solar wind 10

8/3/2019 Solar Wind 10

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The solar wind

Lindeman 1919: Quasi-neutral gas emissions from the Sun

Chapman 1929: Solar flares emit plasma clouds

Chapman and Ferraro 1931: Sun emits particle bursts which cause magnetic

storms

Solar wind-induced tail (ions)

Radiation pressure tail

(neutral/dust)Hale-Bopp

Ludwig Biermann 1951: Cometary tails

require a fast corpuscular flow in addition

to radiation pressure

continuous solar wind

Why solar wind?

There must be a mechanism to transfer solar activity to the Earth:


2/18

2

Theory of solar wind formation

Lets first investigate coronal plasma in the gravitational field of the Sun

Tool: MHD

Continuity Eq. and equation of momentum:

0t

pt

v

vv J B g

Assume steady plasma flow and spherical symmetry

(physical properties functions ofronly),

neglect magnetic forces

2

2

2

10

S

dvr

r dr

GMdv dpv

dr dr r

Chapmans attempt to solution (1957)

Assume heat outflow through a sphere (radius r)

where the heat conduction coefficient isconst.

Letting T0 = 106 K, the temperature at 1 AU is 105 K, which is quite OK.

With the boundary conditions: T = T0, when r=R, and T 0 when r

the pressure becomes

which at r approaches to a constant that is much larger than the

pressure in the interstellar space

However, assuming a hydrostatic equilibrium


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3

Parkers solution (1958):Isothermally expanding solar wind

Assume a spherically symmetric time-independent outward flow.

Equations of continuity, momentum and state are:

Although the solar wind certainly cools

when expanding, assume that the

expansion is isothermal (T= const.)

const

where

is the isothermal sound speed (= 1)

This equation has a critical point:

Integration gives a family of curves:

Five regimes of solutions

unphysical

unphysical

not consistent

with observations

stellar breeze (subsonic: v < vc)

Solution IV through the critical point ( C= 3) is the solar wind:

subsonic near the Sun supersonic beyond the critical point


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Observations of solar wind First observations: Soviet Lunik-2 and Lunik-3 probes in 1960

Mariner 2 while flying towards Venus confirmed the continuous solar wind and

observed in it fast and slow streams repeating at 27-day interval

Skylab 1973-1974: coronal holes sources of fast solar wind streams

Ulysses: latitudinal variations of the solar wind (October 1990s ->)

- perihelion 1.3 AU

- aphelion 5.3 AU

Helios 1 & 2:

launches: Helios 1 December 1974Helios 2 January 1976

perihelion within the orbit of Mercury, 0.3 AU

Currently monitoring the upstream solar wind: SOHO, Wind, ACE, STEREO

Lagrangian points: Five positionswhere the gravitational pull of the

two large masses precisely cancels

the centripetal acceleration required

to rotate with them

Satellites at L1 monitoring the

solar wind:

- Wind (launched Nov 1994)

- ACE (launched Aug 1997)

- SOHO (launched Dec 1995)

Astronomical observatories at L2:

- Herschel (Infrared astronomy)

- Planck (Cosmic microwave

background)


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Energy considerations

& thermal energy

of the gas in volume V

The gas is in the gravitational potential:

5.0

E

Assuming T= 2 106 K Not enough for expansion!

There must be (a) mechanism(s) to

pump extra energy (Q) to the gas

Observations: 25.1QE

Heat transfer is important!

Assume: e, p+, let n = n(r), T= T(r), ne np n

pressure

Thermal energy lifts the gas up when the volume Vexpands.

At the same time the internal pressure pushes new gas into

this volume and does work pV.

The free energy is the enthalpy:

Toward more realistic models

Accept the fact that there is enough energy for the solar wind expansion

and write the energy equation as:

= 0T5/2 ; 0 10

11 Wm1K1 ; T is given in Kelvin

F is the observed energy flux far from the Sun

Combination of Parkers expanding wind and Chapmans heat transfer

At 1 AU:The real solar wind is

much more compicated

heating (in corona) and cooling

(with expansion) are different

fore and i+

effects of the magnetic field

etc.

Average is a quite meaningless concept here!


