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The Solar Wind
The solar wind is ionized gas emitted from the Sun flowing radially
outward through the solar system and into interstellar space.
The solar wind is the extension of the solar corona to very large
heliocentric distances.
1
Homework
6.3, 6.5, 6.9, 6.10, 6.11
8.1, 8.3, 8.7
8.2*
2
Solar Atmosphere Solution
Assume "hydrostatic equilibrium. Possible?
GM 
p
p
2k B
  g    2  , and substitute  
, R
r
r
RT
mp
GM  dr
dp

p
R r 2T  r 
 GM r dr 

p  p exp  

2



R
r
T
r


R



 refers to the base of the corona
 6.2 
3
n
R 
If we assume T  r   T    , the integral in (6.2) can be solved
 r 
(problem 6.1). For n = 0 (isothermal corona T = T ) the pressure
profile becomes
 GM   1 1  
p  r   p exp  

 RT  R  r  
 GM  
-8
2
p     p exp 
10
N
m

 RT R  
 6.5 
The interstellar medium is at pISM  10 13 N / m 2 , i.e., p     pISM .
This is not possible in equilibrium. One can try other reasonable
temperature profiles with n < 2 7. They all produce a finite pressure > 0.
We need a dynamic solution of the momentum equation!
4
• The Earth’s atmosphere is stationary. The Sun’s
atmosphere is not static but is blown out into space as the
solar wind filling the entire heliosphere.
• The first direct measurements of the solar wind were in the
1960’s but it had already been suggested in the early
1900s.
– To explain a correlation between auroras and sunspots Birkeland
[1908] suggested continuous particle emission from these spots.
– Others suggested that particles were emitted from the Sun only
during flares and that otherwise space was empty [Chapman and
Ferraro, 1931].
– Observations of comet tails lead to the suggestion of a continuous
solar wind.
– The question of a continuous solar wind was resolved in 1962
when the Mariner 2 spacecraft returned 3 months of continuous
solar wind data while traveling to Venus.
5
6
Solar Wind Solution
•
The solar wind exists because the Sun maintains a 2x106K corona as
its outer most atmosphere.
The Sun’s atmosphere “boils off” into space and is accelerated to
high velocities (> 400 km s-1).
Parker [1958] proposed that the solar wind was the result of the
high temperature corona and developed a hydrodynamic model to
support his idea. Based on this Dessler developed a simple
gravitational nozzle which demonstrates the basic physics.
•
•
–
Simplifying assumptions:
1. The solar wind can be treated as an ideal gas.
2. The solar wind flows radially from the Sun.
3. Acceleration due to electromagnetic fields is negligible.
4. The solution is time stationary (i.e. the time scale for solar wind
changes is long compared to the time scale for solar wind
generation).
7
1.
Conservation of mass -  vr2  const.
2.
Conservation of momentum -  v dv   dp   GM Sun
dr
3.
dr
r2
dp
Speed of sound - cs2  dr  dp
d d
dr
Combining (1), (2), (3) gives
 2 GM Sun 
2cs 

dv v 
r 

dr r
v 2 cs2

GM Sun
and v 2  cs2
r
GM Sun
2
Or 2cs 
and v 2  cs2
r

If 2cs2 
then
dv
0
dr
8
• The transition from subsonic to supersonic occurs at a critical radius rc
wherev  cs
• In order for a real continuous solution to exist at rc
GM Sun
rc 
2cs2
• The form of solutions for the expansion of the solar wind
• Solution A is the “observed” solar wind. It starts as a subsonic flow in
the lower corona and accelerates with increasing radius. At the critical
point the solar wind becomes supersonic.
• For solution F the speed increases only weakly with height and the
critical velocity is not reached. For this case the solar wind is a “solar
breeze”.
• For solution C the flow accelerates too fast, becomes supersonic before
reaching the critical radius and turns around and flows into the Sun. 9
• Solution B starts as a supersonic flow in the lower corona and becomes
subsonic at the critical point.
• If the flow decelerates less as in D it would still be supersonic at the
critical point and be accelerated again.
• Solution E is an inward blowing wind that is subsonic. The flow
accelerates as it approaches the Sun, turns back and leaves the Sun
supersonically.
• Quantitative solutions (after Parker [1958])
10
• For the solar wind to continue to accelerate then the mean thermal
energy must exceed the gravitational energy.
• To have a solar wind a star must have a cool lower atmosphere and a
hot outer atmosphere.
• How is the corona heated?
cp

