1B11 Foundations of Astronomy The Sun

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1B11 Foundations of AstronomyThe Sun

• Silvia Zane, Liz Puchnarewicz
• emp_at_mssl.ucl.ac.uk
• www.ucl.ac.uk/webct
• www.mssl.ucl.ac.uk/

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1B11 The Sun a source of mystery to the human
race
Newgrange, outside Dublin
Winter Solstice
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1B11 The Sun a composite schematic illustration

• Radius 700000 km
• Core 0-25
• Radiative Zone 25-80
• Convective Zone 80-100
• Then photosphere, active corona (T 5770 K),..

Like all stars, the sun is in equilibrium between
the force of gravity (collapse) and the expansion
produced by the heat released through nuclear
reactions (expansion).
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1B11 The Sun what is a radiative zone

• Consider a spherical shell of area A4 ? r2, at
  radius r of thickness dr
• Radiation Pressure (momentum flux)

(i)
(ii)

• Rate of deposition of momentum in region r ? r
  dr

• Define opacity k m2/kg, so the fractional
  intensity loss by a beam of radiation is ( ?
  mass density)

• Rate of momentum absorption in the shell

(iii)

• Equating (iii) with (ii) and using (i)

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1B11 The Sun what is a convective zone

• Convection occurs in liquids and gases when the
  temperature gradient exceeds a typical value.
• There is no generally accepted theory of
  convective energy transport at present. There is
  however a stability criterion that can be checked
  to know if convection is going on.
• Criterion for stability against convection
  (Schwarzschild criterion)

• Consider a bubble with initial ?, P, rising by
  an amount dr in a medium with a stratification
  Pr, ?r.
• The bubble expands adiabatically, until it
  reaches pressure equilibrium with the new layer.
  Thus, the density of the bubble changes P???
• If the new density is lower than that of the
  surrounding medium, the bubble sink back ?
  equilibrium

Mathematically
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1B11 The Sun what is a convective zone
In a convective zone

• Motions are turbulent (but too slow to disturb
  the hydrostatic equilibrium).
• Highly efficient energy transport.
• Turbulent mixing so fast that the composition of
  convective regions is homogeneous at all times.
• The actual dT/dr is very close to that at which
  the stability criterion breaks

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1B11 The Sun Vital Statistics, 1

• Sun is 5 billion years old (5 x 109 yrs) - a G2
  V star.
• Earth distance is 1.5x108 km ( 1 Astronomical
  Unit)
• Energy source is by fusion of H to He
• Tcore 15. 106 K, Tsurface 5778 K,
• Energy is transported from the core to the
  surface by radiation and convection
• Mass 2. 1030 kg, Radius 7. 105 km,
• Density 1.4. 103 kg/m3, Luminosity 4. 1023
  kW
• Rotation period 26 - 36 days (differential
  with latitude)
• Extended outer atmosphere (corona) with T 1-
  3. 106 K but up to 50. 106 K for solar flare
  plasma
• Mass outflow (Solar Wind v 300 - 800 km/s)

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1B11 The Sun Vital Statistics , 2

• We measure
• the Suns size from its distance (1AU) and
  angular scale (0.5 )
• the Suns mass from the motion of planets
• the Suns age by the abundances of heavy
  radioactive elements in meteorites. The Suns age
  is the least well-determined quantity, with an
  accuracy of 2.

These parameters can be used in input in a
mathematical model (standard model) to determine,
i.e., how density, pressure, temperature vary
from the centre to the surface.
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1B11 The Sun Energy Source , p-p chain
The Energy source is at the Suns core (T15MK,
ne1.5x105kg/m3). The Sun
is a big Nuclear Reactor! The dominant energy is
produced from the proton-proton chain. 4 protons
are fused together to produce one heavier He
nucleus.

• Starts with p p?2De?e, where the deuteron
  consists of a proton and neutron.
• Then 2Dp ?3He?, where the isotope of He
  consists of 2 protons and 1 neutron.
• Finally 3He3He ? 4Hepp, which is a common
  alpha particle.

