Lecture 16:Lecture 16:The life of a low-mass star

Astronomy 111

Main sequence membershipMain sequence membership

• For a star to be located on the Main Sequence in the H-R diagram: q g– must fuse Hydrogen into Helium in its core.– must be in a state of Hydrostaticmust be in a state of Hydrostatic

Equilibrium.

• Relax either of these and the star can no longer remain on the Main

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no longer remain on the Main Sequence.

The main sequence is a mass sequencemass sequence

• The location of a star along the M-S is determined by its Mass.y– Low-Mass Stars: Cooler & Fainter– High-Mass Stars: Hotter & BrighterHigh Mass Stars: Hotter & Brighter

• Follows from the Mass-Luminosity yRelation:

• Luminosity ~ Mass3.5

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• Luminosity ~ Mass3.5

Main sequenceMain sequence

106 High106

104

L sun

)

gMass

102

osity

(L

1

102Lum

ino

104

L

LowMass

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40,000 20,000 10,000 5,000 2,500Temperature (K)

Mass

Internal structureInternal structure

• Nuclear reaction rates are very sensitive to core temperature:p– P-P Chain: fusion rate ~ T4

– CNO Cycle: fusion rate ~ T18 !CNO Cycle: fusion rate T !• Leads to:

Differences in internal structure– Differences in internal structure.– Division into Upper & Lower M-S by mass.

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Proton-proton chainProton-proton chain

(twice)eHpp e2 ( )pp e

(twice) HepH 32 ppHeHeHe 433

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CNO cycleCNO cycle

12C + N1312C + p NN C e e

13

13 13

N C eC p N

e

13 14

N p OO N

14 15

15 15

O N eN p C He

e

15 15

15 12 4

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N p C e

Upper main sequenceUpper main sequence

• Upper Main-Sequence stars:– M > 1.2 MsunM 1.2 Msun

– TCore > 18 Million K• Generate Energy by the CNO Cycle• Generate Energy by the CNO Cycle• Structure:

C ti C– Convective Cores– Radiative Envelopes

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Upper Main Sequence Star

Radiative

Envelope

Convective

Core

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Lower main sequenceLower main sequence

• Lower Main-Sequence stars:– M < 1.2 MsunM 1.2 Msun

– TCore < 18 Million K• Generate Energy by the Proton-Proton• Generate Energy by the Proton-Proton

ChainStructure:• Structure:– Radiative Cores

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– Convective Envelopes

Lower Main Sequence Star

Convective

Envelope

Radiative

Core

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The lowest mass starsThe lowest mass stars

• For 0.25 < M* < 0.08 Msun:• Generate energy by the P-P ChainGenerate energy by the P P Chain• Fully Convective Interiors:

C ti C dConvective Core andConvective Envelope

• Reddest main sequence Stars

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Red Main Sequence Star

Convective

Envelope

Convective

Core

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Brown dwarfs

Failed Stars

Brown dwarfs

Failed Stars

(no fusion)

MBD<0.08 Msun

Many many more BDs than massive tstars.

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Structure along the Main SequenceSequence

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Main sequence lifetimeMain 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

Lif ti M L i it• Lifetime = Mass Luminosity• Recall:

Mass-Luminosity Relationship:• Luminosity ~ Mass3.5

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Main sequence lifetimeMain sequence lifetime

• Therefore:• Lifetime ~ 1 / M2.5• Lifetime ~ 1 / M

• The higher the mass, the shorter its life.• Examples:

Sun: ~ 10 Billion Years30 Msun O-star: ~ 2 Million years0.1 Msun M-star: ~ 3 Trillion years

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sun

Higher Mass = Shorter Life

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ConsequencesConsequences

• If you see an O or B dwarf star, it must be young as they only live for a few y g y yMillion years.

• You can’t tell how old an M dwarf isYou 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• The Sun is ~ 5 Billion years old, so it will last only for ~ 5 Billion years longer.

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Structure & mixingStructure & 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– Surface composition is constant over lifetime.

• Red Main Sequence Stars:– Fully mixed: core & envelope are convectiveFully mixed: core & envelope are convective.– Enhances surface helium composition?

