solar wind 10
TRANSCRIPT
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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:
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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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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)
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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:
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Transient solar wind component
coronal mass ejections
Bmag
Gosling et al., 1987
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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
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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