Prsentation PowerPoint EGUNice2004

1
Coupling siphon and solar wind flows (or how
Alfvén waves accelerate wind and generate siphon
flows) Grappin, R. Léorat, J. Observatoire de
Paris, CNRS, Luth Habbal, S. Univ. Aberystwyth,
Wales
thanks G. Aulanier, A. Mangeney
Poster presented at EGU meeting 2004, session ST13
2
Take a quasi-stationary isothermal MHD wind (with
external dipole) and shake periodically the two
solar hemispheres around the polar axis gt (1)
fast wind (2) siphon flows
1
output Alfvén waves pushing a faster solar wind
input Alfvén waves at chromospheric level ltgt
periodic oscillations around the polar axis
2
output Alfvén waves pushing siphon flows along
closed line
cf. Grappin Léorat Habbal 2002, 2003
How can Alfvén waves trigger siphon flows ?
NB fluctuations are mainly transverse to the
meridian plane and largely exaggerated
3
Siphon flows require pressure imbalance
1. Open wind clear case Alfvén waves give
additional momentum to wind because average
gradient of wave pressure (ltBf2/2gt) is negative,
due to stratification. 2. Closed loops unclear
case Systematic flow requires permanent pressure
imbalance between pairs of footpoints (periodic
pressure oscillations don't do the job...)
Wave pressure gt average pressure gradient from
bottom to top of a loop ... but no average
pressure imbalance expected between footpoints,
except if strong dissipation and only one
footpoint excited Simulations (Grappin Léorat
Habbal 2002) show siphon flows appear with Alfvén
waves with equal amplitudes injected at both
footpoints if non zero phase difference between
both footpoint injection How can Alfvén waves
with same amplitude, same frequency, generate
permanent pressure imbalance between footpoints?
4
Method Integrate MHD equations with axisymmetry,
spherical coordinates R, q, and gravitation. Add
an external dipolar field. Temperature uniform
(isothermal) Domain chromosphere (above
transition) up to 15 solar radii. Non-uniform
radial grid to cope with stratification. Boundarie
s are transparent (we use characteristics) to
plasma and waves advantage downflows and
outflows are free to develop (as in real
corona) drawback more difficult to control
numerically gt Perturb static atmosphere and let
a quasi-stationary wind develop ... then start
injecting Alfvén waves, first north, then
south see R. Grappin, J. Léorat, S.R. Habbal,
Large amplitude Alfvén waves in open and closed
coronal structures, CP679, Solar Wind Ten Proc.
of the Tenth International Solar Wind Conference,
p.277, 2003. R. Grappin, J. Léorat, S.R. Habbal,
Large amplitude Alfvén waves in open and closed
coronal structures a numerical study, J.
Geophys. Research, 2001JA005062, 2002 R. Grappin,
J. Léorat, A. Buttighoffer, Alfvén wave
propagation in the high solar corona, Astron. and
Astrophys., vol 362, p.342, 2000
5
The mother Alfvén wave (Uf) - series of snapshots
Shake north hemisphere
... then shake also south
t10.17
t10.01
t10.1
unit time 8 h 23 ?t0.1 ltgt ?t50 mn
waveperiod t0.035 or 20 min
6
t10.5
Wave interference and flow in the closed
region (t10.5 ltgt 14 Alfvén periods)
Mother wave (Uf)
Streamlines in meridian plane
open flow (solar wind)
siphon flow
...How is the siphon generated?
7
Wave pattern (Bf) in R-q coordinates
t10.5
Bf
open field
Bf contours note asymmetry w/r equator
?
Equator
cut
Note radial coordinate is non-uniform low corona
is emphasized
open field
R/R_s
1
4.4
outward propagation of interference pattern
(three waveperiods t10.15-10.25)
Bf
dBf/B
R
R
8
t10.5
Wave, flow and magnetic structure after 14 periods
Flow velocity u
Magnetic field B (projected)
open flow (solar wind)
?
(Contours of Bf superposed)
well developed siphon flow
R/R_s
1
4.4
R
Contours of parallel flow u// white u// 5
km/s black u// -5 km/s
open flow
?
u// (urBru?B?)/(Br2B?2)1/2
siphon
open flow
R
9
t10-10.3
Forming the siphon flow (u//)
wind
closed region
wind
t10, Stationary corona Solar windblack and
white note weak downflows within closed region
t10.1 due to north wave overpressure, parallel
flow in closed region is mainly north to south
t10.15 illustrates the movement of plasma into
three radial condensations ("ridges")
t10.18 larger regions of uniform parallel
velocity form
t10.24 a continuous siphon forms
t10.3 south-north siphon completed two B-lines
have been added
white gt 5 km/s black lt - 5 km/s)
10
Forces along flux tubes the wave pressure

• Explaining the siphon requires several steps
• a) Identify the relevant forces along the flux
  tubes
• b) Show how they are distributed
• c) Explain why they are so
• Total field is the sum of the meridional and
  azimuthal field
• B BmBfêf.
• In the stationary state with no Alfvén wave (Bf
  0), Lorentz force J x B is perpendicular to the
  magnetic loop. Its contributes in balancing
  gravity, pressure gradient and inertial forces
  due to shear flow along the closed region.
• The wave contribution (Bf) to Lorenz force is
• êr (Bf/r)?r(rBf) - ê??(Bf/rsin?)??(sin??Bf)
• Component parallel to Bm usual wave pressure
  term curvature terms
• - ?/?s (B?2) - (Br/B cot? B?/B)B?2/r
• Dominant first term usual gradient of wave
  pressure -?/?s (B?2)