– Assume an ideal gas p  const. where  
= ration of specific
cv
heats.
5
– If there is no heat gain or loss then the system is adiabatic and   3
 p
– cs2 

– Taking the spatial derivative of
GM Sun
 2cs2we find
r
0
0
d 2
cs r
dr
d
(r  1)
dr
11
• Solving
  r0 
 
0  r 
1
 1
Where  is the density at the base of the atmosphere r0.
0
• From the conservation of mass we get
2
  r0 
 
0  r 
• These two conditions cannot be solved for   53 and
therefore the lower atmosphere can’t be adiabatic.
• Heat must be supplied from the cooler stellar surface!
12
• In summary the outer layer of the solar atmosphere will accelerate
outward provided a suitable heating source adds enough energy to
overcome the Sun’s gravitational energy.
•
There is a limit to how hot the atmosphere can be and still produce a
supersonic solar wind!
dp kT
 kT
2
– For an ideal gas p  nkT 
and cs 
where m is the mass of the

d m
m
gas particles.
– Using this the equation for the solar wind expansion becomes
2kT GM Sun

dv v m
r

kT
dr r
v2 
m
– For very hot stars the numerator is always positive and the denominator is negative
so that as the atmosphere expands the velocity decreases and never becomes
supersonic.
– For cool stars both numerator and denominator start negative and flow accelerates
outward. At some time v approaches the sonic velocity. At this point the
acceleration will only continue if the thermal energy exceeds the gravitational
energy.
13
• The most detailed observations of the solar wind have been
made from spacecraft near the Earth.
Observed Properties of the Solar Wind near the Orbit of
the Earth (after Hundhausen, [1995])
Proton density
6.6 cm-3
Electron density
7.1 cm-3
He2+ density
0.25 cm-3
Flow speed (nearly radial)
450 km s-1
Proton temperature
1.2x105K
Electron temperature
1.4x105K
Magnetic field
7x10-9T
14
• It is useful to describe the solar wind in terms of quantities
that are conserved in the plasma flow.
Flux Through a Sphere at 1AU
(after Hundhausen, [1995])
Protons
8.4x1035 s-1
Mass
1.6x1012 g s-1
Radial momentum
7.3x1014 N (Newton)
Kinetic energy
1.7x1027 erg s-1
Thermal energy
0.05x1027 erg s-1
Magnetic energy
0.025x1027 erg s-1
Radial magnetic flux
1.4x1015 Wb (Weber)
15
• The solar wind speed and density have large variations on time scales
of days. Of special interest are high speed streams.
– The flow speed varies from pre-stream levels (400 km/s) reaching a
maximum value (600 km/s – 700 km/s) in about one day.
– The density rises to high values (>50 cm-3) near the leading edges of the
streams and these high densities generally persist for about a day. The
peaks are followed by low densities lasting several days.
– The proton temperature varies like the flow speed.
– The high speed streams tend to have a dominant magnetic polarity.
– The dominant source of high speed streams is thought to be field lines that
are open to interplanetary space. These regions are known as coronal
holes.
16
The Solar Wind is Highly Variable – V[m/s]
fast streams
Historical
Note:
Recent observations
shock
The solar
wind was
first
sporadically
detected by
the Soviet
space
probes
Lunik 2 and
3.
17
Solar Wind Statistics
“slow”
“fast”
18
• Intermixed with the outflowing solar wind is a weak magnetic field –
the interplanetary magnetic field (IMF).
– On the average the IMF is in the ecliptic plane at the orbit of the Earth
although at times it can have substantial components perpendicular to the
ecliptic.
– The hot coronal plasma has extremely high electrical conductivity and the
IMF becomes “frozen in” to the flow.
– If the Sun did not rotate the resulting magnetic configuration would be
very simple: magnetic field lines stretching radially from the Sun.
– The Sun rotates with a sidereal rotation period of 27 days.
– As the Sun rotates the base of the field line frozen into the plasma rotates
westward turning the radial field lines into an Archimedean spiral.
19
Loci of a
succession
of fluid parcels
(eight
of them in this
sketch)
emitted at a
constant
speed from a
source
fixed on the
rotating
Sun.
Loci of a succession of fluid
particles emitted at constan
speed from a source fixed
on the rotating Sun.
20
• Assume a plasma parcel on the Sun at a source longitude of  0 and a
source radius of r0.
– At time t the parcel will be found at the position  (t )   Sunt   0 and
r (t )  vswt  r0
– Eliminating the time gives r  vsw
  0
 r0
 Sun
21
• Let us express the
 magnetic field in the equatorial plane in polar
coordinates as B  ( Br , B )
 1  2
– Gauss’s Law in spherical coordinates is   B  2
r Br  0 since the
r

