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Home , Chandrasekhar limit, Giant star, Gravitational collapse, Iron star, Neutron star, Pulsar

10: Twinkle, Twinkle Little 17: Black Holes and Extreme • The is a star, powered by reactions (H → He) in the core • Stars form when a cloud of gas collapses under the force of (the mutual attraction of every part of the cloud to every other part) • Nuclear fusion begins when gravity compresses the core to high enough , & • When fuel runs out in the core, the core collapses under gravity, heats the envelope, which expands, forming a giant • High stars form red supergiants. High enough reached to fuse elements beyond hydrogen • Elements up to are formed by nuclear fusion in red supergiants Goals • Understand what happens when stars come to the ends of their • See how can save lower mass stars from ultimate collapse • Introduce stars and • Find out how stars collapse into black holes Reading

Begelman & Rees

• Chapter 2 • Stars (p24-41) • Neutron stars and formation (p41-49) Butterfly Nebulae • As stars come to the ends of their lives, gas pressure and pressure (Lecture 7) from the hot, collapsing core can cause the outer layers of the star to be ejected in a wind Dumbbell Nebula • Can form a Cat’s Eye Nebula • In a Sun-like star, the core stops collapsing and forms a , inside the nebula

Ring Nebula Supernovae SN 1987A

• For stars > 8�⨀ • After fusion reactions all the way to iron, star can no longer extract nuclear in fusion reactions — there is no longer a source to heat the gas and resist the pull of gravity • Star collapses extremely rapidly (final burning takes ~1 day, collapse in seconds) • Enormous release of • Blows outer layers of star away — leaves behind expanding remnant of gas • One star can outshine the whole when it explodes in NGC 4526 Supernovae are an important part of Energy release in a supernova the galactic ecosystem 1044 J per of material, travelling at 10,000 km s-1. It • As the star collapses, ~1046 J energy is released travels ~10 ly before it decelerates: • Is the core gets compressed, from the edge of combine with in the nucleus, forming in core • Heats interstellar gas ! � + � → � + �" • Make new stars (the kinetic energy • This beta process releases — collapsing gas is so dense, pushes the interstellar gas and can cannot escape, but weakly interacting neutrinos can — stimulate it to collapse) much on the energy is released in neutrinos • Disseminate heavy elements that are • Neutrinos transfer kinetic energy into the collapsing envelope of made in nuclear reactions in the star the star — drives out the infalling gas at 10,000 km s-1, which is — the material the Sun, and 44 10 J kinetic energy per solar mass of ejected material — this is the are made of must have once been through a previous • A heats the gas and makes it shine with peak power generation of stars and then scattered 1036 W for ~10 days. This is 1042 J in (outshines galaxy) in a supernova explosion BigI BigI What happens next???

• The fate of the star depends upon how much mass remains in the core that’s left behind after the supernova explosion (high mass stars) the nebula is blown off (low mass stars)

• Massive stars (~20�⊙) can lose up to 40% of their mass in winds during the ref supergiant phase • Several Solar can be blown off in the supernova • The gravitational force pulling the core together gets stronger, so the core will keep collapsing, unless another force can balance gravity WILtY Particle-wave duality Quantum Mechanics in 1 slide • can be described as either a wave or as particles (photons) (as well as the high wave, The (squared) amplitude • Particles can also be described as a low frequency component is the probability of describes the localization) finding the particle at waves — the wavefunction of the each position particle A particle no longer has a location, but a probability of finding it in a given place The wavelength/frequency (and, likewise, a probability of it being represents the momentum found with a particular momentum) Heisenberg’s Uncertainty Principle: We cannot simultaneously and Quantum mechanical effects become precisely know both a particle’s position and momentum (because if important on small scales (~atoms) the wavefunction above is localized to one position and is zero everywhere else, we cannot define its wavelength/momentum) While it seems strange, quantum ℏ mechanics is a well-tested physical ∆� ∆� ≥ 2 theory that have complete ! $%& ℏ = ⁄"#, where Planck’s constant ℎ = 6.63×10 J s faith in The Chandrasekhar mass limit White Dwarfs • As the electrons are confined to smaller spaces, their momenta increase • As the remnant of a star collapses, each (in the atoms) is confined to a smaller space — ∆� gets small, so ∆�, the uncertainty in the • Eventually they will become relativistic, � = momentum gets large (� = �� — Lecture 3) ���" becomes important, and they cannot • a single frequency wave is not localized, the more confined the electron, the move faster than the more frequency components (momentum states) we need in the wavefunction • The supporting force provided by the • The Pauli Exclusion Principle: no two (electrons, protons…) may degeneracy pressure of the electrons reaches occupy the same quantum state a limit • As the star collapses, to obey the exclusion principle, all each electron must • If the mass of the stellar remnant is greater occupy a different state, starting at the lowest energy state, up to the Fermi energy than the Chandrasekhar Mass Limit, electron degeneracy pressure cannot contend with • Some of the electrons must occupy high energy states. They have high gravity, a white dwarf would be unstable, and WILtY momentum and high kinetic energy. We must do work to give the electrons this energy, so as we try to compress the electrons, they push back (degeneracy the star continues to collapse pressure) • As the star collapses, the degeneracy pressure eventually equals the A low mass star will collapse into a gravitational pressure collapsing the star. This quantum mechanical force white dwarf, supported by quantum saves the star from further collapse, and forms a white dwarf mechanical forces from the electrons if • Stable stellar remnant, heated by the collapse, gradually cools over time � < 1.46�⊙ BigI Neutron Stars for stars that produced a core-collapse supernova

