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					                  Solar-Terrestrial Relations


 The sun can influence the Earth in several ways:
 1. Evolutionary changes
 2. Luminosity variations (spots, plage)
 3. Particles (flares, solar wind)



1 Occurs on timescales of ~109 years, so only 2 and 3 are important
for humans
           I. Solar Activity and Climate Changes
The solar irradiance change by no more than 0.1–0.3% during the sunspot
cycle. What is the corresponding temperature change at the Earth?




                                              0.07 %




          Let„s take the solar irradiance changes of the
          last 30 years which gives DL = 0.00073
          Intercepted flux, Fin = radiated flux, Fout


              L                              RE = radius of Earth
      Fin =          pRE   2   (1– A)        A = Albedo of Earth
              4pd2
                                             d = distance to sun

  Fout = sT4 · 4pRE2               s = Stefan-Boltzmann constant


                               L(1 – A)
                                             = sT4
                               16pd2

                       DT = constants x (1/4) L–3/4 DL

                                        DT           DL
                                               =
                                         T           4L

         T ≈ 300 K                  DT = 0.05 !!!

Naively we would expect that solar activity has little influence
on the Earth„s climate. But the real story is different.
Evidence for the influence of Solar Activity on Climate:

  1 The Maunder minimum coincided with the “Little Ice Age” in
  Europe. Baliunas and Jastrow estimate that the solar irradiance
  during the Maunder minimum was about 0.4% less than it is now
  (based on studies of solar-type stars). This could account for the
  climate change observed during the Maunder minimum


                                       During the Little Ice Age:
                                       1. Glaciers in Switzerland advanced
                                          crushing villages
                                       2. The Thames River and Canals in The
                                          Netherlands often froze
                                       3. New York Harbor froze allowing
                                          people to walk from Manhattan to
                                          Staten Island
2. S. Bjorck of Lund University looked at tree rings and ice drillings in
Greenland and found that there was a 200-year cold spell 10.300 years
ago. This coincided with a large increase in the amount of 10Be in the
Greenland ice sheet. 10Be is produced via cosmic rays colliding with
nitrogen and oxygen in the atmosphere. During high levels of solar
activity the Earth's magnetic field is stronger so less cosmic rays can
penetrate.
3. Abnormally high solar activity during 1100–1250 coincided with
   a period of warming in Europe. During this time:
    a) Viking settled in Northern Europe, traveling to Greenland
       and America over seas usually filled with dangerous ice
    b) Grapevines grew as far north as England
    c) Higher tree lines in the Alps




 The Modern Maximum is comparable to the Medieval Maxium in
 strength
Temperatures seem to be correlated with sunspot maximum
Wilson claimed in 1997 that the level of solar activity is
increasing from one cycle to the next and that this can
account for 0.7–1.4 deg warming over the next 100 years.
Higher levels of solar activity increases the amount of ozone
in the upper atmosphere. Schindell argued that this warms
the upper atmosphere and the warm air affects winds from the
stratosphere to the surface.



Postmentier, Soon, and Baliunas have claimed that there is a
correlation with the size of coronal holes and the Earth's temperature.
Large coronal holes allow more charged particles to strick the Earth.
Presumably these affect the properties of clouds.
Coronal Holes are „open“ field lines on the Sun where
the X-ray emission is less
It is clear that solar activity has some influence on climate. Since 1950
the sun has been in an enhanced maximum similar to the Grand
Maximum that caused the Medieval Warm Period in the 9th to 13th
centuries. So, can solar activity account for the observed „global
warming“? Keep in mind that carbon dioxide in the atmosphere has
increased by more than 25% in the last century.



                  Is it the sun or is it humans?
To answer this Solanki & Krivova at MPS did a study.