Very high Temperature (gt 107 K) is required for p
to overcome their mutual electric repulsion!
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1B11 The Sun p-p chain, efficiency
Energy balance

• 4He has a mass of only 99.3 \ of 4 protons !
• Remaining 0.7\ is converted in energy via Emc2

EFFICIENCY of this reaction 0.7\

• Lsun 3.86 x10 26 J/s
• From Emc2, mass converted into L is

3.86 x10 26 /(3x108)2 4.3 x109 kg/s

• But the efficiency is only 0.007, so the mass
  converted is

4.3 x109 kg/0.007 6.14 x 10 11 kg/s or 600
million tonnes/s!
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1B11 The Sun how long ?

• 0.1 MSun of H is available in the core for
  fusion
• So the core will support fusion for a time

? 0.1 x 1.99 x 10 30 kg/6.14 x 1011 kg/s
3.2 x 10 17 s 10 x 10 9 yrs

• More detailed calculations yield 12 x 10 9 yrs
• So the Sun is at 40\ of his life
• This is the main sequence lifetime after that,
  the Sun will become a Red Giant and then cool
  down as a white dwarf

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1B11 The Sun study of the interior
The Sun is the only star for which we can measure
internal properties

• Composition (heavy elements) from meteorites
• Central conditions from neutrinos
• Density, internal rotation from helioseismology

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1B11 The Sun detecting neutrinos ?

• In addition to the standard p-p chain there are
  reactions which produce 8B neutrinos.

3He4He ? 7Be ? (Be Beryllium) p 7Be
? 8B ? (B Boron, unstable!) 8B ? 8Be
e ?e

• 8B neutrinos are rarer than those produced by
  p-p chain, but have greater energy and it is
  likely they are easier to detect.
• Neutrinos interact weakly with matter and have an
  optical depth 20 orders of magnitude weaker than
  a typical photon.

However, the probability of absorption does
increase with their energy!
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1B11 The Sun detecting neutrinos ?

• Studying Solar neutrinos is a direct way to test
  our theory of stellar structure and evolution.
  Also, we can test particle physics and determine,
  for instance, if neutrinos have zeros mass.
• First experiment Raymond Davies collegues put
  378000 lt of Chlorine in a huge tank 1.6 km
  below the Earth surface, in an old gold mine in
  S. Dakota. Energetic neutrinos react with
  chlorine to produce argon.

37Cl ?e ? 37Ar e-

37Ar ? 37Cl e ?e
But 37Ar is unstable
And this decay can be detected ? the mass of
argon that is produced can be measured!
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1B11 The Sun detecting neutrinos ?

• Nuclear theory predicts 7SNUs while the
  experimental results giving 2.2 SNUs (1SNU 10
  -36 interactions/s/atom, Bahcall)1/3!
• Whats wrong?

Other experiments (e.g. Kamiokande, GALLEX) cover
a wide range of neutrino energies and give
roughly the same results Kamiokande 1/2 then
predicted Gallex 60 than predicted
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1B11 The Sun un-detecting neutrinos !

• The deficit of neutrinos seems to be real,
  although the exact amount is still uncertain
• This is telling us that either

1) the standard solar model is uncorrect (so
physicists are right) 2) something yet unknown
happens to neutrinos (so astronomers are right)

• Nuclear fusion has stopped?
• The interior temperature is lower than has been
  predicted?
• Neutrinos can oscillate from one flavour to
  another?

Hundreds of proposals, no really satisfactory
explanation!
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1B11 The Sun helioseismology
The Sun oscillates in a complicated manner. The
solar oscillations are caused by the turbulent
convection near the Sun surface. Waves
(somewhat like the seismic waves on the Earth)
resonate in the solar interior and appear on the
surface. There are different type of waves
sounds or pressure waves (p-waves) and gravity
waves (g-waves).
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1B11 The Sun helioseismology
p-waves have periods between 2 minutes and hours
g-waves are predicted to have much longer period
and have not yet been observed! Measuring
p-waves it is possible need to measure Doppler
shift relative to their width to an accuracy
1106 Possible with good resolution
spectrometers and long integration times (to
average out noise) Observational measures of
p-waves allow us to probe the interior of the
Sun, obtaining information about the temperature
and the motion from the deeper regions to the
surface.
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1B11 The Sun helioseismology
The Sun acts as a resonant cavity - bounded by a
density drop near the surface and at the bottom
by an increase in sound speed. The speed of
sound increases because the Sun is hotter at
greater depths (V?T1/2), hence the wave front is
refracted (the deepest part is travelling at
greater speed than the shallowest part).
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1B11 The Sun helioseismology
Leighton, Noyes and Simon first observation of
solar oscillations (1960s) at the Mount Wilson
Observatory.