r
field depends only on r so that r 2 Br  r02 B0 .


– The magnetic flux through radial shells is conserved and the radial
component of the field decreases as
2
 r0 
Br  B0  
r
 
– The frozen-in field condition  (v  B)  0 gives
1 
(r (v Br  vr B ))  0
r r

or r (v Br  vr B ))  const. If we assume that B is radial at r0 we get
rv Br  rvr B  r02 SunB0
B 
rv Br  r02 B0
B 
rvr
v  r Sun
vr
Sun
Br
22
– At large distances r
Sun
 v and B   r Sun Br vr .
– The radial component falls off as r-2 while the azimuthal component falls
off as r-1.
2
  Sunr 
B0 r0

B(r )  2 1  
r
 vr 
• The angle between the magnetic field direction and the radius vector
from the Sun is tan   B Br . For typical solar wind parameters at the
Earth it is about 450 with respect to the radial direction.
• The stretched out heliospheric configuration is maintained by an
equatorial current sheet. The magnetic field lines and current lines are
plotted below.
23
Magnetic-field lines deduced from the isothermal MHD coronal
expansion model of Pneuman and Kopp (1971) for a dipole field at
the base of the corona. The dashed lines are field lines for the
pure dipole field.
MHD modeling shows that the
inner magnetic field lines (R <
2) near the equator are closed,
and that at higher latitudes the
field lines are drawn outward
and do not close.
These field lines that do not
close nearly meet at low
latitudes, but do not reconnect;
this abrupt change in the
magnetic field polarity is
maintained by a thin region
of high current density called
the interplanetary current sheet. This current sheet separates the plasma
flows and fields that originate from opposite ends of the dipole-like field.
24
• The IMF can be directed either inward or outward with
respect to the Sun.
• One of the most remarkable observations from early space
exploration was that the magnetic field polarity was
uniform over large angular regions and then abruptly
changed polarity.
– This polarity pattern repeated over succeeding solar rotations. The
regions of one polarity are called magnetic sectors.
– In a stationary frame of reference the sectors rotate with the Sun.
– Typically there are about four sectors.
– The sector structure gets very complicated during solar maximum.
25
• The sector structure inferred from IMP satellite
observations. Plus signs are away from the Sun and minus
signs are toward the Sun.
26
THE INTERPLANETARY MEDIUM AND IMF
Intermixed with the streaming solar wind is a weak magnetic field,
the IMF.
The solar wind is a
“high-b” plasma, so
the IMF is "frozen in”;
the IMF goes where
the plasma goes.
Consequently, the "spiral"
pattern formed by
particles spewing from
a rotating sun is also
manifested in the IMF.
The field winds up because
of the rotation of the sun. Fields in a low speed wind will be
more wound up than those in high speed wind.
27
• Until the 1990’s our knowledge of the heliosphere was limited to the
ecliptic.
• The Ulysses spacecraft observed flow over both the northern and
southern poles of the Sun.
• No latitudinal gradient in Br.
– Magnetic flux is removed from the poles toward the equatorial regions.
– Sketch showing equatorial current sheet and magnetic field lines coming
from the polar regions toward the equator. [Smith et al., 1978]
28
• Plasma measurements show a
dramatic change in velocity
with latitude in observations
taken between 1992 and 1997.
[McComas et al., 1998].
– The velocity increases from
about 450 km/s at the equator
to about 750 km/s above the
poles.
– Above 500 only fast solar
winds streaming out of coronal
holes were observed.
– Up to about 300 a recurrent
CIR was observed with a
period of about 26 days.
– Near the equator, the curvature
force due to the magnetic field
reduces the solar wind speed.
29
Plasma leaves the sun predominantly at high latitudes and flows
out and towards the the equator where a current sheet is formed
corresponding to the change in magnetic field polarity.
The Sun’s magnetic field is dragged out by the high-beta solar
wind. The current sheet prevents the oppositely-directed fields from
reconnecting.
The current sheet is tilted with respect to the ecliptic (about 7°),
ensuring that earth will intersect the current sheet at least twice during
each solar rotation. This gives the appearance of "magnetic sectors".
1
j=
2

