The Astrophysical Journal, 738:29 (9pp), 2011 September 1 doi:10.1088/0004-637X/738/1/29C© 2011. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

AN ESTIMATE OF THE NEARBY INTERSTELLAR MAGNETIC FIELD USING NEUTRAL ATOMS

J. Heerikhuisen and N. V. Pogorelov

Department of Physics and Center for Space Physics and Aeronomic Research, University of Alabama, Huntsville, AL 35899, USA; jacob.heerikhuisen@uah.eduReceived 2011 January 6; accepted 2011 June 7; published 2011 August 10

ABSTRACT

The strength and orientation of the magnetic field in the nearby interstellar medium have remained elusive, despitecontinual improvements in observations and models. Data from NASA’s Voyager mission and the Solar WindANisotropies (SWAN) experiment on board Solar and Heliospheric Observatory (SOHO) have placed observationalconstraints on the magnetic field, and the more recent Interstellar Boundary Explorer (IBEX) data appear to alsobear an imprint of the interstellar magnetic field (ISMF). In this paper, we combine computational models ofthe heliosphere with data from Voyager, SOHO/SWAN, and IBEX to estimate both the strength and direction ofthe nearby ISMF. On the basis of our simulations, we find that a field strength of 2–3 μG pointing from eclipticcoordinates (220–224, 39–44), combined with an interstellar hydrogen density of ∼0.15 cm−3, produces resultsmost consistent with observations.

Key words: ISM: magnetic fields – Sun: heliosphere

Online-only material: color figures

1. INTRODUCTION

The study of the interaction between the solar wind (SW) andthe local interstellar medium (LISM) grew out of early works bythe likes of Parker (1961), Axford et al. (1963), Holzer (1972),Baranov et al. (1971), Fahr (1974), and Wallis (1975). The SWflow expands into the partially ionized plasma of the LISM,whereupon the relative motion of the Sun and the LISM resultsin a teardrop shaped heliosphere with a well-defined “nose”and “tail.” The SW and the ionized component of the LISMare separated by a tangential discontinuity called the heliopause(HP). Before the SW can be turned toward the tail by the HP, itmust become subsonic at the termination shock (TS). The LISMflow is also supersonic, but for strong interstellar magnetic field(ISMF) the flow becomes sub-fast magnetosonic preventing abow shock BS from forming. While the SW magnetic fieldis dynamically of little importance in the supersonic SW, theISMF plays an important role in shaping the region of space justoutside the HP. Various LISM models suggest the magnetic fieldstrength is a few micro-Gauss (see a review by Frisch 2000).At the higher end of this range of field strengths, the low fast-magnetosonic Mach number in the LISM results in the absenceof a fast-mode bow shock. Parker (1961) also considers an evenmore extreme limit, where the ISMF pressure dominates overthe dynamic pressure and “squashes” the heliosphere to suchan extent that there is no clear nose or tail. This “magneticpressure dominated” regime has recently been invoked as apossible explanation for the CASSINI/Ion and Neutral Camera(INCA) (Krimigis et al. 2009) data. McComas et al. (2009a), onthe other hand, suggest that the Interstellar Boundary Explorer(IBEX) data point more to a situation where the dynamic andmagnetic pressures on the HP are approximately equal.

The direction and strength of the ISMF, BLISM, are two ofthe key unknown LISM quantities. We do know from three-dimensional simulations, however, that the way the magneticfield drapes over the HP creates north–south and east–westasymmetries in the distance to both the HP and TS (Ratkiewiczet al. 1998; Pogorelov & Matsuda 1998; Pogorelov et al. 2004;Izmodenov et al. 2005; Opher et al. 2006; Pogorelov et al.

