Heliosphere - Lectures 5 September 27, 2005 Space Weather Course Solar Wind, Interplanetary Magnetic Field, Solar Cycle Chapter 12-Gombosi (The Solar Wind) Chapter 6 - Kallenrode (The Solar Wind) Chapter 12- Parker (The Solar Wind) - PowerPoint PPT Presentation

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Heliosphere - Lectures 5 September 27, 2005 Space Weather Course Solar Wind, Interplanetary Magnetic Field, Solar Cycle Chapter 12-Gombosi (The Solar Wind) Chapter 6 - Kallenrode (The Solar Wind) Chapter 12- Parker (The Solar Wind)

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Title: Heliosphere - Lectures 5 September 27, 2005 Space Weather Course Solar Wind, Interplanetary Magnetic Field, Solar Cycle Chapter 12-Gombosi (The Solar Wind) Chapter 6 - Kallenrode (The Solar Wind) Chapter 12- Parker (The Solar Wind)


1
Heliosphere - Lectures 5September 27, 2005 Space
Weather CourseSolar Wind, Interplanetary
Magnetic Field, Solar CycleChapter 12-Gombosi
(The Solar Wind)Chapter 6 - Kallenrode (The
Solar Wind)Chapter 12- Parker (The Solar Wind)
2
Before we start
3
Overview of what we will see in Lecture 05
  • Lecture 5 (Sep. 27, 2005)
  • Solar wind formation and acceleration
  • (how the Sun generates its solar wind. Why
  • Does the Sun has a wind?)
  • - Interplanetary magnetic field
  • (How the Magnetic Field from the Sun is carried
  • into space? How does it look?)

_at_P.Frisch
4
  • Lecture 6 (Oct. 4, 2005)
  • Corotating interaction regions
  • (what are they? How do they form?)
  • Heliosphere during the solar cycle
  • (the Sun changes every 11 years-so how the
    Heliosphere
  • Reacts to that?)
  • -CMEs in the interplanetary space (magnetic
    clouds),
  • (How CMEs propagate in the heliosphere)
  • -interplanetary shocks
  • (CMEs pile up material forming shocks-how those
    shocks propagate in space)
  • -shock physics
  • (what happens at a shock?)

_at_P.Frisch
5
Lecture 7 (after John Guillary) -energetic
particles in the heliosphere (galactic, anomalous
cosmic rays and solar energetic particles) (who
are they? Where do they come from? Which ones are
the most hazardous to Earth?) -Solar wind
interaction with the nearby interstellar
medium. (the solar system interacts with the
interstellar medium-how this interacts happens?
How it affects the Heliosphere, Earth and Space
Weather?
_at_P.Frisch
6
The Heliosphere
A global view of the Heliosphere
7
Magnetic Structure of the Sun
Magnetic Structure of the Sun
Streamer Belt
Coronal Holes
Helmet streamer
Helmet Streamers
Fast Wind
Slow Wind
Open and closed Field Lines
8
The Solar Wind
At the beginning of the twentieth century, a
particle of flow from the Sun Towards Earth was
suggested by Birkeland (1908) to explain
the Relationship between aurorae and sunspots
(The Norwegian aurora Polaris expedition
1902-1903 On the cause of magnetic storms and
the Origin of terrestrial magnetism)
Chapman (1919) (an outline of a theory of
magnetic storms) and Chapman and Ferraro (1931)
(A new theory of magnetic storms) suggested
the emission of clouds of ionized particles
during flares only. Except for these plasma
clouds, interplanetary space was assumed to be
Empty.
(Description is in chapter 04 Gombosi) (Also
chapter 6 from Kallenrode)
9
Cont. of historic background
Evidence to the contrary came from observations
of comet tails the tail of a comet neither
follows the path of the comet nor is
directed Exactly radially from the Sun but
deviates several degrees from The radial
direction. Hoffmeister (1943) suggested that
solar particles and the solar light pressure
shape the comet tails.
Characteristics of the Solar Wind
It is a continuous flow of charged particles. It
is supersonic With a speed of 400 km/s (x 40
the sound speed) (a parcel of plasma travels from
Sun-Earth in 4 days). The Solar wind carry the
solar magnetic field out in the Heliosphere the
magnetic field strength amounting to nanoteslas
at Earth. Two distinct plasma flows are observed
Fast and Slow Wind
10
Solar Wind Bi Modal Structure
Solar Wind Bi-Modal Structure
Property (1 AU) Slow Wind Fast Wind Flow
Speed 400 km/s 750 km/s
Density 7 cm-3
3 cm-3 Variance "large", gt50 Variance
"small", lt50 Temperature T(proton, 1AU)
200,000 K T(proton, 1 AU) 50,000 K
11
Fast and Slow Wind
Fast Solar Wind originates in coronal holes (the
dark parts of the Corona dominated by open field
lines) The streams are often stable over a long
time period. Has flow speeds between
400-800km/s average density is low 3 ions/cm3
(1AU) 4 of the ions are He The proton
temperature is about 2x105 K The electron
temperature is about 1x105K
Slow Solar Wind Speeds between
250-400km/s Average density is 8 ions/cm3
(1AU) Solar Minimum -slow wind originates from
regions close to The current sheet at the
heliomagnetic equator. 2 of the ions are He
(highly variable) Solar Maxima - slow wind
originates above the active regions in
the Streamer belt and 4 of the ions are
He Compared to the fast wind, the slow wind is
highly variable and turbulent The proton
temperature is 3x104 K (low!) The electron
temperature is similar to fast
12
More on the slow and fast winds..
(to the magnetic field)
For the fast and slow winds
Also the momentum flux
on average is similar.
Same is true for the total energy flux (despite
the fact that Kinetic energy, potential energy,
thermal energy, electron and proton heat flux,
wave energy, are different.
Charge states of heavy ions indicate a T 106K
in the corona The photosphere is only 5800K - So
one of the basic questions in understanding the
corona and solar wind is how can the corona be
heated up to a Million Kelvin?
13
Origin of Solar Wind
  • First theory of an extended corona was by Chapman
    (1957)
  • Static atmosphere with energy transfer by
    conduction alone.