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Main sequence phaseMain sequence phase

• Energy Source: H fusion in the core• What happens to the He created by HWhat happens to the He created by H

fusion?– Too cool to ignite He fusion– Too cool to ignite He fusion– Slowly build up an inert He core

Lifetime:• Lifetime:~10 Gyr for a 1 Msun star (e.g., Sun)

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~10 Tyr for a 0.1 Msun star (red dwarf)

Hydrogen exhaustionHydrogen exhaustion

• Inside: He core collapses & starts to heat up.H burning zone shoved into a shellH 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 coolsOutside: Envelope expands and cools

Star gets brighter and redder.• Becomes a Red Giant Star

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Red Giant Star

InertHe

Core

H Burning

Sh llCool, Extended

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Shell,

Envelope

Climbing the Red Giant BranchClimbing the Red Giant Branch

106106

104

sun)

Red Giant102

osity

(L

Red Giant

Branch

1

10 -2Lum

ino H-core

exhaustion10

10 -4

L

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40,000 20,000 10,000 5,000 2,500Temperature (K)

Climbing the Red Giant BranchClimbing 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:p– Tcore reaches 100 Million K– Ignite He burning in the core in a flash.

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The Sun as a red giant starWeak gravitational hold on outer layers

The Sun as a red giant star

hold on outer layers

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Helium flashHelium flash

• Triple- Process:Fusion of 3 4He nuclei into 1 12C (Carbon):

BeHeHe 844

( )

CBeHe 1284

Secondary reaction with 12C makes 16O (Oxygen):4 12 16He C O

Secondary reaction with 12C makes 16O (Oxygen):

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Leaving the giant branchLeaving the giant branch

• Inside:– Primary energy from He burning core.Primary energy from He burning core.– Additional energy from an H burning shell.

• Outside:• Outside:– Gets hotter and bluer.

Star shrinks in radius getting fainter– Star shrinks in radius, getting fainter.• Moves onto the Horizontal Branch

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Horizontal Branch Star

HeBurning

Core

H Burning

Sh ll EnvelopeASTR111 Lecture 16

Shell Envelope

Horizontal branchHorizontal branch

106 Helium106

104

Red Giant

HeliumFlash

sun)

102

Red GiantBranchHorizontal Branch

sity

(Ls

1

10 -2umin

os H-core exhaustion

10

10 -4

L

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40,000 20,000 10,000 5,000 2,500Temperature (K)

Horizontal branch phaseHorizontal branch phase

• Structure:– He-burning coreHe burning core– H-burning shell

• Triple- Process is inefficient can only• Triple- Process is inefficient, can only last for ~100 Myr.Build up a C O core but too cool to• Build up a C-O core, but too cool to ignite Carbon fusion

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Horizontal branch star

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Asymptotic giant branchAsymptotic giant branch

• After 100 Myr, core runs out of He– C-O core collapses and heats upC O core collapses and heats up– He burning shell– H burning shellH burning shell

• Star swells and coolsClimbs the Giant Branch again but at higher TClimbs the Giant Branch again, but at higher T

• Asymptotic Giant Branch Star

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Asymptotic Giant Branch Star

InertH Burning C-O

CoreH Burning

ShellHe Burning

Sh llCool, Extended

Shell

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ShellEnvelope

The asymptotic giant branchThe asymptotic giant branch

106Asymptotic

106

104

L sun

)

Red GiantGiant Branch

102

sity

(L BranchHorizontal Branch

1

10 -2umin

o

H-core exhaustion10

10 -4

Lu

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40,000 20,000 10,000 5,000 2,500Temperature (K)

Asymptotic giant branch starAsymptotic giant branch star

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The instabilities of old ageThe instabilities of old age

• He burning is very temperature sensitive:

• Triple- fusion rate ~ T40!• Consequences:• Consequences:

– Small changes in T lead toL h i f i t t– Large changes in fusion energy output

• Star experiences huge Thermal Pulses

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that destabilize the outer envelope.

