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The Sun:The Sun: A Nuclear A Nuclear

PowerhousePowerhouse

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Happy SunHappy Sun

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Why Does the Sun Shine?Why Does the Sun Shine?The Sun gives off energyThe energy must come from somewhere — there’s no free lunch

Conservation of energy is a fundamental tenet of physics

Where does the energy come from?Until the 20th century only 2 possibilities were known:

Chemical reactionsGravity

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The Sun’s Energy The Sun’s Energy OutputOutput

How bright is the Sun? The Sun produces 4x1026 watts

The watt is the unit for the rate of energy use, commonly seen on light bulbs and appliances

Our largest power plants produce around 5 x 109 watts of power (5,000 megawatts)Sun’s power = 8 x 1016 of these power plants (10,000 trillion)

Anyway you look at it, the Sun gives off a lot of energy

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Is the Sun Powered by Is the Sun Powered by Chemical Reactions?Chemical Reactions?What are chemical reactions? Examples:

Rearrange the atoms in molecules, as in 2H2+O2 2H2O This reaction combines hydrogen and oxygen (gases) to produce water plus energy

Reverse the process: 2H2O 2H2 + O2

By adding energy, we can dissociate water into hydrogen and oxygen

The energy factor is often left out of chemical-reaction formulas, for convenience

If the Sun is powered by burning coal or oil, how long could its fuel last?

Only a few thousand years!A process that uses fuel more efficiently is needed — something that gets more energy out of every kilogram of material

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Gravity Squeeze?Gravity Squeeze?The Sun’s interior experiences contraction due to its own gravity

This gravitational contraction converts gravitational potential energy into heat energy

Drop a book noise (gravitational potential energy turns into sound energy)

A contraction of 40 m per day would account for the Sun’s energy output

Efficiency ~ 1/10,000 %

Gravity could power the Sun for about 100 million years

but the Sun is thought to be at least 4 billion years old!

So gravity cannot be the Sun's main energy sourcealthough it did help ignite the Sun when it formed

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Nuclear Physics and Theory of Nuclear Physics and Theory of RelativityRelativity

To understand the way the Sun produces its energy, we need to learn a little about nuclear physics and the special theory of relativityNuclear physics deals with the structure of the nuclei of atomsThe special theory of relativity deals with the behavior of things moving at close to the speed of light

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Converting Mass to EnergyConverting Mass to EnergyOut of the special theory of relativity comes the most famous equation in science: E = m cE = m c22

This equation tells us that mass (m) is just another form of energy (E)!

The c2 is the square of the speed of light

For example, 1 gram of matter is equivalent to the energy obtained by burning 15,000 barrels of oil

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……But There Are RulesBut There Are RulesWe can’t simply convert atoms into energyWe rearrange the protons and neutrons in nuclei to get a lower-mass configurationThe difference between initial mass and final mass is converted to energy

Chemical energy comes from rearranging atoms to configurations of lower energy (mass)Nuclear energy comes from rearranging nuclei to configurations of lower mass (energy)In each case, we get out the energy difference

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Elementary ParticlesElementary Particles5 particles play a fundamental role inside the Sun

Protons and neutrons make atomic nucleiElectrons orbit nuclei of atomsPhotons are emitted by the SunNeutrinos are also emitted

Particle name

Mass (MeV/c2)

Charge (e)

Proton 938.272 +1

Neutron 939.565 0

Electron 0.511 -1

Neutrino <10-6 0

Photon 0 0

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Atomic NucleusAtomic NucleusTwo ways to rearrange nuclei and get energy:

Fission produces energy by breaking up massive nuclei like uranium into smaller nuclei like barium and kryptonis used in A-bombs and nuclear reactorsneeds uranium-235 and plutonium-238cannot occur inside the Sun: it has no uranium or plutonium

Fusionproduces energy by fusing light nuclei like hydrogen to make more massive nuclei like heliumis used in H-bombscan occur inside the Sun: it has lots of hydrogen!!

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How Does Fusion Work?How Does Fusion Work?Nuclear fusion is a process by which two light nuclei combine to form a single, larger nucleusHowever, nuclei are positively charged

Like charges repelTwo nuclei naturally repel each other and thus cannot fuse spontaneouslyFor fusion, electrical repulsion must be “overcome”

When two nuclei are very close, the strong nuclear force takes over and holds them togetherHow do two nuclei get close enough?

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Fusion Needs Fast-Moving Fusion Needs Fast-Moving NucleiNuclei

Fast moving nuclei can overcome the repulsion

They get a running start

Lots of fast moving nuclei implies high temperaturesThe core of the Sun has a temperature of 15 million kelvin

Low speed

High speed

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Fusion Powers the SunFusion Powers the SunTemperatures in the cores of stars are estimated to be above the 8 million K needed to fuse hydrogen nuclei togetherCalculations have shown that the observed power output of the Sun is consistent with the power produced by the fusion of hydrogen nucleiThe observed neutrinos from the Sun produced are expected as one of the byproducts of fusion reactionsWe can, therefore, hypothesize: all stars produce energy by nuclear fusion

