The Life of Stars

The Life of Stars

Terms Defined

• Degeneracy Pressure: Pressure from the Pauli exclusion principle prevents electrons/neutrons from occupying the same state, supporting white dwarfs and neutron stars.
• Flare Star: A star exhibiting sudden, intense brightness increases due to magnetic activity.
• Helium Flash: The abrupt initiation of helium fusion within the core of a low-mass red giant star.
• Horizontal Branch: A stage in a low-mass star's life where helium is burned in its core, visible on the HR diagram following the red giant phase.
• Neutron Star: An extremely dense remnant of a collapsed massive star core, composed mainly of neutrons.
• Nova: A white dwarf experiences a sudden brightening caused by a surface explosion of accumulated hydrogen from a companion.
• Planetary Nebula: A dying low-mass star ejects a glowing gas shell, leaving behind a white dwarf core.
• Red Giant: A large, cool, luminous star that forms after core hydrogen is depleted and fusion continues in a surrounding shell.
• Supernova: An intense explosion marking the end of a massive star's life.
• Supernova Remnant (SNR): The expanding cloud of gas left over after a supernova explosion.
• White Dwarf: A small, dense, hot remnant of a low-mass star, supported by electron degeneracy pressure.

Star Mass, Fusion, and Convection

• Higher mass stars fuse hydrogen at a faster rate, resulting in shorter lifespans.
• Low-mass stars have a radiative core and a convective envelope.
• High-mass stars are characterized by a convective core and radiative envelope.

After Hydrogen Fusion Ends (Low-Mass)

• The core contracts and heats up.
• Hydrogen fusion continues in a shell surrounding the core.
• Outer layers expand turning the star into a red giant.
• Helium fusion begins abruptly, known as the helium flash.
• The star becomes stable again, positioning itself on the horizontal branch.

Why Stars Expand Off the Main Sequence

• The core contracts, heats up, and initiates fusion in shells surrounding the core.
• Increased energy output causes the outer layers to expand.

Triple-Alpha Process

• The fusion of 3 helium nuclei (alpha particles) forms 1 carbon nucleus.
• The process occurs in hot cores of red giants at temperatures of ≥100 million K.

Helium-Core Fusion Stars vs Red Giants

• Helium-core fusion stars are smaller, hotter, and located on the horizontal branch of the HR diagram.
• Red giants are larger, cooler, and situated above the main sequence.

Fate of Low-Mass Stars (like the Sun)

• The star evolves into a red giant, ejects a planetary nebula, and leaves behind a white dwarf.

After Hydrogen Fusion Ends (High-Mass)

• The core fuses elements into progressively heavier elements, up to iron, in layers.
• There is no helium flash; each element fuses smoothly.
• The iron core collapses, leading to a supernova.

The CNO Cycle

• A process by which high-mass stars fuse hydrogen into helium.
• Uses carbon, nitrogen, and oxygen as catalysts.
• It is a faster process than the proton-proton chain in low-mass stars.

Heaviest Elements Formed in Stars

• Low-mass stars primarily form elements up to carbon and oxygen.
• High-mass stars can create elements up to iron (Fe).

Why Fusion Stops at Iron

• Fusing iron does not release energy; it consumes energy.

Evidence for Stellar Element Production

• The spectra of stars and nebulae match predicted element abundances.
• Supernova remnants contain heavier elements formed during the explosion.

High-Mass Star Supernova (Type II)

• The iron core collapses, rebounds, creates a shock wave, and expels the outer layers.
• A neutron star or black hole is left behind.

Death of High-Mass Stars

• Core collapse leads to a supernova, leaving behind a neutron star or black hole remnant.

Formation of Neutron Stars

• Core collapse crushes protons and electrons into neutrons.
• Neutron degeneracy pressure halts the collapse, resulting in the formation of a neutron star.

The Special Theory of Relativity

Term

• Reference Frame: A viewpoint from which measurements of position and time are made.

People

• Albert Einstein developed the Special Theory of Relativity.
• Michelson & Morley's experiment demonstrated the constant speed of light.

