Stellar evolution

The structure of a star gravity 300,000 earth masses

How do stars work? Gravity wants to collapse star ⇒ Star heats up ⇒ Pressure increases ⇒ Pressure force stops the collapse

How do stars work? gravity Gravity wants to collapse star ⇒ Star heats up ⇒ Pressure increases ⇒ Pressure force stops the collapse “Hydrostatic equilibrium”: ⇒ Hottest and densest in center ⇒ Highest pressure in center pressure

How do stars work? Gravity wants to collapse star ⇒ Star heats up ⇒ Pressure increases ⇒ Pressure force stops the collapse “Hydrostatic equilibrium”: ⇒ Hottest and densest in center ⇒ Highest pressure in center higher pressure lower pressure net force “Buoyancy”

How do stars work? Gravity wants to collapse star ⇒ Star heats up ⇒ Pressure increases ⇒ Pressure force stops the collapse “Hydrostatic equilibrium”: ⇒ Hottest and densest in center ⇒ Highest pressure in center “Buoyancy”

How do stars work? Gravity wants to collapse star ⇒ Star heats up ⇒ Pressure increases ⇒ Pressure force stops the collapse “Hydrostatic equilibrium”: ⇒ Hottest and densest in center ⇒ Highest pressure in center Pressure stratification

The structure of a star Artist’s rendition gravity pressure 30 million degrees F 12,000 degrees F

But stars radiate! Anything with temperature > 0 radiates ⇒ Stars lose heat and cool Their pressure should decrease They should contract under gravity As they contract, they heat back up ⇒ With just gravity: stars “slowly” shrink lifetime for the sun (“Kelvin- Helmholtz”): solar age t ~ 15 million years gravity pressure

But stars radiate! Anything with temperature > 0 radiates ⇒ Stars lose heat and cool Their pressure should decrease They should contract under gravity As they contract, they heat back up ⇒ With just gravity: stars “slowly” shrink lifetime for the sun (“Kelvin-Helmholtz”): solar age t ~ 15 million years Actual solar age: t > 1 billion years (fossils)

Solution: Heating Sun, like rest of universe, is made mostly of hydrogen Four hydrogen nuclei can fuse into one helium nucleus ( + stuff ) Einstein (1905): E = mc 2

Solution: Heating Sun, like rest of universe, is made mostly of hydrogen Four hydrogen nuclei can fuse into one helium nucleus ( + stuff ) Einstein (1905): E = mc 2 4 x m H > m HE ΔE = 0.8% mc 2 4xH→He fusion releases energy! (Eddington 1926) Fusion reactions heat stars (Bethe, Chandrasekhar 1939)

Artist’s rendition Solution: Heating Stellar equilibrium: Gravity balanced by pressure Radiation balanced by fusion gravity pressure

Main sequence stars Most stars we see are burning hydrogen This makes them all similar: Stellar structure mostly determined by stellar mass Mass determines temperature and luminosity “Main sequence” They evolve slowly ( not along the main sequence) The stellar “main sequence”: Determined by mass low mass high mass

Main sequence stars What happens when fuel runs out? For sun: t fuel ~ 10 billion years More massive stars burn more quickly Once hydrogen is gone, collapse?

Main sequence stars We could burn 3 x Helium to 1 x Carbon... We could burn 1 x Carbon + 1 x Helium to 1 x Oxygen... Can we go on like this forever? net energy loss net energy gain It becomes harder to fuse (requires more pressure) Gain energy until we hit iron Above iron: it takes net energy to fuse Iron is the end of the line!

So: Without fuel... Stars lose heat and cool Their pressure should decrease They should contract under gravity As they contract, they heat back up Then cool some more... ⇒ With just gravity: stars collapse ⇒ Where does it stop? Does any other form of pressure appear? Does the star collapse to R<R S

Particles are social animals: Pauli exclusion principle “Bosons” like each other Photons Easy to cram them into tight spaces “Fermions” don’t like each other Electrons, neutrons Each particle requires some space Quantum “degeneracy” pressure, independent of temperature! Quantum degeneracy

White dwarfs: After sufficient compression: Electrons become “degenerate”, (too close together) Resist further compression No more contraction No more burning (stops at carbon or oxygen) Just cooling New equilibrium where gravity is balanced by degeneracy pressure a white dwarf Normal gas (50 km thick) Degenerate matter (helium, carbon, oxygen) 5000 km A carbon white dwarf: The largest diamond possible Size comparison with regular stars

Neutron stars More mass = more gravity More gravity = smaller star Denser electrons get crammed into protons no electrons = no degeneracy pressure collapse! All matter converted to neutrons Neutron degeneracy pressure Neutrons take less space + proton electron neutron - neutron star 10 km radius

A neutron star: A giant atomic nucleus

Neutron stars White dwarf more massive than 1.4 suns: Collapse Supernova explosion Formation of neutron star Neutron are little magnets Neutron stars are super- magnets! ~ 1 trillion times stronger than typical bar magnet

Neutron stars Exact structure of neutron stars unknown For 1.4 M sun : R ~ 10 km Compare: R s ~ 4.5 km

Neutron stars Exact structure of neutron stars unknown Complicate particle physics But we know: More massive = smaller Upper mass limit: ~ 3 solar masses Then: Black hole! How to make a black hole: Take a very massive star and let it run out of fuel How massive? About 40 solar masses. How long does this take? About 10 million years. black hole limit

The fate of a dying star gravity <12 white dwarf (a carbon or oxygen ball)

The fate of a dying star >12 neutron star (a neutron ball)

The fate of a dying star >40 black hole (an “event horizon”)

Stellar mass black holes Now we know that massive stars make black holes Black hole mass: A few solar masses But how do we find such black holes? Gravity on other star? Light bending? Radiation?

Most stars are “binaries” They have a stellar companion They orbit each other following Kepler’s laws Most massive stars should have a companion Massive stars evolve into black holes Some hold on to their companions when they make black holes ⇒ Some black holes have stellar companions

Accretion When a black hole comes close enough: It can syphon off matter from the companion star! This matter must ultimately fall into the black hole This process is called accretion This is how black holes grow This is how we find and study most black holes