“How does the Sun work?” Dr Vincent Smith, Department of Physics

(1) Some Facts and Figures

(2) Energy source

(3) Magnetism and Sunspots

“The Sun shines and warms and lights us and we have no curiosity to know why this is so;

but we ask the reason of all evil, of pain, and hunger, and mosquitoes and silly people”

Ralph Waldo Emerson (1803-1882)

But he also said:“There are many things of which a wise man might wish to be ignorant.”

Distance from Earth to Sun = 1.50 x 1011 m (150 million km)

(The light from the Sun takes 8 minutes to reach us)

Diameter of Sun = 1.4 x 106 km (>100 times diameter of Earth)

Mass = 2 x 1030 kg ( 2 billion billion billion tonnes; ≈ 333,000 times Earth)

Average density = 1.4 tonnes per cubic metre (density of Earth = 5.5)

Surface Temperature = 6000 K (Central Temperature 16 x 106 K)

Central pressure = 3.4 x 1016 Pa (340 billion x Earth’s atmosphere)

Composition = Hydrogen (71%), Helium (27%), heavier elements (2%)

Power output = 3.8 x 1026 W(380 Yotta Watts)

Power received at Earth = 1.4 kW / m2 (called the Solar Constant)

Where does its power come from ?

It can’t be chemical burning:

Example: Coal (Carbon) + Oxygen

Heat of combustion = 400 kJ/mole (12 g of C)But power needed = 4 x 1026 WThis needs (4x1026/4x105) x12 g per second= 12x1021 g/sec = 12x1018 kg/secBut mass of Sun = 2 x 1030 kg,so fuel lasts 2x1030/12x1018 sec = 16x1010 sec = 5000 years.

Where does its power come from ?

It can’t be chemical burning:

Example: Coal (Carbon) + Oxygen

Heat of combustion = 400 kJ/mole (12 g of C)But power needed = 4 x 1026 WThis needs (4x1026/4x105) x12 g per second= 12x1021 g/sec = 12x1018 kg/secBut mass of Sun = 2 x 1030 kg,so fuel lasts 2x1030/12x1018 sec = 16x1010 sec = 5000 years.

(Just right for Creationists !)

Does Gravity supply the energy ?

Infalling meteors ?(It needs 3x1022 kg per year: surface area of Earth’s orbit = 30x1022 m2; that’s 100g per m2 per year, we would be smashed to bits!)(Actual rate = 3 mg per m2 per year.)

Contracting Sun? (releases gravitational p.e.) g at surface = 274 m/s2

Suppose: the mass (2x1030 kg) falls a distanceh each year: mgh = 4x1026x3x107 J. h = 20 m per year.

But radius = 7x108 m, so lifetime = 7x108/20 = 35 million years.

Still not enough ! Lord Kelvin

Is it Radioactivity ?

(NB Radioactivity keeps us warm on Earth: it gets hotter as you go deeper.)

Still not enough (especially given the small fractions of heavy elements in the Sun.)

In the 1920s and 1930s it was realised it was Nuclear Fusion:

Hydrogen nuclei (protons) combine to make Helium nuclei, releasing lots of energy.

Fritz Houtermans was one of the pioneers:

In the 1920s and 1930s it was realised it was Nuclear Fusion:

Hydrogen nuclei (protons) combine to make Helium nuclei, releasing lots of energy.

Fritz Houtermans was one of the pioneers:

“One Summer evening he was strolling with his girlfriend at his side. She looked up at the stars and said, ‘Aren’t they beautiful?’‘Yes,’ he said, ‘and yesterday I became the first man to know why they shine!’ ”

Fusion Reactions

The details were worked out by Hans Bethe,(who worked for 6 months in 1934 at Bristol University.) He received the Nobel prize for Physics in 1967.

There are three steps:

(1) p + p d + e+ + (two protons combine to form a deuteron)(the e+ rapidly annihilates with an e-)

(2) p + d 3He + (the deuteron combines with another proton)

(3) 3He + 3He 4He + p + p(two 3He combine to make 4He, and release two protons.)

The net effect is: 6p + 2e 4He + 2p + 2

In this process, 26 MeV is released. Why is this?

Remember Einstein’s famous equation: E = mc2

Note the masses: 1H mass = 1.007825 u 4He mass = 4.002603 u

(NB 1 u = 931.5 MeV)

4x 1H - 4He = 0.0287 u = 26.7 MeV

(1 eV = 1.6 x 10-19 J)

So in order to produce 4x1026 W, we need to convert(4 x 4x1026)/(26x1.6x10-13) = 4x1038 protons per second.

This is equivalent to 4x1038 x 1.67x10-27 kg = 6x1011 kg of hydrogen converted per second,and a mass loss of 4x1026/(3x108)2 = 4x109 kg per second.

NB The Sun is so huge, that this energy release is only about 0.2 mW per kg of the Sun ! (Compare the metabolism of your body, of order 0.2 kW in 100 kg, ie 10,000 times greater.)