• They measured Doppler shifts in the wavelengths
  of absorption lines in the photosphere spectrum.
• Patches appear to oscillate intermittently with
  period close to 5 minute, which makes the gas
  rise and fall at about 0.4 km/h.
• Patches occupy ?1/2 of the star surface and
  persists for around 30 minutes.
• Oscillations have an amplitude of ?1 km/s.

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1B11 The Sun helioseismology
With computer simulations it is possible to
reconstruct resonant tones in the Sun interior
(different colors are expanding and contracting
regions).
Comparing with mathematical models, we can also
mimic the rotational splitting of different waves
induced by large scale flows.
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1B11 The Sun helioseismology, latest results

• The angular velocity at the surface extends
  through the convection zone.
• Depth of the convection zone is 0.28 R
• The tachnocline is the region where the angular
  velocity adjusts to the solid body rotation of
  the deep interior.
• Rotation in the core is slow, almost like a solid
  body (bad a rapidly rotating solar core could
  decrease the neutrino flux)
• The He abundance in the interior affects the
  tuning of the suns vibration best match
  requires 20 helium (higher than in the
  atmosphere!)

Bad the high helium model imply an even higher
production rate for neutrinos, aggravating that
problem!
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1B11 The Sun helioseismology, future

• Much progresses have been made in understanding
  the interior of the Sun, and it is clear with the
  long term observing capabilities of the ground
  based and space based observatories that these
  discoveries will continue!
• g-modes are still trapped lower in the Suns
  interior, below the convection zone
• To date, elusive g-modes have not been observed
  and this is an area that will continue to be
  investigated until they have been successful
  found, analyzed and investigated.

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1B11 The Sun Active Regions. What they are?
Events of active Sun are localized, short-lived
phenomena on or near the solar surface. In
general, the area of solar activity are named
active regions and include Photosphere,
Chromosphere and an hot Corona
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1B11 The Sun Active Regions. What they are?
Photosphere Tsurface 5700K Granules, sunspots
(T 4000-4500K) Chromosphere Complex time
varying structures seen (e.g. spicules) T is up
to 10,000K Transition Region
T ranges from 10,000K to few 105
K Dynamic behaviour (small brightenings/active
regions) Corona T gt 1. 106
K Bright points , active regions, flares, large
scale structures (streamers), coronal holes,
solar wind, CMEs
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1B11 The Sun Active Regions. Why study them?

• How are they heated?
• Small scale reconnection events or waves?
• Do they contribute to the solar wind?
• modest but significant plasma outflow observed
• Do they contribute to quiet Sun heating?
• What is the behaviour of different temperature
  structures in active regions?

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1B11 The Sun Active Regions. Photosphere
Photospheric Granulation. The photosphere has a
bubbly look. Each bubble has an irregular shape,
about 2000 km across and lasts for about 10
minutes.

• Granuli
• Cores - radiation from up-flowing gas
• Dark lanes - downflowing cool gas
• Cell dimensions 1100km

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1B11 The Sun Active Regions. Photosphere

• This is the region where the optical radiation
  is coming from. Astronomers have analysed tens of
  thousands of absorption lines in the solar
  spectrum. Iron produces most of the lines other
  strong lines come from hydrogen, calcium and
  sodium. Famous Na D lines at 5896 and 5890Å, the
  Ca H and K lines at 3968 and 3934Å.
• Through these lines we can reconstruct the
  chemical abundances in the photosphere.

Fraunhofer Spectrum covers a complete range from
the red to the violet
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1B11 The Sun Active Regions. Chromosphere

• Chromosphere get its name from its red color due
  to emission of H? (?656.3 nm). This is the first
  line of the Balmer series of hydrogen, and falls
  in the red region of the optical spectrum.
• The Chromosphere is an active place. It is
  constantly pierced by long, thin jets of gas,
  called spicules, that reach up to 10000km and
  die out in a few minutes.
• Spicules are clearly seen during eclipses !