 B
0
3
1
j
B
 j =  B =  1 iˆ
o3
x 3
2
1976 (max 1979) 1986
1998 (max 2001) 2008
30
• That the IMF has sector structure suggests that plasma in a given
sector comes from a region on the Sun with similar magnetic polarity.
• The sector boundaries are an extension of the “neutral line” associated
with the heliospheric current sheet (HCS).
– The dipolar nature of the solar magnetic field adds latitudinal structure to
the IMF.
– The radial magnetic field has one sign north of the HCS and one sign
south of the HCS.
– The current sheet is inclined by about 70 to the rotational equator.
– As the Sun rotates the equator moves up and down with respect to the
solar equator so that the Earth crosses the equator twice a rotation. [From
Kallenrode, 1998].
31
Wavy Structure of the Interplanetary Current
Sheet
Where Earth’s orbit intersects this current sheet determines whether
Earth “sees” a positive or negative magnetic sector.
32
Two Classes of Solar Particle Events
33
•
•
•
•
•
•
The Archimedean spiral associated
with slow streams is curved more
strongly than for a fast stream.
Because field lines are not allowed
to intersect at some point an
interaction region develops
between fast and slow streams.
Since both rotate with the Sun
these are called corotating
interaction regions (CIR).
On the Sun there is an abrupt
change in the solar wind speeds but
in space the streams are spread out.
At the interface between fast and
slow streams the plasma is
compressed.
The characteristic propagation
speeds (the Alfven speed and the
sound speed) decrease.
At some distance between 2AU and
3AU the density gradient on both
sides of the CIR becomes large and
a pair of shocks develop.
•
The shock pair propagate away
from the interface.
– The shock propagating into the
slow speed stream is called a
forward shock.
– The shock propagating into the fast
wind is called a reverse shock.
34
• Changes in the solar wind plasma parameters (speed V, density N,
proton and electron temperatures TP and TE, magnetic-field intensity
B, and plasma pressure P) during the passage of an interplanetary
shock pair past the ISEE 3 spacecraft. [Hundhausen, 1995].
35
Acceleration of High-Energy Particles:
Near the Sun & in Interplanetary Shocks
The measured spectra of
energetic particles near Earth
indicate 2 spectral regimes.
The time history indicates
the high-energy component
was accelerated near the Sun,
and the low-energy
component in interplanetary
space, probably in association
with shocks.
36
• Coronal mass ejections in
interplanetary space still carry
the magnetic signature of the
filament that formed them on
the Sun.
– These closed magnetic field
structures are called magnetic
clouds.
– Magnetic and plasma data
from a magnetic cloud.
Magnetic field magnitude,
elevation, azimuth, solar wind
speed, plasma density, and
proton temperature.[Burlaga,
1991]
– Decrease in B in the cloud.
– Rotation of the magnetic field
vector.
– Decreases in the density,
plasma speed, and plasma
temperature
37
• The magnetic field configuration of a magnetic cloud can
be inferred from the variation in the elevation.
– At the beginning of the event the field is perpendicular to the ecliptic
plane.
– After the cloud has passed the field has almost reversed direction.
– This is an indication of a magnetic field wrapped around the structure –
sometimes called a flux rope.
– The orientation of the magnetic cloud (i.e. whether is it north then south or
vice versa depends on the field at the source).
– How long the cloud stays connected to the Sun is not known.
– Magnetic clouds are the main cause of geomagnetic disturbances called
magnetic storms at Earth.
38
Coronal Holes and Solar
Wind Speed and Density
The interplay between the inward
pointing gravity and outward pointing
pressure gradient force results in a
rapid outward expansion of the
coronal plasma along the open
magnetic field lines.
At low latitudes the direction of the
coronal magnetic field is far from
radial. Therefore the plasma cannot
leave the vicinity of the Sun along
magnetic field lines. At the base of
low-latitude coronal holes, however,
the magnetic field direction is not far
from radial, and the expansion of the
hot plasma can take place along open
magnetic field lines without much
resistance  fast solar wind.