2008, 2009b). One of the restrictions placed on BLISM throughobservations comes from Solar and Heliospheric Observatory(SOHO)/Solar Wind ANisotropies (SWAN) data. By lookingat Lyα backscatter from interstellar hydrogen atoms in the SW,it is possible to deduce the direction in which LISM hydrogentravels in the inner heliosphere. This hydrogen has been filteredby the outer heliosphere, and so its direction is not simply that ofthe LISM inflow as inferred from helium measurements (sincehelium interacts only weakly with the heliosphere). The factthat the LISM hydrogen stream is on average offset from thehelium stream caused Lallement et al. (2005) to suggest thatBLISM belongs to the plane, the so-called hydrogen deflectionplane (HDP), mapped out by these two streams. Computationalmodels confirm that the hydrogen stream is deflected from thehelium stream approximately in the plane that contains the ISMFand velocity vectors (Izmodenov et al. 2005; Pogorelov et al.2008), though simulations generally predict smaller deflectionsthan suggested by the data. Other clues to BLISM come fromthe Voyager 1 and 2 crossings of the TS in 2004 and 2008,respectively (Stone et al. 2005, 2008). A difference of 10 AUin the distance to the TS between those locations and betweenthose times suggests an asymmetry in the heliosphere causedby BLISM exerting more pressure on one side of the HP than theother. Computational models back up this claim, whose effect issomewhat reduced when neutrals are included (Pogorelov et al.2007, 2009b; Izmodenov et al. 2009). Of course, BLISM is onlypartly responsible for the asymmetry in the Voyager crossings,time-dependent effects related to the SW dynamic pressurelikely also caused the TS to move inward during this time(McComas et al. 2003; Richardson et al. 2008a). An approachbased on considering the average flow velocities observed byVoyager 2 after crossing the TS suggests that BLISM may in factbe directed out of the HDP (Opher et al. 2009). While thesethree approaches do not yield a consensus on the directionand strength of BLISM, it should be noted that the Voyagermeasurements are subject to highly temporal fluctuations, whilemost computational models have so far assumed a steady-state(some recent exceptions are Pogorelov et al. 2009a, 2010, andPogorelov et al. 2011). This suggests that the HDP orientation

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of BLISM predicted using SOHO/SWAN data is the more robustmeasure since it is not subject to the short timescale fluctuationsof the SW.

The first all-sky maps from NASA’s IBEX mission (McComaset al. 2009b) were dominated by an unexpected “ribbon” ofenhanced energetic neutral atom (ENA) flux. The only clue tothe ribbon’s origin was that it appeared to be related to locationsjust outside the HP where the ISMF is oriented perpendicular tothe line of sight (Pogorelov et al. 2009b). One of the six ribbonmechanisms postulated in McComas et al. (2009a) involvesso-called secondary ENAs which are created outside the HPfrom pick-up ions (PUIs) which were “primary” ENAs thatescaped the heliosphere. This idea was implemented into a three-dimensional simulation of the heliosphere by Heerikhuisen et al.(2010b), who demonstrated that a ribbon forms with propertiessimilar to those of the ribbon in the IBEX data, provided anassumption on the scattering of PUIs was made. This modelassumes that PUIs which are picked up by the LISM plasma atan angle close to 90 deg to the magnetic field will not scatter toan isotropic shell distribution before they capture an electronfrom a passing H-atom and become secondary ENAs. Thisassumption was tested by Florinski et al. (2010), who used a one-dimensional “hybrid” (particle proton, fluid electron) simulationto show that the turbulence generated by PUIs scatters these ontoa shell on a timescale of a few days. This is far shorter than thetimescale of years on which re-neutralization occurs. One keyfactor not included in the Florinski et al. (2010) simulation,however, is the transfer of turbulence from parallel modeswhich scatter PUIs to perpendicular modes which do not. It ispossible, for example, that the parallel turbulence generated bythe PUIs is transferred to perpendicular modes on timescalesshorter than a day, and hence very little scattering wouldoccur. Testing this will require a three-dimensional simulationof PUI scattering. Another recent paper (Gamayunov et al.2010) employed a quasi-linear analysis of the PUI distributionfunction and showed that under some conditions, backgroundLISM turbulence could couple to the turbulence generated bythe PUIs themselves and prevent the PUI distribution frombecoming isotropic. Overall, the secondary ENA mechanismpredicts a ribbon with many of the quantitative features seenin the IBEX data: shape, thickness, relative intensity along theribbon, and spectrum in the ribbon (Heerikhuisen et al. 2010b).It should be noted, however, that the simulated ribbon tends tobe brightest in the southwest part of the ribbon, while the ribbonin the IBEX data is generally brightest at high latitudes, withthe formation of a bright “knot” in the northern hemisphere atenergies above 1 keV. While this effect is not reproduced in thebasic version of our mechanism used in this paper, we do expectsimilar features to develop once we include time-dependenteffects related to the solar cycle (Pogorelov et al. 2011), whichwould introduce primary ENAs from the supersonic SW withenergies of several keV at high latitudes. Since the secondaryENA mechanism involves the magnetic field outside the HP, itprovides a new way of estimating BLISM. The same mechanismwas investigated by Chalov et al. (2010) in the scatter-free limit,though no quantitative predictions were made.

In the following sections, we use the ribbon mechanismimplemented by Heerikhuisen et al. (2010b) to test a variety ofLISM boundary conditions, with particular emphasis on tryingto determine the strength and orientation of BLISM by matchingthe simulated ribbon to the IBEX data. Additionally, we willquantify the amount and direction that hydrogen in the innerheliosphere has deflected from the LISM boundary condition.

