Lecture 16: The life of a low-mass star Astronomy 111
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 ~ Mass 3.5
Main sequence Lumino osity (L sun ) High 10 6 Mass 10 4 10 2 1 10 2 10 4 40,000 20,000 10,000 5,000 2,500 Temperature (K) Low Mass
Internal structure Nuclear reaction rates are very sensitive to core temperature: P-P Chain: fusion rate ~ T 4 CNO Cycle: fusion rate ~ T 18! Leads to: Differences in internal structure. Division into Upper & Lower M-S by mass.
Proton-proton chain 2 p H p p 2 3 H e He e (twice) (twice) 3 He 3 He 4 He p p
CNO cycle 12 C + p 13 N 13 13 N C e e 13 14 C p N 14 15 N p O 15 15 O N e 15 12 4 N p C He e
Upper main sequence Upper Main-Sequence stars: M > 1.2 M sun T Core > 18 Million K Generate Energy by the CNO Cycle Structure: Convective Cores Radiative Envelopes
Upper Main Sequence Star Radiative Envelope Convective Core
Lower main sequence Lower Main-Sequence stars: M < 1.2 M sun T Core < 18 Million K Generate Energy by the Proton-Proton Chain Structure: Radiative Cores Convective Envelopes
Lower Main Sequence Star Convective Envelope Radiative Core
The lowest mass stars For 0.25 < M * < 0.08 M sun : Generate energy by the P-P P Chain Fully Convective Interiors: Convective Core and Convective Envelope Reddest main sequence Stars
Red Main Sequence Star Convective Envelope Convective Core
Brown dwarfs Failed Stars (no fusion) MBD<0.08 Msun Many many more BDs than massive stars.
Structure along the Main Sequence
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 it Recall: Mass-Luminosity Relationship: Luminosity ~ Mass 3.5
Main sequence lifetime Therefore: Lifetime ~ 1 / M 2.5 The higher the mass, the shorter its life. Examples: Sun: ~ 10 Billion Years 30 M sun O-star: ~ 2 Million years 0.1 M sun M-star: ~ 3 Trillion years sun
Higher Mass = Shorter Life
Consequences If you see an O or B dwarf star, it must be young as they only live for a few Million years. You can t tell how old an M dwarf is because their lives can be so long. The Sun is ~ 5 Billion years old, so it will last only for ~ 5 Billion years longer.
Structure & mixing Upper & Lower M-S Stars: Core & Envelope are separate. No mixing of nuclear fusion products between the deep core and the envelope. Surface composition is constant over lifetime. Red Main Sequence Stars: Fully mixed: core & envelope are convective. Enhances surface helium composition?
Main sequence phase Energy Source: H fusion in the core What happens to the He created by H fusion? Too cool to ignite He fusion Slowly build up an inert He core Lifetime: ~10 Gyr for a 1 M sun star (e.g., Sun) ~10 Tyr for a 0.1 M sun star (red dwarf)
Hydrogen exhaustion Inside: He core collapses & starts to heat up. H burning zone shoved into a shell. Collapsing core heats the H shell above it, driving the fusion faster. More fusion, more heating, so Pressure > Gravity Outside: Envelope expands and cools Star gets brighter and redder. Becomes a Red Giant Star
Red Giant Star Inert He Core H Burning Shell Cool, Extended Envelope
Climbing the Red Giant Branch 10 6 sun) Lumino osity (L 10 4 10 2 1 10-2 H-core exhaustion Red Giant Branch 10-4 40,000 20,000 10,000 5,000 2,500 Temperature (K)
Climbing the Red Giant Branch Takes ~1 Gyr to climb the Red Giant Branch He core contracting & heating, but no fusion H burning to He in a shell around the core Huge, puffy envelope ~ size of orbit of Venus Top of the Red Giant Branch: T core reaches 100 Million K Ignite He burning in the core in a flash.