   • The created a model which reconstructs the solar irradiance.
   This is a four component model which including quiet sun,
   umbra, penumbra, and faculae
   • Assumed that all terrestrial temperature changes prior to
   1970 were due entirely to the sun
Krivova & Solanki reconstruction of Solar irradiance
Global Temperatures



    Measured irradiance


    Reconstructed curve




Conclusion:
•     Less than 30% of the
      Earth„s temperature rise
      can be attributed to the
      sun
•     A large part of the global
      warming may be due to
      CO2
There have been many attempts to try to correlate solar activity with
other things. Some might not be too crazy…




                                                       Solar activity might
                                                       incluence climate so
                                                       you can argue there
                                                       should be a correlation




   Others are total „rubbish“
 Like the claim that solar activity influences world events




There has been claims that Solar activity (maxima) has caused political
and economic crises. The End of the Century was written by Francois
Masson in 1979-1980. A publisher was never found (for good reason)
but it was transcribed into English and published on the internet
Dates of Maximum Solar Activity corresponding to revolts, famine,
depressions and other catastrophes. Below are the events chronicled
by Masson with additions by me in boldface:

1702: Protestant Revolts in France, general wars in Europe

1715: Scottish rebellion, depression and famine in Europe. Death of
Louis XIV and big political changes
1725: Revolt in Scotland, Peter the Great dies. Russia enters 50
years of strife
1738: Workers revolt in England. Wesley founds the first Methodist
Society
1729: Tax Revolt in England
1760: Founding of Freemasonry. Condemnation of the Encyclopedists
in France.
1776-77: Declaration of Independence, American War of Independence
1787-88: True beginning of the French Revolution. Rioting in Paris.
Economic Crisis in French State.
1803: French economic crisis. Napoleon renews wars with England
1814-15: Liberal rebellions in France and other European countries.
Uprising in France in favor of Napoleon on his return from Elba.
Waterloo.
1827: Serious depression in Europe
1836: Riots in France. TEXANS DEFEATED AT ALAMO. TEXANS
GAIN INDEPENDENCE AT BATTLE OF SAN JACINTO
1848: Revolution and depression in Europe
1860-61: Revolutions in Italy, South Carolina secedes, Civil War begins
in USA.
1870-71: Franco Prussian War
1882: Major Depression
1892-93: European Tariff war. Stock Market crash in U.S.
1905-06: Russo-Japanese War. Imporant revolts in Russia. Einstein
1917-18: Revolution and total change in Russia. Rebellion in French
and Italian armies. Mutiny of the German fleet. Sun Yat-Sen„s
revolution in China.
1928-29: Great Depression begins. Peasant revolts in Russia
against collectization of land. Famin, bloody purges. Revolts in
Serbia, Yugoslavia
1936-37: Franco„s rebellion in Spain, civil war. General strikes in
France. Start of ideological wars Fascism vs. Communism
1947-48: Revolts in Eastern satellite nations, revolts in Indo-China,
revolt of Chinese communists against Chiang Kai-Shek.
1957-58: First uprising of French colonists in Algeria, Castro„s revolt
in Cuba. A. HATZES BORN: SPUTNIK LAUNCHED. TV DINNERS
INTRODUCED
1968-69: World youth revolt. The Prague Spring. Height of Vietnam
war. Gold crisis. MAN LANDS ON MOON: BEATLES RELEASE
LAST ALBUM FOLLOWED BY BREAKUP
1979-80?: New economic crisis. Numerous localized wars. First sign
of new religion in USSR. REAGAN ELECTED PRESIDENT:
HATZES STARTS GRADUATE SCHOOL: JOHN LENNON
ASSASINATED.
1990-91: End of USSR. Berlin wall falls (1989)
2000-2001: HATZES BECOMES DIRECTOR OF TLS: BUSH GETS
ELECTED. TERRORISTS ATTACKS ON U.S. GEORGE
HARRISON DIES.

  Conclusions. Solar Activity has been
  1. bad for The Beatles
  2. good for A. Hatzes
  3. Mostly affects events in France and England
 1865: Lincoln assassinated
 1914: Assassination of Archduke Ferdinand. Start of WWI
 1939-40: Start of WWII
 1963: Kennedy assassinated
 1986: Challenger shuttle disaster
 2003: Iraq war starts, Columbia shuttle disaster
 2004: Bush gets re-elected. Madrid train bombings
 2005: London terrorist bombings
 2007: G8 Protests

Lessons:
1. With so many historical events one can always find correlations
   between these and solar maxima or minima
2. Don„t believe everything you read on the internet.
                            II. The Solar Wind

Spacecraft moving outside of the Earth„s magnetic field have demonstrated
that a continuous flux of charged particles streams outwards from the sun


