Influence of the time-dependent heliosphere on global
structure
G.P. Zank and H.-R. Müller †
Institute of Geophysics and Planetary Physics, University of California, Riverside
†
Bartol Research Institute, University of Delaware, Newark
Abstract. The solar cycle leads to important changes in the solar wind, which can have an important effect on the structure
of the global heliosphere. In the ecliptic, the ram pressure can vary from one cycle to the other, being greater during periods of
minimum activity. We investigate the response of the heliosphere to a temporally varying solar wind. Since neutral hydrogen
is a key component in determining the global structure of the heliosphere, we employ a multi-fluid model in which the selfconsistent charge-exchange interaction between neutral hydrogen and protons is included self-consistently. The variability of
the termination shock location is described and the response of the hydrogen wall to the temporal solar wind is discussed.
INTRODUCTION
Belcher [3], who modeled neutrals as a second fluid following the approach developed by Pauls et al. [6]. Here,
we consider more carefully the implications of the ram
pressure varying with solar cycle on global heliospheric structure, using the somewhat more sophisticated description of the neutral component developed by Zank et
al. [7]. This multi-fluid neutral description includes the
neutral heating of the outer heliosheath regions, which is
necessary to determine the bow shock stand-off distance.
The use of the multi-fluid description allows us to consider the distribution of neutral hydrogen throughout the
heliosphere, which was not discussed at all in [3].
The solar wind varies on many spatial and temporal
scales and some aspects of this variation have been considered in the context of global heliospheric structure.
Most studies have concentrated on the response of the
termination shock to relatively short ( 180 day and less)
variations in the solar wind ram pressure, often associated with interplanetary shocks (see [1] for references).
These results, which are 1D, have been extended in a limited way to 2D by Steinolfson [2] and Wang & Belcher
[3]. Less attention has been devoted to determining the
global structure of the heliosphere as it responds to either
long-term variation in ram pressure or very long-lived spatial variation.
As has been discussed extensively, the inclusion of interstellar neutral hydrogen (H) has a profound effect on
global heliospheric structure. Of particular importance to
time-dependent models of the global heliosphere is the
role of pickup ions in the outer heliosphere. As discussed
by numerous authors, pickup ions exert a profound influence on the dynamics of the steady solar wind, causing it
to decelerate and thereby reduce the ram pressure of the
wind (see [1] for an exhaustive review). Observations of
the solar wind by the Voyager spacecraft [4] indicate that
the ram pressure (ρ u 2 , where ρ denotes the solar wind
density and u the radial solar wind speed) varies by a
factor of 2 with solar cycle. This observation prompted
Karmesin et al. [5] and Wang & Belcher [3] to consider the response of the global 2D heliosphere to variations in solar wind ram pressure with a 22 year period.
Karmesin et al. [5] did not include interstellar neutrals
in their simulation, and this was redressed by Wang &
SIMULATION MODEL
The heliospheric-LISM plasma environment is composed of three thermodynamically distinct regions: (i)
the supersonic solar wind, with a relatively low temperature, large radial speeds, and low densities; (ii) the shockheated subsonic solar wind with much higher temperatures and densities, and lower flow speeds, and (iii) the
LISM, where the plasma flow speed and temperature is
low. As discussed in detail in [7], each of the thermodynamically distinct regions contributes a distinct population of neutral atoms produced by charge exchange with
the ambient plasma and neutrals entering the region. The
self-consistent inclusion of neutral hydrogen in models
of the solar wind-LISM interaction is fundamental to understanding the large-scale structure of the heliosphere.
Two basic classes of model have been developed to
describe neutral H in and around the heliosphere: multifluid models of varying degrees of sophistication [3, 6–
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
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10] which treat the neutral atoms as a multi-fluid, and kinetic models which solve the neutral atom kinetic equation, either by a Monte-Carlo technique [11, 12], or by
a particle-mesh method [13, 14]. The long charge exchange mean free path for neutral hydrogen may mean
that the fluid description for neutrals within the heliosphere is not completely justifiable. Multi-fluid and
Boltzmann models differ in the detailed predictions that
each admits for the neutral atom distribution and this can
lead to 10-15% differences in predicted neutral H densities and temperatures within the heliosphere. Nevertheless, the basic morphological predictions of both models
remain the same.
The kinetic codes, when coupled self-consistently to
the background solar wind and LISM plasma, are computationally intensive, and so both kinetic approaches are
restricted to steady-state conditions so far. However, the
solar wind properties vary on an 11-year scale. Since
the time for a neutral atom to enter the heliosphere and
reach 1 AU is 15-20 years, the local neutral atom distribution has experienced both a variable charge exchange
and photoionization rate, as well as a supersonic solar
wind whose extent, velocity and density is highly variable. Thus, the problem of neutral atom interaction with
the solar wind is inherently time-dependent and nonstationary. Neutral atom characteristics will therefore depend on solar cycle, with the overall distribution being
a mixture of atoms created in temporally different solar
wind environments, since they cannot be lost to the system on time scales shorter than the solar cycle. This requires a time dependent approach to the modeling of the
solar wind-LISM neutral atom interaction. Accordingly,
since the multi-fluid models provide a computationally
feasible approach to investigating time-dependent problems in the solar wind, we adopt this approach here.