39
• The heliospheric current sheet shows marked variation during the solar
cycle.
– The “waviness” of the current sheet increases at solar maximum.
– The current sheet is rather flat during solar minimum but extends to high
latitudes during solar maximum.
– During solar minimum CIRs are confined to the equatorial region but
cover a wide range of latitudes during solar maximum.
– The average velocity of the solar wind is greater during solar minimum
because high-speed streams are observed more frequently and for longer
times
40
How does the corona acquire the necessary energy for the
mean thermal energy of the coronal gas to increase outward
from the sun and overcome the sun's gravity ? A source of
coronal heating is required. Four possibilities have been
suggested:
•
•
•
•
Acoustic wave dissipation
Alfven wave dissipation
MHD wave dissipation
Microflares “magnetic carpet”
The currently favored mechanism, evolved from multi-instrument
observations from SOHO, is that “short-circuit” electric currents
flowing in the loops of the “magnetic carpet”, and extending into
the corona, provide the energy necessary to raise the coronal
temperatures to millions of degrees K. Microflares are thought to
accompany these intense currents.
41
Small magnetic loops permeate the surface of the Sun,
much like a magnetic carpet
Each loop carries as much energy
as a large hydroelectric plant
(i.e., Hoover Dam) generates in
about a million years !
More sensitive instruments are
needed to actually observe the
microflares thought to exist.
Energy flows from the loops when
they interact, producing electrical
and magnetic “short-circuits”. The
very strong currents in these short
circuits are what heats the corona
to high temperatures.
42
• Waves and turbulence?
– One possibility is that the corona is heated by compressional waves
at or just below the surface. Oscillatory motion of the Sun’s
surface could drive pressure waves. In theory fast mode waves
could propagate up to 20RSun. Experiments designed to detect
sound waves propagating into the corona have not detected them.
• Impulsive energy release?
– The Sun has a magnetic field that contains magnetic energy.
Magnetic energy can be converted into thermal energy. This is
done by reconnection. The granularity of the photosphere as the
top of the convection zone is caused by bubbles rising and falling.
These might reconnect. X-ray bursts may be evidence of this
happening.
• We still don’t know how the corona is heated!
43
The Heliosphere and its Interaction with the Interstellar Medium
Heliopause
Interstellar Medium
Termination Shock
Heliosphere
Heliospheric Bow Shock ?
The heliosphere and heliopause represent the region of space influenced
by the Sun and its expanding corona, and in some respects encompass
the true extent of the solar system.
44
The radially-expanding supersonic solar wind must
be somehow diverted to the downstream direction to
merge with the flow of the interstellar medium. This
diversion can only take place in subsonic flow, and
therefore the supersonic expansion of the solar wind
must be terminated by an “inner shock” or
“termination shock”.
Flow lines of the
interstellar plasma
do not penetrate
into the region
dominated by the
solar wind flow but
flow around a
“contact surface”
called the
heliopause,
which is
considered to be
the outer boundary
of the heliosphere.
The interstellar
medium (ISM) will
form a heliospheric
bow shock if it is
supersonic with
respect to the
heliopause
26 km/sec
45
46
47
•The solar wind forms a
bubble, called the
heliosphere, in the partially
ionized local interstellar
medium (LISM).
•We do not know if the LISM
is subsonic – the LISM flow
will be diverted around the
heliospheric obstacle either
adiabatically or by forming a
bow shock.
•The boundary separating the
heliosphere from the LISM is
the heliopause (HP).
•The solar wind is supersonic
and a shock (the termination
shock-TS) forms within the
heliosphere as it approaches
the heliopause.
•The region of shocked
plasma between the TS and
the heliopause is called the
inner heliosheath.
•In the simulation below the
LISM flow was assumed to
be supersonic and no
interstellar neutral hydrogen
was assumed.
Contours of temperature and
flow streamlines- from Zank et48
al., 2001
49