Power generation in stars

Astronomy 100

Energy transfer• As the names of the layers

imply, it is not the composition of the sun that is interesting, but the manner in which energy is transmitted from layer to layer.

• This difference in manner of energy transfer will be a direct result of the lessening density of the Sun outwards; in fact, the outer edge of the convective zone (the photosphere) is far less dense than the Earth’s atmosphere!

The Sun’s energy is generated by thermonuclearreactions in its core

• Thermonuclear fusion occurs at very high temperatures• Hydrogen fusion occurs only at temperatures in excess of

about 107 K• In the Sun, hydrogen fusion occurs in the dense, hot core

Proton-Proton Chain Reaction•The Sun’s energy is produced by hydrogen fusion, a sequence of thermonuclear reactions in which four hydrogen nuclei combine to produce a single helium nucleus; called proton-proton chain reaction

Proton-Proton Chain Reaction: Step 1

Proton-Proton Chain Reaction: Step 2

Proton-Proton Chain Reaction: Step 3

Proton-Proton Chain Reaction

4 H He + energy + neutrinos

Mass of 4 H > Mass of 1 He

•In every second, 600 million tons of hydrogen converts into helium to power the Sun

•At this rate, the Sun can continue hydrogen fusion for more than 6 billion years.

Solar neutrinos

How do we know about the interior of the sun and how it produces power?

One answer is neutrinos. We, on Earth, can measure neutrinos produced

within the solar core. This is because neutrinos almost never interact with matter.

Neutrino detection

Neutrinos DO interact with matter, but their cross- section is small, meaning they don’t

hit other matter very much.

• ~7 × 107 neutrinos pass through your thumbnail (which is an area about 1 cm2) each second. But your body interacts with a neutrino only about once in 70 years. This length is jokingly referred to as the……....

Neutrino Theory of Death! (human lifespan and all, heh, heh)

Neutrino detection

The first actual detection of a neutrino was made by Frederic Reines and Clyde Cowan.

They didn’t actually measure a neutrino, just the by product of its reaction with a proton (1 in 1018 chance of occurring).

e + p n + e+ e+ + e- 2

In 1956 they measured these gamma rays from a nuclear reactor at Hanford in E. Washington and (conclusively) Savannah River in South Carolina.

Why do we care about neutrinos?

Reason 1: Neutrinos are produced in the core of the Sun in HUGE amounts (about 1038 neutrinos/s).

Reason 2: Most neutrinos escape the Sun without interacting with the Sun’s matter, so they reach the Earth in 8 minutes ! They travel at very close to the speed of light.Reason 3: Neutrinos are produced by several reactions in the proton-proton chain and depend on solar core composition, pressure, and temperature.

Reason 4: They provide another boundary condition for the standard model (i.e., the way we describe subatomic particles).

Complete fusion process in the solar core (colored boxes show neutrino production)

The solar neutrino spectrum

p+ p D+ e+ +

[ 3He + 4He 7Be]

7Be + e- 7Li +

[ 7Be + P 8B]

8B 7Be + e+ +

neutrino reactions in the Sun:

The relative contributions of the different neutrino reactions depend on conditions in the solar core.

8B7Be7Be

(1MeV = 1.6 x 10-13 J)

p + e- + p D +

First detection of solar neutrinos

Homestake Mine experiment led by Ray Davis in South Dakota 1.5 km underground 1965-1987:

378,000 liters of cleaning fluid (ultra-pure carbon tetrachloride).

When neutrino interacts argon is produced.

37Cl + 37Ar + e-

[E = 0.8 MeV]

Measures ~ one neutrino every 2 days.

(17p+ + 20n) (18p+ +19n)

The solar neutrino problem

• Standard Model of the Sun says that Homestake should detect ~1.5 –2 neutrinos per day, but it only detects 0.5 per day. Factor of 3 to 4 difference.

• Either we don’t understand the sun like we thought we did, or something else is going on. Hopefully not the first thing, because then the Standard Model would be hopelessly wrong.

The solar neutrino problem

Adding up all the neutrinos does not get the amount predicted in the Standard Model, regardless of the

detection method used.

Solution to solar neutrino problem: neutrino oscillations

There are three flavors of neutrinos: electron neutrino (e), muon neutrino (), and the tau neutrino()

MSW Effect: neutrinos oscillate between flavors as they travel through space. This is effect is strongly enhanced when neutrinos pass through matter (Mikheyev, Smirnov, and Wolfenstein, 1986)

Homestake Mine could only detect electron neutrinos

Neutrino oscillations require that the neutrino has mass (changes the Standard Model of particle physics)

How do we know if neutrinos oscillate?

Using very large omni-directional sensors of water and heavy water (D2O). Measure a lack of e and overabundance of other flavors

Water Based: SuperKamiokande in Japan, 50,000 tons of ultra-pure water

Able to detect e above 7.5 MeV

e scatter with e- in water, producing e- that travel faster than c in water (called Cherenkov radiation) which produces radiation detected by thousands of photomultiplier tubes (PMT)

Measured lack of e (like Homestake)

Confirmed that neutrinos can oscillate, but were unable to detect all the solar neutrinos

The solar neutrino observatories

Neutrino observatories are defined mainly by the energy range and flavors they can sample.

