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 lower 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
Fermi 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? • Degenerate pressure exists whether matter is present or not. • In a degenerate gas pressure varies rapidly with time. • In a degenerate gas, pressure does not depend on temperature. • 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 • 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
HR diagram Giant phase is when core has been fully converted to Helium
A star moves into the giant phase when: • It eats three magic beans • The core becomes helium and fusion in the core stops. • Fusion begins in the core • 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 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
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 • 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 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
When on the horizontal branch, a solar-mass star • 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…
In which order will a single star of one solar mass progress through the various stages of stellar evolution? • Planetary nebula, main-sequence star, white dwarf, black hole • Proto-star, main-sequence star, planetary nebula, white dwarf • Proto-star, red giant, supernova, planetary nebula • Proto-star, red giant, supernova, black hole
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 • temperature • density • luminosity • gravity Do mass on spring demo
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.
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? • 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?