Mass Statistics Add mass for main sequence to our plot Masses vary little Model: Stars are the same: mass determines rest Heavy stars hot, luminous

Mass-Luminosity Relation Find approximately Borne out by models: Mass compresses star increasing rate of fusion If amount of Hydrogen available for fusion is near constant fraction, big stars run out sooner OB stars are young!

Main Sequence Stars Stellar modeling matched to data tells us about how stars work Main-Sequence stars fuse Hydrogen to Helium in core Hydrostatic Equilibrium determines rate of fusion and density profile from mass

CNO Chain In large stars core hot and CNO chain dominates fusion Rate rises rapidly with temperature

Size Matters Mechanisms of heat transfer depend on mass In small stars, entire volume convective so all available to fuse in core In large stars, radiation and convection zones inverted CNO Simulator

Expansion by Contraction As a main sequence star ages core enriched in Helium Rate of fusion decreases – temperature and radiation pressure decrease Number of particles decreases – thermodynamic pressure decreases Core contracts and heats Fusing region grows Luminosity increases Envelope expands Sun now 25% brighter than when it formed Core now 60% Helium Continues to brighten – heating Earth In 1-3Gy could be uninhabitable? Orbit stable out to 1Gy?

Questions For 90% of stars we have a good understanding of how they work This comes from careful observation and detailed modeling Where do the rest come from? What happens when core is all Helium??

Modelling Collapse Model a cloud of mass Within a few Ky form opaque radiating photosphere of dust and later H- Photosphere contracts from to at constant fueled by Kelvin-Helmholtz and deuterium fusion over 600Ky

Pre-Main Sequence Initial photosphere contracts at constant T decreasing L Rising ionization in center reduces opacity creating radiative zone increasing L When fusion begins L decreases initially as core expands In 40My settle down to MS equilibrium: KH time! Larger stars go faster 105 106 107

Too Small Below effective fusion does not occur is a brown dwarf type L, T, Y How Many? 1:1? 1:5? BD: 13-80 MJ 229 T

Too Big? Models suggest that collapse with fails as radiation pressure fragments cloud Recent record Eddington Limit 2010 discovery in Tarantula Nebula (LMC)- VV IR

On the Main Sequence Hydrogen fusion in core supports envelope by thermal and radiation pressure Luminosity, surface temperature determined by mass, composition, rotation, close binary partner, atmospheric and interstellar effects Main Sequence thickened by variations in these Over time core contracts and heats Fusion rate increases Envelope expands slowly with little change in temperature Evolutionary track turns away from Main Sequence

Running Out of Gas Inner 3% inert Helium core is isothermal Hydrogen fusion in shell exceeds previous core luminosity Envelope expands and cools Inert core grows

Sub-Giant Branch In isothermal core pressure gradient maintained by density gradient If core too large cannot support outer layers. Core collapses rapidly (KH scale) Gravitational energy expands envelope Temperature decreases Sub-Giant Branch Procyon A: M=1.42, R = 2 L = 7

Red Giant Core collapses Compression heats shell increasing luminosity Envelope expands and cools, H- opacity creates deep convection First dredge-up brings fusion products to atmosphere Mass loss up to 28% Ad-debran M=1.7 R = 44 L = 520

Then What? Core does not collapse due to electron degeneracy pressure Quantum effect of Pauli exclusion principle Squeezing electrons into small space requires occupying higher energy states Produces temperature-independent contribution to pressure This is smaller than thermal pressure in Hydrogen core today In compressed inert Helium core degeneracy pressure stops collapse

Helium Core Flash When core temperature reaches 108K Helium fusion via triple-α process occurs explosively in degenerate core For a few seconds produce galactic luminosity absorbed in atmosphere, possibly leading to mass loss Expands shell decreasing output Envelope contracts and heats

Horizontal Branch Deep convection rises Convective core fusing Helium to Carbon, Oxygen Shell fusing Hydrogen to Helium Core contracts Envelope contracting and heating

Early Asymptotic Giant Branch Inert CO core collapses to degeneracy Helium fusion in shell Hydrogen shell nearly inactive Envelope expands and cools Convective envelope deepens: second dredge-up Mass loss in outer layer Core: 8e-4 He shell 9 e-4 Inert He: 2.9e-3 H shell: 5.6e-3 R = 44

Thermal Pulse AGB Hydrogen shell reignites Helium shell flashes intermittently Flash expands Hydrogen shell, luminosity drops and envelope contracts heats Hydrogen reignition increases luminosity envelope expands cools Convection between shells and deep convective envelope: third dredge-up and Carbon stars Rapid mass loss to superwind s-process neutron capture nucleosynthesis produces heavier elements Flash expands H shell stopping fusion. Reignites on contraction, collects He to flash, repeat every 100Ky Carbon stars M> 2Modot. Mdot sim 10^{-4}Modot/yr! Mira M = 1.18, R = 330-400, L = 8400-9360 Variable later

The End Pulses eject envelope exposing inert degenerate CO core Initially hot core cools Expanding envelope ionized by UV radiation of white dwarf glows as ephemeral planetary nebula

M57

Ghost of Jupiter (NGC 3242)

Cat’s Eye

Hubble 5

NGC-2392 (Eskimo)

Clusters and the Model Model predicts how clusters will evolve Massive stars evolve faster Later stages of evolution rapid Can find cluster age from Main-Sequence turnoff Main Sequence Matching leads to distance: Spectroscopic Parallax and other cluster distance measures sclock

Does it Work? IC 1795 – OB Association NGC 2264 8My Cone nebula

Older Orion Nebula Cluster 12My M45 130My

And Older NGC6494 300My M44 800My

Oldest M67 3.5Gy M13 12Gy

Blue Stragglers Some MS stars found past turnoff point Mechanism: Mass Transfer in close binary Collision and Merger Likely both NGC-6397

Populations Astronomers distinguished Population II from Population I stars based on peculiar motion Differ in metallicity: Population II metal-poor formed early Globular Clusters are Population II Population III: Conjectured first stars – essentially metal free

Variable Stars Some Giants and Hypergiants exhibit regular periodic change in luminosity Mira (Fabricius 1595) changes by factor of 100 with period of 332d LPV like Mira not well modelled

Instability Strip A nearly vertical region traversed by most massive stars on HB RR Lyrae: PII HB stars with periods of hours. Luminosity varies little (!) Cepheids (PI) , W Virginis (PII) periods of days.

Why They Pulse Cepheids oscillate in size (radial oscillation) Temperature and luminosity peak during rapid expansion Eddington: Compression increases opacity in layer trapping energy and propelling layer up where it expands, releases energy Problem: compression reduces opacity due to heating Solution: compression ionizes Helium so less heating. Expansion reduces ionization – κ-mechanism Instability strip has partially ionized Helium at suitable depth Shapley thought so Schwarzschild found it

Why We Care Later: W Virginis PLR less luminous for same period Leavitt 1908: Period-Luminosity Relation for SMC cepheids Luminous cepheids have longer periods With calibration in globular clusters cepheids become standard candles Later: W Virginis PLR less luminous for same period

Discovery Surface Gravity Bessel 1844: Sirius wobbles: a binary Pup hard to find. Clark 1846 Orbits: Spectrum (Adams 1915): Surface Gravity Spectrum: Very broad Hydrogen absorption lines Estimate: No Hydrogen else fusion

Degenerate Matter White dwarves are the degenerate cores of stars with Composition is Carbon Oxygen Masses Significant mass loss Chandrasekhar: Relativity:

Mass-Radius