Neutrinos are hard to measure, so the detectors are large and omni-directional.

Heavy Water: Sudbury Observatory (SNO) in Canada 1000 tons of D2O (UW Physics main US participator):

Can detect all flavors of neutrinos (e, μ ,and τ) above ~5 MeV

Measured lack of νe and abundance of μ and/or τ

Best evidence for neutrino oscillations and thus massive neutrinos

Solar neutrino problem: solved!

• In June of 2001, the SNO team reports that the neutrino deficit is solved

• Our model of the solar core is correct

• Neutrino mass needed to be added to the Standard Model

Neutrino astrophysics

SN 1987A (supernova): Three hours before observing light, neutrinos were detected in a 13 second burst.

Kamiokande II: 11 antineutrinos

IMB: 8 antineutrinos

Baksan: 5 antineutrinos

Dark Matter: One candidate for DM is the sterile (truly non-interacting) neutrino.

Cosmic Neutrino Background: Big Bang Nucleosynthesis, constraints on matter distribution

Astronomy 100 23

Nucleosynthesis – Triple Alpha reaction

4 4 8 02 2 4 08 4 12 * 04 2 6 0

He+ He Be+

Be+ He C +

The triple alpha reaction

(3 He’s are involved)

Carbon is formed in an excited state, originally predicted before it was known that this could happen.

Requires temperatures on the order of .810 K

How are elements heavier than helium produced?

Astronomy 100 24

Results of nucleosynthesis: the cosmic abundances of the elements (not all due to stellar processes)

Abu

ndan

ce r

elat

ive

to h

ydro

gen

Mass number (number of baryons in nucleus)

Figure: Shu, The Physical Universe

Astronomy 100 25

Hotter fusion and heavier elements

• Could stars in principle live forever simply by contracting gravitationally and increasing their temperature to ignite the next heavier source of nuclear fuel whenever they run out?– No. The strong interaction’s range is smaller than the

diameters of all but the smaller nuclei, but the range of the Coulomb interaction still covers the whole nucleus.

– If nuclei get large enough the increase in electrostatic repulsion of protons becomes greater than the increase in binding energy from the strong interaction.

– Thus there is a peak in the binding-energy-per-baryon vs. atomic mass number relationship, that turns out to lie at iron (Fe).

Astronomy 100 26

Hotter fusion and heavier elements (continued)

Implication:Once a star’s core is composed completely of iron, it can no longer replenish its energy losses (from luminosity) by fusion. Stars therefore must die, eventually.In other words, you get energy by fusion all the way up to production of iron but not beyond.B

indi

ng e

nerg

y pe

r ba

ryon

Atomic mass number

Figure: Shu, The Physical Universe

The high mass track

1) Proto Star

• While on the main sequence what do high mass stars burn in their cores?– Hydrogen

• What fusion process?– CNO

HIGH MASS TRACK

2) Main sequence

The CNO cycle

• Low-mass stars rely on the proton-proton cycle for their internal energy

• Higher mass stars have much higher internal temperatures (20 million K!), so another fusion process dominates– An interaction involving Carbon,

Nitrogen and Oxygen absorbs protons and releases helium nuclei

– Roughly the same energy released per interaction as in the proton-proton cycle.

– The C-N-O cycle!

High mass stars – the end• Onion structure of the core

.

Astronomy 100 33

Nucleosynthesis (continued)

• The triple alpha reaction makes carbon. • Add a helium to carbon and you get an oxygen.• Two carbons can make a magnesium.• To fuse heavier elements generally require higher

temperatures.• Energy is released all the way up to the formation of iron.• Nuclei are fused at higher and higher temperatures in the

core of a massive star until an iron core forms. • If the star doesn’t reach high enough temperatures in its core

then it can stop at triple alpha process (lower mass stars).• Eventually stars cannot burn anything more. So how are very

heavy elements made in the universe?

Summary• For the majority of stars (~95%, corresponding to stars with

initial masses of less than 8 M-Sun), direct nuclear fusion does not proceed beyond helium, and carbon is never fused.

• Most of the nucleosynthesis occurs through slow neutron capture during the asymptotic giant branch (AGB), a brief phase (~106yr) of stellar evolution where hydrogen and helium fuse alternately in a shell.

• These newly synthesized elements are raised to the surface through periodic "dredge-up" episodes, and the observation of short-lived isotopes in stellar atmospheres provides direct evidence that nucleosynthesis is occurring in AGB stars.

Supernovae• A supernova is a massive explosion of a star

that occurs under two possible scenarios. The first is that a white dwarf star undergoes a nuclear based explosion after it reaches its Chandrasekhar limit from absorbing mass from a neighboring star (usually a red giant).

• The second, and more common, cause is when a massive star, usually a red giant, reaches iron in its nuclear fusion (or burning) processes.

Supernovae

• Iron has one of the highest binding energies of all of the elements and is the last element that can be produced by nuclear fusion, exothermically.

• All nuclear fusion reactions from here on are endothermic and so the star loses energy.

• The star's gravity then pulls its outer layers rapidly inward. The star collapses very quickly, and then explodes.

Composite image of Kepler's supernova from pictures by the Spitzer Space Telescope, Hubble Space Telescope, and Chandra X-ray Observatory.