2. HOW THE MODEL RIBBON CHANGES WITHLISM PARAMETERS

The ribbon model we employ in the our simulations(Heerikhuisen et al. 2010b) is based on the idea that “primary”ENAs born in the supersonic and subsonic SW exit the helio-sphere and create PUIs in the nearby LISM. These PUIs can bere-neutralized after a charge-exchange collision with a LISMH-atom, resulting in a “secondary” ENA that has the same en-ergy as the primary ENA. The direction of the secondary ENA’svelocity depends on the phase-space filled by the parent PUI.The assumption in our model is that the PUI’s velocity is re-stricted to a “partial shell” oriented perpendicular to the ambientmagnetic field. In our approximation, the area of the shell de-pends on the angle the primary ENA makes with the magneticfield, such that angles close to perpendicular result in a verynarrow shell, while pick-up close to parallel results in a nearlyisotropic shell distribution (Heerikhuisen et al. 2010a). Due tothis choice of isotropization, locations where we have a narrowshell whose phase space is aligned with a line of sight from theinner heliosphere will produce a stronger secondary ENA signalthan other locations. Hence we expect the ribbon ENAs to comefrom locations in nearby interstellar space, where the ambientmagnetic field is close to perpendicular to our line of sight (i.e.,B · r � 0). We should point out that apart from the partial shellassumption, our ribbon model contains no parameters, and theribbon we simulate is a direct result of secondary ENA’s beinggenerated in the outer heliosheath from PUI’s that in turn werecreated by primary ENA’s. As discussed in the introduction, thevalidity of the assumption made in this model regarding a partialshell distribution for PUIs is still an open question.

In this section, we investigate the effects of changing either thedensity or the magnetic field strength in the LISM, while keepingall other conditions, including the magnetic field orientation,fixed. Since in this paper we are mainly interested in the ribbon,which in our model is driven by physics outside the heliosphere,we assume fairly simple boundary conditions at the innerboundary surrounding the Sun. These are vE = 450 km s−1,nE = 7.3 cm−3, TE = 51,100 K, and the radial component ofthe magnetic field BE = 37.5 μG. On the outer boundary (a1200 AU sphere surrounding the Sun), in the LISM, we assumevelocity of 26.4 km s−1 relative to the Sun coming from 5 degabove the ecliptic plane and a temperature of 6527 K. Thesevalues fall within the range deduced by Witte (2004), based onobservations using the ULYSSES/GAS instrument. The otherLISM boundary conditions vary between runs and are listedwith each result and in Table 1. We have also run simulationsbased on a non-uniform SW boundary condition, but since theshape of the resulting ribbon is very similar to one obtainedusing a uniform SW, we do not discuss those results here.

Our simulations are based on a numerical code that couplesan MHD description of ions (Pogorelov et al. 2004), with akinetic description of neutral hydrogen (Heerikhuisen et al.2006, 2008; Pogorelov et al. 2008, 2009b). Our model employsa Lorentzian (or “κ”) distribution for the total population ofions in the inner heliosheath. For the simulations in this paper,we have used κ = 1.63 throughout this region, which is inapproximate agreement with the power-law slope observedfor ENA measurements from the heliospheric nose and polardirections, while the observational data suggest a steeper slopein the heliotail direction (McComas et al. 2009a; Funstenet al. 2009). Future versions of our model will include avariable κ value to better match these observations. The use

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Table 1Summary of Parameters Used in our Simulations, Along with Computed Quantities that can be Compared to Observational Data

np (cm−3) nH (cm−3) |B| (μG) Direction B Average H–He nH (cm−3)Points from Deflection (deg) at TS in Nose

0.04 0.19 3 (224,41) 2.1 0.1050.05 0.16 3 (224,41) 2.1 0.0950.06 0.15 3 (224,41) 2.4 0.0900.07 0.15 3 (224,41) 2.6 0.0860.06 0.15 1.5 (224,39) 1.1 0.0850.06 0.15 2 (222,39) 1.5 0.0880.06 0.15 2.5 (224,41) 1.9 0.0880.06 0.15 3 (220,44) 2.1 0.0900.06 0.15 4 (211,48) 1.8 0.0950.06 0.15 5 (207,51) 1.1 0.100

Note. The first four columns represent the LISM boundary conditions—ion and neutral densities, magnetic field strength anddirection (in ecliptic coordinates)—used for each simulation we considered. Column five shows the corresponding computedaverage deflection between the hydrogen and helium streams in the supersonic SW towards the nose of the heliosphere. The lastcolumn shows the density of neutral hydrogen obtained in each simulation at the TS in the nose direction.

of a κ-distribution is an attempt to include PUIs in the parentpopulation for ENAs, since the Maxwellian core of the κ-distribution represents the “core” SW, and the power-law tail actsas a proxy for PUIs. The net effect is an increase in the numberof ENAs at keV energies, with a spectrum in the heliosphericnose direction that matches the IBEX data reasonably well(Heerikhuisen et al. 2008). A more detailed formalism for theproton distribution function in the inner heliosheath was recentlydevised by Zank et al. (2010). Those authors demonstratedthat by incorporating some of the micro-physics of how ionsinteract with the TS, a multi-component distribution can bederived that in many ways resembles a κ-distribution for energyrange relevant to IBEX. The cross-section we employ is givenby Lindsay & Stebbings (2005).