Key Concepts

• Speed of Information: The speed of light (c) is the ultimate speed limit.
• Time Dilation: Moving clocks tick slower relative to stationary observers.
• Simultaneity: Events that are simultaneous in one frame may not be in another.
• Length Contraction: Objects appear shorter in the direction of motion.
• Relativistic Mass: Mass increases as speed approaches the speed of light.

Einstein's Methods

• Utilized thought experiments, not physical ones, to develop his theories.

“Motion is Relative”

• There is no absolute fixed point in the universe; all motion is measured relative to something else.

Inertial vs Non-Inertial Frames

• Inertial frames have constant speed.
• Non-inertial frames are accelerating.

Two Core Principles

• The laws of physics are the same in all inertial frames.
• The speed of light is constant for all observers.

Time Dilation Formula

• Time runs slower for objects in motion.

Simultaneity

• Events that appear simultaneous in one frame may not be in another.

Length Contraction

• Moving objects contract along the direction of motion.

Rest Mass

• Mass increases with speed, reaching infinite mass at the speed of light.

Mass and Light Speed

• It takes infinite energy to reach the speed of light.

Experimental Support

• Evidenced by GPS clocks (time dilation), particle accelerators (mass changes), and muon decay.

Thought Experiments

• Examples include the "twin paradox" or "light clock" to illustrate how motion affects time and space.

General Relativity

Terms

• Dimension: A direction in space or time (e.g., x, y, z, time).
• Event Horizon: The boundary of a black hole; beyond it, nothing can escape.
• Gravitational Lensing: The bending of light due to massive objects.
• Hyperspace: A space with more than three spatial dimensions.
• LIGO: Laser Interferometer Gravitational-Wave Observatory.
• Schwarzschild Radius: The distance from the center of a black hole to its event horizon.
• Singularity: The point in a black hole where density becomes infinite.
• Spacetime: A 4D combination of space and time.
• Wormhole: A hypothetical tunnel through spacetime.

People

• Einstein, Wheeler popularized the term "black hole”.
• Schwarzschild solved Einstein's equations.

Key Concepts

• Gravity is the curvature of spacetime.
• Time Dilation: Clocks tick slower near massive objects.
• Black Holes are regions where gravity is so strong that not even light can escape.
• Gravitational Waves are ripples in spacetime caused by moving masses.

Equivalence Principle

• Gravity is locally indistinguishable from acceleration.

Three Types of Geometry

• Flat: Normal geometry.
• Spherical: Like a globe.
• Hyperbolic: Saddle-shaped.

Universe Geometry Implications

• Affects the fate of the universe, determining whether it will expand forever or collapse.

Gravity Source

• Caused by the warping of spacetime due to mass/energy.

Gravity & Time

• Stronger gravity results in slower time, proven using GPS satellites.

Confirmed Predictions

• Precession of Mercury's orbit.
• Gravitational lensing by galaxies.
• LIGO detection of gravitational waves.

Gravitational Redshift

• Light loses energy as it leaves a gravity field, causing it to become redder.

Building Blocks of the Universe

Terms

• Antimatter: Matter with the opposite charge to regular matter.
• Annihilation: The process where matter and antimatter combine to produce pure energy.
• Baryon: Heavy particles, such as protons and neutrons.
• Boson: Force-carrying particles (e.g., photons).
• Degeneracy: Quantum resistance to compression.
• Fermion: Matter particles (e.g., electrons).
• Hadron: Particles made of quarks.
• Lepton: Lightweight particles, such as electrons.
• Meson: Hadrons made of a quark and an anti-quark.
• Pair Production: The creation of a particle and its antiparticle from energy.
• Spin: A quantum property of particles, similar to angular momentum.
• Quantum State: A complete description of a particle.
• Quark: Basic building blocks of hadrons.
• Virtual Particle: A temporary particle due to quantum fluctuation.
• Vacuum Energy: Energy from empty space.

People

• Includes Democritus, Bohr, Einstein, Hawking, Heisenberg, Gell-Mann, Higgs, and Rutherford.