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1B11 The Sun Active Regions. Chromosphere
Spicules - we can tune a spectroscope to the H?
line, to see these small jets of gas.
They dileneate the boundaries of the
Chromospheric Network
Network cells are 20,000 km in size
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1B11 The Sun Active Regions. Chromosphere
Jan 4 2001 - image in H? - filaments are clearly
seen.
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1B11 The Sun Active Regions. Chromosphere

• The chromosphere has a density about 100 times
  less than the photosphere, but it is much hotter
  in the chromosphere the temperature rises from
  5700K to more than 10000K.
• This rise to high temperatures produces the
  emission lines from this region.
• The emission lines from different metals,
  produced in the photosphere, pass unchanged
  through the chromosphere. In fact this region has
  a low density and is trasparent to the light
  passing through it. It only adds a little
  emission to the photospheric spectrum.
• Why the chromosphere is hotter than the
  photosphere? Not certainly because is irradiated
  from below! Some other energy source, probably
  magnetic dissipation, must do the heating. On the
  other hand, this is a small ring the problem in
  the corona is even worse!

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1B11 The Sun Active Regions. Corona
The splendid coronal emission is also seen during
eclipses!

• The corona consists of photospheric light which
  is scattered by electrons and dust.
• Associated phenomena include the Zodiacal light,
  Radio emission, X-ray emission.
• Coronal e/p plasma flows away as solar wind at
  hundreds km/s
• Normally 103eV, but solar flares eject particles
  at 107 -1010 eV
• ?
  terrestrial aurorae!

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1B11 The Sun Active Regions. Corona heating

• The coronal emission line 5303Å was discovered
  in 1869, and named coronium. Another one at 6375Å
  was found.
• In 1939 Grotian determined that the latter was
  due to Fe IX ? highly ionized material ? this
  means high temperature, around 500,000 K !
• Hence the coronal heating problem was born.

WHY THE CORONA IS SO HOT?
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1B11 The Sun Active Regions. Corona heating
Understanding why the corona is so much hotter
than the surface of the Sun has been one of the
main goals of solar physicists since the problem
was discovered more than fiftly years
ago! Although the energy that is required to
heat the corona is only 0.01 of the Suns total
luminosity, the actual mechanism is still
unknown. Biermann, Schearszchild Schartz
(1940) Sound waves? No the flux of acoustic
waves has been measured and found to be a factor
100-1000 too low to heat the corona Most
probably a magnetic dominated mechanism!
TODAY, 2 big classes of models 1) Alternating
current (AC) models, I.e. dissipation of waves 2)
Direct currents (DC) models, I.e. dissipation of
stressed magnetic fields
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1B11 The Sun Active Regions. Corona heating
Yohkoh SXT Active Region Observations
Yohkoh X-ray images during Jan 92. On the other
hand, soft X-ray images of the Sun demonstrate
the magnetic complexity of the coronal
emission. Notice the complex bright active
regions. Loops appear temporarily to connect
active regions to other active regions, and there
are also large diffuse loops which exists in
their own right.
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1B11 The Sun Active Regions. Sunspots
Sunspot appear as dark blotches on the solar
disk. With a temperature of about 4200K, a
sunspot is cooler than the photosphere and so
appears dark in contrast. In fact a sunspot is
almost 4 times fainter than the photosphere.
Sunspots have the tendency to form in groups.
When photospheric granules separate, a tiny spot
appears betweem them as a dark pore. Such pores
have B?1T- enormous. Usually more pores soon
become visible and coealesce over a period of
several hours to form a sunspot!
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1B11 The Sun Active Regions. Sunspots
Whats going on? Magnetic Flux Tube Emerge from
below Photosphere
The magnetic field has his own pressure,
B2/(8?). This pressure push the plasma out the
magnetic flux tube, until it reaches pressure
balance with the gas outside
Pext Pint B2/(8?)
Loss of mass inside the flux tube ? resulting
magnetic buoyancy causes flux tubes to rise!

• Sunspot contains strong B fields
• These inhibit convection, hence Tspot lt Tphot.
• For Bspot 0.4 Tesla, Tspot 3700 K.
• Size of Umbra 20,000 km

This occurs when B reaches a critical value!
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1B11 The Sun Active Regions. Sunspots
The Magnetic Carpet
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1B11 The Sun Active Regions. Flares!
Eventually, twist and kinks in the magnetic
loops produce flares!

• Magnetic loops extend into the corona emerging
  from active regions
• Magnetic reconnection occurs above the
  photosphere, joining field lines of opposite
  polarity
• The point of reconnection moves up the field
  lines, driving a flare of plasma outwards!
• EXPLOSIVE EVENTS!

