Scatter-free pickup ions beyond the heliopause as a model for the Interstellar Boundary Explorer (IBEX) ribbon

The collision of the supersonic solar wind with the interstellar plasma flow results in formation of a complex interaction region or heliospheric interface. This region includes the termination and, possibly, bow shocks decelerating the solar wind (SW) and interstellar plasma, respectively, and the heliopause separating the two plasmas. The region of the heated SW behind the termination shock (TS) is known as the inner heliosheath, while the region behind the heliopause is called the outer heliosheath. The local interstellar medium (LISM) is a partly ionized medium consisting mainly of neutral atoms. It has become evident within recent years that the interstellar atoms have a pronounced effect on the global structure of the interface region and on the physical processes operating in the heliosphere. Apart from the fact that the position and shape of the TS and heliopause are significantly determined by the action of the atoms, they give rise to a specific hot population of pickup ions (PUIs). The first direct measurements of pickup helium (Möbius et al., 1985) and pickup hydrogen (Gloeckler et al., 1993) showed that the velocity distributions of the PUIs differ in significant ways from the velocity distributions of primary solar wind ions.

The first measurements of the IBEX (Interstellar Boundary Explorer) spacecraft (McComas et al., 2009; Fuselier et al., 2009; Funsten et al., 2009; Schwadron et al., 2009) show results that were entirely unexpected. The objective of the IBEX mission is to image the complex interaction between the local interstellar medium (LISM) and the outflowing solar wind by measuring the fluxes of energetic neutral atoms (ENAs) originating in the outer parts of our heliosphere and beyond. The first scan of the whole sky showed that maxima of ENA fluxes form a long ($\sim 250-300^{\circ}$) and narrow ribbon-like feature that was not predicted by any model prior to the IBEX observations.

The speed of the original interstellar atoms entering the heliosphere is $\sim$26.4 km/s, which for hydrogen atoms corresponds to the kinetic energy of about 3 eV. Some portion of the atoms experiences charge exchange with shock heated solar wind protons and PUIs, and a new population of energetic atoms, created as a result of this process, has the broad energy distribution extending over several keV. These ENAs represent the energy distributions of the parent charged particles and, therefore, when measured at the Earth’s orbit, can be used as a remote sensing of the ions in the interaction region.

Current theoretical models of the SW/LISM interaction fall into two categories: standard models which assume instantaneous assimilation of pickup ions in the SW (Baranov & Malama, 1993), and the compound or multi-component model (Malama et al., 2006) in the framework of which the pickup particles are considered as separate isotropic (in the solar wind rest frame) populations with their specific energy distributions. Izmodenov et al. (2009) presented an extension of the Malama et al. (2006) model by introducing a non-thermal population of pickup protons in the interstellar medium. These authors showed that the interstellar pickup protons form significant fluxes of ENAs dominating at energies above $\simeq 1$ keV. Although the multi-component models are more comprehensive, all of the current numerical models predict that the ENA fluxes have maxima near the upwind direction of the heliosphere and minima at the flanks, though, of course, the position of maxima can slightly deviate from the upwind direction due to effects of the interstellar magnetic field and solar wind asymmetry (e.g. Izmodenov et al. 2009).

McComas et al. (2009) presented six possible concepts for the formation of the ribbon observed by IBEX. Among these concepts was the idea that neutralized solar wind propagates out beyond the heliopause, becomes ionized, gyrates about interstellar magnetic field lines, and then charge exchanges again to become ENAs. Some of these ENAs move back in toward the Sun where they can be imaged by IBEX. The advantage of this mechanism is that it produces sharply peaked ENA emissions in directions roughly perpendicular to the interstellar magnetic field beyond the heliopause - the same alignment inferred by comparing the IBEX ribbon to an MHD simulation of the heliosphere (Schwadron et al., 2009). Another concept suggested by McComas et al. (2009) is that compression of the interstellar magnetic field beyond the heliopause may cause ions to align preferentially perpendicular to the interstellar magnetic field through conservation of the first adiabatic invariant and conservation of energy. This will also lead to a special orientation of peaked ENA emissions perpendicular to the interstellar magnetic field, and may help to explain both how the ribbon is formed and the even more surprising fine structure observed in it (McComas et al., 2009). The basic idea of secondary ENA generation of the IBEX ribbon was further examined by Heerikhuisen et al. (2010). These authors assumed that pickup protons in the outer heliosheath have and retain a partial shell distribution and that their re-neutralization is effectively instantaneous. This approach is significantly different from ours in this study since we solve consistently for the motion of pickup protons along magnetic field lines in the scatter-free limit, and thus include the motion of PUIs along the field line between their pickup and reneutralization.

