Download Observed Properties of the Solar Wind near the Orbit

ESS 200C
Lectures 6 and 7
The Solar Wind
• The Earth’s atmosphere is stationary. The Sun’s
atmosphere is not stable but is blown out into space as
the solar wind filling the solar system and then some.
• 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.
•Bierman, 1951: Cometary tails point directly away from Sun
regardless of comet’s velocity
=> must be ionized gas pushed away by solar ionized gas, the solar wind
To Sun
Solar Wind forms the ion tail. Solar
wind must have very high speed relative
to comet, to align tail with sun direction.
Radiation pressure on micro-size
dust grains forms the diffuse dust tail.
Grains have less sunward force, move
further away from Sun, but fall behind
the radial direction because their angular
speed is lower than closer in. Dust tails
curve around (lag from radial direction).
Image of Hale Bopp (Courtesy: John Gleason and NASA)
• Measured solar wind speeds (heavy lines) and
densities (light lines) with Mariner 2 in 1962
[Hundhausen, 1995].
• 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
• 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)
•
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).
Assume hydrostatic equilibrium:
- no flow (u=0)
- no forces (true for radial fields)
Not possible !
Solar Wind Acceleration 4
1.
Conservation of mass -  vr2  const.
2.
Conservation of momentum -  v dv   dp   GM2 Sun
dr
3.
dp
dp
2kT
Speed of sound - cs2  dr 

d d
m
dr
Combining (1), (2), (3) gives
 2 GM Sun 
2cs 

dv v 
r 

dr r
v 2 cs2

If

dv
GM Sun
2
2
2
0
 2cs and v  cs then
dr
r
dr
r
• The transition from subsonic to supersonic occurs at a critical
radius rc where v  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.
• 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])
• 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.
• Following derivation in Ch.3 but using  =5/3 you can show that there is no
solution that reaches supersonic speed, i.e., the solar wind does not
accelerate unless there is heating. Actually only for
 <=3/2 can reach supersonic speeds.
– The solar wind heating is provided by electrons:
•
•
•
•
•
At 10^6 degrees, electrons have thermal speeds >1000km/s
At 10^6 degrees, ions have thermal speeds < 100km/s
Electrons move along field lines fast, create an electric field, pull ions
Heating of the base in the solar corona provides energy for acceleration
Using equation of energy conservation you can prove that
– The initial energy in the enthalpy minus potential energy in the solar gravity
– Final energy is in the kinetic energy of solar wind
– Energy transformation depletes enthalpy and increases solar wind
speed to supersonic speeds.
• 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!
• Motion of granules and magnetic structures –
Hinode observations
• As the feet of the field lines move they are
twisted and since they can’t cross current
sheets develop. Reconnection across these
current sheets is thought to heat the corona.
• 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!
2kT
 2kT and 2 dp
– For an ideal gas p  2nkT 
where m is the
cs 

m
d
m
mass of the gas particles, =1 for isothermal plasma.
– Using this the equation for the solar wind expansion becomes
4kT GM Sun

dv v m
r

dr r v 2  2kT
m
– For very hot stars the numerator is always positive and the denominator is
initially 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. Past
this point the acceleration will only continue if the thermal energy exceeds
the gravitational energy.
• 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.
– As the Sun rotates (sidereal period 27 days) the base of the field line
frozen into the plasma rotates westward creating an Archimedean
spiral.
• 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
  0
r

v
 r0
– Eliminating the time gives
sw

Sun
In order to determine the radial falloff of the magnetic field and the
shape of the field lines, we can use flux conservation and the
frozen in condition either in a rotating frame (book) or a fixed frame
• Let us express the magnetic field
in the equatorial plane in