 Composition: 95% (by number) protons and electrons, the rest are a
 particles
  Density: 3–20 particles cm–3 (mean = 10)
  Plasma Temperature (velocity dispersion): 100.000 – 150.000 K.      a
  particles 4–5 times higher
  Velocity: 350 – 750 km/sec. Speed varies little between 1– 20 AU
  Magnetic field strength: 2 – 10 g (g = 10–5 Gauss)

   In 1958 Eugene Parker worked out the model for a
   continuously expanding corona
The radial outflow of the solar wind would follow the
magnetic field lines radially, except that the sun
rotates. Streamlines are given by:

          1   dr   Vr    Vr
              df =    =
          r        Vf   –wr
    The solar radial
    component of the
    magnetic field switches
    polarity several times

           +


                       -


-

                  +
Note: „Solar Sails“ do not use the Solar Wind!




 Solar Sails use radiation pressure! The solar wind is very
 tenuous and does not exert much force on anything it hits.
 The solar wind has 1.000 – 10.000 less force that the
 radiation pressure of sunlight
              III. The Solar Wind – Earth Interaction

Magnetosphere: The Earth has a weak dipole field that
is inclined by 11o from the spin axis. Forcing by the solar wind
modifies this field creating a cavity called the magnetosphere.
Inner magnetosphere: extends from the “nose” to a distance
of 8 RE on the night side. It does not include the poles. This is a
stable region populated by the inner and outer radiation belt. Typical
densities of ions is 1 per cubic cm. In outer radiation belt the energy of an
ion is about 50 keV. The electrical current associated with the plasma is
the ring current circling the Earth.




Plasma Sheet: Thick layer of hot plasma centered on the tail's equator.
Typical thickness is 3–7 RE, density 0.3–0.5 ions per cubic cm and an
ion energy of 2–5 keV.

Electrical currents flows across the plasma sheet and then closes
along the magnetosphere boundary. In a substorm this current is
diverted earthwards along the magnetic field lines.
Tail Lobes: Regions of relatively smooth magnetic fields north and
south of the plasma sheet. The region is a good vacuum with a density
of 0.01 ion/cubic cm. It has strong magnetic fields and thus stores
appreciable magnetic energy.




Ionosphere: Region 70–500 km above the Earth containing free electrons
and ions.
 Motion of a Charged Particle in the Earth„s Magnetic Field

Cyclotron Motion:

               dv
             m    = qv x B
               dt

Take B to be in the z-direction

                dvx
               m    = q Bvy
                 dt
                dvy
               m    = –q Bvx
                 dt
 Motion of a Charged Particle in the Earth„s Magnetic Field


Differentiate the equation for x:
                                                        2
                  d2vx q B dvy                     qB
                                               (
                                         = –
                                                        (   vx
                  dt = m dt                        m


This is the equation for a harmonic oscillator frequency:


         wc = |q| B         =
                                |q| BG        Cyclotron Frequency
               m                 mc
      BG = magnetic field strength in Gauss
 Motion of a Charged Particle in the Earth„s Magnetic Field

Lamor Radius:

                    vx = v┴ e ±iwct           v┴ is the velocity of
                                              the particle
                                              perpendicular to the
                       vy = v┴ e ±iwct        magnetic field



     vy = ± 1 dvx       = ±iv┴    eiwct
                                                dy
                                              = dt
            wc dt

Integrating:                      And the same for x:


 y – y0 = ± v┴ eiwct                     x – x0 = –i v┴ eiwct
            wc                                       wc
Motion of a Charged Particle in the Earth„s Magnetic Field

Defining the Lamor Radius:
                           v┴         mv┴ c
                      rL =        =
                           wc         |q| BG


                    x – x0 = rL sin wct

                    y – y0 = ± rL sin wct


            Where ± is due to the sign of the charge
     Motion of a Charged Particle in the Earth„s Magnetic Field

             Bz



                                    Charge particles cannot
                                    move across the field
One charge                          lines, but are free to move
                                    along the magnetic field
                                    lines

                      RL

Opposite charge
The Ring Current
  Gradients in the magnetic field causes a drift in the “guiding
  center” defined by the Lamor radius. This is because in regions of
  stronger magnetic field the Lamor radius is smaller. The guiding
  center drift velocity is given by:
                                              D
              vDB = ± 1 v┴ rL B x B
                      2         B2
                       Increasing magnetic field strength

                                                            Lamor radius is smaller
Lamor radius is larger where                                where the field strength is
the field strength is smaller                               higher




