The Solar Wind

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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.
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Solar Atmosphere Solution
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• The Earths atmosphere is stationary. The Suns
  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 1960s 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.

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Solar Wind Solution

• The solar wind exists because the Sun maintains a
  2x106K corona as its outer most atmosphere.
• The Suns atmosphere boils off into space and
  is accelerated to high velocities (gt 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
• The solar wind can be treated as an ideal gas.
• The solar wind flows radially from the Sun.
• Acceleration due to electromagnetic fields is
  negligible.
• 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).

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• Conservation of mass -
  
• Conservation of momentum -
  
• Speed of sound -
• Combining (1), (2), (3) gives
• If and then

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• The transition from subsonic to supersonic occurs
  at a critical radius rc where
• In order for a real continuous solution to exist
  at rc
• 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.

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• 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)

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• 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?
• Assume an ideal gas
  where ration of specific heats.
• If there is no heat gain or loss then the system
  is adiabatic and
• Taking the spatial derivative of
  we find

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• Solving
• Where is the density at the base of the
  atmosphere r0.
• From the conservation of mass we get
• These two conditions cannot be solved for
  and therefore the lower atmosphere cant be
  adiabatic.
• Heat must be supplied from the cooler stellar
  surface!

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• In summary the outer layer of the solar
  atmosphere will accelerate outward provided a
  suitable heating source adds enough energy to
  overcome the Suns gravitational energy.
• There is a limit to how hot the atmosphere can be
  and still produce a supersonic solar wind!
• For an ideal gas
  and where m is the
  mass of the gas particles.
• Using this the equation for the solar wind
  expansion becomes
• 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.

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• 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) 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
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• 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) 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)
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• 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 (gt50 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.

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The Solar Wind is Highly Variable Vm/s
fast streams

• Historical Note
• The solar wind was first sporadically detected by
  the Soviet space probes Lunik 2 and 3.

Recent observations
shock
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Solar Wind Statistics
slow
fast
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• In summary the outer layer of the solar
  atmosphere will accelerate outward provided a
  suitable heating source adds enough energy to
  overcome the Suns gravitational energy.
• There is a limit to how hot the atmosphere can be
  and still produce a supersonic solar wind!
• For an ideal gas
  and where m is the
  mass of the gas particles.
• Using this the equation for the solar wind
  expansion becomes
• 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.

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• 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.

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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 constant speed from a source fixed on the
rotating Sun.
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• Assume a plasma parcel on the Sun at a source
  longitude of and a source radius of r0.
• At time t the parcel will be found at the
  position and
• Eliminating the time gives

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• Let us express the magnetic field in the
  equatorial plane in polar coordinates as
  
• Gausss Law in spherical coordinates is
  since the field
  depends only on r so that
  .
• The magnetic flux through radial shells is
  conserved and the radial component of the field
  decreases as
• The frozen-in field condition
  gives
• or If
  we assume that is radial at r0 we get

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• At large distances and
  .
• The radial component falls off as r-2 while the
  azimuthal component falls off as r-1.
• The angle between the magnetic field direction
  and the radius vector from the Sun is
  . 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.

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• 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.

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• The sector structure inferred from IMP satellite
  observations. Plus signs are away from the Sun
  and minus signs are toward the Sun.

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THE INTERPLANETARY MEDIUM AND IMF Interm
ixed 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.
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• Until the 1990s 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

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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 lt 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.
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• 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.

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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 Suns 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".
2
3
1
j
1976 (max 1979) 1986 1998 (max 2001) 2008
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• 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.

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Wavy Structure of the Interplanetary Current Sheet
Where Earths orbit intersects this current sheet
determines whether Earth sees a positive or
negative magnetic sector.
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Two Classes of Solar Particle Events
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• 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.

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• 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.

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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.
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• 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

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• 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.

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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.
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• 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

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• 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.
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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.
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• Waves and turbulence?
• One possibility is that the corona is heated by
  compressional waves at or just below the surface.
  Oscillatory motion of the Suns 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 dont know how the corona is heated!

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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.

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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.
The interstellar medium (ISM) will form a
heliospheric bow shock if it is supersonic
with respect to the heliopause
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.
26 km/sec
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• 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.

• 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.

Contours of temperature and flow streamlines-
from Zank et al., 2001
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