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1. Fast wind in high speed streamsHigh speed 400-800 kms-1

Low density 3 cm-3

Low particle flux 2 x 108 cm-2 s-1

Helium content 3.6%, stationary

Source coronal holes

Signatures stationary for long times,

all streams are alike,

Alfvnic fluctuations

2. Low speed wind of "interstream" type

Low speed 250-400 kms-1

High density 10 cm-3

High particle flux 3.7 x 108 cm-2 s-1

Helium content below 2%, highly variable

Source helmet streamers near current sheet,

Signatures generally very variable,

sector boundaries imbedded,

The two basic types of solar wind

solar wind blows out

radially

field frozen-in to the

solar wind

sources of the IMFattached to the

rotating Sun

Interplanetary magnetic

field (IMF)


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Parker spiral

close to the Sun:

radial flow, B is nearly radial

assume, that flow remains radial

B is frozen-in to the rotating surface and to the outflowing plasma

Flow speed ^ B : V = VsinY

Speed of the fl. ^ r : W (rR)For large r:

Archimedes spiralknown in this context

as the Parker spiralV

RrRrV

)(tancos)(sin

Calculation ofB: Assume that B is radial and constant on the surface.

1. Radial component on the equatorial plane

Write B and V in spherical coordinates (r):

Now 2

rB r

2. Azimuthal component in the equatorial plane

Induction equation: 0 V B

Thus at large distances BBrB

and

1

spiral field

The spiral angle is

44 at Earth (1 AU)

57 at Mars (1.5 AU)

88 at Neptune (30 AU)


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3. Off-equatorial (/2) B is more complicated

i.e., the winding opens up toward high latitudes

Thus, far from the Sun:

1

2

B r

B r

in the ecliptic (tight spiral)

in the polar directions

The above analysis assumes that the IMF is too weakto affect the coronal outflow

i.e. the magnetic energy density2

02

B

is much less than the kinetic energy density2

2

v

Close to the base of corona: v


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Angular momentum loss

solar magnetic field plays an important role in the angular momentum loss

magnetic field enforces co-rotation with the Sun out to the Alfvn radius

Write the force balance as

and use Ampres law and multiply by r3 to get

(exercise)

The mass flux r2mVrand the magnetic flux r2Br

are constants and the integration gives

the constant of integration L contains

the mechanical angular momentum and angular

momentum carried with the magnetic field

Use r rB V

B V r

to replaceB:

is the the radial Alfvn Mach number

When r= rA , Vr= VA and MA = 1 Observations: rA 12R

Thus the angular momentum of the Sun decreases due to the solar wind:

Magnetic braking

Solar angular momentum is transferred to the charged particles

To keep V finite when rrA2

AL r

which is the same as the angular momentum (per unit mass)

of a solid body with radius rA


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Sources of the solar wind:

Coronal holes

plasma escapes on

open flux tubes

plasma confined

by magnetic field

helmet streamer

near solar minimum

- clear polar holes

near solar maximum

- holes all over the Sun

Corona seen

during solar

eclipses

solar minimum:

large polar coronal hole


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Coronal holes may remain stable over many solar rotations

How does the real solar wind look like?

Formation of the

heliospheric current sheet(Pneuman and Knopp)


12/18

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The real current sheet is curved Ballerina skirt (Alfvn)

The Earth can be

toward sector or in

away sector

OMNI data, May 2007

red: towards sector

green: away sector


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Minimum

Minimum

Maximum

The ballerina dancing through the solar cycle

The magnetic topology of the

large-scale heliosphere

Hoeksema, 1995

The boundaries of coronal

holes and the streamer

belt, as seen by

EIT and UVCS on SOHO

Older pictures:


14/18

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Transient solar wind component

coronal mass ejections

Bmag

Gosling et al., 1987


15/18

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16/18

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Ulysses observations

Minimum and maximum epochs

are very different!


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Solar wind varies from minimum to maximum and

the last minimum was different from the previous

The heliosphere


18/18

Estimate of the heliospheric boundary in the upstream interstellar wind

Pressure balance:

In solar wind (S)

dynamic pressure dominates everywhere

Vconstant up to termination shock

The interstellar side (G) less well-known

pressure 0.1 pPa or less

Heliopause at 140 AU

Termination shock at about 2/3 of the

distance to heliopause

At the termination shock the supersonic

solar wind becomes subsonic again

Termination shock reached by

Voyager 1 : December 2004 at the distance of94 AU from the Sun

Voyager 2: August 2007 at the distance of 84 AU from the Sun

five crossings!

Termination Shock

Heliopause to be reached about 10 years from

the termination shock (5 billion km)

(more on shocks, see the November 18lecture by Rami Vainio

solar wind 10

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