How Stars Evolve Pressure and temperature Normal gases

How Stars Evolve • Pressure and temperature – Normal gases – Degenerate gases • The fate of the Sun – – – Red giant phase Horizontal branch Asymptotic branch Planetary nebula White dwarf

Normal gas • Pressure is the force exerted by atoms in a gas • Temperature is how fast atoms in a gas move • Hotter atoms move faster higher pressure • Cooler atoms move slower pressure Pressure balances gravity, keeps stars from collapsing

Degenerate gas • Very high density • Motion of atoms is not due to kinetic energy, but instead due to quantum mechanical motions • Pressure no longer depends on temperature • This type of gas is sometimes found in the cores of stars

Pauli exclusion principle • No two electrons can occupy the same quantum state • Quantum state = energy level + spin • Electron spin = up or down

Electron orbits Only two electrons (one up, one down) can go into each energy level

Electron energy levels • Only two electrons (one up, one down) can go into each energy level. • In a degenerate gas, all low energy levels are filled. • Electrons have energy, and therefore are in motion and exert pressure even if temperature is zero.

Which of the following is a key difference between the pressure in a normal gas and in a degenerate gas? 1. Degenerate pressure exists whether matter is present or not. 2. In a degenerate gas pressure varies rapidly with time. 3. In a degenerate gas, pressure does not depend on temperature. 4. In a degenerate gas, pressure does not depend on density.

The Fate of the Sun • How will the Sun evolve over time? • What will be its eventual fate?

Sun’s Structure • Core – Where nuclear fusion occurs • Envelope – Supplies gravity to keep core hot and dense

Main Sequence Evolution • Core starts with same fraction of hydrogen as whole star • Fusion changes H He • Core gradually shrinks and Sun gets hotter and more luminous

Gradual change in size of Sun Now 40% brighter, 6% larger, 5% hotter

Main Sequence Evolution Fusion changes H He He sinks to center of Sun Core depletes of H Eventually there is not enough H to maintain energy generation in the core • Core starts to collapse • •

Red Giant Phase • He core – No nuclear fusion – Gravitational contraction produces energy • H layer – Nuclear fusion • Envelope – Expands because of increased energy production – Cools because of increased surface area

Sun’s Red Giant Phase

HR diagram Giant phase is when core has been fully converted to Helium

A star moves into the giant phase when: 1. It eats three magic beans 2. The core becomes helium and fusion in the core stops. 3. Fusion begins in the core 4. The core becomes helium and all fusion in the star stops.

Broken Thermostat • As the core contracts, H begins fusing to He in a shell around the core • Luminosity increases because the core thermostat is broken— the increasing fusion rate in the shell does not stop the core from contracting

Helium fusion does not begin right away because it requires higher temperatures than hydrogen fusion—larger charge leads to greater repulsion Fusion of two helium nuclei doesn’t work, so helium fusion must combine three He nuclei to make carbon

Helium Flash • He core – Eventually the core gets hot enough to fuse Helium into Carbon. – This causes the temperature to increase rapidly to 300 million K and there’s a sudden flash when a large part of the Helium gets burned all at once. – We don’t see this flash because it’s buried inside the Sun. • H layer • Envelope

Movement on HR diagram

Movement on HR diagram

Helium Flash • He core – Eventually the core gets hot enough to fuse Helium into Carbon. – The Helium in the core is so dense that it becomes a degenerate gas. • H layer • Envelope

Red Giant after Helium Ignition • He burning core – Fusion burns He into C, O • He rich core – No fusion, degenerate • H burning shell – Fusion burns H into He • Envelope – Expands because of increased energy production

Sun moves onto horizontal branch Sun burns He into Carbon and Oxygen Sun becomes hotter and smaller What happens next?

What happens when the star’s core runs out of helium? – – The star explodes Carbon fusion begins The core starts cooling off Helium fuses in a shell around the core

Helium burning in the core stops H burning is continuous He burning happens in “thermal pulses” Core is degenerate

Sun moves onto Asymptotic Giant Branch (AGB)

Sun looses mass via winds • Creates a “planetary nebula” • Leaves behind core of carbon and oxygen surrounded by thin shell of hydrogen • Hydrogen continues to burn

Planetary nebula

Planetary nebula

Planetary nebula

Hourglass nebula

When on the horizontal branch, a solar-mass star 1. 2. 3. 4. Burns H in its core. Burns He in its core. Burns C and O in its core. Burns He in a shell around the core.

White dwarf • Star burns up rest of hydrogen • Nothing remains but degenerate core of Oxygen and Carbon • “White dwarf” cools but does not contract because core is degenerate • No energy from fusion, no energy from gravitational contraction • White dwarf slowly fades away…

Evolution on HR diagram

Time line for Sun’s evolution

In which order will a single star of one solar mass progress through the various stages of stellar evolution? 1. Planetary nebula, main-sequence star, white dwarf, black hole 2. Proto-star, main-sequence star, planetary nebula, white dwarf 3. Proto-star, red giant, supernova, planetary nebula 4. Proto-star, red giant, supernova, black hole

Wolf-Rayet Stars • • Near solar-mass stars undergo heavy mass loss in the asymptotic phase forming planetary nebula. Massive stars undergo heavy mass low in a similar evolutionary phase, i. e. after significant nuclear ash accumulates. Wolf-Rayet stars are among the most massive (typically over 20 solar masses), hottest (surface temperatures over 25, 000 K), and shortest lived stars known. Wolf-Rayet stars represent an evolutionary phase in the lives of massive stars during which they undergo heavy mass loss. They are characterized by spectra dominated by emission lines of highly ionized elements.

