A Consistent Scenario for the IBEX Ribbon , Anisotropies in TeV Cosmic Rays , and the Local Interstellar Medium

The Interstellar Boundary Explorer (IBEX) observes enhanced ∼ keV energy Energetic Neutral Atoms (ENAs) from a narrow “ribbon” that stretches across the sky and appears to be centered on the direction of the local interstellar magnetic field. The Milagro collaboration, the Asγ collaboration and the IceCube observatory have made global maps of TeV cosmic rays. This paper provides links between these disparate observations. We develop a simple diffusive model of the propagation of cosmic rays and the associated cosmic ray anisotropy due to cosmic ray streaming against the local interstellar flow. We show that the local plasma and field conditions sampled by IBEX provide characteristics that consistently explain TeV cosmic ray anisotropies. These results support models that place the interstellar magnetic field direction near the center of the IBEX ribbon.


Introduction
The Interstellar Boundary Explorer Mission (IBEX), launched October 2008, has the objective to discover the global interaction between the solar wind and the local interstellar medium (McComas et al., 2009b).IBEX measures from ∼ 0.01 to ∼ 6 keV neutral atoms.In the ∼ keV energy range these particles, dubbed energetic neutral atoms (ENAs), are created predominantly from charge-exchange between neutral interstellar hydrogen and plasma protons in the solar wind and interstellar medium (McComas et al., 2009b(McComas et al., , 2011)).IBEX also makes measurements of lower en-ergy atoms from the interstellar medium including oxygen, helium and hydrogen atoms (Möbius et al., 2009).
The IBEX maps revealed the existence of a narrow ribbon of higher flux ENA emissions (McComas et al., 2009a;Funsten et al., 2009;Fuselier et al., 2009).The ribbon forms a roughly circular structure centered on (gal.long , gal.lat.b) ∼ (210.5 • ± 2.6 • , −57.1 • ± 1.0), with the center of the ribbon arc varying by ∼ 11 • over the measured energy range (Funsten et al., 2013).The center of the IBEX ribbon likely defines the direction of the local interstellar (LISM) magnetic field (Schwadron et al., 2009).However, until the physical mechanism for the ribbon is identified, it will be difficult to know how the interstellar field direction is related in Published by Copernicus Publications.N. A. Schwadron et al.: A Scenario for TeV Cosmic Ray Anisotropies, the IBEX Ribbon, and the LISM detail to the IBEX ribbon.A number of heliospheric models have been devised with the property that the ribbon may be highly sensitive to the interstellar magnetic field direction (Heerikhuisen et al., 2010(Heerikhuisen et al., , 2014;;Frisch et al., 2010;Ratkiewicz et al., 2012;Schwadron and McComas, 2013).For the purposes of this paper, we take the association of the IBEX ribbon center with the interstellar magnetic field direction as a partially-supported conjecture, and attempt to build a consistent scenario for the TeV cosmic ray anisotropies.Further, this study supplies a test for the association between the IBEX ribbon and the interstellar magnetic field.This paper also discusses another observational signature of this LISM magnetic field in TeV cosmic ray anisotropies (Schwadron et al., 2014).
There are numerous studies that complement the analysis presented here.While Schwadron et al. (2014) studied the global TeV anisotropy, there are also features in TeV cosmic ray maps that may be directly related to heliospheric structure.For example, Desiati and Lazarian (2013) considered the scenario where heliospheric magnetic instabilities (see Pogorelov et al., 2013) cause resonant scattering which may re-distribute the anisotropic cosmic rays in the 10's TeV energy scale.Such scattering processes may produce a complex angular structure in the arrival direction distribution of cosmic rays, that trace the heliospheric structure.Another complementary analysis is presented by Effenberger et al. (2012), which examines Galactic transport models for cosmic rays involving the diffusive motion of these particles in the interstellar medium.Because of the large-scale structure of the Galactic magnetic field, cosmic ray diffusion is found to be highly anisotropic.As a result, significant variability is found in the energy spectra at different positions along the Sun's Galactic orbit.Locally, polarized starlight and the center of the IBEX ribbon arc trace the same interstellar field directions to within uncertainties, suggesting that the ordering of the interstellar field persists over much larger spatial scales than that of the heliosphere (Frisch et al., 2015).These results highlight the need to account for anisotropic diffusion and the need for accurate Galactic magnetic field models.The work presented here offers new insights into local structure of the magnetic field in the interstellar medium.

Interstellar flow and field characteristics
Our understanding of the characteristics of the local interstellar medium (LISM) depend critically on a limited set of observations.Very recent analysis of Interstellar Boundary Explorer observations has allowed us to update estimates of LISM flow using observations of interstellar neutral (ISN) He (e.g., McComas et al., 2015b, a;Schwadron et al., 2015;Bzowski et al., 2015;Leonard et al., 2015;Möbius et al., 2015).A feature of the IBEX data is that the LIC physical characteristics are determined from a narrow tube in parameter space where the interstellar parameters are approx-imately degenerate.However, analysis resulting in a specific solution was associated with large uncertainties along the parameter tube.The more recent IBEX analyses have taken into account a much larger observational baseline, allowing derivation of specific solutions.In the Heliocentric coordinates, Schwadron et al. (2015) found an ISN flow gal.long.= 183.7 • ± 0.8 • , gal.lat.b = −15.0• ± 1.5 • , and speed 25.4 ± 1.1 km s −1 .This yields an angle of 80.4 • ± 5 • between the magnetic field and the velocity expressed with respect to the LSR velocity frame that describes our galactic neighborhood.This angle is 46.6 • ± 2.5 • for velocities given with respect to the Sun.
This yields an angle between that magnetic field and the flow velocity in the LSR frame of 80.4 • ± 5 • .This angle is 46.6 • ± 2.5 • in the Heliocentric reference frame.

Local Interstellar Structure
The heliosphere interacts with a clumpy decelerating interstellar flow that moves away from the Lower Centaurus-Crux (LCC) association near the origin of the Loop I superbubble (Frisch et al., 2011).The Sun is likely located within or near the Local Interstellar Cloud (LIC), less than 0.1 pc from the LIC edge (Wood et al., 2000;Frisch and Mueller, 2011).In the direction facing away from the galactic center, the closest cloud to the LIC is the "Blue Cloud" (BC, Lallement et al., 1994;Hébrard et al., 1999).The conditions for colliding clouds are observed within ∼ 10 pc (Linsky et al., 2008), and relative intercloud velocities are observed up to 50 km s −1 .Gry and Jenkins (2015) model the LIC kinematics by omitting outlying velocity components, and conclude that a shock front is driving into the cloud from the rough location of = 124 Figure 1 provides a rough picture of local interstellar structure near the edge of LIC and at the front of the Loop I superbubble.An interstellar magnetic field entrained in the inhomogeneous interstellar material associated with the expanding Loop I shell provides an explanation for inhomogeneities in the local interstellar magnetic field.Measurements by IBEX and Ulysses of interstellar He inside of the heliosphere provide the LIC velocity (e.g., McComas et al., 2015b, a;Schwadron et al., 2015;Bzowski et al., 2015;Leonard et al., 2015;Möbius et al., 2015) and velocities for 15 local clouds have been determined with the triangulation of the radial velocity component towards different stars behind the clouds (Redfield and Linsky, 2008).The Loop I superbubble shell is centered ≈ 78 pc at galactic coordinates of , b ≈ 346 • , 3 • (Wolleben, 2007).Pressure equilibrium between the gas and magnetic field in the LIC yield magnetic field strength of ∼ 2.7 µG (Slavin and Frisch, 2008).This value is similar to the ∼ 3 µG field strength derived from the globally distributed ENA fluxes (Schwadron et al., 2011).
The IBEX magnetic field direction should be apparent in the light of nearby stars that is linearly polarized in the inter- Nearby stars with polarizations that best agree with IBEX Interstellar Magnetic Field (ISMF) direction are plotted as red dots in Fig. 2; these data for stars within 90 • of the heliosphere nose give a magnetic field direction toward , b = 36 • , 49 • , ±16 • (Frisch et al., 2015).Figure 2 also shows stars with polarization data that do not sample the IBEX ISMF, either because the polarization vectors point in another direction or the polarizations are insignificant (small black dots).The similar locations of the polarizations that best-trace the ISMF direction and the LIC stars suggests that the interstellar magnetic field direction traced by the center of the IBEX ribbon corresponds to magnetic field lines within the LIC.
Taken together, these results suggest that the magnetic field inside the rim of the Loop I superbubble at the solar location is associated with the LIC and is consistent with the magnetic field that orders the IBEX Ribbon (also see Frisch et al., 2015).

Source of Large-scale anisotropy in TeV cosmic rays
We consider a TeV cosmic ray model for the large-scale anisotropy associated with streaming of cosmic rays against the LIC plasma flow.We stress that the anisotropy reported by the IceCube, the Milagro and Asγ collaborations have been corrected for Earth's motion.In practice, the TeV cosmic ray anisotropy maps represent the flux distribution in an inertial reference frame moving with the Sun.Because TeV cosmic rays have large gyro-radii, on the order of the size of the heliosphere, the TeV anisotropy maps are characterized by the cosmic ray velocity distribution incident from outside the heliosphere, and are affected by interactions of cosmic rays with the heliosphere (Schwadron et al., 2014).
We break up the calculation of the anisotropy into two pieces: (1) we use standard diffusion theory to determine the anisotropy incident from beyond the heliosphere; (2) we characterize the interaction of TeV cosmic rays with the heliosphere and solve for the resulting distortion of TeV cosmic ray anisotropies.Both of these calculations are worked in detail by Schwadron et al. (2014).In particular, it was shown the the heliosphere makes small changes to the global anisotropy at energies greater than 10 TeV.In the present work, we focus on the calculation of the global anisotropy incident on the global heliosphere.This calculation of the TeV cosmic ray anisotropy is an idealization that essentially neglects the presence of the heliosphere.The calculation is most important in showing how the local interstellar magnetic field and plasma conditions control the overall magnitude and an orientation of TeV cosmic ray anisotropies.
Standard diffusion theory (e.g., Forman and Gleeson, 1975) specifies the anisotropic component of the distribution in cosmic rays, The anisotropy is related to the streaming S and the isotropic component f 0 of the cosmic ray distribution, ξ = 3S/ (4π wf 0 ).The streaming is S = d wf , where w is the velocity of cosmic rays, and d indicates integration over solid-angle.The diffusion coefficients κ and κ ⊥ are the parallel and perpendicular to the magnetic field.The bulk velocity of the LISM plasma is u and the term g = ∇ ln(f 0 ) is the gradient of the isotropic density.The quantity g = ( b • g) b is the parallel component of the gradient, and g ⊥ is the perpendicular component.The term κ T = τ κ ⊥ is the off-diagonal diffusion coefficient, τ is the scattering time, and is the gyrofrequency.The Compton-Getting coefficient is defined as follows: Small black dots indicate stars with polarization data collected in the 21st century and within 90 • of the heliosphere nose (from Frisch et al., 2015).The red dots indicate the half of the group of significant polarization position angles that are in best agreement with the dominant ISMF direction near the Sun.Since the dominant ISMF is the same as the IBEX ISMF direction to within the uncertainties, the red dots also trace the extension of the IBEX magnetic field out into interstellar space for the sampled region.Comparisons between the LIC stars and the GCR asymmetries in Fig. 4 show that higher GCR fluxes tend to be associated with sightlines through the LIC, where the red dots show that the IBEX ISMF is also found.Locations are plotted in equatorial coordinates.
The full distribution function is related to the isotropic distribution and the anisotropy, (2) The unit vector p is in the direction of the cosmic ray momentum.Based on this formulation, a solution of the isotropic portion of distribution function, f 0 , including its spatial gradients allows specification of the anisotropy.The needed solution for the isotropic portion of the distribution function f 0 is found from the Parker transport equation, where K is the diffusion tensor.The differential energy spectrum is taken as power-law form of j ∝ T −2.7 where T is kinetic energy.In this case, the distribution function has the power-law, f 0 ∝ p −4.7 , and C = 4.7/3 = 1.6 The anisotropy can be obtained from Eq. ( 1) provided that we have information about the spatial dependence of the distribution function.We take the Local Standard of Rest (LSR) frame where the distribution is scattered toward isotropy.In this frame, we consider the relative plasma flow, u LSR , directed at angle θ relative to the magnetic field.As discussed in Sect. 1 and Table 1, we utilize the local determinations from IBEX for the interstellar plasma flow and the local magnetic field from the IBEX ribbon as proxies for these vectors on the larger parsec-scales needed needed to specify the cosmic ray anisotropy magnitude (Jokipii, 2005(Jokipii, , 2007)).Note that the local flow measured by IBEX, u LISM , is added to the solar apex motion, u , to determine the flow in the LSR frame, u LSR : The Parker transport equation is written as In this case, the x axis is directed along u LSR and κ = κ cos 2 θ + κ ⊥ sin 2 θ is the diffusion tensor projected along the direction of the plasma flow.The solution upstream is and f 0 ∝ constant downstream.Equation ( 6) is an approximation in the limit of 1-D uniform flow and a planar shock geometry.Implications for TeV cosmic ray anisotropies of  departures from this approximation should be explored in the future.The use of the LSR frame to calculate the cosmic ray gradients since the gradient scale, κ xx /u LSR , is typically more than 1000's of parsecs at TeV energies.
As a simple example, we adopt the parallel diffusion coefficient (Büsching and Potgieter, 2008;Ptuskin et al., 2006) where ζ = pc/q is rigidity q is the cosmic-ray charge, and κ 0 = 0.073 (kpc) 2 (Myr) −1 for ζ 0 = 3 GV (these specific values were obtained by Ptuskin et al., 2006).Figure 3 shows the resulting anisotropy broken down by component magnitude in Eq. ( 7) as a function of κ ⊥ /κ at 5 TeV.In this figure we have varied the field-flow angle over the region of uncertainty from 75.4 to 85.4 • .A ∼ 0.1-0.2% anisotropy is approached in the limit of relatively small values of κ ⊥ /κ .The resulting global anisotropy map in TeV cosmic rays is shown in Fig. 4. The full calculation is detailed by Schwadron et al. (2014) and includes the interaction of cosmic rays with the interstellar magnetic field deflected around the heliosphere.Notably, Schwadron et al. (2014) show that the gyroradii of TeV cosmic rays are on the scale or larger than the scale of the heliosphere itself.As a result, the effects of the heliosphere on TeV cosmic rays cannot be modeled using the Parker transport equation, which relies on a diffusive approximation and moment decomposition of the cosmic ray distribution.Instead, Schwadron et al. (2014) detailed the effects of the heliosphere by following individual cosmic ray trajectories and mapping the effects of the local interstellar  2014) is based on a potential approximation.Recent work by Röken et al. (2015) offers a new analytical solution for the interstellar magnetic field in the vicinity of the heliosphere.This provides an opportunity to contrast the influences of different interstellar field models near the heliosphere on the propagation of cosmic rays.The model of Schwadron et al. (2014) does not include stochastic acceleration, heating by magnetic reconnection, or interaction with the magnetic and electric fields inside the heliopause.The main free parameter in the estimates of the global TeV anisotropy is the level of perpendicular diffusion, for which we use a value typical for the ISM, κ ⊥ /κ ∼ 0.001.This level of perpendicular diffusion is similar to that found by Shalchi et al. (2010).
It is important to note that the field-flow angle plays a significant role in determining the maximum anisotropy.In Schwadron et al. (2014), based on knowledge of the LISM at the time of publication, the field-flow angle of 87.6 • was used.This value is slightly above the central value plus uncertainty of 85.4 • cited in Table 1.However, as shown in Fig. 3, a maximum anisotropy of 0.2 % can still be achieved with a field-flow angle of 85.4 • .A more significant issue, however, is whether the "local" value of the field-flow angle returned by IBEX is relevant over the larger pc or 10's of pc scales critical for determining the TeV anisotropies.Based on the agreement between simulated and observed anisotropy, the tentative conclusion is that the local deter- mination of the field-flow angle does appear to be applicable over much larger scales, albeit with some reasonable uncertainty due to small-scale variations in both the field and flow.The large field-flow angle, close to 90 • , should be a natural consequence of the sweeping and subsequent wrapping up of the field at the outer edge of the Loop I superbubble expansion.
Another surprising aspect of the calculation presented here and by Schwadron et al. (2014) is that the global TeV anisotropy appears to agree in both magnitude and overall orientation based on diffusive streaming in response to advection by the local interstellar flow.As a result, the cosmic ray anisotropy is aligned with the spatial configuration of the LIC.The LIC magnetic field coincides with the IBEX magnetic field direction to within the uncertainties and is entrained in the rim of the expanding Loop I leading to streaming of the GCRs along the magnetic field swept up by the expansion of the Loop I/LCC superbubble (see also the schematic in Fig. 1).