In the simulations discussed below, the long-term variation in solar wind ram pressure is introduced at the inner
boundary (1 AU) sinusoidally by varying the flow speed.
We used a base of 400 km/s, an amplitude of 83 km/s and
a period of 11 years. This yielded a ram pressure which
varied by a factor of 2.
T 7.0E+03
[K]
1.7E+04
4.2E+04
1.0E+05
2.6E+05
6.3E+05
Plasma
Temperature
400
AU
200
AU
liop
aus
e
k
S hoc
Bow
He
Termination
Shock
FIGURE 1. The 2D steady-state, 2-shock heliosphere showing the temperature distribution of the solar wind and interstellar plasma, together with velocity streamlines. The plasma
boundaries, termination shock, heliopause, and bow shock are
labeled. The plasma temperature is plotted logarithmically. The
distances along the x and y axes are measured in astronomical
units (AU).
figure is a 2D plot of the plasma temperature showing
the labeled boundaries. The extent of the heliosphere in
the nose direction (the "stagnation axis") is 80 AU to
the termination shock, 110 AU to the heliopause, and
230 AU to the bow shock.
Once the steady-state solution is computed, the inner
boundary velocity at 1 AU is allowed to vary cyclically.
Shortly after the initiation of the time-varying boundary
condition, the heliosphere begins to exhibit an arrhythmic “breathing” as the termination shock begins to move
in and out in response to the varying solar wind ram pressure. The arrhythmic motion of the termination shock is
a consequence of the steady state heliosphere itself being
asymmetric, and the local outward and inward motion of
the TS being asymmetric. We note that, since interstellar neutrals reduce the asymmetry in the global structure
compared to models that do not include neutral H [2, 5],
the “breathing” of the heliosphere is less arrhythmic than
in the corresponding plasma-only case. Also, the movement of the termination shock in the self-consistent case
is somewhat smaller ( 10 AU in the nose direction) than
is exhibited in the plasma-only model. This is due to the
mediation of the solar wind velocity, and hence ram pressure, by pickup ions.
The motion of the termination shock drives pressure
waves into the inner heliosheath (the region between the
termination shock and heliopause) which steepen as they
propagate. Depending on the distance to the heliopause,
the pressure waves may eventually steepen sufficiently
to form weak shocks which then collide with the heliopause. However, the impact of the additional pressure
on the heliopause leads to the transmission and/or emission of weak shocks into the outer heliosheath. This is
illustrated in Figure 2, where differences in the plasma
temperature are seen both in the heliotail and the in-
RESULTS
For reasons of space, we describe only our results from a
2-shock model. In this case, the incident interstellar plasma flows supersonically onto the heliospheric obstacle.
The interstellar flow velocity is set to 26 km/s, at a temperature of 8000 K. An interstellar plasma density of 0.1
cm 3 and neutral density of 0.14 cm 3 is assumed for
the model. Corresponding numbers for the solar wind at
1 AU are 5 cm 3 and 105 K, respectively. The steadystate 2-shock heliosphere is depicted in Figure 1. The
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1.8E+04
4.0E+04
8.9E+04
2.0E+05
4.5E+05
1.0E+06
2.2E+06
10 6
10 -1
-3
np (cm )
600
400
10 5
10 -2
200
10
-3
10
10 1
2
r (AU) 10
Tp (K)
T(K): 8.0E+03
4
10 3
0
-600
-400
-200
0
200
FIGURE 2. A snapshot during the time-dependent solar
wind simulation. Note the presence of transmitted shocks beyond the heliopause and in the heliotail.
FIGURE 3. A 1D profile of the plasma density (solid) and
temperature (dashed) as a function of radial heliocentric distance for Figure 2 along the stagnation axis in the upstream
direction. Observe the train of shocks in the outer heliosheath
(between the heliopause and bow shock).
ner and outer heliosheath (the lighter shading of the colors). The shocks transmitted across the heliopause in the
upwind direction are more easily distinguished in a 1D
cut along the stagnation axis, Figure 3, showing density and temperature, where the train of driven shocks is
clearly apparent. The dynamical pressure associated with
the train of shocks acts to communicate the varying solar wind ram pressure (although on a very much longer
timescale) to the LISM and pushes the bow shock further
out than in the steady-state case. This, of course, reflects
the result that the solar wind ram pressure, suitably averaged, is larger than that of the steady-state wind. The
steady bow shock is located at about 230 AU and the
time-dependent bow shock at about 270 AU.
