APASTRA ProceedingsAPASTRA Proc.2199-3963Copernicus GmbHGöttingen, Germany10.5194/ap-2-9-2015A Consistent Scenario for the IBEX Ribbon, Anisotropies in TeV Cosmic Rays,
and the Local Interstellar MediumSchwadronN. A.n.schwadron@unh.eduhttps://orcid.org/0000-0002-3737-9283FrischP.AdamsF. C.ChristianE. R.https://orcid.org/0000-0003-2134-3937DesiatiP.FunstenH. O.JokipiiJ. R.McComasD. J.MoebiusE.ZankG.University of New Hampshire, Durham, NH, 03824, UKSouthwest Research Institute, San Antonio, TX 78228, USAUniversity of Chicago, Department of Astronomy and Astrophysics, Chicago, IL 60637, USAUniversity of Michigan, Ann Arbor, MI, 48109, USAGoddard Space Flight Center, Greenbelt, MD, 20771IceCube Research Center and Astronomy Department, University of Wisconsin, Madison, WI 53706, USALos Alamos National Laboratory, Los Alamos, NM, 87545, USAUniversity of Arizona, Tucson, AX 85721, USAUniversity of Alabama, Huntsville, AL, Huntsville, AL 35899, USAUniversity of Texas at San Antonio, San Antonio, TX, USAN. A. Schwadron (n.schwadron@unh.edu)8September2015229162April201528July201524August2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://ap.copernicus.org/articles/2/9/2015/ap-2-9-2015.htmlThe full text article is available as a PDF file from https://ap.copernicus.org/articles/2/9/2015/ap-2-9-2015.pdf
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 . 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
. IBEX also makes measurements of lower
energy atoms from the interstellar medium including oxygen, helium and
hydrogen atoms .
The IBEX maps revealed the existence of a narrow ribbon of higher flux ENA
emissions . The ribbon
forms a roughly circular structure centered on (gal. long ℓ, 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 . The center of the IBEX ribbon
likely defines the direction of the local interstellar (LISM) magnetic field
. However, until the physical mechanism for the ribbon
is identified, it will be difficult to know how the interstellar field
direction is related in 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
.
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 .
There are numerous studies that complement the analysis presented here. While
studied the global TeV anisotropy, there are
also features in TeV cosmic ray maps that may be directly related to
heliospheric structure. For example, considered the
scenario where heliospheric magnetic instabilities (see
) 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 , 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 . 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., ). 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 approximately
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,
found an ISN flow gal. long. ℓ=183.7∘±0.8∘, gal. lat. b=-15.0∘±1.5∘, and speed 25.4±1.1kms-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 . The Sun is likely located within
or near the Local Interstellar Cloud (LIC), less than 0.1 pc from the
LIC edge . In the direction facing away from
the galactic center, the closest cloud to the LIC is the “Blue Cloud”
BC, . The conditions for colliding
clouds are observed within ∼10pc, and
relative intercloud velocities are observed up to 50 kms-1.
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 ℓ=124∘, b=-67∘ (or RA,
DEC =13∘, -4∘). Figure 1 provides a rough picture of
local interstellar structure near the edge of LIC and at the front of the
Loop I superbubble.
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.
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., ) and velocities for 15 local
clouds have been determined with the triangulation of the radial velocity
component towards different stars behind the clouds .
The Loop I superbubble shell is centered ≈78pc at galactic
coordinates of ℓ, b≈346∘, 3∘. Pressure equilibrium between the gas and magnetic
field in the LIC yield magnetic field strength of ∼2.7µG. This value is similar to the ∼3µG
field strength derived from the globally distributed ENA fluxes
.
The IBEX magnetic field direction should be apparent in the light of nearby
stars that is linearly polarized in the interstellar medium. The spatial
region of the LIC, as traced by stars with interstellar absorption lines at
the LIC velocity, is shown in Fig. 2 (open circles). Comparisons between
Fig. 2 and Fig. 4 show that the regions with the highest TeV cosmic ray
intensities are also the regions where the LIC is located.
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 ℓ, b=36∘, 49∘, ±16∘. 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 ).
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 . 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 (from ).
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.
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 .
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
. 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., ) specifies the
anisotropic component of the distribution in cosmic rays,
ξ=3wCu-κ∥g∥-κ⟂g⟂-κTg×b^.
