Before we start:

Heliosphere - Lectures 5September 27, 2005 Space Weather Course

Solar Wind, Interplanetary Magnetic Field, Solar CycleChapter 12-Gombosi (The Solar Wind)Chapter 6 - Kallenrode (The Solar Wind)Chapter 12- Parker (The Solar Wind)

Before we start:

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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?)

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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 HeliosphereReacts 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?)

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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

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Magnetic Structure of the Sun



Helmet Streamers

Open and closed Field Lines

StreamerBelt

Helmet streamer

CoronalHoles

Fast WindSlow Wind

The Solar WindAt the beginning of the twentieth century, a particle of flow from the Sun Towards Earth was suggested by Birkeland (1908) to explain theRelationship between aurorae and sunspots (“The Norwegian aurora Polaris expedition 1902-1903: On the cause of magnetic storms and theOrigin of terrestrial magnetism”)

(Description is in chapter 04 Gombosi) (Also chapter 6 from Kallenrode)

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.

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 directedExactly 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 supersonicWith 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



Property (1 AU) Slow Wind Fast WindFlow 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

Slow Solar Wind:Speeds between 250-400km/sAverage 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 theStreamer belt and 4% of the ions are HeCompared to the fast wind, the slow wind is highly variable and turbulentThe proton temperature is 3x104 K (low!)The electron temperature is similar to fast…

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 HeThe proton temperature is about 2x105 KThe electron temperature is about 1x105K

More on the slow and fast winds..

For the fast and slow winds:

Tparallel T (to the magnetic field)

Also the momentum flux

M npmpvp2 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 coronaThe 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 controversialSolar 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

t(m

u )0

mu tm(

u )u

p B2

20

I

B B 0

m

g

B t(

u B

B u )0

32pt

32

(u )p 5

2p(u )0

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)

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

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

1r2

ddr

r2u 0

u dudr

dpdr G MS

r2 0

32

u dpdr 5

2p 1

r2ddr

r2u 0

If we assume stationary solar atmosphere (u=0)

dpS

dr SG

MS

r2 0

Chapman’s assumed isothermal corona; so p=npkT+nekT~

2kTmp

S

Then, we get

dpS

dr S

Gmp MS

2kT1r2 0

That gives,

pS pB expmpgB

2kTRB

RB

r 1

Where the index B indicate the Base of the corona

As r, pcte

p pB exp mpgB

2kTRB

For TB ~ 106 Kp ~ 3 x10-4 pB >> any reasonable interstellarPressure!!! 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 holdthe corona-it must stream outward as the “solar wind”)

Parker Solution: (neglecting electromagnetic effects)

dpdr

53

pu

dudr

103

pr

The momentum equation:

u dudr

dpdr G MS

r2 0

Outflowplasma

Pressuregradient

gravity

Substituting we get:

u2 as2

u

dudr

2as2

r

GRB2

r2

Where

as2 5p /3 is the local sound speed.

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

uas

2

ln uaS

2

4 ln rrc

2GMraS

2 C

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

There is a critical point A where du/dr is undefined:When u=as, so that both coefficient of du/dr and the right hand side vanish.

r rC GMSun /2as2

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 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.

Classes I and II: have double valued solutions which are unphysicalClass III: posseses supersonic speeds at the Sun what are not observedSo we have left solutions IV and V ….

A

v (lnr)1/ 2

n r 2(ln r) 1/ 2

Solar Breeze (Type IV): subsonic

Parker’s solution for differentcoronal 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 constantspeed of 500km/s

The speed increases only weakly with height and the critical Velocity is not acquired at the critical radius. The flowThen 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 coronalTemperature does not remain constant as it expands.

Although the hydrodynamic description of the solar wind is a reasonable and valuableApproach: a fundamental problem that was neglected is the heating of the corona. Some heating mechanism is needed (especially near the critical point)

Limitations and Assumptions:•Isotropy: It is established that T( r) ~ r-

,, where is the polytropic indexAnd still allow for solar wind type solutions. (at earth the typicalPlasma 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 reductionOf the flow speed)•No Magnetic or Electric Field considered. In a MHD modelThe critical point is lowed in the corona (~ 2 Rs) but the general form Of the solution is the same.

Brief notes on Coronal HeatingHeating by Waves and Turbulence: Altough non-thermal broadeningOf some spectral lines indicated the existence of waves or turbulenceIn the lower corona, it is not completely understood which kind of Waves these are, how they propagate outward and whether the observationsAre 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 aheating mechanism. Reconnection happens when field of opposite polarityEncounter. The photosphere is in continuous motion with bubbles rising and fallingAnd plasma flowing in and out. Thus on a small scale magnetic field configurationssuitable for reconnection will form frequently, converting magnetic field into thermal energy.,

Interplanetary Magnetic FieldThe magnetic induction equation

B t(

u B

B u )0

B t(

u B )

can be written

The sun rotates with a period of 27 days. In the rotating frame a vector A:

dA

dt

inertial

dA

dt

rotating

r

A

So the flow speed in the corotating system is

u

u S

r

B

tB tS

B The time derivative of B in the rotating system is:

And the induction equation in the rotating frame is:

B tS

B

(

u S

r )

B

B tS

B

(

u S

r )

B

Expanding the right hand side you get

B tS

r B

u B

The left hand side is the total time derivative of B inthe system rotating with the Sun: DB/Dt

So

DBDt

u B

In the Steady State

DBDt0

u B 0

and

There is a scalar potential :

u

B

Taking the product of

With u and B

This means that that in the rotating frame

u

B 0

u B

The magnetic field and plasma vectors are alwaysParallel in the rotating frame

And some math…Look at page 243 of Gombosi’s book

The Geometry of the Magnetic Field

First: no polar components

u 0

B 0and

Since u’ and B are parallel to each other the ratio betweenB and Br needs to be the same:

BBr

u u r

(r RS )S sinuSW

Where we assumed that uSW is the assymptotic velocity of the solar wind and thatAt large distances r>>RS the plasma velocity is practically radial (in the non corotating frame)

B Br

e r Br

(r RS )S sinuSW

e So:

From Maxwell Equations:

B 0 in spherical coordinate system is

B 1

r2

r

(r2Br )1

rsinB

1r2r

(r2Br ) (r RS )S

ruSW

Br

0

Br

0And so

1r2

r

(r2Br )0 that leads to

Br(r)BSRS

r

2

Substi. In the expression of B we get:

B BS

RS

r

2e r Bs

RS

r

2

(r RS )S sinuSW

e

At large distance from the Sun r>>RS

B BS

RS

r

2e r Bs

RS2

r

S sin

uSW

e

We can see that

Br r 2

B r 1

and (fall more slowly!)

As we go outward in the solar systemthe magnetic field becomes more and moreazimuthal

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 fieldlines

To have a realistic solar magnetic field you need to solve:

u 0

u u p G MS

r2

e r

j B 0

(

u B )0

j 10

B

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:

MHD model Zeus-3D(Asif ud-Duola, Stan Owcki)

Initial State: solid lines-DipoleFinal State: dashed lines

The lines are drawn outward by the plasmaAnd become open

Coronal plasma in static equilibrium: balance betweenPressure gradient and gravity

Field lines from opposite polarities: Heliospheric Current Sheet

Heliospheric Current Sheet



Non alignement of the magnetic axis and the rotation axisproduces the ballerina skirt

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?

7º

B

7º

Global View of the Magnetic Field

Meridional Plane

ISW

Opher et al.

Documents

Before we start: