Submitted Manuscript: Confidential
27 December 2011
Title: A Porous, Layered Heliopause
Authors: M. Swisdak,1* J. F. Drake,1-2 and M. Opher3
Affiliations:
1
Institute for Research in Electronics and Applied Physics, University of Maryland, College
Park, MD 20742.
2
Department of Physics, the Institute for Physical Science and Technology and the Joint Space
Science Institute, University of Maryland, College Park, MD 20742.
3
Department of Astronomy, Boston University, 725 Commonwealth Avenue, Boston, MA 02215
*Correspondence to: swisdak@umd.edu
Abstract: The picture of the heliopause (HP) -- the boundary between the domains of the sun
and the local interstellar medium (LISM) -- as a pristine interface fails to describe the recent
Voyager 1 spacecraft data. Particle-in-cell simulations reveal that the sectored region of the
heliosheath (HS) produces large-scale magnetic islands that reconnect with the interstellar
magnetic field and mix the LISM and HS plasma. Cuts across the simulation data reveal
multiple, anti-correlated jumps in the number density of LISM and HS particles at the magnetic
separatrices of the islands as seen in the Voyager 1 data. Based on the Voyager 1 observations
and simulation data a model is presented of the HP as a porous, multi-layered structure that is
threaded by magnetic fields.
Main Text: The Voyager 1 (V1) and 2 spacecraft have been mapping the structure of the outer
heliosphere on their trajectories out of the solar system. In 2005 V1 crossed the termination
shock (TS) (1-3), where the supersonic solar wind becomes subsonic, and after this time has
been traversing the HS. In the HS the magnetic field has remained dominantly in the azimuthal
direction given by the Parker spiral magnetic field. The outer boundary of the HS is the
heliopause (HP), the magnetic boundary that separates the magnetic field and plasma from the
sun from that of the LISM (4, 5). The location and structure of the HP is unknown. The
expectation is that across the HP the magnetic field will rotate from azimuthal (east-west) in the
HS to a direction with significant North-South and radial components (6). In an ideal (nondissipative) model of the heliosphere the local magnetic field is transverse to the boundary so the
HP is a tangential discontinuity (4, 5). However, whether the HP is a smooth interface or breaks
up due instabilities at the interface has been the subject of substantial discussion in the literature
(7-11). The structure of the HP, and in particular whether the boundary is porous to some classes
of particles, is of great importance because of its likely impact on the rate of transport of galactic
cosmic rays from the LISM into the heliosphere.
Starting on day 210 of 2012 the V1 spacecraft measured a series of dropouts in the intensity of
energetic particles that are produced in the heliosphere, the Anomalous Cosmic Rays and the
lower-energy Termination Shock Particles (TSPs)(12, 13). Simultaneous with the dropouts in the
heliospheric particles were abrupt increases in the Galactic Cosmic Ray (GCR) electrons and
protons and increases in the intensity of the magnetic field (14). Finally, on around day 238 the
heliospheric-produced particles dropped and remained at noise levels and the GCR particles rose
and remained constant. This behavior suggested that V1 might have crossed the HP into the
LISM with the repeated dropouts and increases arising from the inward and outward motion of
the HP resulting from the variability of the solar wind dynamic pressure. However, a key
observation was that during these dropouts and increases the direction of the magnetic field
remained dominantly azimuthal (14), consistent with the spacecraft remaining in the HS. While
MHD models of the global structure of the heliosphere suggested that the rotation of the
magnetic field across the HP at the location of V1 would be small (6), the lack of any significant
change in the magnetic field direction at the dropouts suggested that V1 remained within the
magnetic domain of the HS during all of these events.
We present the results of a global MHD simulations of the heliosphere pared with a local PIC
simulation of the HP that suggest that due to reconnection a complex nested set of magnetic
islands develop at the boundary. Tongues of LISM plasma penetrate into the magnetic domain of
the HS along field lines that connect the domain of the LISM with that of the HS. These tongues
correspond to local depletions of the HS plasma and local enhancements in the local magnetic
pressure. A model of the magnetic structure of the HP at the location of V1 is constructed that
produces particle and magnetic signatures consistent with the V1 observations.