The IBEX observations of an unexpected narrow ribbon of enhanced ENA fluxes raise fundamental questions about the origin of these particles. McComas et al. (2009) considered 6 possible sources of the ribbon including both sources inside and beyond the heliopause. The idea that the source lies in the outer heliosheath has at least two arguments. First, it was recently demonstrated in Izmodenov et al. (2009) that high-energy charged (pickup) protons can arise in the outer heliosheath due to charge exchange between interstellar protons and ENAs originated inside the heliopause. The energy distribution of the pickup protons has maximum near 1 keV and extends to energies of about 10 keV. Secondly, it was noted in McComas et al. (2009) and Schwadron et al. (2009) that the ribbon position, as seen from the Earth, coincides closely with the likely magnetic field direction located just beyond the heliopause, where, according to the recent MHD models, the interplanetary magnetic field is perpendicular to the heliocentric radial direction. The latter circumstance means that the interstellar magnetic field beyond the heliopause¹¹1Note that neutrals from the solar wind will be picked up over a huge range of distances from the heliopause ($\sim$1000 AU). plays a very important role in the formation of the ribbon. This role is twofold. On the one hand, the dynamical effect of the magnetic field essentially changes the shape of the heliosphere and the pattern of the plasma flows in the interface region (see, e.g. Izmodenov 2009). On the other hand, the magnetic field influences the transport of energetic charged particles (PUIs). While the primary interstellar plasma can be considered as a collisional medium and can be described in the framework of the MHD approach (Baranov, 2000), pickup protons originating in the outer heliosheath from heliospheric ENAs with energies of about 1 keV are collisionless. The more comprehensive global theoretical models of the heliospheric interface (Malama et al., 2006; Izmodenov et al., 2009), treated PUIs as a separate population of charged particles, assume that the velocity distributions of the PUIs in both inner and outer heliosheathes are isotropic (in the plasma rest frame). In other words, the isotropization time in these models is considered to be the smallest characteristic time. This is fairly good approximation for the supersonic solar wind and, possibly, for the inner heliosheath. However, in the interstellar medium this time is unknown. Here we consider the opposite limiting case when the scattering of PUIs in the outer heliosheath due to wave-particle interactions is completely ignored. We show that in this limiting case a feature arises from simulations that is qualitatively similar to the observed ENA ribbon, much as Heerikhuisen et al. (2010) found.

The population of pickup protons beyond the heliopause is the product of the charge exchange process between interstellar protons and heliospheric ENAs. The ENAs can be subdivided into two type. Type 1 originates in the supersonic solar wind – the so-called neutral solar wind. The energy of these atoms is about 1 keV. Type 2 originates in the inner heliosheath. The ENAs from this region have a broad energy distribution extending up to several tens of keV.

In the case of negligible scattering, which we consider here, the motion of a pickup proton in the outer heliosheath consists of gyration around a magnetic field line and free motion along this line. Figure 1 shows the spatial distribution of the interstellar magnetic field around the heliopause in the $\mathbf{BV}$ plane, where $\mathbf{B}$ is the magnetic field vector and $\mathbf{V}$ is the vector of the interstellar plasma velocity. The arrows show direction of the magnetic field, while the color indicates the magnetic field magnitude. The results presented here are obtained in the framework of the numerical three-dimensional model, with an MHD description of the plasma flows and a kinetic description of atoms (Izmodenov et al., 2005). The process of generating an ENA in the outer heliosheath is also shown schematically in Fig. 1. An energetic atom from the heliosphere (ENA1) penetrates into the outer heliosheath. Due to the charge exchange reaction between the ENA1 and an interstellar proton, a new pickup proton is ”born”. Once produced, it moves along a magnetic field line until a subsequent charge exchange results in the formation of a new energetic atom (ENA2). Under appropriate conditions this new ENA reaches the vicinity close to the Sun where it can be detected by IBEX.

In Fig. 1 one can see the domains of the increased magnetic field magnitude and domains where the magnitude reaches its minimal values. The transport of pickup protons in the outer heliosheath is substantially determined by these features. The regions of strong magnetic field can be considered as magnetic mirrors or stagnation regions where the motion of charged particles along field lines is decelerated and some portion of the particles is reflected. Figure 2 schematically illustrates the velocities of individual particles in the vicinity of the magnetic field maximum presented in Fig. 1. The maximum of the magnetic field (the magnetic mirror) is marked by the dotted line $\Lambda$. The velocity, $\mathbf{v}$, of a pickup proton originating from a heliospheric energetic atom can be obtained as the sum of velocity along the magnetic field line, $\mathbf{v}_{\parallel}$, and the gyration velocity, $\mathbf{v}_{\perp}$. In the case of no scattering, the magnetic moment of charged particles propagating in the slowly varying magnetic field is an adiabatic invariant; we use this simplification in our model. Furthermore, we ignore the effects of the drift motion of the pickup protons in the charge exchange process. This assumption is well-founded since the speeds of the drift motion are about 20 km s^-1, small compared with the proper speeds of the particles. Thus we have:

Equations (1) determine the motion of a pickup proton in the fixed magnetic field $\mathbf{B}$. Particles that move along the field line in the direction of increasing field magnitude (protons 1 and 2 in Fig. 2), $v_{\parallel}$ decreases, while $v_{\perp}$ increases due to conservation of the first adiabatic invariant and conservation of energy. For some of particles $v_{\parallel}$ may become zero in the region of the increased magnetic field and then these particles are reflected. This is magnetic mirror effect. In any case the parallel velocities of pickup protons near the maxima of the magnetic field magnitude are small, so that the pickup protons spend a comparatively long time in these regions. Therefore, these regions in the outer heliosheath are ideal places for production of ENAs. Note that, as it can be seen in Fig. 1, the radial component of the magnetic field at the maximum equals zero. In other words, the position of these regions coincides with the observed position of the IBEX ribbon in the sky.