Finally we note that computational methods for modeling theheliosphere are not without error. One of the possible causesfor error is due to numerical diffusion of magnetic field acrossthe HP. For the ribbon mechanism we employ that most of theribbon ENAs are generated some distance away from the HP(∼100 AU, see Figure 3(a)), where spurious diffusion will bemuch smaller than at the discontinuity itself. To test this we rantwo calculations with the only difference being a reversal of theISMF vector. Since we keep the SW magnetic field the samefor these runs, diffusion across the HP will happen in differentlocations, potentially altering the solution to such an extent thatthe ribbon moves. However, the ribbons of the two simulationsare indistinguishable, which suggests that magnetic diffusion orreconnection across the HP, due to numerical effects, does notimpact our findings.

2.1. Variations in Interstellar Density

First we perform a number of runs with varying ion andneutral densities in the LISM. For all these runs we havechosen the LISM magnetic field to originate from the eclipticcoordinates (224, 41), which is the same orientation used inHeerikhuisen et al. (2010b). Here, we choose four combinationsof densities that result in hydrogen densities at the TS in therange 0.086 < nH(TS) < 0.105 cm−3. These values are closeto the value of ∼0.9 inferred from measurements in the innerheliosphere (Richardson et al. 2008b; Bzowski et al. 2009).Table 1 summarizes the LISM boundary conditions used in allruns, along with hydrogen densities at the TS for each. For the“best guess” BLISM runs of Section 3, we use np = 0.06 cm−3

and nH = 0.15 cm−3, which also gives a hydrogen density atthe TS consistent with the value predicted by observations.

Figure 1 shows that the simulated ribbon is fairly insensitiveto the choice of hydrogen and proton densities in the LISM.A more careful inspection shows that increasing proton density(decreasing hydrogen density) moves the ribbon more northerlyin the nose, and pulls the ribbon to higher latitudes in thenorthwest. This can be understood in terms of the relativestrengths of the dynamic and magnetic pressures, as discussedin Section 2.3. Generally, these results suggest that the ribbonis only weakly sensitive to changes in the LISM density.

2.2. Variations in Interstellar Magnetic Field Strength

We now look at simulations for six different ISMF strengths,while keeping the LISM densities and magnetic field orientationconstant. The strength of the ISMF is poorly constrained.Models of the interstellar medium suggest it should be afew micro-Gauss (Frisch 2000). In order to account for the10 AU asymmetry in TS distance observed by the Voyagers,global models of the heliosphere imply that |BLISM| > 4 μG(Pogorelov et al. 2006; Izmodenov et al. 2009; Opher et al.2009), if we make the somewhat unreasonable assumption ofa steady-state heliosphere. Richardson et al. (2008a) suggestthat the average asymmetry is more like 7 AU, based on atime-dependent two-dimensional MHD simulation. Washimiet al. (2007) showed, on the basis of a time-dependent three-dimensional simulation of the SW–LISM interaction withoutneutrals, that the average asymmetry could be as little as 3or 4 AU, while still having a difference of 10 AU in thecrossing distances of the two Voyager spacecraft. So while anasymmetry, caused by the pressure of BLISM on the HP, almostcertainly exists, the complicated dynamics of the SW makeit difficult to estimate average asymmetry and hence the fieldstrength required to produce it. Based on these considerations,we choose six magnetic field strengths from 1.5 to 5 μG. Thisrange of values is also consistent with recent simulations byMitchell et al. (2009) of the 2–3 kHz radio emissions observedby the Voyagers, where |BLISM| � 2 μG is required for theirmechanism to work.

Figure 2 shows simulated ENA maps for a range of ISMFstrengths, while keeping all other boundary conditions fixed.There is a general trend that as the field strength is increased,the ribbon moves more southerly in the nose and more westerly

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(a) (b)

(c) (d)

Figure 1. All-sky maps of ENA flux (cm−2 s−1 sr−1 keV−1) at 1.1 keV for BLISM = 3 μG oriented from ecliptic coordinates (224, 41) and for LISM densities:np = 0.04, nH = 0.19 (a); np = 0.05, nH = 0.16 (b); np = 0.06, nH = 0.15 (c); np = 0.07, nH = 0.15 (d). The black line on the maps represents a fit to the ribbonin the IBEX data (Heerikhuisen et al. 2010b). The all-sky maps are shown in a Mollweide projection with the interstellar flow coming from the center of the plot, andthe heliotail at the far left and right. The white fiducial lines show ecliptic latitude and longitude at 30 deg intervals.