We first explore the large-scale structure of the heliosphere to establish the local conditions at
the HP using a global MHD simulation model (15) that includes neutral and ionized components
(see Supplementary material). The MHD simulation did not include the sector zone (where the
solar spiral magnetic field periodically reverses polarity as result of the tilt between the solar
magnetic and rotation axes) since this leads to field reversals that can’t be numerically resolved
upstream of the HP (16-17). The magnetic field strength B from the global MHD simulation
reveals the solar wind compression at the termination shock, the downstream HS and the HP
(Fig. 1). Profiles (solid curves in Fig. S1) along the V1 trajectory of the density of the pick-up
(npui) and thermal (nth) ions and the azimuthal (BT) and normal (BN) magnetic fields near the HP
are used as input for the PIC simulations. In the LISM BN (Fig. S1C) is small at the latitude of
V1. The BT component of B flips direction across the HP but remains the dominant component
on both sides of the boundary (Fig. S1D). Because V1 has continued to measure sector
boundaries in the HS during 2012 and was therefore in the sector zone, the direction of BT in the
HS in the MHD model is irrelevant since a “correct” model should include the reversals
associated with the sectors that fill the HS upstream of the HP (16-17). On the other hand, the
strength of the field in the HS and the strength and orientation of the field in the LISM should be
correct. Therefore V1 should not measure a large rotation of B across the HP.
The initial profiles for the magnetic field density and temperature for the 2-D PIC simulations of
the HP (dotted lines in Fig. S1) were constructed with input from the profiles from the MHD
model. The simulations are evolved in time with no initially imposed magnetic perturbations.
Because of the lower density in the HS, which leads to a locally higher Alfvén speed, magnetic
reconnection first starts in the sectored HS (movie S1). Small magnetic islands grow on
individual current layers in the HS and merge to become larger islands until they are comparable
in size to the sector spacing (Figs. S2A, S3A, 2A) (18). A chain of small islands grows at the HP
(movie S1, Fig. S2A). These islands merged to form larger islands and are then compressed by
islands in the HS pushing against the HP (movie S1, Figs. S3A, 2A). By late time the HS
magnetic field has reconnected with that of the LISM, forming a complex, nested chain of
islands (Fig. 2A) at the HP with sizes scales comparable to the original sector spacing.
In our PIC model we are able to independently track all particles and therefore can explore the
mixing of the LISM and HS particles as reconnection at the HP takes place. Overall,
reconnection at the HP produces a highly structured distribution in the density of LISM (nLISM)
and HS (nHS) plasma with the density of each species undergoing sharp jumps across the
separatrices that bound the outflows of plasma ejected from reconnection sites (Figs. S2, S3, 2AC). The particles initially in the LISM continue to dominate the number density of the unreconnected field in the LISM, have mixed with HS particles in the nested islands formed as a
result of reconnection between the HS and LISM fields, and are largely excluded from islands
that resulted from reconnection of the HS sectored field (Fig. 2B). The particles initially in the
HS dominate in islands resulting from reconnection of the sectored field, are mixed with LISM
particles in the HP islands and are nearly excluded from regions of the LISM with unreconnected fields (Fig. 2C).
Cuts through the simulation data along the radial direction reveal that the increases and decreases
in the number densities of the LISM and HS plasma are typically anti-correlated (Fig. 2E).