The Sun as a red giant star Weak gravitational hold on outer layers
Helium flash Triple- Process: Fusion of 3 4 He nuclei into 1 12 C (Carbon): 4 4 He He 4 8 He Be 8 12 Be C Secondary reaction with 12 C makes 16 O (Oxygen): 4 12 16 He C O
Leaving the giant branch Inside: Primary energy from He burning core. Additional energy from an H burning shell. Outside: Gets hotter and bluer. Star shrinks in radius, getting fainter. Moves onto the Horizontal Branch
Horizontal Branch Star He Burning Core H Burning Shell Envelope
Horizontal branch sun) uminos sity (L s L Helium 10 6 Flash 10 4 Red Giant 10 2 Horizontal Branch Branch 1 10-2 H-core exhaustion 10-4 40,000 20,000 10,000 5,000 2,500 Temperature (K)
Horizontal branch phase Structure: He-burning core H-burning shell Triple- Process is inefficient, can only last for ~100 Myr. Build up a C-O core, but too cool to ignite Carbon fusion
Horizontal branch star
Asymptotic giant branch After 100 Myr, core runs out of He C-O core collapses and heats up He burning shell H burning shell Star swells and cools Climbs the Giant Branch again, but at higher T Asymptotic Giant Branch Star
Asymptotic Giant Branch Star H Burning Inert C-O Core Shell He Burning Cool, Extended Shell Envelope
The asymptotic giant branch sity (L sun ) Lu umino Asymptotic 10 6 Giant Branch 10 4 10 2 1 10-2 Horizontal Branch H-core exhaustion Red Giant Branch 10-4 40,000 20,000 10,000 5,000 2,500 Temperature (K)
Asymptotic giant branch star
The instabilities of old age He burning is very temperature sensitive: Triple- fusion rate ~ T 40! Consequences: Small changes in T lead to Large changes in fusion energy output t Star experiences huge Thermal Pulses that destabilize the outer envelope.
Core-envelope separation Rapid Process: takes ~10 5 years Outer envelope gets slowly ejected (fast wind) C-O core continues to contract: with weight of envelope taken off, heats up less never reaches Carbon ignition temperature of 600 Million K Core and envelope go their separate ways
Planetary nebula phase Expanding envelope forms a ring nebula around the contracting C-O core. Ionized and heated by the hot central core. Expands away to nothing in ~10 4 years. Planetary Nebula Hot C-O core is exposed, moves to the left on the H-R Diagram
Planetary Nebula Phase C-O Core Envelope Ejection Lum minos sity (L sun ) 10 6 10 4 10 2 1 10-2 10-4 White Dwarf 40,000 20,000 10,000 5,000 2,500 Temperature (K)
Degenerate Gas Law At high densities, a new gas law takes over: Pack many electrons into a tiny volume These electrons fill all low-energy states Only high-energy = high-pressure states left Result is a Degenerate Gas : Pressure is independent of Temperature. Compression does not lead to heating.
Core collapse to white dwarf Contracting C-O core becomes so dense that a new gas law takes over. Degenerate Electron Gas: Pressure becomes independent of Temperature P grows rapidly & soon counteracts Gravity Collapse halts when R ~ 0.01 R sun (~ R earth ) White Dwarf Star
Chandrasekhar Mass Mass-Radius Relation for White Dwarfs: Larger Mass = Smaller Radius Maximum Mass for White Dwarf: M ch = 14M 1.4 sun Calculated by Subrahmanyan Chandrasekhar in the 1930s. Above this mass, electron degeneracy pressure fails &th the star collapses.
White Dwarfs Remnant cores of stars with M < 8 M sun. Held up by Electron Degeneracy Pressure. Properties: Mass < 1.4 M sun Radius ~ R earth (<0.0202 R sun ) Density ~ 10 5 6 g/cc No nuclear fusion or gravitational ti contraction
Evolution of White Dwarfs White dwarfs only shine by leftover heat. No sources of new energy (no fusion, nothing) Cools off and fades away slowly. Ultimate State Old, Od,cod cold white dwarf So cold that it is very hard to see Takes ~ 10 Tyr to cool off Galaxy is not old enough for these to exist
White dwarf Gravitational collapse is balanced by electron degeneracy
Sirius B: White Dwarf Sirius B
White dwarf Pauli Exclusion Principle says: No two electrons can be at the same place at the same time with the same energy. At high density, all the low energy states are occupied, leaving only high energy (high pressure) states. Results in Degenerate Electron Gas: Pressure is independent of temperature Compression does NOT lead to heating Works for stellar cores up to 1.4 solar masses.
Summary 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
Summary Stage: Main Sequence Red Giant Horizontal Branch Asymptotic Giant White Dwarf Energy Source: H Burning Core H Burning Shell He Core + H Shell He Shell + H Shell None!
The Stellar Graveyard Q: What happens to the cores of dead stars? A: They continue to collapse until either: A new pressure law takes hold to halt further collapse & they settle into equilibrium. If too massive they collapse to zero radius and become a Black Hole.