(A color version of this figure is available in the online journal.)

(a) (b)

(c) (d)

(f)(e)

Figure 2. All-sky maps of ENA flux (cm−2 s−1 sr−1 keV−1) at 1.1 keV for the LISM parameters np = 0.06, nH = 0.15, with BLISM oriented from ecliptic coordinates(224, 41) with the following field strengths: (a) 1.5 μG, (b) 2 μG, (c) 2.5 μG, (d) 3 μG, (e) 4 μG, (f) 5 μG. The black line on the maps represents a fit to the ribbon inthe IBEX data (Heerikhuisen et al. 2010b).

(A color version of this figure is available in the online journal.)

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(a) (b)

Figure 3. (a) Average distance to the ENA emission site for all OHS ENAs in the simulation shown in Figure 1(b) with energies greater than 0.5 keV. (b) Projectionsonto an all-sky map of the location of B · r = 0 measured 100 AU beyond the HP for the six simulations shown in Figure 2. The colored lines correspond to thestrength of the ISMF in the following way: blue 1.5 μG, magenta 2 μG, green 2.5 μG, orange 3 μG, cyan 4 μG, red 5 μG. The dashed line represents BLISM · r = 0,the great circle in the sky created by the plane that intersects the Sun perpendicular to the magnetic field vector of the pristine LISM.

(A color version of this figure is available in the online journal.)

in the ecliptic. The ribbon also appears to become narrower andbrighter for high magnetic field strengths. These features canbe understood in terms of the relative strengths of the dynamicand magnetic pressures, which we discuss in Section 2.3. Ingeneral though, it is clear that the magnetic field strength playsan important role in determining the width and location of theribbon, under the assumptions of our model.

2.3. Pressure Changes Caused by Changing Density andField Strength

The trends seen in Figures 1 and 2 are likely a consequence ofchanges in the relative magnitudes of the dynamic and magneticpressures just outside the HP. As the pressure increases due toincreased density or magnetic field strength, the shape of theHP and the relative effectiveness of magnetic draping over theHP changes. These changes alter the shape of the B · r = 0surface, and consequently move the ribbon generated in thesimulation.

In Figure 3(a), we show the average distance from the Sun tothe location in the outer heliosheath where the ENA emission iscoming from in our simulation, for the 3 μG case with magneticfield oriented from ecliptic coordinates (224, 41). We haveoverplotted the same fit to the IBEX data shown in Figures 1and 2, and comparison with Figures 1(b) and 2(d) shows that thesimulated ribbon is just to the south and west of the best-fit line.Given that the HP is located about 150 AU from the Sun in theribbon direction near the nose, this shows that in our simulationmost of the emission in the brightest parts of the ribbon comefrom 50 to 100 AU beyond the HP. This distance is less thanthe mean free path of primary ENAs exiting the heliosphere,mainly because emission from farther away will appear morediffuse, and also because ENAs created farther into the LISMhave a lower probability of surviving the trip to IBEX withoutbeing ionized by the relatively high LISM proton density. Thisrelationship between ribbon brightness and the distance to ENAsource also explains why the simulated ribbon becomes fainteraway from the heliospheric nose.

Figure 3(b) shows the location on an all-sky map of B · r = 0measured 100 AU beyond the HP, which Figure 3(a) suggestsis approximately the location of most of the ribbon emissionin our simulations. For |BLISM| < 3 μG, the location ofB · r = 0 is roughly the same, but that for |BLISM| = 4 μGand |BLISM| = 5 μG the increased magnetic pressure startsto significantly alter the structure of the outer heliosheath and

V LISM

60 N

30 N

ecliptic

180

(254.5,5)

240 210

μ1.5 G

μ2.5 G

μ5 G

μ3 Gμ4 G

μ2 G

HDP (2005)

HDP (2010)

Figure 4. Red asterisks show the locations from which the BLISM originates forour “best guess” orientations for the field at 1.5, 2, 2.5, 3, 4, and 5 μG. Thesecorrespond to ecliptic coordinates: (224, 39), (222, 39), (224, 41), (220, 44),(211, 48) and (207, 51), respectively. The green and blue lines represent thepredicted plane containing BLISM and VLISM on the basis of the angle betweenthe observed hydrogen and helium flows for both the original (Lallement et al.2005) and revised (Lallement et al. 2010) analysis (see Section 3.1).

(A color version of this figure is available in the online journal.)