Moving from a pure HS magnetic island into an island or outflow jet where LISM and HS
plasma has mixed reduces nHS and increases nLISM. On a cut from the HS to the LISM the first
drops in nHS take place just downstream of magnetic separatrices where HS particles have an
open path to the LISM along open field lines (ΔR/di ~13 in Fig. 2D). Such mixing behavior has
been documented in satellite measurements at the Earth’s magnetopause (18) and is one of the
striking observations on V1’s approach to the HP – the variation of the flux of ACRs and TSPs
are anti-correlated with galactic electrons and GCRs (12-13). The cuts through the simulation
data further reveal that when crossing a magnetic separatrix the sharp increases and decreases of
the number density of the LISM and HS plasma do not correspond to a directional change in the
magnetic field (Fig. 2D). The absence of a direction change in B in the simulations at locations
with strong variation of the particle density is consistent with one of the most significant of the
recent V1 observations (14). In the simulation the change in field direction to that of the LISM
occurs across the midplanes of the chain of magnetic islands at the HP (ΔR/di ~31 in Fig. 2D).
Finally, the cuts through the simulation data reveal that local decreases in the HS density
correspond to increases in the local magnetic field (Figs. 2D-E). The total pressure across the HP
is balanced. While the dominant pressure in the HS is from pickup particles heated at the
termination shock (20), the dominant pressure in the LISM is magnetic. Thus, when reconnection
opens a path for HS plasma to escape into the LISM and mix with the lower-pressure LISM
plasma, there is nothing to balance the total pressure and, as a result, the region undergoes a local
compression to increase the magnetic field amplitude. This behavior is primarily seen at
separatrix crossings remote from where reconnection locally reduces the magnetic field strength
(Fig. 2D). In the V1 data the magnetic field strength is also observed to increase where the local
fluxes of HS plasma decrease (12-14).
Thus, based on our simulations we suggest that the V1 observations of simultaneous drops
(increases) in HS (LISM) particle fluxes take place at a series of separatrix crossings associated
with a nested set of magnetic islands that formed at the HP (Fig. 3). At such crossings the
magnetic field direction will not change significantly while particle fluxes can change sharply, as
seen in the satellite data. Three active reconnection sites at the HP and associated separatrices
with two nested islands are sufficient to explain the sequence of Voyager events. On day 168 the
spacecraft crossed a broad current layer, on day 190 the flux of HS electrons dropped, on day
208 a narrow current layer was crossed and on days 210, 226 and 238 three successive drops
(increases) in the HS (LISM) particle fluxes occurred . The day 190 drop in the HS electrons
suggests that the magnetic field after this time was no longer laminar so that these electrons
could leak into the LISM. In the Voyager observations the highest energy ACRs suffered the
largest drops and the size of the drop increased in each successive event until the third event
when the HS particles dropped to noise levels. Such behavior is consistent with our schematic.
Islands and x-lines flowing away from an active x-line (right-most x-line in Fig. 3) correspond to
reconnection sites that developed earlier in time. Thus, the day 210 drop in HS particles occurred
on field lines that had just reconnected and formed an open path to the LISM. The drop in
intensity was therefore modest. The intensity rose as the spacecraft approached field lines that
were close to the separatrix of the right-most HP magnetic island. This is because the effective
length of a field line increases dramatically when it wraps around an island and passes close to
the x-line where the field line moves mostly in the out-of-plane direction. HS particles in the
separatrix region therefore must move farther to escape into the LISM so their intensity recovers.
The drop in HS particles on day 226 was greater than on day 210 because reconnection with the
LISM field had occurred earlier in time. The final drop of the HS particle fluxes on day 238
occurred downstream of the oldest x-line. Essentially all of the HS particles had drained into the
LISM on these field lines.
If the schematic with nested magnetic islands (Fig. 3) is correct, the dropout in the HS particle
fluxes occurred on the HS side of the HP on field lines that had a solar source. The V1 spacecraft
therefore has not yet crossed the HP where the magnetic field will undergo a rotation from
λ~180° to λ~90° (Fig. 2D). Thus, the results suggest that just outside of the HP the T component
of the B will be positive.
References and Notes:
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bubbles? Astrophys. J. 734, 71 (2011).
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heliosheath: observations and modeling, Astrophys. J. Lett. 728, L21 (2011).
