Model of An Expanding Heliosphere

P. Song1, and V. M. Vasyliūnas1,2

1. Space Science Laboratory and Department of Physics, University of Massachusetts Lowell

2. Max-Planck-Institut für Sonnensystemforschung,

Göttingen,Germany

2015 Fall AGU, SH41A-2374

1

Differences Between the Heliosphere and Planetary Magnetospheres

• The heliosphere is created predominantly by mass outflow from the Sun in form of solar wind plasma; it is affected by the magnetic field which in the outer solar wind (and into the heliosphere at least in part), although nominally of solar origin, is created primarily by solar rotation combined with solar wind outflow and is predominantly in the azimuthal direction, the magnetic flux closing mainly on itself.• Planetary magnetospheres, in contrast, even for planets with large mass outflow (Jupiter, Saturn), are created primarily by planet’s magnetic field, modified in some cases appreciably by plasma effects including outflow.• Because the Sun is surrounded on all sides by solar wind flow which is supersonic, no MHD stresses can be transmitted inward from the termination shock to the Sun. All external forces on the heliosphere must therefore be balanced within the heliosphere.• External force balance may affect location and shape of the termination shock, but the integrated force on the entire termination shock remains zero. • Planetary magnetospheres, in contrast, are anchored to their massive planets, which take up all the external forces.

2

Expansion of the Heliosphere• The continuing outflow of solar wind over a very long time (possibly up to a

significant fraction of the age of the Sun) implies that the volume occupied by plasma from the Sun is very large and continues to expand with time.

• The averaged rate of mass outflow at the present epoch is • A continuing expansion of the heliosphere can be terminated only if plasma of

solar origin effectively loses its identity, either being neutralized by recombination or becoming assimilated into and indistinguishable from the interstellar medium.

• Given the comparatively low density and initially high energy of solar wind plasma, neutralization is unlikely to be important.

• As noted later (p. 16), magnetic field geometry is unfavorable for reconnection (except on very small scales); hence extensive assimilation of heliospheric into interstellar magnetic field is improbable.

• It follows that a steady heliosphere of finite size is not possible: the heliosphere must be expanding continuously, with nonzero outward velocity over at least some portions of its outer boundary (the heliopause).

• Geometry and rate of expansion may change when solar conditions, or interstellar conditions, or both, change.

3

Size and Shape of the Heliosphere• If the expansion is more or less spherical (including ellipsoidal – the essential

point is that the expansion is in all directions, albeit possibly at different rates), the extent of the heliosphere is 1000’s or 10000’s AU after 1000 years (depending on density distribution) and growing (examples on p.5). In such a case the plasma interaction at Voyager distances would be not with the interstellar plasma but with plasma of solar wind origin from earlier times.

• Quasi-spherical expansion is expected if there is neither significant interstellar flow nor other (e.g., magnetic) asymmetric external stress. Ellipsoidal expansion may result from the latitude dependence of the solar wind magnetic field.

• If there is interstellar flow, the expansion can be deflected sideways, in the direction of the flow, by linear momentum transfer from the associated asymmetric stresses.

• A relatively close distance of the heliopause is then possible on the front side over a limited range of angles, most of the expansion taking place at the distant end of a long tail/wake attached to a quasi-spherical front-side region.

• In this case, the simplest model is a cylinder of more or less fixed radius but with steadily increasing length. If density and flow of interstellar medium are assumed known, the minimum dimensions of the cylinder can be estimated (examples on p. 6). The scale of the cylinder is still very large.

4

Expansion of a Spherical Heliosphere• Solar wind mass output rate

• For spherical expansion (heliopause at r = R3 )

• If density is approximately constant downstream of termination shock (r = R1),

• If density varies as 1/r,

20 0 04M mN V R

5

Expansion of a Cylindrical Heliosphere• The expansion forms a long tail or wake, modeled most simply as a cylinder of

radius Rcl and length LT

• In a quasi-steady state, the interstellar wind flow speed may be taken as an upper limit on the expansion speed at the distant end of the tail

• Assuming the expansion conditions are determined at the termination shock,

• If

• If

• The radius of front side heliopause is plausibly a significant fraction of Rcl

2 2 2 20 0 0 0 0 04 , 4T

T cl T cl TdLN R N V R N R L N R V tdt

2

0 03

0

, 4872 , 4 10

clTT ISM T ISM

T ISM

R N VdL tV V L V t AUdt y R N V

0 0 011

0 1 1

, 4 2000 clT

cl ISM

R N V RRN N AUR R N V R

1 , 440 T clN N R AU

6

Photoionization of Interstellar Neutrals• The ionization fraction of the interstellar medium is difficult to determine

observationally; it is commonly assumed to be 1/4 ~ 1/3.• The interstellar plasma continuity equation (NISM = ISM plasma density):

Terms on RH side: photoionization, electron impact ionization, recombination.• Estimated stellar photoionization rate near the Sun [Vallerga, 1998]:

• Solar photoionization rate [Siscoe and Mukherjee, 1972]:

For distances < 10000 AU, solar photoionization dominates over stellar.• For estimated heliospheric plasma parameters, electron impact ionization is

smaller than photoionization• The interstellar ionization fraction near the Sun is estimated as 15% [Vallerga,

1998] and may be much smaller – sufficiently low to raise the question:• Is the heliosphere/interstellar-medium interaction primarily with neutrals?

( )ISMISM ISM ph n eii n r ISM ISM

N N N N V N V Nt

V

15 1~ 2.3 10ph s

7

Relative Role of Interstellar Neutrals and Interstellar Plasma/Magnetic Field

• Neutrals are unaffected by electromagnetic fields. They interact with plasma by collisions, which for hydrogen are primarily charge-exchange collisions.

• The estimated plasma densities in the heliosphere are sufficiently small so that neutrals can penetrate essentially through the entire volume, with almost no significant change of density except near the Sun ( ) where the photoionization rate by solar radiation is sufficiently high to reduce the neutral density exponentially.

• Photoionized neutrals are picked up by the solar wind electric field and become a component of the solar wind. Their contribution to plasma density may become significant because they are “snowplowed” by the plasma flow.

• Termination shock: there is an established and observed effect of neutrals (via pickup ions) on solar wind speed and temperature. We estimate an upper limit on the distance to the termination shock, due to interaction with neutrals alone and independent of any assumptions about interstellar plasma.

• Effect on plasma temperature: charge exchange acts to heat the plasma when the flow of plasma relative to neutrals is faster than thermal speed, and to cool it when the flow is slower (dissipation equation, p. 9); when there is no differential flow, charge exchange acts to equalize plasma and neutral temperatures. We are looking into the possibility that formation of the observed heliocliff may be related to the cooling expected in the subsonic flow downstream of the termination shock, but have no specific model yet.

8

Photoionization and Collision Effects• Mass conservation with solar photo ionization included:

• With the MHD approximation (electron collision frequency << gyro frequency) Faraday’s law:

• With photoionization and plasma-neutral collisions (including charge exchange), plasma momentum equation (w=δV = relative speed of colliding particles):

• Leading terms of the energy (dissipation) equation are [after Vasyliūnas and Song, 2005]

20

0 2( ) nRN N N

t r

V

2

2 00 2

0 0

1 1 ( ) ( )2 i n N

RmN mN p B w N mN mNt r

V V V B B V V g

2

2002/ 3 2

2 1 3log3 2 2

ni n n

N Rd T w N m T Tdt N NT r

V V

t

B V B

9

Steady State Spherically Symmetric Radial Flow

• Combining all the above, the flow equation is

• Solution of the equation requires one boundary condition• [LH]=0 and RH=0 (dV/dr undetermined): critical point• RH=0 but [LH]≠0, dV/dr=0: velocity extremum• [LH] =0 but RH≠0, dV/dr=∞: unphysical (multivalued) solution

