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Exam #3 Study Guide • The Hertzsprung-Russell (H-R) Diagram – Plot of Luminosity vs. Temperature for stars. • Features: – Main Sequence (most stars) – Giant & Supergiant Branches – White Dwarfs • Luminosity Classification H-R Diagram Supergiants Luminosity (Lsun) 106 104 102 Giants 1 10 -2 10 -4 40,000 White Dwarfs 20,000 10,000 Temperature (K) 5,000 2,500 Main Sequence • Most nearby stars (85%), including the Sun, lie along a diagonal band called the • Main Sequence • Ranges of properties: – L=10-2 to 106 Lsun – T=3000 to >50,0000 K – R=0.1 to 10 Rsun Giants & Supergiants • Two bands of stars brighter than Main Sequence stars of the same Temperature. – Means they must be larger in radius. • Giants R=10 -100 Rsun L=103 - 105 Lsun T<5000 K • Supergiants R>103 Rsun L=105 - 106 Lsun T=3000 - 50,000 K White Dwarfs • Stars on the lower left of the H-R Diagram fainter than Main Sequence stars of the same Temperature. – Means they must be smaller in radius. – L-R-T Relation predicts: R ~ 0.01 Rsun (~ size of Earth!) • Main Sequence: – Strong correlation between Luminosity and Temperature. – Holds for 85% of nearby stars including the sun • All other stars differ in size: – Giants & Supergiants: Very large radius, but same masses as M-S stars – White Dwarfs: Very compact stars: ~Rearth but with ~Msun! Mass-Luminosity Relationship • For Main-Sequence stars: L M Lsun M sun 3.5 In words: “More massive M-S stars are more luminous.” Not true of Giants, Supergiants, or White Dwarfs. • Observational Clues to Stellar Structure: – H-R Diagram – Mass-Luminosity Relationship – The Main Sequence is a sequence of Mass • Equation of State for Stellar Interiors – Perfect Gas Law – Pressure = density temperature • Stars are held together by their self-gravity • Hydrostatic Equilibrium – Balance between Gravity & Pressure • Core-Envelope Structure of Stars – Hot, dense, compact core – cooler, low-density, extended envelope • Stars shine because they are hot. – need an energy source to stay hot. • Kelvin-Helmholtz Mechanism – Energy from slow Gravitational Contraction – Cannot work to power the present-day Sun • Nuclear Fusion Energy – Energy from Fusion of 4 1H into 1 4He – Dominant process in the present-day Sun • Energy generation in stars: – Nuclear Fusion in the core. – Controlled by a Hydrostatic “thermostat”. • Energy is transported to the surface by: – Radiation & Convection in normal stars – Conduction in white dwarf stars • With Hydrostatic Equilibrium, these determine the detailed structure of a star. • Main Sequence stars burn H into He in their cores. • The Main Sequence is a Mass Sequence. – Lower M-S: p-p chain, radiative cores & convective envelopes – Upper M-S: CNO cycle, convective cores & radiative envelopes • Larger Mass = Shorter Lifetime Putting Stars Together • Physics needed to describe how stars work: • • • • • Law of Gravity Equation of State (“gas law”) Principle of Hydrostatic Equilibrium Source of Energy (e.g., Nuclear Fusion) Movement of Energy through star Proton-Proton Chain: p p H e e (twice) 2 H p He (twice) 3 3 4 He He He p p 2 3 3-step Fusion Chain CNO Cycle: C + p N 12 13 13 13 14 N C e e C p N 14 N p O 15 15 15 13 O N e e 15 N p C He 12 4 Main Sequence Membership • For a star to be located on the Main Sequence in the H-R diagram: – must fuse Hydrogen into Helium in its core. – must be in a state of Hydrostatic Equilibrium. • Relax either of these and the star can no longer remain on the Main Sequence. The Main Sequence is a Mass Sequence. • The location of a star along the M-S is determined by its Mass. – Low-Mass Stars: Cooler & Fainter – High-Mass Stars: Hotter & Brighter • Follows from the Mass-Luminosity Relation: • Luminosity ~ Mass3.5 Main Sequence Lifetime • How long a star can burn H to He depends on: – Amount of H available = MASS – How Fast it burns H to He = LUMINOSITY • Lifetime = Mass Luminosity • Recall: Mass-Luminosity Relationship: • Luminosity ~ Mass3.5 Main Sequence Lifetime • Therefore: • Lifetime ~ 1 / M2.5 • The higher the mass, the shorter its life. • Examples: Sun: ~ 10 Billion Years 30 Msun O-star: ~ 2 Million years 0.1 Msun M-star: ~ 3 Trillion years Summary of Post-Main Sequence Evolution •Stage: •Energy Source: •Main Sequence •Red Giant •Horizontal Branch •Asymptotic Giant •White Dwarf •H Burning Core •H Burning Shell •He Core + H Shell •He Shell + H Shell •None! Post-Main Sequence Evolution of a High Mass Star • End of the Life of a Massive Star: – Burn H through Si in successive cores – Finally build a massive Iron core • Iron core collapse & core bounce • Supernova explosion: – Explosive envelope ejection – Main sources of heavy elements Stellar Remnants • White Dwarf: – Remnant of a star <8 Msun – Held up by Electron Degeneracy Pressure – Maximum Mass ~1.4 Msun • Neutron Star: – Remnant of a star < 18 Msun – Held up by Neutron Degeneracy Pressure – Pulsar = rapidly spinning neutron star The Milky Way: • The Milky Way is our Galaxy – Diffuse band of light crossing the sky – Galileo: Milky Way consists of many faint stars • The Nature of the Milky Way – Philosophical Speculations: Wright & Kant – Star Counts: Herschels & Kapteyn – Globular Cluster Distribution: Shapley The Milky Way and Other Galaxies: • Disk & Spheroid Structure of the Galaxy • Pop I Stars: – Young, metal-rich, disk stars – Ordered, nearly circular orbits in the disk • Pop II Stars: – Old, metal-poor, spheroid stars – Disordered, elliptical orbits in all directions • Gives clues to the formation of the Galaxy.