11
t10-10.3
Wave pressure pattern (Bf2/2)
Time to reach the top of the shortest flux tube
Alfvén ?A/2 0.017 Sound wave 0.1
?
1
4.4
R/R_s
t10.1 wave fronts become tilted due to
gradients of Alfvén speed (minimum at equator)
and at inner boundary
t10.15 the second wave pattern (also tilted)
emitted south interferes with the first one
Interference pattern is built in ?t0.05 after
starting southern wave time to reach top of
closed region Once formed, the pattern simply
drifts rightward toward larger R, due to larger
delay in reaching top of longer flux
tubes Time-averaged pattern made of ridges
parallel to the radial
t10.18 the interference pattern is complete
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t10-10.3
Gas pressure pattern
Second relevant force parallel to flux tubes is
the gas pressure gradient, triggered by the wave
pressure With both waves, wave pressure pattern
partially balances the time-average wave pressure
pattern
t10.1 due to wave pressure, matter is pushed
ahead of the wave front
t10.15 radial ridges form in the interference
region
dP/P (P(t)-P)/P PP(t10)
t10.18 radial ridges grow and stabilize
t10.3 (time of siphon completion)
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t10-10.3
Sum wave gas pressure PB?2/2
Note low-pressure pattern asymetric w/r equator
the two B-lines always have higher pressure at
south foot
t10.1 due to wave pressure, matter is pushed
ahead of the wave front
t10.15 pressure decreases in the region close
low corona around equator
P PB?2/2 Images Pressure difference,
relative to initial P field dP/P
(P(t)-P)/P
t10.18 low pressure region persists, but
dissymmetric w/r equator south footpoint has
larger pressure
t10.3 B-lines still have south footpoint at
higher pressure
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Discussion

• Key formation of permanent low-pressure in
  inner B-loops, not symmetric w/r equator
• Why lower pressure?
• because B-loops are stretched by Alfvén waves.
• Differential stretching gt pressure decrease or
  increase
• Why stretching B-loops?
• because NL coupling with Alfvén waves want to
  conserve (approximately) B modulus
  arc-polarized wave (Barnes Hollweg, 1974,
  Grappin et al., 2000)
• gt average decrease of B component not parallel
  to wavevector gt stretching

2
?
B Loop differential stretching B-lines before
(1) and after (2) wave injection in low corona
all lines are stretched by Alfvén waves, but
more in northern regions
1
Equator
R/R_s
1
1.3
C Wave pressure radial profile at equator (one
Alfvén period) rarefaction coincides with
positive gradient
Bf2/2
r
D Rarefaction induced by stretching radial
profile at equator thick (1) no wave plain (2)
wave injection
1
2
B?
(1) Lin. pol. Alfvén
Region with density decrease
A Hodograph components perpendicular to
wavevector Arc-polarized wave gt lower mean Bq gt
loop stretching
(2) arc pol. Alfvén
R/R_s
1
1.3
B?
15
t10.3
Summary
lower pressure at north footpoint
4. South-north acceleration gt flow along loops
1.Interference pattern of Alfvén waves (Bf) phase
difference gt north shift
2.Nonlinear coupling in Alfvén wave gt lower mean
Bq gt loop stretching (more north than south)
3.Stretching gt lower pressure of inner loops -
with north shift gt acceleration northward
?
?
?
1
1.6
R/R_s
1
1.6
R/R_s
1
1.6
R/R_s
higher pressure at south footpoint
NB bold lines are two sample B-lines taken
within the siphon region
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Conclusion
We have explained how coherent monochromatic
Alfvén waves can excite siphon flow. The basic
process is stretching of loops due to nonlinear
coupling in Alfvén waves. Stretching is
nonuniform, because Alfvén waves injection is non
uniform this leads to gradients of the pressure
field which can induce siphons, as soon as waves
at footpoints are not in phase. 1. About the
validity The siphon generation by Alfvén waves
first found in Grappin et al.( 2002) became
doubtful when the same method of wave injection
in a 1D version of the model was proved to lead
to artificial siphon flows due to spurious
coupling of waves at boundaries (Grappin, Léorat,
Ofman, 2003, SW10). However the two-dimensional
(axisymmetric) results studied here have been
comforted, as we recently re-obtained them using
a completely different method of wave injection
(volume forcing), to be reported elsewhere
(Grappin Léorat Aulanier 2004). 2. Application
to solar atmosphere In the present simulations,
the siphon flow is continuously accelerated as
soon as the interference pattern forms. This
phase ends when siphon flow becomes supersonic
either a shock develops within the domain, or
not, but pressure balance is no longer required.
In solar conditions, this supersonic phase (and
as well a third one in which the siphon flow
destabilizes the whole closed region, see
Grappin, Léorat Habbal 2002) might be difficult
to reach it would require Alfvén waves with
coherence time long compared to the waveperiod,
which is perhaps unrealistic. How siphon flow
evolve in presence of Alfvén injection with
finite correlation time remains to be
investigated. However, the differential
stretching effect might explain several aspects
of observed loops (work in progress).
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Conclusion (2)
Differential stretching due to localized areas
excited by Alfvén waves might explain some
observed features of loops a) they would become
visible when excited b) excitation would induce
thinning Loop B stretched by Alfvén waves hence
loop B pushes loop A above gt plasma between
loop A and B is compressed gt loops between A
and B become visible AND thinner gt plasma
betwwen loop B and C is depressed
compressed tube
loop stretching
B
A
C
local excitation by Alfvén waves