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1B11 The Sun Active Regions. Flares

• Solar Flares are short-lived, violent discharges
  of energy.
• A large flare blows off about 1025 J, as a bomb
  of 2 billions megatons!
• On 6 March 1989, the largest flare in 20 yrs
  blasted detectors on satellites.
• A week later, storms in the Earths magnetosphere
  ignited auroras, disrupted radio communications
  and caused black out for 6 millions of people in
  Quebec.
• That flare released 1030 J!

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1B11 The Sun Solar cycle

• The level of activity of the Sun varies
  periodically.
• The most obvious feature that changes with time
  are the number of sunspots visible on the surface
  of the Sun.
• The famous butterfly diagram shows that
  sunspots do not appear randomly, but they are
  concentrated in two latitude bands on either side
  of the equator.

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1B11 The Sun Solar cycle

• There is a cyclic activity going on here.
  Discovered by Walter Maunder (1851-1928).
• At each side of the equator, sunspots first
  emerge at relatively high latitude (?30?) and
  then appear at lower and lower latitude. They
  finally die away along the equator in ?11yrs.

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1B11 The Sun Solar cycle
The 11 yrs cycle is not the only periodicity!

• In 1908 G. H. Hale detected intense magnetic
  fields associated with sunspots

The strongest magnetic sunspots have Bgt0.4T,
about 8000 times the average field at the Earth
surface

• Hale noticed that sunspot groups contain spots
  of opposite polarity, east and west (for example,
  east has north polarity and west has south
  polarity).
• At each time, the situation is reversed in the
  southern emisphere.
• Every 11 yrs the cycle starts again, but with
  opposite global polarization.

If a spot group has the west spot with south
polarity, in the next sunspot cycle the west spot
will have a north polarity and in the following
cycle, south polarity again
The complete cycle repeats every 22 yrs!
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1B11 The Sun Solar cycle. Babcock Model

• Babcock published a semi-observational model of
  the variation of the Suns magnetic field in
  early 1960s.
• Initially the field lines are poloidal,
  connecting north and south poles.
• This occurs ?3 yrs before the onset of the Suns
  cycle.
• Differential rotation, with a rate of ?25 d at
  the equator and ?30 d at the poles, stretches
  the field lines horizontally around the Sun.
• This takes the form of a spiral pattern in the
  north and south hemisphere.

The field is more intense around latitudes of
?30?, due to a sin2 ? term in the Suns
differential rotation, and this is the location
of the first sunspots!
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1B11 The Sun Solar cycle. Periodic Reversal of
the field
The final stage of Babcocks model describe the
reversal of the poloidal field due to the fact
that active regions tends to have the leading
polarity at lower latitude of the following
polarity.

• The following polarity can migrate toward the
  nearest pole, whereas the leading polarity has
  more chance to move towards the equator and
  cancelling with opposite polarities from the
  opposite hemisphere.
• The following polarity that makes it to the poles
  first cancel the existing magnetic field and then
  replace it with flux of the opposite polarity
• After 11 years the field is poloidal again (but
  reversed!) and after 22 years the polarities will
  return to the initial starting point ? 22 years
  is the real periodicity!

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1B11 The Sun Solar cycle. Not so simple, so far
...

• In reality the cycle period also varies from peak
  to peak, with intervals in the range 8-15 yrs,
  making difficult to predict when the peak of
  solar activity will occur.
• There have been years with no sunspot at all.

• It has been argued that the phase of the solar
  cycle may be coupled to a periodic oscillation
  of the solar interior shorter cycle are
  generally followed by longer ones.
• The dataset however cover only a few hundreds
  years, and it is not long enough to define the
  phase exactly.

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1B11 The Sun solar cycle. And in the past?

• Sunspots where discovered by Galileo in 1613..
  And before??

? Little historical evidence!

• From 1645 for 70 years there was a period in
  which very few sunspots have been observed
  Maunder Minimum.

This corresponded to an unusual cold spell,
sometimes called the Little Ice Age (the average
T of the Earth dipped about 0.5 K), that extended
from the sixteenth to the eighteenth century.

• The relative consistency of the cycle in modern
  times may be a brief phase that recurs over
  longer times..
• Overall, solar activity behaviour may be more
  complex than we have inferred from the limited
  time spans investigated so far!