis et al. 2013). Because the HEP intensity changes occurred on short time scales (comparable to rg /V1 , where rg is the cyclotron radius of a typical HEP ion, about 0.005 AU for a 5 MeV proton, and V1 is Voyager 1’s speed), a model must be capable of resolving scales of the order of rg and smaller. A diffusive approach is obviously invalid here because the particle populations were highly anisotropic immediately beyond the boundary. Using a fully kinetic approach in a simple numerical model, we show below that a flattened pitch-angle distribution is a natural consequence of gyrating particles overcoming the magnetic shear barrier that stops particles streaming at small pitch angles. The particles then escape by scatter-free motion along nearly straight (laminar) field lines into the interstellar medium. We also suggest a possible parallel between fast and slow stream interaction regions in the solar wind (Intriligator & Siscoe 1995; Intriligator et al. 2001) and the heliopause.

1. INTRODUCTION Since the end of 2004, the Voyager 1 space probe has been exploring the region of space downstream of the solar wind termination shock, known as the heliosheath (e.g., Stone et al. 2005; Decker et al. 2005; Burlaga et al. 2005). The mean magnetic field magnitude in the heliosheath was increasing with heliocentric distance from some 1 μG just beyond the shock (94 AU) to about 3 μG by mid-2012, when the spacecraft was at 122 AU from the Sun (Burlaga et al. 2013). Turbulent fluctuations were very weak in 2010, with the ratio of the magnetic energy in 1–10 hr fluctuations to the mean magnetic energy δB 2 /B 2 of under 0.026 (Burlaga & Ness 2012). The heliosheath is permeated by energetic ions with MeV energies, produced inside the heliosphere from interstellar material (neutral atoms) and observed to be accelerated at the termination shock (Decker et al. 2008; Florinski et al. 2009; Giacalone & Decker 2010). In the following we shall call these ions heliosheath energetic particles, or HEPs, a term that also includes anomalous cosmic rays (Pesses et al. 1981; Jokipii 1986). From 2012 August, HEPs experienced a series of rapid drops and recoveries, after which they disappeared altogether (Webber & McDonald 2013; Stone et al. 2013; Krimigis et al. 2013). The unexpectedly sharp transition was dubbed the “heliocliff” or “edge.” At the interface, the magnetic field strength increased rapidly from under 3 μG to over 4 μG without a significant change in the field direction (Burlaga et al. 2013). Remarkably, the magnetic field became very smooth, or laminar, after crossing the boundary, with magnetic fluctuations virtually absent. This transition was expected to occur across the heliopause, because it was generally thought that interstellar turbulence existed on vastly greater scales (Armstrong et al. 1995). The heliopause hypothesis was corroborated by the detections of electrostatic oscillations that could only originate in a relatively dense plasma, characteristic of the interstellar medium (Gurnett et al. 2013). In this Letter we examine the process of energetic charged particle crossing a magnetic interface between the weakly turbulent heliosheath and a laminar regions that is part of the

2. THE KINETIC TRANSPORT MODEL To provide context for the transport model, we first discuss a possible large-scale geometry of the heliosheath in the direction of Voyager 1’s travel. Consider a localized intrusion of the interstellar gas into the heliosheath, resulting from a Rayleigh–Taylor like instability driven by a difference in the charge exchange rates across the heliopause (e.g., Florinski et al. 2005; Borovikov et al. 2008). Magnetic fields, which were essentially parallel on the two sides of the “cliff,” would not impede surface wave propagation in the direction orthogonal to B, which does not involve bending of the field lines. The large-scale magnetic geometry for the model adopted here is illustrated schematically in Figure 1 as a projection onto the ecliptic plane. One should keep in mind that the intrusion is also localized in its latitudinal extent (perpendicular to the plane of the page), and that magnetic field lines can wrap around it. 1