B · r = 0 moves southwest. In fact, for 5 μG the ribbon in thenose of the heliosphere has almost converged to the limiting caseof BLISM · r = 0. This suggests that the surface B · r = 0, whichbecomes a plane perpendicular to BLISM at large distances, issignificantly distorted in the region where most ribbon ENAsare generated only for |BLISM| < 5 μG. For |BLISM| � 5 μG,most ribbon ENAs are created in a region that resembles theasymptotic great circle in the sky given by BLISM · r = 0. Sincethe thickness of the ribbon is in part due to the warping on theB · r = 0 surface, the latter strong ISMF case also results in amuch narrower ribbon.

3. BEST GUESS MAGNETIC FIELD ORIENTATION AS AFUNCTION OF FIELD STRENGTH

In this section, we look at six LISM magnetic field strengthsand vary the orientation of the field so that the model ribbon bestmatches the IBEX data. Figure 4 shows these field orientationson an all-sky map, along with two estimates of the HDP from

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(a) (b)

(c) (d)

(e) (f)

Figure 5. All-sky maps of ENA flux (cm−2 s−1 sr−1 keV−1) at 1.1 keV for LISM conditions np = 0.06, nH = 0.15, with the following field strengths (in μG) (fromtop-left to bottom-right): 1.5, 2, 2.5, 3, 4, 5; and corresponding BLISM oriented from ecliptic coordinates: (224, 39), (222, 39), (224, 41), (220, 44), (211, 48), (207,51). The black line on the maps represents a fit to the ribbon in the IBEX data (Heerikhuisen et al. 2010b).

(A color version of this figure is available in the online journal.)

Lallement et al. (2005) and Lallement et al. (2010). Since theseplanes are formed by the observed hydrogen velocity vectorin the supersonic SW, combined with the known helium flowdirection (254.7, 5.2), both planes pass through the “nose” ofthe heliosphere. All other boundary conditions are held fixed,with nH = 0.15 cm−3 and np = 0.06 cm−3 in the LISM.

Figure 5 shows six all-sky maps where we have chosen theorientation of the ISMF to best match the ribbon’s crossing of theecliptic (in the west) and meridional (in the south) planes. Theseplots show similar trends to those of Figure 2, with the ribbonwidth decreasing and intensity increasing as the ISMF strengthincreases. Additionally, while all six plots show reasonably goodagreement with the data west and south of the nose (sincethis was the criterion by which we chose the magnetic fieldorientation), for strong ISMF the northwest part of the ribbonagrees less well with the shape of the ribbon in the data. Thisis because, as mentioned in Section 2.3, for large field strengthsthe ribbon becomes more like a great circle in the sky, whileribbon in the IBEX data has a radius close to 70 deg (Funstenet al. 2009). The best matches between the model and the IBEXdata are for |BLISM| < 3 μG, so the shape and thickness of theribbon tend to rule out a strong LISM magnetic field, under theassumptions of our model.

3.1. The Deflection of the Flow of Interstellar Hydrogen fromthe Flow of Interstellar Helium

As interstellar hydrogen drifts into the heliosphere, some ofthe atoms charge-exchange in the disturbed plasma flow just

upstream of the HP. This process removes particles from theprimary distribution that exists in the LISM and creates a sec-ondary interstellar population of H-atoms that have velocityand thermal properties that resemble the slower, hotter plasmaof the outer heliosheath. Many of these secondary interstellarneutrals are deflected around the heliosphere, but some havevelocities that bring them into the inner heliosphere. This pro-cess both creates a new population of interstellar H-atoms andremoves particles from the distribution of LISM H-atoms thatenters the heliosphere. If the structure of the outer heliosphereis sufficiently asymmetric, this process will preferentially re-move certain parts of the LISM distribution and replace theseby slower hotter H-atoms created in the outer heliosheath. Theresult is a shift in the bulk velocity that manifests itself as anapparent deflection from the pristine LISM flow vector given byhelium atoms, which interact only very weakly with the helio-sphere. The apparent deflection between LISM hydrogen andhelium streams, as determined by SOHO/SWAN (Lallementet al. 2005) and ULYSSES/GAS (Witte 2004), led Lallementet al. (2005) to suggest that the asymmetry of the heliosphereis maximal in the plane of deflection, the so-called hydrogendeflection plane (HDP), and further that, since the ISMF is thedominant source of asymmetry, BLISM belongs to the HDP. Asstated in the introduction, three-dimensional models of the he-liosphere generally support this view.

In this section, we investigate the deflection of hydrogen fromits direction VLISM at the LISM boundary of our simulation. Toquantify the deflection we plot two-dimensional histograms of

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Figure 6. Two-dimensional distributions of velocity of neutral Hydrogen, in the LISM direction of the supersonic solar wind, with deflections in the HDP shownvertically and deflection perpendicular to the HDP plane shown horizontally. These are for the six “best guess” magnetic field orientations shown in Figure 5, withfield strengths (in μG) 1.5, 2, 2.5 (top, left to right) and 3, 4, 5 (bottom, left to right). The colors represent counts of computational particles within the volume of theSW in the LISM direction (as described in the text) on a normalized scale.