0

2 2 22 2 00 0 0 0 0 0 0 0 0 0

0 0

( )1 ( ) ~ 1200

rn

ph nR

N r AUr NV R N V r N dr R N V r R R N VV N AU

2 22 2 2 0

02 2 20

1 ( ) ( cos )2

ss n i n

c RV N GMNV c N B r N w N V V mNr r r m r r r r

0 0 0rVB R V B

2

2 2002/3 2

2 1 3log 2 cos3 2 2

ni n n n

N Rd T w N m V VV V T Tdr N NTV r

10

Types of Solutions and Singular Points

• Solutions of equation

• We define the sonic speed as fast mode, or magnetosonic, speed, or

• (A) If two boundary conditions are specified, upstream and downstream, solution is possible only if a shock forms (within which additional dissipation effects operate). The solution jumps from one solution (blue, downstream boundary condition) to another (green, upstream boundary condition). The requirement that the jump satisfy the Rankine-Hugoniot relations determines the location of the shock.

• (B) When both LH and RH reach 0 at the same point, the flow goes smoothly from subsonic to supersonic (e.g., Parker’s solar wind solution)

• (C) If a supersonic flow decelerates so that it reaches the magnetosonic speed, the solution is unphysical. For a physical solution, a shock must be formed (and matched to an appropriate subsonic solution) before the magnetosonic speed has been reached.

LH RHdVdr

2 2 2 2 2LH s A msV c c V c

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Location of the Termination Shock• For supersonic flow, the leading terms of the flow equation are

• Since

• The maximum flow speed at RH=0:

• The flow starts decelerating after about 5 AU and undergoes rapid decrease at distance of order

• This is (slightly below) the upper limit to location of the termination shock. • To determine the actual location, the subsonic downstream solution must be

obtained (under investigation) and matched using the Rankine-Hugoniot relations. It is expected that the subsonic solution will further decelerate the flow and cool the sheath by charge exchange. 12

20 0 0 0 0 0 0 0

0 0 020 0 0 0 0

( ) ~ , ~ 200n

n

N N V V R L V Nr N rr R N L AUR V V V L R R N

2 2 2

0 00 02 2

2 20

23

/ ~ 200 / ( / 1) ~ 5

sn i n

m m m

m s

c R RN w N

r V Nr r N

r R V c

0 0 0

00

0 0 0

200~ ~ 105

/ 20044 11 3 2623i n

r R L r Rr AU

r RN LrR R R

Formation of Sunward-Moving Neutral Particles• Neutrals produced by charge exchange of the

original solar wind ions (solid circle in (A) and (B)) with ISM neutrals move antisunward with solar wind velocity.

• Pickup ions produced by charge exchange and photoionization of ISM neutrals in the solar wind have gyrovelocity equal to solar wind speed (dashed circle in (B)), or antisunward velocity ranging from 0 to .

• Pickup ions produced downstream of the TS likewise have antisunward velocity ranging from 0 to twice the local plasma flow speed

• Pickup ions produced in the solar wind and crossing the TS undergo decrease of drift velocity and increase of gyrovelocity (dashed circle in (C), see p. 14) and now have sunward velocity over a significant segment of their gyration orbit.

• Charge exchange of these ions with ISM neutrals produce sunward-moving energetic neutrals.

• These may constitute some of the ENA observed by IBEX.

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2 swV

Sunward-Moving Neutral Particles• Pickup ions have always drift velocity =(perpendicular) plasma bulk flow

and initial gyrovelocity = plasma-neutral bulk flow difference.• Pickup ion energy in solar wind:• After a pickup ion in the solar wind has crossed the TS, its post-shock

energy is similar to that before shock but reduced slightly (to first approximation by the energy corresponding to difference between solar wind and sheath plasma flows); thus

• Sunward ENA average energy:

• Pickup ion flux produced upstream of the TS (photoionization and charge exchange):

• Secondary charge exchange (pickup ions on ISM neutrals) rate in sheath:

1

0

2 22 20 0 0 0 1

0

1R

sw in i nPCR

Vr NV N dr R w Nr N R R

2 2

1 1

2

1

22 2 00 0 1

0

2 2 2 200 1 0 1 0 2 1 0 0

0

1

1

R Rsw i i

i PC nENAshR R

Rsw i sh sh

n i n i sw ish shR

V Nr NV N r dr R N R drV

V N w wN R R dr N R R R R V NV V

2

( )1 1.2 12ENA gyro post shock sh swE m V V E keV

2 2 21 1 22 2sw gyro sw swmV mV mV E

22 2( )