                                                      Center of motion shifts


 At the Earth‟s magnetic equator this causes one charge to drift
 eastward, the other westward creating a ring current.
Reflection at the Poles:

The magnetic moment of a gyrating particle is an invariant:

                          1 m v┴2
                       m=
                          2  B


     As a particle moves from weaker to stronger fields its v┴
     increases.To keep the energy constant the motion parallel to the
     field must decrease. Eventually it comes to stop and gets
     reflected. The force causing this reflection is that on a
     diamagnetic particle:


                           F = –m
                                    D
                            ║        ║   B
Motions of particles in the Earth„s magnetic field
                Geomagnetic Storms


The term “geomagnetic storm” (world-wide disturbance) was
coined by Alexander von Humboldt. Humboldt convinced the
Czar to set up a network of magnetic observations across
Russian lands. Other sites in throughout the world established
that the magnetic storms were the same all over the world.
There is a steep increase in the field (50-300 nanotesla) out of a
total intensity of 30-60.000 nT occurring over 12-24 hours,
followed by a recovery lasting 1– 4 days.
    Magnetic storms are caused when high energy particles
   from solar flares collide with the particles in the ionosphere
   changing the level of ionization. These events are
   associated with


     • increased Aurora activity
     • fluctuations in compass needle
     • disruption of short wave radio communications
     • induced currents that blow fuses, damage power lines
     • disruption of communications
     • decay of satellite orbits


In other words, solar flares can cause significant damage and cost
a lot of money to humans.
Aurora:

     Aurorae occur when the charged solar particles from the
    solar wind interact with the Earth's magnetic field. These
    particles can only spiral along the field lines and thus strike
    the polar regions in what is called “the ring of fire”.

     In times of solar flares this ring of fire expands and extends
    to much lower latitudes.
The Aurora taken from
Tautenburg by Christian Högner
The colors of the aurora result when charged particles strike
molecules in the upper atmosphere causing collisional excitation of
emission lines. Most are due to oxygen and nitrogen:

    O2 emission occurs at 200 km this is due to the 6300 Å, and
6364 Å lines (Red)

      O2 emission occurs at 100 km and is due to the 5557 Å line
(yellow green).

    N2+ causes the blue colors due to the emission line at 4652 Å

    N2 also causes some red colors
Important historical events in the studies of Aurora:

• 500 BC Hippocrates suggest it is reflected sunlight
•1600 Gilbert discovers that the Earth is a magnet.
•1620 Galileo terms expression Aurora Borealis.
•1774 Dortous de Mairan relates auroral displays to solar activity.
•1790 Cavendish measures height at 80-110 km.
Important historical events in the studies of Aurora:
.
• Alexander von Humboldt notes auroral displays coincide with magnetic storms.
•1817 Biot proves aurora is self luminous.
•1868 Angstrom uses a prism to show that the aurora is different from sunlight. Finds
auroral green line.
• Störmer used triangulation to confirm a height of at least 100km for displays
• 1912-23 Oxygen and nitrogen lines identified
• 1939 Hydrogen lines discovered.
Auroral displays exhibit kinks, curls, and spirals.
These are due to the magnetic field produced by
the moving charged particles interacting with the
Earth's field.
The Geocorona:

     The outermost part of the Earth's atmosphere
consists of a huge cloud of hydrogen gas extending a
distance of 4-5 Earth radii.
Collisions with this cloud removes the ion particles
added during a geomagnetic storm.




                                             Picture of the
                                             geocorona taken
                                             by the Apollo
                                             astronauts
Solar Flare Effect or Magnetic Crochet:

     A magnetic crochet arises from increased ionisation in the
D and E layers of the ionosphere caused by the massive
increase in X-ray radiation flux generated by a solar flare. The
ionisation changes the conductivity of the ionospheric layers
causing the electrical currents to flow more easily. The
magnetic field produced by these currents causes a jump in
the Earth's field.

     These events are rare because they are only observed by
large flares that rise to a peak quickly.
                              Substorms

 These are much more frequent (hours apart) than magnetic
storms. These last about 1 hour during which energy is rapidly
released in the magnetospheric tail.

     These are observed mainly over the polar regions unlike the
larger magnetic storms which are observed globally. They do not
inject as many particles into the ring current.