polar coordinates as
B  ( Br , B )
 1 
– Gauss’s Law in spherical coordinates is   B  2 r 2 Br   0
r r
2
2
field depends only on r so that r Br  r0 B0 .
since the
– 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
– 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 sketched below.
At the edges of the heliosphere the radial field drops off as r2
and the azimuthal component as r, both approach zero as r -> 
The mach number u/cs goes to infinity either because the flow
increases or because the temperature decreases
The only way to stop the supersonic wind is for a shock to form
at the interface with the interstellar medium.
At the “termination” shock the dynamic pressure of the flow
balances the interstellar gas pressure.
•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 et
al., 2001
• Observations from Voyager 1 as it crossed the
termination shock.
– (left) Energetic particle measurements show increase in
particle fluxes at shock (A, B, D) and change in first order
anisotropies (C) and radial velocity (F). (Decker et al., 2005)
–(right) The magnetic field magnitude increased (A) and the
galactic cosmic ray intensity increased. (Burlaga et al., 2005)
• The Voyager passage through the termination shock
– Voyager moving at a speed of 3.6 AU/year was 94AU from
the Sun when it encountered the shock.
–The shock was moving toward the Sun possibly because
decreasing solar wind dynamic pressure.
– As of December, 2005 Voyager 1 was still in the heliosheath.
• 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.
• The sector structure inferred from IMP satellite
observations. Plus signs are away from the Sun and
minus signs are toward the Sun.
• A meridian view of the IMF
– The rotation and dipole axes are
along the left edge of the figure
and the solar equator is
horizontal
– The dipole component of the
solar magnetic field (dashed
lines) is distorted by the solar
wind flow
– The expected IMF is shown by
solid lines.
– Beyond a distance of about 2
solar radii the solar wind is
stronger than the tension in the
field lines and the field lines are
pulled outward
– The IMF that reaches the Earth
has its foot-points rooted at
middle latitudes
– The antiparallel field lines in the
equatorial plane require a
current sheet between them.
• 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].
• As the Sun rotates the three dimensional current
sheet becomes wavy. This is sometimes called the
Ballerina skirt model of the heliosphere.
• 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.
750
100 250
10
1
104 105
Temp. (K) Density (cm-3)
– Velocity, density
and proton
temperature of two
high speed streams
– Speed and
temperature have
similar variations
with time
– Note that low speed
corresponds to high
density and vice
versa
Flow Speed (km/s)
• Observations of high speed streams
•
•
•
•
•
•
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.
• Time series of parameters associated with a CIR
– Between the two shock waves, and
centered on the interface, the plasma is
compressed
– This implies a higher density of S’ plasma
than unshocked S plasma
– Similarly the shocked F’ plasma is higher
density than unshocked F plasma, but the
density of F’ < density S’ since fast plasma
has lower density than slow plasma
– The S’ plasma is moving faster than S, but
slower than F’ which is slower still than F
– The S’ plasma has a positive azimuthal
velocity, the interface a zero azimuthal
velocity, and the F’ a negative azimuthal
velocity
– The magnitude of the magnetic field is
compressed between the shocks
– There is increased magnetic turbulence
and temperature in the interaction region
– Not shown is a tipping of the IMF out of the
ecliptic plane
• 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].
• Until the 1990’s our knowledge of the heliosphere was limited to
the ecliptic.
• The Ulysses spacecraft observed the 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]
• 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.
• 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
• A coronal mass ejection in space
– A time sequence of differences
between four images taken with the
Solar Maximum Mission
coronagraph during a coronal mass
ejection on 14 April 1980 and a
single "pre-event" image.
– Positive differences (brightenings of
the corona since the pre-event
image) are shown in red and
orange, negative differences in
blue.
– A pair of bright (red) loops moved
outward through the corona
between 0544 and 0709 UT, leaving
a wedge of depleted (blue) corona
behind them (as at 0847 UT).
– Coronal features to the sides of the
loops were progressively pushed
away from the ejection during its
passage through the coronagraph
field of view, and are thus visible on
these difference images
• Observations of a CME in space
–
–
–
–
•
CMEs are often referred to as
magnetic clouds, bottles, or flux ropes.
At 1 AU they take about a day to pass
the Earth.
The axis of these may have any
orientation. The simplest rope lies in
the ecliptic plane orthogonal to the
Earth-Sun line
Their identifying characteristic is a
region of nearly constant magnetic
field strength with slow sinusoidal
changes in the two field angles. N is
generally low.
If the cloud is traveling fast relative to
the solar wind a shock will form ahead
of the cloud. The shock is evident from
the increase in B, N, T (VT), and V.
These are called Interplanetary
Shocks (IPS).
In the sheath between the shock and
cloud the field and density are
compressed and turbulent.
• 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.
– Note the increasing helicity of the field from the inside out.
– The orientation of the magnetic cloud (i.e. whether is it north
then south or vice versa depends on the field at the source).
•
–
–
•
•
•
In some CMEs there are
both forward and reverse
shocks.
The forward shock forms in the
slow solar wind speeding it up
relative to the Earth, but slowing
the flow as seen by the CME.
The reverse shock propagates
into the magnetic cloud slowing it
down relative to the Earth.
The cloud may be rotated an
any angle about the Earth-Sun
line.
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.