The anisotropy is related to the streaming S and the isotropic
component f0 of the cosmic ray distribution, ξ=3S/4πwf0. The streaming is S=∫dΩwf, where w is the velocity of cosmic
rays, and ∫dΩ 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(f0) 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 κT=Ωτκ⟂ is the off-diagonal diffusion
coefficient, τ is the scattering time, and Ω is the
gyrofrequency. The Compton–Getting coefficient is defined as follows: C=(-1/3)[∂lnf0/∂lnp].
The full distribution function is related to the isotropic distribution and
the anisotropy,
f(p)=f0(p)×1+ξ⋅p^.
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, f0, including its spatial gradients allows
specification of the anisotropy.
The needed solution for the isotropic portion of the distribution function
f0 is found from the Parker transport equation,
∂f0∂t+u⋅∇f0-∇⋅K⋅∇f0-∇⋅u3p∂f0∂p=0,
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, f0∝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,
uLSR, 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
. Note that the local flow measured by IBEX,
uLISM, is added to the solar apex motion,
u⊙, to determine the flow in the LSR frame,
uLSR:
uLSR=u⊙+uLISM.
The Parker transport equation is written as
∂∂xuLSRf0-κ∂f0∂x=0.
In this case, the x axis is directed along uLSR and
κ=κ∥cos2θ+κ⟂sin2θ is
the diffusion tensor projected along the direction of the plasma flow. The
solution upstream is
f0∝expuLSRκxxx
and f0∝ constant downstream. Equation () 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,
κxx/uLSR, is typically more than 1000's of parsecs at TeV
energies.
We apply the upstream solution because the flow is a partof the Loop I
superbubble expansion. The anisotropy is given by
ξ=3wCuLSR-κ∥κxxuLSRcosθb^-κ⟂κxxuLSRsinθe^⟂1-κTκxxuLSRsinθe^⟂2
and the unit vectors e^⟂1=x^-cos(θ)b^/sin(θ) and e^⟂2=x^×b^/sin(θ) are
orthonormal. The components b^, e^⟂1, and
e^⟂2 form a basis with projections of associated with
parallel diffusion (b^), perpendicular diffusion
(e^⟂1), and drift (e^⟂2).
As a simple example, we adopt the parallel diffusion coefficient
κ∥=κ0ζ/ζ00.6,
where ζ=pc/q is rigidity q is the cosmic-ray charge, and κ0=0.073(kpc)2(Myr)-1 for ζ0=3GV (these
specific values were obtained by ). Figure
shows the resulting anisotropy broken down by component magnitude in
Eq. () 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∥.
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.
(Taken from .) 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.
Local interstellar parameters.
Mag.Gal.Gal.(kms-1)Long. ℓ (∘)Lat. b (∘)LISM (HC framea), uLISM25.4±1.1183.7±0.8-15.0 ±1.5Solar apex motion in LSRb, u⊙18.0±0.947.8±2.923.8±2.0LISM (LSR frame), uLSR17.2±1.1141.6±3.72.3±2.9LISM Mag. Fieldc210.5±2.6-57.1 ±1.0
a From and in Heliocentric rest frame. b Solar apex motion in Local Standard of Rest, LSR .c Field direction taken from the IBEX highest energy steps (1.79
and 2.73 keV, ) which shows ribbon coherence
and a long Line-of-Sight. hello world.
The resulting global anisotropy map in TeV cosmic rays is shown in
Fig. . The full calculation is detailed by
and includes the interaction of cosmic rays with the
interstellar magnetic field deflected around the heliosphere. Notably,
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,
detailed the effects of the heliosphere by following
individual cosmic ray trajectories and mapping the effects of the local
interstellar magnetic field deflected about the heliosphere on the cosmic ray
distribution function. The magnetic field structure calculated by
is based on a potential approximation. Recent work by
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
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
.
It is important to note that the field-flow angle plays a significant role in
determining the maximum anisotropy. In , 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. , 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
determination 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
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. ).
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 ) and a flow direction
taken from recent interstellar neutral He measurements (e.g.,
). 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.
Acknowledgements
We are deeply indebted to all of the outstanding people who have made the
IBEX mission possible and have contributed to the Asγ, IceCube and
Milagro projects. This work was carried out as a part of the IBEX project,
with support from NASA's Explorer Program.
Edited by: K. Scherer
Reviewed by: H. Fichtner and one anonymous referee
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