1 1 122 2 2gyro sh sw sh sw shmV E mV m V V

14

Density Structures and Flow Speed at 120 AU• When ionization is included, mass conservation and magnetic conservation equations

are, for spherically symmetric radial outflow (not clear to what extent that is a good approximation beyond the termination shock)

• The predicted average plasma density at 120 AU is

• The sporadically occurring high density structures, N~0.11 cm-3, observed by Voyager I at 120 AU, are about a factor 20 greater than this average. They could be produced by periods of high density structures of solar wind (first term) or of ISM neutrals (second term); how far this is consistent with the long-range (“snowplowing”) geometry has not yet been examined.

• The predicted average flow speed is , below the detectability threshold of Voyager I detector.

0

2 2 2 2 20 0 0 0 0 0 0 0 0 0 0

( )( ) ~ 1200

r

ph n nR

r AUr NV R N V r N dr R N V N r R R N VAU

230 0 0 0 0 0

020 0 0 0 0

0.45 5 120~ 1 ~ 1 ~ 0.006120 5 200

nn

R V r R BN NrN N N cmr V V rB R V N

0 0 0R B VVrB

0 0 0 5 400~ 37 /120 0.45

R B VV km srB

15

Magnetic Field and Solar Cycle Effect• The magnetic flux that crosses a meridian plane (in one hemisphere) from start of supersonic solar wind to distance reached by solar wind plasma after a time is larger than the net magnetic flux leaving the Sun by factor Ω✕t (~ 100 for distance to termination shock, ~ 1000 for distance reached

during one solar cycle). • The magnetic field threading the plasma that has left the Sun during the current

solar cycle forms in principle an essentially toroidal structure; the predominantly azimuthal magnetic flux (opposite polarity in the two hemispheres) closes mostly on itself, with only a small fraction (~ 0.1%) connecting to the other hemisphere and an equally small fraction connecting to the Sun.

• The large-scale (quasi-dipolar) solar magnetic field reverses with solar cycle every 11 years. As a result, magnetic fields threading plasma that left the Sun during earlier solar cycles are no longer connected to the Sun.

• Ideally, consecutive solar cycles may thus form distinct shells of wrapped magnetic fields, disconnected from each other and only the innermost one connected weakly to the Sun.

• Such quasi-toroidal magnetic field structures, however, are subject to classical MHD instabilities (except inward of the termination shock, where they can be maintained by dynamically dominant plasma flow). Their development and ultimate fate are thus highly uncertain.

16

Conclusions • Unless some as yet unknown effective mechanism can be found to assimilate into

the ISM the plasma and magnetic field carried out from the Sun, the heliosphere must occupy a very large and continually expanding volume in space.

• The shape of the heliosphere, as well as the nature and distance of a transition from the inner region of quasi-spherical outflow to an outer region possibly aligned with interstellar flow, are very uncertain. The order of magnitude of the overall spatial scale, however, is much greater than 120 AU; thus Voyager I may not have reached the interstellar plasma.

• Photoionization by solar EUV radiation and charge exchange in the heliosheath, together with the (very poorly known) ionization fraction of the ISM, play essential roles in determining the structure of the heliosphere.

• The termination shock need not be formed by proximity of the heliopause or ISM plasma but may result from interaction with ISM neutrals, which slow down the solar wind via ion pickup.

• The heliocliff may be formed by transition from plasma-dominated to magnetic-field-dominated regime as a result of cooling by charge exchange, but a specific theory has not yet been developed.

• The ENAs observed by the IBEX may be produced by charge exchange of ISM neutrals with pickup ions from the supersonic solar wind that are heated as they cross the termination shock. (Whether this can account for the ribbon remains a topic of investigation.)

• The observed episodes of high plasma density might be produced by periods of high solar wind density or high ISM neutral density; they do not necessarily constitute evidence for encountering ISM plasma

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Preprints • Name Institution email

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