      The first sign of a substorm is that increase in polar auroras
in the midnight zone.

     In space synchronous orbit satellites in the midnight zone
see the magnetic field drop by half and they detect the arrival of
many ions in the 5–50 keV range.
 Energy of the substorms:

 Substorms are believed to be due to a form of magnetic reconnection
in the magnetospheric tail:

•The cusp of the magnetosphere, where the field lines part between
those pulled to the equator and those pulled to the tail, moves closer to
the equator. Fewer field lines go sunward and more into the tail.

•The shift in the cusp weakens the Earth's magnetic field near the
 noon side

•More energy is drawn to the tail and the tail lobes of the
 magnetosphere expand.

•The ``stretched'' magnetic field lines in the tail reconnect causing the
tail to ``rebound'' like a slingshot.

•A plasma bubble known as a ``plasmoid'' moves down the tail.
A Magnetic Plasmoid
Source of the substorms:

• In 1904 Maunder proposed that substorms tended to occur in
intervals of 27 days. Searches for features on the sun that could
have been responsible for such storms yielded only bland and
featureless regions, so called “M- regions”

• In 1962 Mariner 2 on its way to Venus established that the solar
wind contained recurrent fast streams whose sources rotated with
the sun. The arrival of such streams triggered moderate
substorms.

• When X-ray observations of the sun began (starting with
Skylab) it was established that the the elusive “M- regions”
coincided with coronal holes. Coronal holes are regions
where the magnetic field lines of the sun are open, not closed,
allowing the particles comprising the solar wind to escape along
the field lines.
                             IV. Space Weather
Example:

     Solar wind: 300.6 km/s, density = 3 protons per cubic cm

     X-ray flares: One C2 class and one M2 class:

           X-class: big, large radio blackouts and radiation storms

           M-class: medium, brief radio blackouts

           C-class small: few noticeable affects

     Active Regions: Region 9802 harbors energy for a class X-flare.
     There is a 10% chance of a class X flare, and a 50% chance for
     class M-flare in the next 24 hours.

          Sunspot 9821 is rapidly growing and poses a threat for
     Earth-directed flares (12.2.2002)
Interplanetary magnetic field: 6.0 nT

Coronal Holes: A substantial coronal hole is crossing the Earth-
facing side. Expect strong gusts in the Solar wind.

11.2.2002: Solar wind gusts buffeted the Earth's
magnetosphere last week. The encounter triggered mild
geomagnetic storms and Nothern Lights.

Geomagnetic storms. Measured via a K index. Ranges
from 0--9 (minor storm has K=5, Severe storm has K > 6). The
probability for a severe storm is 0.01
The study of space weather and the sun are important because:

•    Induced currents from large geostorms can cause massive blackouts
    (1989 Quebec)

1. March 24, 1940: Storm disrupted power service in New England, New York,
   Pennsylvania, Minnesota, Quebec, and Ontario

2. Feb 9-10, 1958: Power transformer failed in British, Columbia

3. Aug, 1972: Reclamation power station experienced swings of power line voltages
   of 25.000 volts. A 230.000 volt transformer exploded. Manitoba Hydro recorded
   power drops of 164 – 44 megawatts in minutes.

4. 1989: 9 hour power blackout in Quebec

5. Costs: $100 Million damage to power transformer of Minnesota Power and
   Electric. Estimated cost of a storm slightly more severe than the 1989 storm: $9
   Billion!
•   Radiation dosages lethal to astronauts

•   Magnetic storms can interfere with GPS, compasses

• Currents in pipelines enhance the rate of corrosion

     In June 1989 a powerful pipline explosion demolished
part of the Trans-Siberian Railroad engulfing two trains. 800 people
died. Alaskan pipeline has safeguards against geomagnetic storms.
•     Magnetic storms can damage satellites

1. 1982: GOES-4 Weather satellite has radiometer disabled for 45
   min.

2. 1989: GOES-7 loses half its solar cells to proton release from
   flare.

3. Two Canadian satellites disabled due to activity

4. 1997: Telstar 401 experienced massive power failure


    Shorten the lifetime of low orbit satellites (e.g. Hubble Telescope)

    Bad news: Predictive abilities poor, only up to 1 hour in advance
    can we geta reliable prediction.

         Good news: It takes particles 2-4 days to get here.