Compare this rate of conversionof hydrogen (6x1011 kg/sec)with the mass of the Sun (2x1030 kg),and we see that the Sun can keepgoing for a long time!

In fact the reactions only take placein the core of the Sun, so only about 10%of its mass will be converted.

The estimated age of the Sun is about5 billion years, and it will keep going foranother 5 billion or so.

So the Sun is currently only middle-aged!

What sets the rate of the Sun’s energy conversion, ie its lifespan and its brightness?(Or, why doesn’t it use up all its hydrogen straight away?)

Notice that the first reaction, p + p d + e+ + , is a weak interaction, since it has to convert a proton into a neutron.

So the reaction is very slow: the protons collide billions of times per second, but only once in 1010 years do they create a deuteron!

We need very high pressure to get the protons to collide frequently.

Also, we have to get the protons to approach each other very closely in order to react (they are positively charged, so they repel each other.) This means the temperature has to be very high (millions of degrees Kelvin), so that their kinetic energies are high.

So these nuclear reactions only take place in the core of the Sun.

(1) p + p d + e+ +

(2) p + d 3He +

(3) 3He + 3He 4He + p + p

After step 1, the newly-formed deuteron has to find a proton to react with, but there are plenty of these with enough energy to reach it. Also, step 2 is electromagnetic, not weak.

Finally, the two 3He nuclei have to find each other, with enough energy to overcome their repulsion, but they are quite rare, so this step takes of order 106 years, even though it is a strong interaction.

NB We can monitor the rate of step 1 by observing the neutrinos produced,

when they interact in large terrestrial detectors to produce electrons.

In the Sun and other stars, as well as the H He (or pp) reaction

described, there is a small proportion of a different reaction:

e + 7Be + 7Li.

(A proton in a beryllium nucleus absorbs an electron, converting into a

neutron and emitting a neutrino.)

These neutrinos are higher in energy than those from the pp reaction, but

the rate of this reaction depends critically on the conditions in the centre of

the star.

They can be detected on Earth by the inverse reaction:

+ 37Cl e + 37Ar*

Ray Davis used a large tank

of dry-cleaning fluid (C2Cl4)

and counted the number of

radioactive argon atoms

produced each month, over

many years. He consistently

found less than half of the

expected number.

Does this mean the reactions in the centre of the Sun have slowed down?

This was a big puzzle for more than 30 years: has the Sun “gone out”?

Or do we really understand the conditions of temperature and pressure at

the centre of the Sun?

Or are we losing neutrinos on the way from the Sun to the Earth?

Recently, experiments have succeeded in measuring the (lower energy)

pp neutrinos, finding there is still a shortfall. The idea that neutrinos were

disappearing began to look more likely.

There are three types of neutrinos, depending

on their related charged particle: electron,

muon, or tau.

(Muons are just like electrons, but 200 times

heavier; taus are 3000 times heavier.)

What if some of the electron neutrinos produced

in the Sun, were changing to a different type on

their way? They would not have enough energy

to produce muons or taus, so they would be

‘sterile’.

Fortunately, it is possible to resolve this

question by simultaneously observing

the rate of conversion of neutrinos into

electrons, and collisions of neutrinos

with nuclei of deuterium (in heavy

water) which break up, but the neutrino

remains a neutrino. The SNO (Sudbury

Neutrino Observatory) in Ontario,

Canada, has found that solar neutrinos

do indeed change their ‘flavour’. So

now we are confident that the Sun is

still shining!

Magnetism and the Sun

The Sun is rotating (once in 24 days near the equator; once in 30 days near the poles: also probably with different rates at different depths.)

It is made of an ionised plasma, positive and negative particles, which have different mobilities. It is not difficult to imagine large net circulating currents being produced: these produce large magnetic fields.

NB The Earth also has a (very much smaller) magnetic field, due to currents in its liquid core, while the Moon does not.

But the currents are unstable: whirlpools are created, with corresponding magnetic fields. The field lines loop out and back in at sunspots (often in symmetric pairs, above and below the equator.)

Sunspots are the Sun’s weather systems!

NB the magnetic field lines continue beyond the photosphere (visible surface of the Sun), into the chromosphere and corona. This is much hotter (106 K), but much less dense than the photosphere. It is probably heated by these magnetic field lines whipping through it.

The number of sunspots cycles through maximum and minimum, usually every 11 years, and the direction of the magnetic field reverses in the same cycle. (Compare the Earth’s magnetic field, which only reverses on a timescale of many thousands of years.)

NB Galileo observed sunspots in 1610, which led him to discard the idea that the Sun was

perfect. But from 1650 – 1700 there were almost none: he was very lucky!

From time to time, material from the surface is projected at high speed (solar flares and coronal mass ejections.) These consist of ionised particles, which reach out far into the solar system, and can enter the Earth’s atmosphere, causing auroras as they excite molecules in the air, and affecting the ionosphere and radio propagation.

The End

I would like to express my thanks for the many images taken from the World Wide Web.