• As massive stars collapsed, electrons in atoms combined with protons, leaving behind a core of neutrons — a • Neutrons must also obey the Pauli exclusion principle, so when they are compressed, they exert pressure • Mass ~2�⊙ • Radius ~10 km, 3 times bigger than black hole • Neutrons are more massive than electrons, so exert a larger degeneracy pressure than electrons • Core density ~10 kg m The mass of a star, compressed into a volume the size • Can support a stellar remnant up to 2~3�⊙ of a city! • The exact mass limit is not known because we do not fully understand the structure of the core, which has similar density to A high mass star will explode as a an — the forefront of supernova, then collapse into a neutron • Likely the core is not composed of individual neutrons — star if the remaining mass in the core neutrons interact with one another via the strong nuclear force � < 2~3�⊙ BigI BigI Pulse observed when beam Pulsars Rotation passes Neutron stars can support strong magnetic fields • As the neutron star spins, magnetic spins with it • Moving magnetic fields create a voltage (electrical Jocelyn Bell-Burnell and Tony Hewish (1967, generator) Cambridge UK) discovered sources of radio • Electrons ripped from the waves emitting regular pulses, seconds apart surface and accelerated, producing radio waves (and Radiation from Jokingly named LGM-1 (‘’) gamma rays) magnetic poles Quickly associated with spinning neutron stars Radio waves are beamed along the axis of the magnetic (predicted by & Baade soon after the field – we see the pulse when the beam from the spinning in the 1930s) star crosses our line of sight, like a lighthouse WILtY Neutron stars are extreme laboratories!

• at extremely high (nuclear) • Strong (108~1015 x Earth’s field) • Superconducting — electrical currents flow forever • Superfluid — no viscosity • Strong gravity at surface • Gravitational of light emitted • ~0.5c • Relativity is important on a neutron star! BigI The Final Collapse

If the mass of the core that remains after the supernova explosion exceeds ~3�⊙, no force is able to counteract the of the star. The stellar remnant continues to collapse, until it becomes smaller than the for its mass, � 2�� � = �# � The remnant disappears inside its and forms a black hole The material inside the event horizon continues to collapse. Reaches extreme densities (more dense than an atomic nucleus) which will require to describe – the singularity BigI

≲ 2�⨀ left White Dwarf behind Low Mass Star Planetary Nebula Neutron Star

Giant Star ≳ 8�⨀ Red Supergiant Supernova Explosion Black Hole

≳ 2�⨀ left behind The Crab Nebula • One of the brightest sources of X-rays in the sky • The nebula shines with luminosity ~1031W • Extended nebula of hot gas, discovered in 1731 • In 1054, a bright star, visible in the daytime, was seen at the same location in the sky • Emits pulses of radio waves 30 times per second

• How did the Crab nebula form? • What is at the center? • What is the source of the energy? • What will happen to the time interval between the pulses as the Crab Nebula ages? The Crab Nebula • A — the nebula is formed from the of the supernova explosion at the end of the of a • Radio pulses come from a (neutron star) at the center that was formed when the core of the star collapsed during the supernova • The energy output from the pulsar is heating the nebula • The source of the energy is the rotation of the pulsar. Rotational (kinetic) energy is transferred into electromagnetic energy in the pulsar’s magnetic field, which accelerates electrons and produces the radio and gamma rays • As energy is released, the spin of the pulsar slows down. The period between the pulses increases as it ages Binary Stars

Unlike our Sun, many stars in our Galaxy are not found alone. They exist in binaries, triples or higher order systems

In a binary, 2 stars each other and lose energy over time, slowly spiraling towards each other

One star may come to the end of its life before the other. The supernova explosion an disrupt the binary, but it is also possible that the remaining star ends up in a binary with a black hole, neutron star, or white dwarf Cataclysmic Variables TMI

Formed when a star is in a binary orbit with a white dwarf companion

As they get closer, the star is deformed by the gravitational pull of the white dwarf (tidal forces – Lecture 6)

Gas from the star is pulled towards the white dwarf. When it hits the surface, it is compressed and heated, leading to a thermonuclear burst, producing a flash of X- rays

If enough gas from the star accretes onto the white dwarf to increase its mass above the , the white dwarf becomes unstable and explodes as a (a core collapse supernova is Type II) X-ray Binaries (e.g. Cyg X-1) TMI

Formed when a star is in a binary orbit with a black hole or neutron star companion

Low mass companion star: gas is drawn from the surface onto the black hole or neutron star

High mass companion star: the black hole accretes from material blown off the star in the clumpy

Gas from the star (or stellar wind) forms a hot, glowing disc (Lecture 7), an X- ray emitting corona and (sometimes) a jet (Lecture 8)

X-ray binaries are (Lecture 8) TMI X-ray Binaries are messy eaters! Quiescence Gas flows slowly to Gas does not flow smoothly from the star to black hole the black hole or neutron star

X-ray binaries spend a lot of time in quiescence with gas flowing slowly from the star to the black hole/neutron star, but go Outburst High/Soft State through bright outbursts, lasting 2-3 months, Gas quickly accretes through hot, as the gas builds up glowing accretion disc The outburst begins with the gas forming a hot disk that we see emitting black body radiation at X-ray wavelengths Outburst Low/Hard State The inner part of the disk then overheats and Inner disc overheats. Accretion slows may inflate, slowing down the flow of gas to down. Corona formed, producing high the black hole. It then produces a corona, energy X-rays emitting higher energy X-rays than the disk

The X-ray binary then fades away, returning to quiescence BigI • Giant stars explode as supernovae at the ends of their lives • Final fate of the star depends on how much mass remains in the core • Quantum mechanical forces can support the stellar remnant against gravitational collapse • Low mass stars form white dwarfs • Neutron stars formed after supernova explosion from high mass star if low mass left behind • Spinning, magnetized neutron stars form pulsars • If too much material remains, nothing can stop the gravitational collapse to a black hole