(A color version of this figure is available in the online journal.)

the direction in which H-atoms in the simulation travel, relativeto VLISM. As in Pogorelov et al. (2008), we collect particlevelocities from our Monte Carlo code in a 45 deg cone, withits open end pointing at the source of the LISM flow, fromthe Sun to 80 AU. We then collect statistics on the angleeach particle’s velocity makes with respect to VLISM both inthe HDP and perpendicular to it. Distributions of deflectionangles for the six “best guess” orientations of BLISM describedin Section 3 are plotted in Figure 6. These distributions showthat the smallest field strengths have the least deflection, aswould be expected given that the key driver for deflection is anasymmetric heliosphere caused by magnetic pressures on theHP. Surprisingly, however, the amount of deflection appears tomaximize around 3–4 μG, and then drops off slightly for 5 μG.In all cases, an average deflection of a few degrees is observedand occurs almost exclusively in the plane mapped out by BLISMand VLISM. Table 1 lists the average deflection observed in eachrun considered here.

The somewhat surprising result that the deflection for 5 μGis less than the deflection at 3 μG can be understood in terms ofthe disturbed region of LISM plasma just upstream of the HP.Figure 7 compares the plasma conditions along a radial line inthe LISM inflow direction from the HP to the LISM boundaryfor simulations with BLISM set to 2 μG, 3 μG, 4 μG, and 5 μG.When the magnetic field is weak, a bow shock forms at around250 AU beyond the HP, resulting in a significant increase inplasma density and a sudden decrease in plasma velocity. Atlarge values of BLISM, the bow shock disappears, the densityincrease becomes very small, and the velocity decrease is slower

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

distance beyond HP in AU

T/5x104K

ρ/0.1cm−3

−v/30km/s

2μG3μG4μG5μG

Figure 7. Plots of the plasma velocity, density, and temperature along a line inthe upwind LISM direction for interstellar magnetic field strengths of 2, 3, 4,and 5 μG. These quantities have been normalized to −30 km s−1, 0.1 cm−3,and 5 × 104 K. At low field strengths a bow shock is present, which allows theplasma to change significantly as it approaches the HP. As the field strengthincreases, this region get smeared over ever larger distances.

(A color version of this figure is available in the online journal.)

and starts at much larger distances from the HP. The temperaturegradient does not change much with increasing field strengthbecause it is mainly due to primary ENAs depositing energy

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The Astrophysical Journal, 738:29 (9pp), 2011 September 1 Heerikhuisen & Pogorelov

into this region. The result is a complicated interplay betweenthe level of asymmetry of the heliosphere, which increases withincreasing magnetic field strength, and the parameters of theplasma in the region just outside the HP. At low field strengths,for example, a clearly-defined region forms just outside theHP where secondary interstellar neutrals are created with abulk speed that is relatively slow compared to their thermalspeed. A relatively slow bulk speed allows secondary atomscreated at different latitudes, where the bulk flow is mainlyparallel to the HP, to still enter the heliosphere and be seen ashighly deflected H-atoms. Conversely, at high field strengths, theregion where most secondary interstellar atoms are created hasa relatively high bulk speed, compared to the thermal speed,so that secondary atoms tend to travel on trajectories thatare more parallel to the LISM bulk flow. However, when thefield strength is large, the disturbed region extends far outsidethe HP, and incoming atoms are deflected sooner. A morein depth investigation is required to determine the interplaybetween these effects, but clearly this combination of effects isresponsible for the somewhat surprising result that the level ofdeflection peaks for BLISM � 3–4 μG.

Recently Lallement et al. (2010) revised their earlier re-sults (Lallement et al. 2005), based on observational data fromSOHO/SWAN, of the deflection of the LISM hydrogen and he-lium streams, but the overall HDP orientation remains withinthe error bars of the previous result. As can be seen in Figure 4,all six of the magnetic field orientations that produce the bestagreement between the simulated and observed ribbon lie be-tween the two predictions for the HDP. Hence we conclude thatour model agrees with the orientation of the HDP predicted byobservations. However, quantitatively the observations predictan average deflection for interstellar hydrogen of about 4 deg,while the deflection obtained in the simulations shown here donot exceed about 2.5 deg. One possible explanation for this dis-crepancy is the different rates of Lyα absorption/emission byprimary and secondary LISM Hydrogen atoms. In our kineticsimulation, these two populations travel at different velocities,while the analysis of the SOHO/SWAN data models all hydro-gen as a single population. The different speeds and velocitydirections of primary and secondary LISM H-atoms mean thatthe radial velocities of these two populations are different, andhence they will experience different absorption/emission rates(see, for example, Bzowski 2008). While the deflection peakof secondary LISM H-atoms is around 5 deg (Pogorelov et al.2008), the much smaller deflection of primary atoms will dilutethis effect. So the way we currently compute deflection in themodel, based on density rather than absorption/emission rates,results only in qualitative, rather than quantitative, agreementwith observations of H-atom deflection.