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Proton-Proton Chain Proton-Proton Chain

eHHH 2

HeHH 32

HHHeHeHe 433

• Fuse two hydrogen (H=1 proton) to make deuterium (2H=1 proton+1 neutron), neutrino, and positron

• Fuse one deuterium and one hydrogen to make helium-3 (3He=1 proton+2 neutrons) and a gamma ray (energetic photon)

• Fuse two helium-3 to make helium-4 (4He) and two hydrogen

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Why a Complicated Chain?Why a Complicated Chain?Fusion would be simpler if four protons would collide simultaneously to make one helium nucleus That is simpler, but less likely

rare for four objects to collide simultaneously with high enough energy chance of this happening are very, very smallrate too slow to power the Sun

The proton-proton chain: each step involves collision of two particles

chance of two particles colliding and fusing is much higher

so nature slowly builds up the helium nucleus

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Fusion and Solar StructureFusion and Solar StructureFusion occurs only in Sun's coreThis is the only place that is hot enoughHeat from fusion determines the Sun's structure

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Heat from Core Determines Heat from Core Determines Sun's SizeSun's Size

There is a force equilibrium inside the Sun, called hydrostatic equilibrium, which is a balance between

thermal pressure from the hot core pushing outward gravity contracting the Sun toward its center

The nuclear-fusion rate — how often fusion can occur — is very sensitive to temperature

A slight increase/decrease in temperature causes the fusion rate to increase/decrease by a large amount

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Gravity and PressureGravity and PressureForce equilibrium

Newton's 1st law states that an object’s acceleration is zero if forces on the object balanceGravity tries to pull the 1/4 pounder toward Earth’s centerNewton’s 3rd law implies that pressure from the table opposes gravity

Hydrostatic equilibrium in the SunThe “cloud of gas” is like 1/4 pounderGravity pulls it toward the centerPressure from below opposes gravity

The heat from fusion in the hot core increases the pressure

Thus the energy output of the Sun controls its size!

pressurpressure from e from tabletable

weight weight from from

gravitgravityy

cloud

pressurpressure from e from hot gas hot gas

weight weight from from

gravitgravityy

Temperature and Temperature and Pressure Pressure

The temperature of a gas corresponds to the random motion of atoms in the gasThe pressure of a gas is the amount of force per unit area on a surface in contact with the gasIn general, pressure increases with increasing temperature

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Balancing Fusion, Gravity, and Balancing Fusion, Gravity, and PressurePressure

If the fusion rate increases, thenthermal pressure increases causing the star to expandthe star expands to a new point where gravity would balance the thermal pressurethe expansion would reduce the pressure inside the corethe temperature in the core would drop the nuclear fusion rate would subsequently slow downthe thermal pressure would then drop the star would shrinkthe temperature would then rise again and the nuclear fusion rate would increasestability would be re-established between the nuclear-reaction rates and the gravity compression

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Hydrostatic EquilibriumHydrostatic Equilibrium

The balance between the fusion rate, thermal pressure, and gravity determines the Sun's sizeBigger stars have cooler coresSmaller stars have hotter cores and, therefore, are more compressed

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Other ParticlesOther ParticlesHelium is not the only product in the fusion of hydrogenTwo other particles are produced

PositronsNeutrinos

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Gamma-Ray Propagation in Gamma-Ray Propagation in the Sunthe SunThe positrons emerging from the fusion reactions in

the core quickly annihilate the electrons near themThe annihilation produces pure electromagnetic energy in the form of gamma-ray photonsThese photons take about a million years to move from the core to the surface This migration is slow because they scatter off the dense gas particles

The photons move on average about only a centimeter between collisions In each collision, they transfer some of their energy to the gas particles

As they reach the photosphere, the gamma-ray photons have become visible-light photons

because the photons have lost some energy in their journey through the Sun

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NeutrinosNeutrinosThese particles have no charge and are nearly masslessThey rarely interact with ordinary matter Neutrinos travel extremely fast

at almost the speed of light if their mass is tiny

Neutrinos pass from the core of the Sun to its surface in only two secondsThey take less than 8.5 minutes to travel from the Sun to the Earth

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Neutrino Abundance & Neutrino Abundance & CountingCountingThe Sun produces a lot of neutrinos

In one second several million billion neutrinos pass through your body

Do you feel them?Not to worry!

The neutrinos do not damage anythingThe great majority of neutrinos pass right through the entire Earth as if it weren’t there

In principle, we can use the number of solar neutrinos received on Earth to get clues about the Sun’s energy output, but

neutrinos have a very low probability of interacting with ordinary matterthey could pass through a light year of lead and not be stopped by any of the lead atoms!

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Detecting NeutrinosDetecting NeutrinosIncrease the odds of detecting neutrinos by using a large amount of a material that reacts with neutrinos in a measurable way

A chlorine isotope changes to a radioactive isotope of argon when hit by a neutrinoA gallium isotope changes to a radioactive isotope of germaniumNeutrinos can interact with protons and neutrons and produce an electron

The electron can be detected

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Neutrino DetectorsNeutrino DetectorsNeutrino detectors use hundreds of thousands of liters of these materials in a container buried under many tens of meters of rock to shield the detectors from other energetic particles from space called cosmic raysEven the largest detectors can detect only a few neutrinos per day