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2011; Stone & Cummings 2011; Decker et al. 2012), although larger, variable VT between 30 km s−1 and −80 km s−1 has been reported after 2012 (Krimigis et al. 2013). For simplicity we do not include plasma convection effects in the transport model. However, a shear of VT across the interface is permitted in principle. The unidirectional mean magnetic field is taken to be BHS = 3 μG and BLISM = 4 μG on the heliosheath side, and the interstellar side of the boundary, respectively, in accordance with the observations (Burlaga et al. 2013). A 2D Boltzmann equation describing energetic particle transport in a magnetized plasma with turbulent fluctuations may be written, in the most general form, as  ∂f ∂f ∂f ∂f + v 1 − μ2 cos ϕ + vμ −Ω = Sf, (1) ∂t ∂x ∂z ∂ϕ where f (x, z, μ, ϕ) is the phase space density, μ is the pitchangle cosine, ϕ is the gyrophase, and Ω is the cyclotron frequency. The operator S on the right hand side describes both scattering in solid angle and perpendicular diffusion as a result of field line meandering, or random walk (FLRW). Both expressions could be obtained from the theory of wave–particle interaction (e.g., Jokipii 1972; Schlickeiser & Miller 1998). Scattering is, in general, a resonant process (depends on the spectral power in the fluctuations at the cyclotron radius scale), whereas FLRW is a non-resonant phenomenon that is caused by field line meandering on large scales. Particles can cross the magnetic field lines via scattering in gyrophase and perpendicular diffusion. Because the flow is essentially incompressible, the energy of the particles is conserved. Because the geometry and spectra of magnetic fluctuations in the heliosheath are poorly known, we adopt a simple model with an isotropic scattering operator and a diffusive FLRW term,     ∂ D ∂ 2f ∂ ∂f 2 ∂f Sf = D (1 − μ ) + K|vz | , + ∂μ ∂μ 1 − μ2 ∂ϕ 2 ∂x ∂x (2) where D is the pitch-angle scattering coefficient and K is the FLRW coefficient. The characteristic mean free paths corresponding to Equation (2) are given by v v λ ≈ ≈ 3K, (3) , λscat , λFLRW ⊥ ≈ ⊥ 2D 2D(1 + Ω2 /4D 2 )

Figure 1. Illustration of the particle transport model geometry with magnetic field lines projected onto the RT plane. The (greatly exaggerated) waviness of the field lines in the heliosheath implies a higher amplitude of magnetic fluctuations on AU and sub-AU scales. The double-headed arrow shows a possible plasma flow pattern inside the intrusion-like structure (see text for details). A narrow “approach region” between the two gray bars is postulated, where the magnetic field inside the intrusion presses against the boundary.

An intrusion like that shown in Figure 1 would introduce a stagnation region ahead of it in the direction of Voyager 1 travel, explaining the apparent absence of plasma convection (Krimigis et al. 2011; Decker et al. 2012) and a decrease in magnetic flux along the Voyager 1 trajectory (Richardson et al. 2013). Another benefit of the intrusion feature is that it would explain an unexpectedly early crossing into the local interstellar medium (LISM). However, the particle transport model discussed below is not rigidly tied to this configuration. For example, the stagnant flow could also be a consequence of solar-cycle effects (Pogorelov et al. 2012). We concentrate on a narrow (∼1 AU in the radial direction) region immediately adjacent to the heliocliff (the gray line in Figure 1) on either side. A two-dimensional (2D) coordinate system is introduced with the x-axis normal to the boundary (i.e., pointing approximately in the radial direction), and the z-axis parallel to the mean magnetic field B (the curvature of the field lines is ignored). The xz plane therefore approximately corresponds to the spacecraft RT plane. It is assumed that the magnetic field lines in the external region are pressed against the boundary for a distance zmax (the “approach region” in Figure 1) after which point they separate from the boundary. As illustrated in the figure, the heliosheath magnetic field has more fluctuations on AU and sub-AU scales than the field inside the intrusion. This does not mean that the turbulence is weaker in the new region. Its total turbulent ratio could be well in excess of 0 reaching the end of the approach region is considered lost to the interstellar space. Indirect measurements of the plasma velocity based on the Compton–Getting effect yielded generally small values for the R and N components from 2010–2011 onward (Krimigis et al.

for resonant scattering and cross-field diffusion due to FLRW. Note that for small D resonant transport is predominantly along the magnetic field (e.g., Forman et al. 1974). Equation (1) is solved numerically along the characteristics using a stochastic integration method (see Florinski & Pogorelov 2009, and references therein). Instead of solving Equation (2) directly, the random walk on a sphere technique of Ellison et al. (1990) is used, which avoids the singularities at μ = ±1. For small scattering angles the process is identical to a 2D random walk on a plane. Integration proceeds backward in time until one of the boundaries is reached. At the left (heliosheath) boundary, a constant isotropic distribution is imposed. Trajectories leaving the simulation box across the right (laminar region) boundary are given a weight of 0 (absorbing boundary signifying escape to the LISM). Particles leaving the box through the sides at (approximately) ±zmax /2 with x > 0 are also considered to have escaped, while those with x < 0 reappear at the opposite boundary (they have therefore completed a full circle along a tightly wound magnetic spiral field line inside the heliosheath). The scattering rate of MeV ions in the heliosheath can be estimated from the data reported by Burlaga & Ness (2012) 2

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Figure 2. Model scattering coefficient D (black) and FLRW coefficient K (red) for a 5 MeV proton near the heliocliff boundary. The region with small K implies that field lines do not cross the boundary, interpreted as a tangential discontinuity. (A color version of this figure is available in the online journal.)

