8 march 2005ast 2010: chapter 151 the sun: a nuclear powerhouse

8 March 2005 AST 2010: Chapter 15 1

The Sun:The Sun: A Nuclear A Nuclear

PowerhousePowerhouse


Happy SunHappy Sun


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


The Sun’s Energy OutputThe Sun’s Energy OutputHow bright is the Sun?

The Sun produces 4x1026 wattsThe 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


Chemical ReactionsChemical ReactionsWhat are chemical reactions? An example:

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


Is the Sun Powered by Chemical Is the Sun Powered by Chemical Reactions?Reactions?

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


Gravity Squeeze?Gravity Squeeze?Gravitational contraction: falling layers of the Sun's material compresses the Sun 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 can't be the Sun's main energy sourcebut it did help ignite the Sun when it formed


Mass, Energy, and the Theory of RelativityMass, Energy, and the Theory of Relativity

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


Converting Mass to EnergyConverting Mass to EnergyOut of the special theory of relativity comes the most famous equation in science: E = mcE = mc22

This equation tells us that mass (m) is just another form of energy (E)!The c2 is the square of the speed of light1 gram of matter is equivalent to the energy obtained by burning 15,000 barrels of oil


……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


Elementary ParticlesElementary Particles5 particles play a fundamental role in the SunProtons 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


The Atomic NucleusThe Atomic NucleusTwo ways to rearrange nuclei and get energy:

Fission It produces energy by breaking up massive nuclei like uranium into less massive nuclei like barium and kryptonA-bombs, nuclear reactorsFission needs uranium-235 and plutonium-238Problem: no uranium or plutonium in the Sun

FusionIt produces energy by fusing light nuclei like hydrogen to make more massive nuclei like heliumH-bombThe Sun has lots of Hydrogen!!


How Does Fusion Work?How Does Fusion Work?Nuclear fusion:

a process by which two light nuclei combine to form a single larger nucleus

However, 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?


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 means high temperatureThe core of the Sun has a temperature of 15 million degrees kelvin

Low speed

High speed


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 reactionsHypothesize: all stars produce energy by nuclear fusion


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


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


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


Heat from Core Determines Sun's Heat from Core Determines Sun's SizeSize

Force equilibriumHydrostatic equilibrium: balance between

thermal pressure from the hot core pushing outwards gravity squeezes the star collapse to the very center

Nuclear-fusion rate is very sensitive to temperatureA slight increase/decrease in temperature causes fusion rate to increase/decrease by a large amount


Gravity and PressureGravity and PressureForce equilibrium

Newton's second law: F = ma Static equilibrium: no acceleration if forces on object balanceGravity tries to pull 1/4 pounder to center of the EarthPressure from table opposes gravity

Hydrostatic equilibrium in the Sun“Cloud of gas" (like 1/4 pounder)Gravity pulls cloud to the centerPressure from gas below opposes gravityHeat from fusion in the hot core increases pressure Energy output controls size of sun!

pressure from table

weight from gravity

cloud

pressure from hot gas

weight from gravity


Temperature and Temperature and Pressure Pressure

Temperature corresponds to the random motion of atoms in a gasPressure is the amount of force per unit area on piston from gasGenerally pressure increases with increasing temperature


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

If the fusion rate increases, thenthermal pressure increases causing the star to expandstar expands to a new point where gravity would balance the thermal pressurethe expansion would reduce compression of 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 rise again and the nuclear fusion rate would increasestability would be re-established between the nuclear reaction rates and the gravity compression


Hydrostatic EquilibriumHydrostatic Equilibrium

The balance between pressure, heat from fusion, and gravity determines the Sun's sizeBig stars have cooler coresSmall stars have hotter cores and, thus, are more compressed


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

PositronsNeutrinos


Gamma-Ray Propagation in the Gamma-Ray Propagation in the SunSun

The positrons quickly annihilate the electronsPhotons produced in core of the Sun take about a million years to move to the surface This migration is slow because they scatter off the dense gas particles

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

As they reach the photosphere, gamma rays have become visible photons

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


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 the distance from the Sun to the Earth


Neutrino CountingNeutrino CountingIn principle

We can use neutrino count at Earth as indicator of the Sun’s energy output

The problem:Neutrinos have a very low probability of interacting with matterThey could pass through a light year of lead and not be stopped by any of the lead atoms!


Neutrino AbundanceNeutrino AbundanceThe Sun produces a lot of neutrinosIn 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


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


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


Solar Neutrino Production (1)Solar Neutrino Production (1)Number of neutrinos produced in the Sun is directly proportional to the number of nuclear reactions taking place in the Sun's core

Same principle with neutrinos produced via the Carbon-Nitrogen-Oxygen chain

The more reactions there are, the more neutrinos are produced and the more that should be detected here on the Earth Physicists find that the number of neutrinos coming from the Sun is smaller than expected

Early experiments detected only 1/3 of the expected number of neutrinosThese experiments used hundreds of thousands of liters of cleaning fluid (composed of chlorine compounds) or very pure water


Solar Neutrino Production (2)Solar Neutrino Production (2)Later experiments using many tons of gallium were able to detect the more abundant low-energy neutrinosHowever, those experiments also found the same problem

Too few neutrinos (the gallium experiments found about 2/3 the expected number)

The puzzling lack of neutrinos from the Sun is called the solar neutrino problem


The Solar Neutrino ProblemThe Solar Neutrino ProblemPhysicists evaluated a number of possible reasons for the problem

Nuclear fusion is not the Sun's power source? Not supported by observations, not likely to be the correct reason

The experiments were not calibrated correctly?Unlikely that all carefully-tuned experiments were tuned in the same wrong way. Experiments independently verified by many other scientists; astronomers think that the results are correct.

The nuclear reaction rate in the Sun is lower than what our calculations say?

Possible, but many people have checked and re-checked the physics of the reaction ratesStrong constraints in how much one can lower the temperature in the core of the Sun to slow down the reactions


Solar Neutrino SolutionSolar Neutrino SolutionThree types of neutrinos existThe Sun produces only one type, called electron neutrinosThe experiments detect only the electron typeOn their way from the Sun, neutrinos can transform from one type to another

This can explain why we only detect 1/3 of the mix at Earth

This also implies that neutrinos have mass, which is very small, but not zero

8 march 2005ast 2010: chapter 151 the sun: a nuclear powerhouse

Documents

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gravitational potential

rate of energy use