Summary
We detail here a simple model for the TeV cosmic ray anisotropy based on a diffusive anisotropy created in response to advection by the local interstellar flow.The global configuration of the anisotropy is strongly ordered by the interstellar magnetic field.By assumpition, the model uses a orientation for the interstellar magnetic field taken from the center of the IBEX ribbon (see Funsten et al., 2013) and a flow direction taken from recent interstellar neutral He measurements (e.g., McComas et al., 2015b, a;Schwadron et al., 2015;Bzowski et al., 2015;Leonard et al., 2015;Möbius et al., 2015;Bzowski et al., 2014;Wood et al., 2015).The fact that model results appear to agree with the general organization of the observed TeV anisotropy strengthens our assumption for the interstellar field direction, and suggests that the local determinations are indicative of large-scale characteristics within the local interstellar medium.
There is a significant factor that may help create conditions conducive to aligning local and global organization of the magnetic field and flow.Our Sun's position within the LIC appears to be near the outskirts of the Loop I superbubble.At this position, the expansion of the interstellar plasma from the center of the Loop I superbubble sweeps up the interstellar magnetic field, thereby maintaining a field-flow angle close to 90 • .This field direction is consistent with that inferred from the center of the IBEX ribbon.
Clearly the local interstellar conditions observed by the Interstellar Boundary Explorer provide fundamental insights into the magnetic and flow characteristics that order TeV cosmic ray anisotropies.