Figure 3. Simulated intensity profiles of μ = 1 (orange), μ = 0 (blue), and μ = −1 (turquose) particles as a function of distance from the heliocliff (the dotted line). The circle is a gyro-orbit of a 5 MeV proton. (A color version of this figure is available in the online journal.)

using the following arguments. That study covered frequencies in the range of 1.75 × 10−3 –1.75 × 10−2 s−1 . Assuming the waves travel with the Alfv´en speed, va ∼ 200 km s−1 upstream the heliocliff, we find that these measurements cover most of the relevant range of fluctuations capable of resonantly interacting with a 5 MeV proton, which has a cyclotron radius rg = 1.1 × 1011 cm in a 3 μG field. However, the fluctuations were also highly compressive, with the average magnetic compressibility CB = δBz2 /δB 2  ∼ 0.87, according to Burlaga & Ness (2012). Clearly, conventional solar-wind diffusion models based on incompressible slab+2D turbulence are invalid in the heliosheath. Of the four principal plasma wave modes (Alfv´en, fast, slow and mirror/entropy), the first is only weakly compressible for all angles of propagation, whereas the last two are strongly damped in a warm isotropic plasma. Therefore it appears natural to assume that the observed fluctuations are fast mode waves traveling obliquely to the mean magnetic field. A sensible first approximation is an isotropic ensemble of such waves, which has CB = 2/3 in the MHD limit. While this is less than reported by Burlaga & Ness (2012), the isotropic model is the only one for which a scattering theory has been developed (Schlickeiser & Miller 1998). From Equation (99) of their paper we obtain rg B 2 λ 0.1 δB 2 



kmin rg va v

turbulence is generated by the instability. In addition, the value of K is greatly reduced within a distance ±xm from the boundary, corresponding to a region the field lines are not allowed to cross. In our interpretation, the heliocliff is a tangential discontinuity where the normal component of B is zero. A parallel may be drawn with the interfaces between fast and slow solar wind streams inside of corotating interaction regions, or CIRs, where the random walk of magnetic field lines is reduced by a factor of 150–300 (Intriligator et al. 2001). A velocity shear of 50–100 km s−1 is typical of CIR stream interfaces, believed to be tangential discontinuities (Crooker et al. 1999), and comparable values are not ruled out for the heliocliff (Krimigis et al. 2013). Smoothing of the field lines due to a shear in the plasma flow is expected to be even more pronounced at the heliopause, where more time is available for the process to work. 3. HEP INTENSITIES AND PITCH-ANGLE DISTRIBUTIONS To gain insight into the problem, a series of simulations were performed where some of the transport coefficients, not fixed by the observations, varied over a wide range. Figure 3 shows a typical result for 5 MeV protons obtained with DHS = 10−4 s−1 , DLISM = 2 × 10−7 s−1 , zmax = 70 AU, and xm = 0.007 AU. The width of the FLRW suppression region, 2xm used here is about equal to the thickness of the magnetic field increase at the cliff measured by Voyager 1 (∼0.02 AU, assuming the nominal Voyager 1 radial speed V1 = 17.3 km s−1 ). Intensity profiles of μ = 1, 0, and −1 ions are shown with different colors. The particle distribution was assumed to be isotropic at the left (heliosheath) boundary of the simulation and all three curves are almost identical up to x = 0. The right boundary plays no role in the simulation because all particles exit the simulation box (escape to the LISM) before reaching it. Because the LISM region is essentially scatter-free, and FLRW transport is inhibited across the “cliff,” particles traveling at small angles to the magnetic field are only able to penetrate a very short distance into the new region. However, ions traveling near 90◦ pitch angles are able to overcome the barrier because of gyration, and enter the interstellar region where

1−q ,

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where kmin is the fluctuation outer scale, which we take to correspond to the 10 hr time interval, the longest used in Burlaga & Ness (2012), and q = 5/3 is the power spectral index of the fluctuations in the inertial regime. The normalization factor (0.1) was read off from Figure 7 of Schlickeiser & Miller (1998). Using δB 2 /B 2 = 0.026 in Equation (4), we obtain λ = 1.2 × 1013 cm for a 5 MeV proton, which we round up to 1 AU. The model transport coefficients D and K are shown in Figure 2. The parallel mean free path increases to 520 AU beyond the “cliff.” The FLRW coefficient was taken to be 6 × 10−4 AU in the heliosheath and some 10 times smaller in the LISM. The degree of magnetic field meandering on large (tens to hundreds of AU) scales is comparable on both sides of the boundary in the approach region, where a small amount of 3