The time-dependent response of the heliosphere to dynamical variations in ram pressure is illustrated in Figure
4. Figure 4 is a color plot of the plasma temperature along
the stagnation axis (upwind and downwind directions) as
a function of time/phase. Since Figure 4 is a space-time
diagram, the dynamical response of the boundaries is exhibited clearly and structures such as transmitted shocks
or driven pressure waves which heat the plasma as they
propagate can be discerned easily. The most striking feature of Figure 4 is the enormous excursions made by the
termination shock in the downwind direction about its
mean, steady-state location. The downwind termination
shock can move by as much as 50 AU compared to
10AU in the upwind direction over a solar cycle. The
larger downwind than upwind termination shock movement is a consequence of the additional interstellar ram
pressure in the upwind direction. Within the orange band
(hot plasma in the inner heliosheath) one can observe
lighter colored streaks. The back of a light-colored streak
corresponds to a steepening pressure pulse or shock front. The darker orange color corresponds to heliosheath
material that has been compressed and heated by the
driven shock wave. The light orange is therefore the am-
bient steady-state temperature of the heliosheath plasma
in the absence of temporal solar wind driving. By comparing the temperatures (not the colors!) of Figures 1 and
2 or 3, the maximum temperature for the steady-state is
1:8 106 K, compared to 3:5 10 6 K for the temporal solar wind case. Clearly, both the upwind inner heliosheath and the heliotail within 500 AU experience
considerable additional heating by steepening pressure
waves and shock waves driven by the solar cycle varying solar wind ram pressure. In the upwind direction,
the bands continue beyond the inner heliosheath into the
cooler outer heliosheath (shocked LISM plasma) but, as
can be seen from the changed gradient of the bands, at
a much slower speed (the light blue streaks now correspond to heated plasma). As illustrated in Figure 3, the
slow structures are weak shock waves. The shock waves
propagating into the heliosheath in the downwind direction also slow and weaken with increasing distance, as illustrated in Figure 4 by the slowly decaying exponentiallike tracks. At any given time, multiple shocks can be
present in the outer heliosheath and in the heliotail.
The solar cycle varying solar wind has some impact on
the characteristics of neutral H entering the heliosphere.
The increased separation distance between the BS and
HP leads to a greater deceleration and heating of the hydrogen wall compared to its stationary counterpart. The
wall amplitude is slightly larger (0.321 vs. 0.316 cm 3 )
and the filtration of interstellar H is a little more pronounced. Both the neutral H density and temperature exhibit variability beyond 20 AU. The 1D stagnation axis
profiles of Figure 5 show neutral density and temperature
for two phases within a solar cycle. The change in neutral
H temperature about half a period apart is most remarkable, and reflects the change in heliosheath and ISM plasma temperature due to the propagation of weak shocks.
The front of the hydrogen wall, located approximately
at the heliopause, exhibits some variation. Propagating
764
60000
50000
0.40
T(K): 8.0E+03
1.8E+04
4.1E+04
9.3E+04
2.1E+05
4.8E+05
1.1E+06
2.4E+06
0.35
40000
0.30
30000
0.25
-3
nH (cm )
250
20000
r (AU)
0.15
TH (K)
0.20
0
0.10
10000
0.05
-250
0.00
10 1
2
r (AU) 10
10 3
-500
0
0.5
1
1.5
FIGURE 5. 1D plot of neutral hydrogen density (solid) and
temperature (dashed) along the stagnation axis, for two representative phases within a solar cycle.
2
phase
FIGURE 4. "Space-time" plot of the plasma temperature along the stagnation axis (upwind and downwind directions)
over two solar cycles, illustrating the response of the termination shock, heliopause, and bow shock to variation in solar wind
ram pressure. Note the much larger excursions of the termination shock in the downwind direction than in the upwind, the
smaller response of the heliopause than the termination shock,
and the formation of pressure waves and weak shocks driven
by the motion of the termination shock.
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structures can also be seen, moving slowly outward toward the bow shock but decaying before then. These are
the result of enhanced charge exchange due to the higher
density and temperature of the plasma at and behind the
weak transmitted shocks.
CONCLUSIONS
On the basis of a multi-fluid description of the solar
wind-LISM interaction, we have investigated the structure of the global heliosphere when the observed solar
cycle variation in ram pressure is included. We describe
here only results obtained for a 2-shock model. The varying ram pressure moves the termination shock 10 AU
in the upwind direction and 40 - 50 AU in the downwind direction, and the heliosphere itself exhibits a highly arrhythmic “breathing.” Weak shocks are driven by
the temporal solar wind, propagating into the outer heliosheath and heliotail, and acting to further heat these
regions. The neutral hydrogen distribution is also found
to vary beyond 20 AU in its density and temperature.
ACKNOWLEDGMENTS
This work was supported in part by an NSF-DOE grant
ATM-0296114 and a NASA grant NAG5-611621.
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