Many magnetic mirrors can exist in the vicinity of the heliopause. In Fig. 1 we show two of them. In this way a charged particle can be trapped between two mirrors until the charge exchange reaction results in the formation of a ENA.

Results of our calculations of fluxes of energetic hydrogen atoms at 1 AU from the outer heliosheath at the energy about 1 keV are shown in Fig. 3. The numerical model makes use of the simplified guiding center approach for pickup protons, which is based on conservation of the magnetic moment and energy, and on the magnetic mirror effects. The interstellar pickup protons are calculated using the Monte Carlo method (a similar code used to simulate H atoms). The ENA fluxes are calculated directly in the Monte Carlo code. There is a significant difference between our model and the model by Heerikhuisen et al. (2010), which also attempts to explain the ribbon-like feature considering pickup protons in the case of weak scattering. However, they assume that pickup protons in the outer heliosheath have a partial shell distribution and that re-neutralization is instantaneous. In other words, the motion of the pickup protons along the magnetic field lines is not included.

The ribbon-like structure, similar the IBEX ribbon, is clearly seen in Fig. 3A. This figure shows the all-sky map of calculated differential ENA fluxes in the energy range from 0.83 to 1.39 keV in Mollweide projection in ecliptic coordinates. We note that our 3D model currently treats pickup and solar wind protons in the inner heliosheath as a single fluid with a Maxwellian velocity distribution (a 3D multi-component model is under development). Thus the dominant contribution to the fluxes in Fig. 3A is due to pickup protons, originating from heliospheric ENAs of type 1 (supersonic solar wind ENAs). Only this population is responsible for the appearance of a ribbon-like feature in our current simulations. Because fluxes of ENAs of type 2 from the inner heliosheath are low for the Maxwellian distribution of the mixture of pickup and solar wind protons, we artificially added background fluxes of 100 (cm² s sr keV)^-1. In a forthcoming study based on a 3D multi-component model, the background fluxes will be calculated self-consistently.

Our estimates show that the magnetic mirror effect producing multiple reflections of particles is not very important for pickup protons, originating from heliospheric ENAs of type 1. Taking this effect into account produces a 25% increase in ENA fluxes from the outer heliosheath. However, the mirroring can be very important for pickup protons, originating from heliospheric ENAs of type 2 (from the inner heliosheath). Figure 3B shows the calculated ratio of ENA fluxes from the outer heliosheath to ENA fluxes from the inner heliosheath for a Maxwellian distribution approximating the mixture of pickup and solar wind protons. The ENAs in the outer heliosheath arise as a result of charge exchange between interstellar atoms and pickup protons, which, in turn, are produced due to ionization of ENAs of type 2 from the inner heliosheath. Thus, ENAs of type 1 (supersonic solar wind ENAs) in Fig. 3B are excluded as parent atoms for pickup protons in the outer heliosheath. Since, in reality, the velocity distributions of protons (solar wind + pickup) in the inner heliosheath are far from Maxwellian and have substantial suprathermal tails, we consider the current results as only illustrative of the mirroring and accumulation effects of pickup protons in the nonuniform magnetic field, which is schematically shown in Fig. 2. Figure 3B shows that these effects result in the formation of a pronounced ribbon-like structure even with a Maxwellian velocity distribution in the inner heliosheath.

Here we have reported a new model without scattering, but including the effects of ion transport for the pickup protons generated in the region outside of the heliopause by charge exchange of the thermal interstellar protons and heliospheric ENAs. The results of the model yield a feature qualitatively similar to the IBEX ribbon. In future studies the results of simulations will be quantitatively compared to IBEX ENA observations. These further studies need to take into account ENAs for the inner heliosheath in proper kinetic way as it was done in Malama et al. (2006).

Acknowledgements. The work of S.C., D.A., Y.M. was supported in part by Rosnauka under goskontrakt 02.740.11.5025 and by the RFBR in the frames of the projects 08-02-91968-DFG, 10-01-00258, 10-02-01316 and the Program for Basic Researches of OEMMPU RAS. V.I. was supported by President Grant MD-3890.2009.2 and Dynastia Foundation. Work in the USA was supported by the IBEX mission, which is a part of NASA’s Explorer Program.