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4. DISCUSSION

1

In this Letter we proposed a simple kinetic model to explain the large second-order anisotropy of MeV heliosheath ions observed immediately beyond the heliocliff (now identified as the heliopause), crossed by Voyager 1 in August of 2012 (Gurnett et al. 2013). The model is based on two highly probable assumptions: (1) that particle scattering rates are much smaller in the LISM than in the heliosheath, and (2) that magnetic field lines do not intersect the boundary (no mixing). Ions gyrating near μ = 0 are able to penetrate some distance (a few tens of rg ) into the interstellar region because their larger gyro-radii permit them to travel across the boundary without the assistance of FLRW, whereas particles traveling with small pitch angles cannot overcome the barrier. The heliopause in our model is a canonical tangential discontinuity, similar to stream interfaces inside CIRs that also exhibit very large gradients of energetic particle intensities, indicating great difficulty in overcoming the barrier (Intriligator & Siscoe 1995; Intriligator et al. 2001). The idea of a large-scale convex intrusion is complimentary to the concept proposed by Krimigis et al. (2013), involving an invasion of flux tubes filled with cold dense LISM plasma into the hot heliosheath region as a result of an interchange instability. The particle anisotropy model proposed here would apply equally well to both cases, assuming the turbulence level inside the abovementioned flux tube is low. The model is also in agreement with the generally sharp nature of the ion intensity profiles measured by Voyager 1 (even at 90◦ pitch angle the thickness of the “cliff” is less than 1 AU). The model does not require magnetic mirrors on either side of the Voyager crossing point, but only a region where the magnetic fields of solar and interstellar origin are approximately parallel to each other for a distance of a few tens of AU in the azimuthal direction. The measured difference in the particles streaming in the opposite directions (first-order anisotropy) could be readily accounted for by the approach region extending farther in one direction. The true radial extent of the particle intensity decrease region is unknown because of a large uncertainty in the radial plasma speed measurement. If the flow was slightly anti-sunward, the region could be very thin (perhaps of the order of a few rg of MeV protons). An agreement with observations could still be achieved in that case by reducing the FLRW coefficient, which is essentially a free parameter in the model as it cannot be measured directly. We recognize that a more elaborate model could be constructed for the scattering in the heliosheath, perhaps based on an anisotropic turbulence concept with an excess of fluctuations with wavevectors perpendicular to the mean field. Irrespective to this, the authors believe that the basic premise of the model (gyrating particle escape into the LISM medium at a magnetic shear interface between a weakly turbulent and a laminar regions) adequately describes the fundamental physics of particle transport across the newly discovered boundary.

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Figure 4. Simulated pitch-angle distributions of HEPs in the heliosheath (x = −0.05 AU, solid line) and the LISM (x = 0.025 AU, dashed line, and x = 0.075 AU, dot-dashed line). The intensity is normalized to unity at the left boundary of the simulation. The inset shows a “sector” diagram illustrating a simulated response of a particle detector measuring intensity in the RT plane, at x = 0.05 AU. (A color version of this figure is available in the online journal.)

FLRW facilitates their cross-field transport. The difference in penetration depth is of the order of 0.2 AU, which is consistent with the time the gyrating ions were observed past the heliocliff, 25 days × V1 = 0.25 AU. This result relies on the existence of (weak) perpendicular diffusion in the LISM; without it gyrating ions would only be able to travel a distance ∼2rg farther than the streaming ions (this was confirmed by performing the simulations without the FLRW term). Figure 4 plots the simulated HEP pitch-angle distributions at three different positions relative to the “cliff”: on the heliosheath side and at two locations is the LISM. The initially isotropic ion population becomes highly anisotropic beyond the boundary as space becomes depleted of μ = ±1 particles (large secondorder anisotropy). Some μ = 0 particles have also scattered and escaped from the system, so that the total intensity is significantly reduced. The inset of Figure 4 shows a model scan plane intensity diagram binned into eight 45◦ sectors to simulate the low energy charged particle (LECP) instrument response. The distribution in this plane is consistent with Voyager 1 observations of a flattened (pancake or double loss cone) pitch-angle ion distribution beyond the boundary (Krimigis et al. 2013). In addition to second-order anisotropy, Voyager 1 measured some preferential streaming in the −T direction (first-order anisotropy) on the interstellar side of the boundary. This could develop if the distances from the spacecraft to the escape boundaries in the +x and −x directions are different, or if another effect, such as magnetic mirroring, prevents particle escape in one of the directions along B. In our simulations the escape boundary was set 45 AU from the detection point in the +T direction (μ = −1) and at 70 − 45 = 25 AU in the −T direction (μ = 1). As expected, more particles are streaming toward the closer escape boundary, which is also evident from the figure and the inset.

This work was supported, in part, by NASA grants NNX10AE46G, NNX11AO64G, NNX12AH44G, and NNX13AF99G, by NSF grant AGS-0955700, and a cooperative agreement with NASA Marshall Space Flight Center. V.F. and J.R.J. acknowledge support from the International Space Science Institute in Bern in the framework of the Heliopause team meeting. The authors would like to thank R. B. Decker for making Voyager 1 LECP data available, and J. Heerikhuisen, N. V. Pogorelov, J. F. Drake, and G. P. Zank for valuable theory discussions. 4

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