4. DISCUSSION AND CONCLUSIONS

We have used our three-dimensional MHD-plasma/kinetic-neutral model of the interaction between the SW and the LISMto investigate how various scenarios for the conditions of theLISM affect one of the mechanisms proposed for the IBEXribbon. In addition, we also looked at the degree of deflectionbetween the LISM hydrogen and helium flows, and the level ofLISM hydrogen that enters the SW, for each of the scenarios.

We use the numerical model for the ribbon described inHeerikhuisen et al. (2010a, 2010b), in which ENAs in the ribbonare created from neutralized PUIs in the outer heliosheath.Due to the partial shell distribution we assume for PUIs inthis model, regions in the outer heliosheath where the ambient

ISMF is perpendicular to our line of sight (i.e., B · r = 0)will produce enhanced levels of ENA flux. We find that theshape of the surface B · r = 0 about 100 AU beyond the HP,where most ENA flux in the simulation originates, is a keyindicator of the shape of the ribbon. We also find that changesin the interstellar ion density result in only small changes in theshape and location of the ribbon produced by the simulation.Changing in the strength of the magnetic field in the simulation,for 1.5 � |BLISM| � 5 μG, has a larger effect, especially for|BLISM| > 3 μG. For strong magnetic fields, the increasedmagnetic pressure causes the B · r = 0 surface to approacha plane in the main ENA creation region, as opposed to themore warped surface that exists there for weaker fields. Thiseffect is responsible for a thinner ribbon that appears more likethe great circle in the sky, for strong ISMF. On the basis ofthis, our model tends to support conditions in the LISM where|BLISM| < 3 μG.

In addition to the shape of the ribbon, we also investigated thedeflection between the hydrogen and helium flows predicted byour simulations. None of the configurations we used here wereable to produce a deflection angle in the upwind supersonic SWas large as that implied by the combination of SOHO/SWAN andULYSSES/GAS experiments. Qualitatively, however, the agree-ment is good, with all cases producing an average deflection ofa few degrees almost exclusively in the plane containing BLISMand VLISM. There are a number of modeling details in obtainingthis deflection, both in our simulation and in the measurements,which may account for some or all of the discrepancy. We hopethat new results from the IBEX mission on the direction of theLISM Helium flow will help to further constrain the observa-tions.

In this paper, we did not investigate any aspects of timedependence related to secondary ENAs. Recent results fromIBEX (McComas et al. 2010) indicate that the location of theribbon is mostly stable over timescales of a year, while the fluxintensity in the north and south polar regions has decreased by10%–15%. These findings are largely in agreement with whatwe expect from the secondary ENA mechanism assumed inthis paper. Since we assume that the geometry of the ribbon isdriven by the orientation of the ISMF, we would expect onlysmall changes in the ribbon as pressure pulses from the solarcycle disturb the nearby LISM (Pogorelov et al. 2011). Wewould, however, expect changes in the flux at high latitudesover the solar cycle as primary ENAs are created in either fastor slow SW and eventually become secondary ENAs at thesame latitude. We are currently working on a time-dependentsimulation with corresponding time-dependent ENA maps.

In summary, our results suggest that in order to match theshape of the ribbon, the ISMF strength should be less than3 μG, with 2 μG pointing from ecliptic coordinates (222, 39)resulting in a ribbon obtained from the simulation that bestmatches the shape of the ribbon in the IBEX data. The deflectionof LISM hydrogen from helium in our model occurs withinthe hydrogen deflection plane inferred from observations. Thegreatest deflection occurs in the simulations for 2.5–4 μG,though the magnitude is only about half that inferred fromobservations. Along with these constraints on the magnetic field,we also find that we should have nH � 0.15 cm−3 in the LISM,in order to have nH � 0.09 cm−3 at the TS as required to matchobservations of PUIs in the inner heliosphere.

This work was supported by NASA grants NNX09AG63G,NNX09AG29G, NNX09AW44G, NNX09AG62G, and

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The Astrophysical Journal, 738:29 (9pp), 2011 September 1 Heerikhuisen & Pogorelov

NNX11AB48G. Calculations were performed on super-computers from NASA (SMD-09-1148), NSF’s Teragrid(MCA07S033), and ORNL (PSS003), as well as our local clus-ter “Bladerunner” at CSPAR/UAH.

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