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for the generation of anomalous cosmic rays, Astrophys. J. 709, 963-974 (2010).
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magnetopause, J. Geophys. Res. 86, 10049-10067 (1981).
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Acknowledgments: The authors acknowledge the support of NSF grant AGS-1202330 to the
University of Maryland, and NSF grant ATM-0747654 and NASA grant NNX07AH20G to
Boston University. The PIC simulations were carried out at the National Energy
Research Super Computer Center and the MHD simulations at the NASA Supercomputer Center
at Ames. We acknowledge fruitful discussions with L. F. Burlaga, R. B. Decker, M. E. Hill and
E. C. Stone on the Voyager observations. This research benefited greatly from discussions that
were held at the meetings of the Heliopause International Team at the International Space
Science Institute in Bern, Switzerland.
Fig. 1. A meridional cut from the global MHD simulation of the heliosphere showing the
magnetic field amplitude B (background), the flow streamlines (solid curves with arrows) and
the V1 trajectory. The HP is where the flows from the LISM and the HS come together. The blue
line in the HS is the heliospheric current sheet.
Fig. 2. The structure of the HP and adjacent LISM (top) and HS (bottom) at late time. In the R/T
plane in (A) the magnetic field lines and in (B) and (C) the number density nLISM (nHS) of
particles that were originally in the LISM (HS), respectively. In (D) and (E) the magnitude of B
(solid), the azimuthal angle of the magnetic field λ (dashed), the number density nLISM (solid) and
the number density nHS (dashed) versus radius along the vertical lines marked in (A-C).
Fig. 3. A schematic of the inferred magnetic structure of the HP during the time at which V1
documented the strong variability in the HS and LISM particles based on the results of our
simulations. The time corresponding to several of the documented Voyager events of 2012 are
marked by the days when they occurred.
Supplementary Materials:
We first explore the large-scale structure of the heliosphere to establish the local conditions at
the HP using a global MHD simulation model (14) that includes neutral and ionized components
(both thermal and pick-up ions in the case of the solar wind). The LISM magnetic field, BISM, has
a value of 4.4 μG. The direction of BISM is defined by [αBv=15.9°, βBv=51.5°], where αBv and βBv
are the angles between the BISM and the flow velocity of the interstellar wind vISM and the BISMvISM plane and the solar equator, respectively (6). In the coordinate system of our MHD model,
the Z-axis is along the rotation axis of the Sun and the X-axis is chosen so that vISM lies in the XZ plane. The MHD simulation did not include the sector zone (where the solar spiral magnetic
field periodically reverses polarity as result of the tilt between the solar magnetic and rotation
axes) since this leads to artificial dissipation of the HS magnetic field upstream of the HP (15).
The solar magnetic field corresponds to solar cycle 24 with the azimuthal angle λ (between the
radial and T direction in heliospheric coordinates) 90° in the North and 270° in the South. The
sector region is carried by the flows and fills the HS upstream of the HP (15, 16). The magnetic
field strength B from the global MHD simulation reveals the solar wind compression at the
termination shock, the downstream HS and the HP (Fig. 1).
From the MHD simulation profiles (solid curves in Fig. S1 with the scale on the left) along the
V1 trajectory of the density of the pick-up (npui) and thermal (nth) ions and the azimuthal (BT)
and normal (BN) magnetic fields near the HP are used as input for the PIC simulations. The
pickup ion density decreases from around 0.0007/cm3 in the HS to zero in the LISM and the
thermal ion density rises from 0.003/cm3 in the HS to around 0.08/cm3 in the LISM. In the LISM
BN (Fig. S1C) is small at the latitude of V1. The BT component of B flips direction across the HP
but remains the dominant component on both sides of the boundary (Fig. S1D). Because V1 has
continued to measure sector boundaries in the HS during 2012 and was therefore in the sector
zone, the direction of BT in the HS in the MHD model is irrelevant since a “correct” model
should include the reversals associated with the sectors. On the other hand, the strength of the
field in the HS and the strength and orientation of the field in the LISM should be correct.