WR stars on HR diagram

WR spectrum • WC indicates WR star with carbon lines. • C, N, O produced by nuclear burning, transported to surface by convection. • Roman numeral indicates ionization state: I = neutral, II = one electron missing, III = two electrons missing, etc.

Pulsating stars • Hydrodynamic equilibrium • Pulsating stars • Distance indicators

If a star is neither expanding nor contracting, we may assume that throughout the star there is a balance between pressure and 1. 2. 3. 4. temperature density luminosity gravity Do mass on spring demo

Pulsating stars

Pulsating stars • This should happen in all stars • We already know there are small oscillations visible on the surface of the sun that represent sound waves that travel deep into the interior • In most stars, the pulsations damp out

Pulsating stars • To have large amplitudes need driven oscillations • Pulsations in Cepheids and RR Lyrae stars are driven by opacity changes: – – – – Layer near surface is heated to ~40, 000 K which ionizes He+ to He++ Freed electrons scatter, opacity shoots up Base of opaque layer absorbs light, increasing temperature and pressure Increased pressure makes layer expand Expansion leads to cooling, He++ recombines to He+ Opacity drops, trapped photons leave layer Layer contracts Oscillations grow to large amplitude because period for opacity changes matches period of acoustic waves

Pulsation cycle Rate of fusion in the core stays constant. Transport of energy through outer layers of star oscillates.

Pulsating stars

Pulsating stars

Why is this useful? Flux versus luminosity relation We can figure out the luminosity of a pulsating star by timing the pulsations. Since, we can measure its flux, we can then find the distance to the star.

A Cepheid has the same pulsation period, but is 1/16 the brightness of another Cepheid known to be at a distance of 2 kpc. How far away is the dimmer star? 1. 2. 3. 4. 5. 2 kpc 4 kpc 8 kpc 16 kpc 32 kpc

Death of stars • • Final evolution of the Sun Determining the age of a star cluster Evolution of high mass stars Where were the elements in your body made?

Higher mass protostars contract faster Hotter

Higher mass stars spend less time on the main sequence

Determining the age of a star cluster • Imagine we have a cluster of stars that were all formed at the same time, but have a variety of different masses • Using what we know about stellar evolution is there a way to determine the age of the star cluster?

Turn-off point of cluster reveals age

The HR diagram for a cluster of stars shows stars with spectral types A through K on the main sequence and stars of type O and B on the (super) giant branch. What is the approximate age of the cluster? 1. 2. 3. 4. 1 Myr 100 Myr 1 Gyr

Higher mass stars do not have helium flash

Nuclear burning continues past Helium 1. Hydrogen burning: 10 Myr 2. Helium burning: 1 Myr 3. Carbon burning: 1000 years 4. Neon burning: ~10 years 5. Oxygen burning: ~1 year 6. Silicon burning: ~1 day Finally builds up an inert Iron core

Multiple Shell Burning • Advanced nuclear burning proceeds in a series of nested shells

Why does fusion stop at Iron?

Fusion versus Fission

Advanced reactions in stars make elements like Si, S, Ca, Fe

Supernova Explosion • Core degeneracy pressure goes away because electrons combine with protons, making neutrons and neutrinos • Neutrons collapse to the center, forming a neutron star

Core collapse • Iron core is degenerate • Core grows until it is too heavy to support itself • Core collapses, density increases, normal iron nuclei are converted into neutrons with the emission of neutrinos • Core collapse stops, neutron star is formed • Rest of the star collapses in on the core, but bounces off the new neutron star (also pushed outwards by the neutrinos)

If I drop a ball, will it bounce higher than it began? Do 8 B 10. 50 - Supernova Core Bounce

Supernova explosion

Crab nebula

Cas A

In 1987 a nearby supernova gave us a close-up look at the death of a massive star

Neutrinos from SN 1987 A

Where do the elements in your body come from? • Solar mass star produce elements up to Carbon and Oxygen – these are ejected into planetary nebula and then recycled into new stars and planets • Supernova produce all of the heavier elements – Elements up to Iron can be produced by fusion – Elements heavier than Iron are produced by the neutrons and neutrinos interacting with nuclei in the supernova explosion

Energy and neutrons released in supernova explosion enable elements heavier than iron to form, including Au and U

Types of Supernovae • Type I – no hydrogen absorption lines – Ia – no hydrogen lines, no helium lines, late in decay strongest lines are iron – Ib – strong helium lines, still no hydrogen • Type II – hydrogen absorption lines • Collapse of massive stars (previous slides) leads to type II and Ib, only difference is whether or not star sheds outer hydrogen layer before exploding

Type Ia supernova • Thought to be result of a white dwarf under going fusion of carbon and oxygen into iron. Star is evaporated and no remnant remains. • Occurs either when matter accretes onto a white dwarf or two white dwarfs collide.

Review Questions • What are the evolutionary stages of a one solar mass star? • How does the evolution of a high mass star differ from that of a low mass star? • How can the age of a cluster of stars, all formed at the same time, be determined? • Why does fusion stop at Iron? • How are heavy elements produced?