The mathematical theory was put forward by Eugene
Parker (Astrophysical Journal 1958) - very
controversial Solar wind was first sporadically
detected by Lunik 2 and 3 (soviet space probes)
but the first continuous observations was made
with Mariner 2 Spacecraft (Neugebauer, M.
Snyder, C.W., JGR 1966)
(further reading M. Velli ApJ 1994)
Mariner 2 data
14
MHD equations
The equations that describe a magnetized
conducting fluid (ideal MHD) are
continuity
momentum
magnetic field
energy
Whole gas as a single conducting fluid Maxwell
equations (here dE/dt0) (?m?0 conduction ??)
(Description is in chapter 04 Gombosi)
15
More on solar wind
If you neglect the effect of heat conduction and
magnetic fields
If we assume stationary solar atmosphere (u0)
Chapmans assumed isothermal corona so
pnpkTnekT
(further reading M. Velli ApJ 1994 Priest, E.
chapter 12)
16
Problems with Static corona
Then, we get
That gives,
Where the index B indicate the Base of the corona
As r??, p?cte
p? 3 x10-4 pB gtgt any reasonable
interstellar Pressure!!! So a Hot Static Corona
cannot exist
For TB 106 K
17
Parker (1958) Astrophys, J 128, 664 -gt Corona
cannot be in static equilibrium but instead it
is continuously expanding outwards
(In the absence of a strong pressure at infinity
(lid) to hold the corona-it must stream outward
as the solar wind)
Parker Solution (neglecting electromagnetic
effects)
The momentum equation
Outflow plasma
Pressure gradient
gravity
18
More on parker solution
Substituting we get
Where
is the local sound speed.
There is a critical point A where du/dr is
undefined When uas,
so that both coefficient of du/dr and the
right hand side vanish.

Assuming aScte
(isothermal solar corona) and integrating in both
sides
Depending on the constant C this equation have 5
different solutions
19

