The plasma boundaries in the outer heliosphere are illustrated schematically in Figure 20.2.
Figure 20.2: Schematic of the plasma boundaries expected in the outer heliosphere.
The solar wind is supersonic and superalfvenic and its ram pressure varies as 
,
thereby eventually becoming less than the effective pressure (the sum of ram, thermal and magnetic
pressures - see Eq. (19.4), for instance) of the VLISM. Accordingly, the solar wind must
undergo a shock transition in its interaction with the VLISM. This shock, called the
``termination shock'', is where the solar wind is compressed, heated, deflected, and made subalfvenic.
As described in the last section, the VLISM gas and plasma are believed to flow at a speed of
26 km s 
relative to the Sun and the heliosphere. If this speed is supersonic or
superalfvenic in the VLISM plasma, then there will be a (outer) ``bow shock'' for our solar system.
This flow is supersonic ( 
km s ), but it is presently unknown experimentally whether the
VLISM flow is superalfvenic. Current theoretical estimates predict that 
.
The heliopause, the other major plasma boundary, is a tangential discontinuity between the shocked
solar wind and the possibly shocked VLISM plasma. It is analogous to planetary magnetopauses and to
the pressure-balanced structure discussed in Lecture 14 and Assignment 8. To recap, from the
point of view of MHD theory
the plasmas remain separate because (1) they are highly conducting with frozen-in fields that resist encroachment
by the field of another region and (2) the gyromotion of individual charged particles leads to a current
in the interface region which experiences a 
force that separates the plasmas.
From the viewpoint of kinetic theory the plasmas remain separate because the particles from the low field
region only undergo half a gyration in the high field region before being returned to the low field
region with oppositely directed velocity, leading to a current layer.
The inner and outer heliosheaths are the regions between the termination shock and the heliopause and between the heliopause and the bow shock/VLISM plasma, respectively. The inner heliosheath is thus filled primarily with shocked solar wind plasma, with the outer heliosheath containing either shocked VLISM plasma or unshocked VLISM plasma depending on whether the bow shock exists or not.
The termination shock, heliopause, bow shock, and inner and outer heliosheaths are the well-accepted global plasma structures expected in the outer heliosphere. Where are they located and what are the properties of their plasmas? Detailed predictions require the use of global gasdynamic (GD) simulation codes, with or without pick-up ions, or MHD codes. Before describing these results, it is appropriate to provide some approximate estimates of the locations of the heliopause.
The simplest way to estimate these locations is to use the momentum/pressure balance result written in Eq. (19.4), or simpler versions in Lectures 13 and 14:
A more general equation is
where 
is the pressure in cosmic rays and P' represents the pressure in magnetic
turbulence, dust, and any other effects [Zank, 1999].
First, balance the solar wind ram pressure against the thermal pressure of the VLISM neutral gas,
ignoring the effects of pick-up ions on the solar wind flow:
where 
is the heliocentric distance in AU, 
is the solar wind number density at 1 AU,
and the subscripts n correspond to the VLISM neutral gas. Substituting in 
cm 
and
km s and the results in Table 1 yields a characteristic distance
with 
N m 
.
This estimate varies substantially when other pressures are considered in Eq. (20.2).
Adding thermal electrons and protons to the VLISM with the same temperature and with a number density 
cm reduces this estimate by a factor 
to about 210 AU. Subsequently adding
magnetic pressure in the VLISM, with an estimate of 0.2 nT (they range from 
nT), yields
a magnetic pressure of 
N m and a further decrease in the predicted
distance to the heliopause. Note also the theoretical prediction of a factor of 2 increase in magnetic
field strength due to the current layer at the heliopause, which multiples the above magnetic pressure by
a factor of 4. Similarly, the canonical estimate for the pressure of cosmic rays in the local ISM is
N m [Zank, 1999]. It is thus clear that all the above contributions to the pressure
are possibly important and that the associated predictions for location of the heliopause range widely, from
numbers 
AU.
Standard MHD theory predicts that the distance between a bow shock and its magnetopause obstacle
should be about 
of the distance to the heliopause [e.g., Spreiter et al.,
1966]. This suggests that the distance between the termination shock and the
heliopause is likely to be at least 20 AU.
Figure 20.3 shows the results of 2-D GD simulations with multiple fluid components for the pick-up ions that originate in different regions [Zank et al., 1996].
Figure 20.3: Simulation results of Zank et al. [1996] for the temperature (colour coding) and the plasma density
relative to the VLISM plasma density (contours), with arrows showing the direction of the plasma flow.
The heliopause (HP), termination shock (TS), and bow shock (BS) are clearly visible.
The solar wind and VLISM parameters are similar to those in Table 1. Note that in the upwind direction the termination shock and heliopause are about 95 AU and 140 AU from the Sun, respectively, and that they are at greater distances in other directions. These and similar calculations show that neglecting pick-up ions, or varying the description of the pick-up ions, or the inclusion of magnetic field effects do not affect the qualitative nature of these plasma boundaries but do affect their locations and the associated changes in plasma parameters.
Figure 20.4 shows the radial variation of the plasma density in various directions in Figure 20.3 [Zank et al., 1996].
Figure 20.4: Simulation results of Zank et al. [1996] for the plasma density as a
function of heliocentric distance in the upwind (full line), transverse (dotted line), and
downwind (dashed line) directions.
directions.
The variation in the solar wind plasma density is clearly seen, as is the step-like increase in
plasma density at the termination shock, a small rise in density in the inner heliosheath, the large
rise in plasma density at the heliopause, and the subsequent decrease in plasma density beyond the bow
shock in the undisturbed VLISM. The heliopause is therefore expected to separate the relatively fast
(subsonic), dilute shocked solar wind plasma from the relatively dense but slow plasma of the (shocked?)
VLISM. The rapid and large increase in 
that occurs as a shock or observer moves up and beyond the
heliopause is directly relevant to the radio emissions discussed below.