Particle Properties

• Spin: e.g., 1/2 or 1
• Charge: e.g., ±1, 0

Fermions vs. Bosons

• Fermions are matter particles; bosons are force-carrying particles.
• Fermions follow the Pauli exclusion principle; bosons do not.

Classify Particles

• Electron is a fermion.
• Photon is a boson.

Quark Flavors

• Up, Down, Strange, Charm, Top, and Bottom.

Standard Model

• A theory describing all known particles and forces (except gravity).

Quarks vs. Leptons

• Quarks feel the strong force, while leptons do not.
• Quarks cannot exist alone, whereas leptons can.

Lepton Examples

• Electron and neutrinos.

Antimatter

• Has the same mass but opposite charge as matter.

Four Fundamental Forces

• Gravity: Weak, the carrier is the Graviton, and it has infinite range.
• EM: Medium, the carrier is the Photon, and it has infinite range.
• Weak: Weak, the carriers are W/Z Bosons, and it has a short range.
• Strong: Strong, the carriers are Gluons, and it has a very short range.

Heisenberg Uncertainty

• It is impossible to know both the position and momentum of a particle precisely.

Wave-Particle Duality

• All particles behave as both waves and particles.

Electron Behavior

• Electrons act like standing waves in atoms, forming orbitals.

Pauli Exclusion

• No two fermions can occupy the same quantum state.

Wave Behavior

• Applies to small particles; not noticeable for big objects.

Pressure Types

• Thermal: Pressure from heat.
• Degeneracy: Pressure from quantum laws.

Degeneracy's Role in Astronomy

• Prevents the collapse of white dwarfs/neutron stars.

Quantum Tunneling

• Particles can pass through barriers, explaining fusion in stars.

Virtual Particles

• Pairs of particles appear and vanish due to energy fluctuations.

Hawking Radiation

• Black holes emit radiation due to quantum effects, causing them to slowly evaporate.

The Stellar Graveyard

Terms

• Accretion Disk: Gas spiraling into a star or black hole.
• Black Hole: A region of infinite density with gravity so strong that not even light can escape.
• Chandrasekhar Limit: The maximum mass (~1.4 solar masses) for a stable white dwarf.
• Degeneracy Pressure: Prevents the collapse of dense objects.
• Frame-Dragging: The effect of a rotating black hole pulling space with it.
• Gamma-ray Burst: A flash of gamma rays from stellar collapse or neutron star mergers.
• Neutron Star: The remnant core of a massive star.
• Nova: A bright outburst from a white dwarf accreting material.
• Pulsar: A spinning neutron star that emits beams of radiation.
• White Dwarf: The dense core of a dead low-mass star.

People

• Includes Baade, Bell, Chandrasekhar, Hewish, Laplace, Michell, and Zwicky.

White Dwarf Properties

• Approximately Earth-sized, ~1 solar mass, and has high density.

Size vs Mass

• More mass leads to a smaller size due to increased gravity.

Types

• White dwarfs can be He, C-O, or O-Ne-Mg composition.

Balance of Forces

• Equilibrium between gravity and degeneracy pressure.

Nova Process

• Hydrogen builds up on a white dwarf and ignites, causing a surface explosion.

Type Ia Supernova

• The entire white dwarf explodes.
• Caused by too much mass or a merger.

Type I vs Type II Supernovae

• Type I supernovae lack hydrogen and occur in binary systems.
• Type II supernovae contain hydrogen and result from massive stars.

Neutron Star Properties

• Have a radius of ~10 km, up to 3 solar masses, and are ultra-dense.

Discovery

• Found through radio pulses (pulsars).

Pulsars

• Neutron stars with beams of radiation that sweep past Earth.

Black Hole Size

• The radius of the black hole (event horizon) increases with mass.

Black Hole Properties

• Possess mass, spin, and charge.

Falling into a Black Hole

• From an outside view, objects appear to freeze at the horizon.

Evidence

• X-ray binaries, stars orbiting unseen mass, and gravitational waves.

Gamma-ray Bursts

• Indicate the birth of a black hole or neutron star.

Gravitational Waves

• Produced by collisions of neutron stars/black holes and detected by LIGO.