Download Heliosphere: Solar Wind, Interplanetary Magnetic Field

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)
Before
we start:
Lecture 5 (Sep. 27, 2005)
-Solar wind formation and acceleration
(how the Sun generates it’s 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?)
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?)
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?
A global view of the Heliosphere
Magnetic Structure of the Sun
Coronal
Holes
Streamer
Belt
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Helmet streamer
Slow Wind
Fast Wind
Helmet Streamers
Open and closed Field Lines
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)
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
Solar Wind: Bi-Modal Structure
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Property (1 AU) Slow Wind
Fast Wind
Flow Speed
400 km/s
750 km/s
Density
7 cm-3
3 cm-3
Variance "large", >50% Variance "small", <50%
Temperature T(proton, 1AU) ~ 200,000 K T(proton, 1 AU) ~ 50,000 K
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…
More on the slow and fast winds..
For the fast and slow winds: Tparallel  T
Also the momentum flux
(to the magnetic field)
M  n p m p v2p on average is similar.
 total energy flux (despite the fact that
Same is true for the
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?
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
The equations that describe a magnetized conducting
fluid (ideal MHD) are:
 m
  (  m u)  0
t

u
B 2  BB 
 m   m (u  )u   p 
  m g
I 
t
 20  0 
B
  (uB  Bu)  0
t
3 p 3
5
 (u  ) p  p( u)  0
2 t 2
2
continuity
momentum
magnetic field
energy
Whole gas as a single conducting fluid + Maxwell equations
(here dE/dt=0) (m0; conduction )
(Description is in chapter 04 Gombosi)
If you neglect the effect of heat conduction and magnetic fields:
1 d 2
r u 0

2
r dr
du dp
MS
u   G 2  0
dr dr
r
3 dp 5 1 d 2
u  p 2 r u 0
2 dr 2 r dr
If we assume stationary solar atmosphere (u=0)
dpS
MS

 S G 2  0
dr
r
Chapman’s assumed isothermal corona;
so p=npkT+nekT~ 2kT 
S
m
p

(further reading M. Velli ApJ 1994; Priest, E. chapter 12)
Then, we get
Gmp M S 1
dpS
 S
0
2
dr
2kT r
That gives,
m p gB RB 
pS  pB exp
RB  1
 r

 2kT

Where the index B indicate the Base of the corona

As r, pcte
 m p gB 
p  pB exp
RB 
 2kT

For TB ~

106
-4 p >> any reasonable interstellar
p
~
3
x10

B
K
Pressure!!! So a Hot Static Corona cannot exist
Parker (1958) Astrophys, J 128, 664 ->
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)
dp
5 p du 10 p


dr
3 u dr 3 r
The momentum equation:

u
du
dp
M
   G 2S  0
dr
dr
r
Outflow
plasma

Pressure
gradient
gravity
Substituting we get:
u2  as2 du 2as2 GRB2
 2

 
r
r
 u dr
2
Where as  5 p /3
is the local sound speed.
There
du/dr is undefined:
 is a critical point A where
When u=as, r  rC  GMSun /2as2 so that both coefficient of du/dr and the right
hand side vanish.

Assuming aS=cte (isothermal solar corona) and integrating in both sides:
2
2
 u 
 u 
r 2GM

ln

4
ln

C
 
 
2
rc
raS
as 
aS 
Depending on the constant C this equation have 5 different solutions:

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 v>>vc, the velocity v  (ln r)1/ 2
And the density fall of as n  r2 (ln r)1/ 2 so that the pressure vanish at infinity.
For T=106K the predicted flow speed at 1AU is 100km/s.
Parker’s solution for different
coronal temperatures
For example, for T=106K, and
coronal density of 2x108cm-3,
rc=6Rs. 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.
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->leading 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)
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.,
Interplanetary Magnetic Field
The magnetic induction equation
B
  (u  B)
t
B
  (uB  Bu)  0
t
can be written
 of 27 days. In the rotating frame a vector A:
The sun rotates with a period
dA 
dA 
  
 r  A
 
dt
dt
 inertial  rotating
So the flow speed in the corotating system is u u  S  r

B B

 S  B
The time derivative of B in the rotating system is:
t t
 frame is:
And the induction equation in the rotating
B
 S  B   (u S  r )  B
t



B
 S  B   (u S  r )  B
t
Expanding the right hand side you get B
 S  r   B   u B
t



 
The left hand side is the total time derivative of B in
the system rotating with the Sun: DB/Dt

So
DB
  u B
Dt

In the Steady State

 u B  0




DB
0
Dt

and
There is a scalar potential :
 u B



Taking the product of  With u and B
And some math…Look at page 243 of Gombosi’s book

This means that that in the rotating frame
u B  0  uB
The magnetic field and plasma vectors are always
Parallel in the rotating frame

The Geometry of the Magnetic Field
First: no polar components
u  0
and
B  0
Since u’ and B are parallel to each other the ratio between
B and Br needs to be the same: B
u (r  R )


B
r


u
r

S
S
sin 
uSW
Where we assumed that uSW is the assymptotic velocity of the solar wind and that
At large distances r>>RS the plasma velocity is practically radial (in the non
corotating frame)

So: B  Brer  Br (r  RS )S sin  e
uSW


From Maxwell Equations:
 B  0
in spherical coordinate system is
1  2
1 B
 B  2 (r Br ) 
r r
r sin  
  1  (r 2 B )  (r  RS )S Br  0
r
r 2 r
ruSW

Br
 0 so
And

1  2
(r Br )  0
2
r r
that leads to
RS 2
Br (r)  BS  
 r 

Substi. In the expression of B we get:


2


RS 
RS
S sin 
B  BS   er  Bs  (r  RS )
e
 r 
uSW
 r 
2
At large distance from the Sun r>>RS
RS2 S sin 
RS 2
B  BS   er  Bs 
e
 r 
 r  uSW
 We can see that B  r 2
r
and
B  r1 (fall more slowly!)
As we go outward in the solar system
the magnetic field becomes more and more
azimuthal

Coronal Structure and Magnetic Field
An assumption that we made was: corona was spherically symmetric!
But close to the Sun it’s a poor approximation: regions of open and close field
lines
To have a realistic solar magnetic field you need to solve:
 u  0
 
 u   u  p  G
MS
er  j  B  0
r2
 (u  B)  0
1
j   B
0
And assuming that at all times the solution only depends on r and 

Pneuman and Kopp (1971) solve iteratively starting with a dipole
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
Heliospheric Current Sheet
Non alignement of the magnetic axis and the rotation axis
produces the ballerina skirt
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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 Sun’s magnetic field is not dipolelike.
How wide is the current sheet?

B
7º
7º
Global View of the Magnetic Field
Meridional
Plane
ISW
Opher et al.