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# 1B11 Foundations of Astronomy The Sun - PowerPoint PPT Presentation

1B11 Foundations of Astronomy The Sun. Silvia Zane, Liz Puchnarewicz [email protected] www.ucl.ac.uk/webct www.mssl.ucl.ac.uk/. 1B11 The Sun: a source of mystery to the human race. Newgrange, outside Dublin. Winter Solstice. 1B11 The Sun: a composite schematic illustration.

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### 1B11 Foundations of AstronomyThe Sun

Silvia Zane, Liz Puchnarewicz

www.ucl.ac.uk/webct

www.mssl.ucl.ac.uk/

Newgrange, outside Dublin

Winter Solstice

• Core: 0-25%

• 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).

• Consider a spherical shell of area A=4  r2, at radius r of thickness dr

(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):

• 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 P[r], [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:

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:

• 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)

We measure:

• the Sun’s size from its distance (1AU) and angular scale (0.5 ˚ )

• the Sun’s mass from the motion of planets

• the Sun’s age by the abundances of heavy radioactive elements in meteorites. The Sun’s 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.

The Energy source is at the Sun’s core (T=15MK, ne=1.5x105kg/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2D+e++e, where the deuteron consists of a proton and neutron.

• Then; 2D+p 3He+, where the isotope of He consists of 2 protons and 1 neutron.

• Finally; 3He+3He  4He+p+p, which is a common alpha particle.

Very high Temperature (> 107 K) is required for p to overcome their mutual electric repulsion!

Energy balance:

• 4He has a mass of only 99.3 \% of 4 protons !

• Remaining 0.7\% is converted in energy via E=mc2

EFFICIENCY of this reaction = 0.7\%

• Lsun = 3.86 x10 26 J/s

• From E=mc2, 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!

• ~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

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

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

3He+4He  7Be +  (Be = Beryllium)

p + 7Be  8B +  (B = Boron, unstable!)

8B  8Be + e+ + e

• 8Bneutrinos 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!

• 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 zero’s 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!

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

• What’s 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

• 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!

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).

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 1:106

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.

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).

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.

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.

• 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 sun’s 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!

• 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 Sun’s 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.

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

• 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 > 1. 106 K

• Bright points , active regions, flares, large scale structures (streamers), coronal holes, solar wind, CMEs

• 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?

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

• 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

• 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 !

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

Jan 4 2001 -

image in H

- filaments are

clearly seen.

• 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!

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!

• 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?

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 Sun’s 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

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.

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!

What’s 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 < Tphot.

• For Bspot ~ 0.4 Tesla, Tspot ~ 3700 K.

• Size of Umbra ~ 20,000 km

This occurs when B reaches a critical value!

The “Magnetic Carpet”

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!

• 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 Earth’s magnetosphere ignited auroras, disrupted radio communications and caused black out for 6 millions of people in Quebec.

• That flare released 1030 J!

• 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.

• 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.

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 B>0.4T, 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!

• Babcock published a semi-observational model of the variation of the Sun’s 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 Sun’s 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!

N

S

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s

N

N

S

S

N

N

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S

N

1B11 The Sun: Solar cycle. Periodic Reversal of the field

The final stage of Babcock’s 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!

• 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.

• 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!