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### Overview of what we will see in Lecture 05

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)

- 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?)

@P.Frisch

- 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?)

@P.Frisch

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?

@P.Frisch

Magnetic Structure of the Sun

Magnetic Structure of the Sun

Streamer

Belt

Coronal

Holes

Helmet streamer

Fast Wind

Helmet Streamers

Slow Wind

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.

Cont. of historic backgroundCharacteristics 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

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", >50% Variance "small", <50%

Temperature T(proton, 1AU) ~ 200,000 K T(proton, 1 AU) ~ 50,000 K

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…

More on the slow and fast winds..

(to the magnetic field)

For the fast and slow winds:

on average is similar.

Also the momentum flux

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?

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

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/dt=0) (m0; conduction )

(Description is in chapter 04 Gombosi)

More on solar wind

If you neglect the effect of heat conduction and magnetic fields:

If we assume stationary solar atmosphere (u=0)

Chapman’s assumed isothermal corona;

so p=npkT+nekT~

(further reading M. Velli ApJ 1994; Priest, E. chapter 12)

Problems with Static corona

Then, we get

That gives,

Where the indexB indicate the Base of the corona

As r, pcte

p ~ 3 x10-4pB >> any reasonable interstellar

Pressure!!! So a Hot Static Corona cannot exist

For TB ~ 106 K

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)

The momentum equation:

Outflow

plasma

Pressure

gradient

gravity

More on parker solution

Substituting we get:

Where

is the local sound speed.

There is a critical pointA where du/dr is undefined:

When u=as, so that both coefficient of du/dr and the right hand side vanish.

Assuming aS=cte (isothermal solar corona) and integrating in both sides:

Depending on the constant C this equation have 5 different solutions:

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 windsolution 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

And the density fall of as so that the pressure vanish at infinity.

For T=106K the predicted flow speed at 1AU is 100km/s.

lachzor page 239 T. Gombosi

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.

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->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

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:

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 :

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

The magnetic field and plasma vectors are always

Parallel in the rotating frame

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 r>>RS the plasma velocity is practically radial (in the non

corotating frame)

So:

From Maxwell Equations:

in spherical coordinate system is

that leads to

And

so

Substi. In the expression of B we get:

At large distance from the Sun r>>RS

(fall more slowly!)

We can see that

and

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:

And assuming that atall 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

Solar Cycle and the Heliosphere

During solar minima: the magnetic field is approximately a dipole. The orientation of the dipole isalmost 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.

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