Core-envelope separationCore-envelope separation

• Rapid Process: takes ~105 years• Outer envelope gets slowly ejected (fast

wind)wind)• C-O core continues to contract:

– with weight of envelope taken off heats up– with weight of envelope taken off, heats up less

– never reaches Carbon ignition temperature of 600 Million K600 Million K

• Core and envelope go their separate ways

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Planetary nebula phasePlanetary nebula phase

• Expanding envelope forms a ring nebula around the contracting C-O core.g– Ionized and heated by the hot central core.– Expands away to nothing in ~104 years.Expands away to nothing in 10 years.

Planetary Nebula• Hot C-O core is exposed, moves to the

left on the H-R Diagram

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Planetary Nebula Phasey

106)C-O Core Envelope Ejection

106106

104

(Lsu

n) 106

104

102

sity

(

102

1

10 -2min

os

Whit

1

10 -210

10 -4Lum White

Dwarf

10

10 -4

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40,000 20,000 10,000 5,000 2,500Temperature (K)

40,000 20,000 10,000Temperature (K)

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Degenerate Gas LawDegenerate Gas Law

• At high densities, a new gas law takes over:– Pack many electrons into a tiny volume– These electrons fill all low-energy statesThese electrons fill all low energy states– Only high-energy = high-pressure states

left• Result is a “Degenerate Gas”:

Pressure is independent of Temperature

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– Pressure is independent of Temperature.– Compression does not lead to heating.

Core collapse to white dwarfCore collapse to white dwarf

• Contracting C-O core becomes so dense that a new gas law takes over.Degenerate Electron Gas:• Degenerate Electron Gas:– Pressure becomes independent of

Temperaturep– P grows rapidly & soon counteracts Gravity

• Collapse halts when R ~ 0.01 Rsun (~ R )Rearth)

• White Dwarf Star

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Chandrasekhar MassChandrasekhar Mass

• Mass-Radius Relation for White Dwarfs:• Larger Mass = Smaller RadiusLarger Mass Smaller Radius

• Maximum Mass for White Dwarf:M 1 4 M• Mch = 1.4 Msun

– Calculated by Subrahmanyan Ch d kh i th 1930Chandrasekhar in the 1930s.

– Above this mass, electron degeneracy f il & th t ll

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pressure fails & the star collapses.

White DwarfsWhite Dwarfs

• Remnant cores of stars with M < 8 Msun.

• Held up by Electron DegeneracyHeld up by Electron Degeneracy Pressure.

• Properties:• Properties:– Mass < 1.4 Msun

Radius R (<0 02 R )– Radius ~ Rearth (<0.02 Rsun)– Density ~ 1056 g/cc

N l f i it ti l

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– No nuclear fusion or gravitational contraction

Evolution of White DwarfsEvolution of White Dwarfs

• White dwarfs only shine by leftover y yheat.– No sources of new energy (no fusion, gy ( ,

nothing)– Cools off and fades away slowly.

• Ultimate State– Old, cold white dwarfO d, co d te d a

• So cold that it is very hard to see– Takes ~ 10 Tyr to cool off

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– Galaxy is not old enough for these to exist

White dwarfWhite dwarf

Gra itational collapse• Gravitational collapse is balanced by electron degeneracyelectron degeneracy

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Sirius B: White DwarfSirius B: White Dwarf

Sirius B

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White dwarfWhite dwarf

Pauli Exclusion Principle says: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

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masses.

SummarySummary

• Main Sequence stars burn H into He in their cores.

• The Main Sequence is a MassSequence.– Lower M-S: p-p chain, radiative cores &

convective envelopes– Upper M-S: CNO cycle, convective cores &

radiative envelopes

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• Larger Mass = Shorter Lifetime

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SummarySummary

•Stage:•Main Sequence

•Energy Source:•H Burning Core•Main Sequence

•Red Giant •H Burning Core•H Burning Shell

•Horizontal Branch•Asymptotic Giant

•He Core + H Shell •He Shell + H Shelly p

•White Dwarf •None!

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The Stellar GraveyardThe 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– A new pressure law takes hold to halt

further collapse & they settle into equilibrium.q

– If too massive they collapse to zero radius and become a Black Hole.

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