A
Classes I and II have double valued solutions
which are unphysical
Class III posseses supersonic speeds at the Sun
what are not observed So we have left solutions
IV and V .
The solar wind solution V it starts as a
subsonic flow in the lower corona, accelerates
with increasing radius. At the critical point rC
it becomes supersonic. (C-3). At large distances
where vgtgtvc, the velocity And the density fall
of as so that the
pressure vanish at infinity. For T106K the
predicted flow speed at 1AU is 100km/s.
20
lachzor page 239 T. Gombosi
Parkers solution for different coronal
temperatures
For example, for T106K, and coronal density of
2x108cm-3, rc6Rs. The solar wind accelerates to
up to 40RS, and afterwards propagates to a
nearly constant speed of 500km/s
Solar Breeze (Type IV) subsonic
The speed increases only weakly with height and
the critical Velocity is not acquired at the
critical radius. The flow Then continues to
propagate radially outward But then slows down
and can be regarded as a solar breeze.
21
More on parker solution
The parker solar wind is a simplified model
because the coronal Temperature does not remain
constant as it expands.
  • Limitations and Assumptions
  • Isotropy It is established that T( r) r-?,,
    where ? is the polytropic index
  • And still allow for solar wind type solutions.
    (at earth the typical
  • Plasma temperature is a factor of 10 lower).
  • Electron and proton temperatures are not theh
    same as it assumed in the model
  • (modify slightly the numbers)
  • Consideration of only one particle species
    (protons).
  • (another set of equations needs to be
    considered-gtleading to a reduction
  • Of the flow speed)
  • No Magnetic or Electric Field considered. In a
    MHD model
  • The critical point is lowed in the corona ( 2
    Rs) but the general form
  • Of the solution is the same.

Although the hydrodynamic description of the
solar wind is a reasonable and valuable Approach
a fundamental problem that was neglected is the
heating of the corona. Some heating mechanism is
needed (especially near the critical point)
22
Brief notes on Coronal Heating
Heating by Waves and Turbulence Altough
non-thermal broadening Of some spectral lines
indicated the existence of waves or turbulence In
the lower corona, it is not completely understood
which kind of Waves these are, how they
propagate outward and whether the
observations Are indicative of wave fields or of
turbulence. March, E. (1994) Theoretical models
for The solar wind, Adv. Space Phys. 14, (4)
(103).
Impulsive Energy Release Even for coronal
heating by MHD waves, The field is only used as
carrier for the waves while its energy is
neglected. The conversion of field energy into
thermal energy could provide a heating mechanism.
Reconnection happens when field of opposite
polarity Encounter. The photosphere is in
continuous motion with bubbles rising and
falling And plasma flowing in and out. Thus on a
small scale magnetic field configurations suitable
for reconnection will form frequently,
converting magnetic field into thermal energy.,
23
Interplanetary Magnetic Field
The magnetic induction equation
can be written
The sun rotates with a period of 27 days. In the
rotating frame a vector A
So the flow speed in the corotating system is
The time derivative of B in the rotating system
is
And the induction equation in the rotating frame
is
24
Expanding the right hand side you get
The left hand side is the total time derivative
of B in the system rotating with the Sun DB/Dt
So
and
In the Steady State
There is a scalar potential
25
Taking the product of
With u and B
And some mathLook at page 243 of Gombosis book
This means that that in the rotating frame
The magnetic field and plasma vectors are
always Parallel in the rotating frame
26
The Geometry of the Magnetic Field
First no polar components
and
Since u and B are parallel to each other the
ratio between B? and Br needs to be the same
Where we assumed that uSW is the assymptotic
velocity of the solar wind and that At large
distances rgtgtRS the plasma velocity is
practically radial (in the non corotating frame)
So
27
From Maxwell Equations
in spherical coordinate system is
And
that leads to
so
Substi. In the expression of B we get
28
At large distance from the Sun rgtgtRS
We can see that
(fall more slowly!)
and
As we go outward in the solar system the magnetic
field becomes more and more azimuthal
29
Coronal Structure and Magnetic Field
An assumption that we made was corona was
spherically symmetric! But close to the Sun its
a poor approximation regions of open and close
field lines
To have a realistic solar magnetic field you need
to solve
And assuming that at all times the solution only
depends on r and ?
Pneuman and Kopp (1971) solve iteratively
starting with a dipole
30
The solution obtained
The lines are drawn outward by the plasma And
become open
Field lines from opposite polarities
Heliospheric Current Sheet
Initial State solid lines-Dipole Final State
dashed lines
MHD model Zeus-3D
(Asif ud-Duola, Stan Owcki)
Coronal plasma in static equilibrium balance
between Pressure gradient and gravity
31
Heliospheric Current Sheet
Non alignement of the magnetic axis and the
rotation axis produces the ballerina skirt
32
Solar Cycle and the Heliosphere
During solar minima the magnetic field is
approximately a dipole. The orientation of the
dipole is almost aligned with the rotation
axis. During declining phase of the solar
activity the solar dipole is most noticeably
tilted relative to the rotation axis During
solar maxima the Suns magnetic field is not
dipolelike.
33
How wide is the current sheet?
?
B


34
Global View of the Magnetic Field
Global View of the Magnetic Field
Meridional Plane
ISW
Opher et al.
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