Figure 1 .
Figure1.Sketch of the local interstellar environment projected in the plane containing the vectors to the galactic center and to the north galactic pole (NGP).The grey curve shows the magnetic field connection from the heliosphere to the front, which provides access of cosmic rays (blue arrow) to the heliosphere.The red arrow shows the direction of the local interstellar flow.We also show rough locations of the LIC and the Blue Cloud, which exist in a region near the front from the LCC where the conditions exist for intercloud collisions.

Figure 2 .
Figure 2. The locations of stars that trace the LIC are plotted in right ascension and declination (open black circles), based on the description of the LIC in the 15-cloud model of Redfield and Linsky(2008).The size of the LIC symbol is inversely proportional to the star distance.Small black dots indicate stars with polarization data collected in the 21st century and within 90 • of the heliosphere nose (fromFrisch et  al., 2015).The red dots indicate the half of the group of significant polarization position angles that are in best agreement with the dominant ISMF direction near the Sun.Since the dominant ISMF is the same as the IBEX ISMF direction to within the uncertainties, the red dots also trace the extension of the IBEX magnetic field out into interstellar space for the sampled region.Comparisons between the LIC stars and the GCR asymmetries in Fig.4show that higher GCR fluxes tend to be associated with sightlines through the LIC, where the red dots show that the IBEX ISMF is also found.Locations are plotted in equatorial coordinates.

Figure 3 .
Figure 3. Components (parallel to B in black, perpendicular to B in the flow plane in blue, and perpendicular to B and the flow in green) of the cosmic ray anisotropy as a function of κ ⊥ /κ at 5 TeV.The field-plasma angle is varied between 75.4 and 85.4 • .The shaded regions correspond to the regions covered by these variations.

Figure 4 .
Figure 4. (Taken from Schwadron et al., 2014.)Based on the anisotropy model, we compare observed (left) and modeled (right) cosmic ray intensities.Below 25 • S latitude we show the IceCube anisotropy map, which has a median energy of 20 TeV.On the left panel, above 20 • S latitude, we show the anisotropy map from AS-γ with 5 TeV median energy.On the right panel, the modeled map at 20 TeV is shown for latitudes below 25 • S and at 5 TeV for latitudes above 20 • S.