Therefore V1 should not measure a large rotation of B across the HP. Since the MHD model
does not include the physics necessary to describe the structure of the HP boundary, the scale
length of this transition is not physical but is a numerical artifact.
The initial profiles for the magnetic field density and temperature for the 2-D PIC simulations of
the HP were constructed with input from the profiles from the MHD model. The PIC code is
written in normalized units based on a magnetic field strength B0 and density n0 (lengths to the
ion inertial length di =c/ωpi, with ωpi the ion plasma frequency, times to the ion cyclotron time
Ωi0-1 and velocities to the Alfven speed cA0). In the HS, thermal (nth=0.25n0, Tth=0.25 micA02) and
pick-up ions (npui=0.01n0, Tpui=15.0micA02) were included as independent species while in the
LISM only a thermal component (nth = 2.0n0, Tth=0.2micA02) was included. The profiles are
shown in Fig. S1 as dotted lines (scale on the right). Not shown in Fig. S1 are the three current
sheets that produce the sectored HS field. All of the current sheets initially have characteristic
half-widths of 0.5di. This scale reflects evidence from satellite measurements from the Earth’s
magnetopause that suggest that such boundaries collapse to kinetic scales (18). Pressure balance
across each reversal is achieved by adjusting the out-of-plane magnetic field BN. The PIC
simulations were carried out in the LT -LR plane on a computational domain of dimensions (LT,
LR)= (409.6di, 204.8di). The ion-to-electron mass ratio was 25 and the velocity of light was
15cA0.
The simulations are evolved in time with no initially imposed magnetic perturbations. Because of
the lower density in the HS, which leads to a locally higher Alfvén speed and effectively thinner
current sheets (when normalized to the local value of di) magnetic reconnection first starts in the
sectored HS (movie S1). Small magnetic islands grow on individual current layers in the HS and
merge to become larger islands until they are comparable in size to the sector spacing (17). At
the HP small islands initially grow but merge to form larger islands. The larger islands of the
sector zone, containing low-density HS plasma, are pushed up against the HP (movie S1, Fig.
S1) and are forced to merge to match the larger, sector-scale islands in the HS (movie S1, Figs.
S1, S2, 2A). Thus, magnetic islands on the HP have scale sizes that are linked to the upstream
HS sector spacing.
An interesting feature of the simulation is the motion of the HP boundary in the direction of the
HS as the simulation evolves (movie S1). This motion occurs as the magnetic field energy in the
HS is converted into thermal energy which causes the total pressure in the HS to drop. From
energy conservation the change in the pressure of the HS plasma when the magnetic energy is
dissipated is given by B2/12π. This is smaller than the initial magnetic pressure B2/8π. The HS is
therefore compressed by the LISM (movie S1) until pressure balance is restored.
Fig. S1. Cuts of various parameters along the V1 trajectory near the HP from the MHD model
(solid with left scale) and as initial conditions for the PIC model (dotted with right scale). Shown
are in (A) the pick-up ion density, in (B) the thermal ion density, in (C) BT and in (D) BN. Note
that the scales on the right and left differ.
Movie S1. A movie showing the time evolution of the total plasma density with the LISM at the
top and the HS at the bottom.
Fig. S2. The structure of the HP and adjacent LISM (top) and HS (bottom) at Ωi0t=150. In the RT plane in (A) the magnetic field lines and in (B) and (C) the number density nLISM (nHS) of
particles that were originally in the LISM (HS), respectively. Note the large islands containing
HS plasma that are pressed against the HP (along the HP at ΔT = 100di, 270di, 360di).
Fig. S3. The same as in Fig. S1 but at Ωi0t=210. The three large HS islands noted in Fig. S1 are
significantly reduced in size as a result of reconnection with the LISM magnetic field.