19. Main-Sequence Stars & Later• End of core hydrogen fusion creates a red giant• Core helium fusion in red giants• Star clusters & red giant evolution• Star evolution produces two star populations• Many mature stars pulsate• Mass transfer can affect close binary stars

Core Hydrogen Fusion Termination• Critical concepts

– Zero-age main-sequence stars ZAMS• On-going hydrogen fusion begins within the core• Hydrostatic & thermal equilibrium are established

– Main-sequence lifetime• The total time hydrogen fusion continues within the core

• Chemical changes in a star’s core– Initial mass ~ 74% H ~ 25% He ~ 1%

“metals”• Atoms ~ 91 H ~ 8 He ~ 1 “metals”

– Final mass ~ 0% H ~ 99% He ~ 1% “metals”• Atoms ~ 0 H ~ 25 He ~ 1 “metals”

• Physical changes in a star’s core– Progressively fewer atoms as He replaces H– Core diameter decreases & temperature increases– Rate of hydrogen fusion gradually increases

Changes In the Sun• Physical changes

– The Sun is ~ 40% more luminous than at ZAMS

– The Sun is ~ 6% larger in diameter than at ZAMS

– The Sun is ~ 300 K hotter than at ZAMS

• Chemical changes– The Sun’s core is already > 50% He

• Position on an H-R diagram– Increased temperature moves it slightly to the left– Increased luminosity moves it slightly upward

H & He In the Sun’s Interior

The Maturing Sun

Main-Sequence Lifetimes• Basic physical relationships

– Einstein’s famous equation…E = f . M . c2

…where f is the fraction of mass lost in fusion– Definition of luminosity…

L = E / tE = L . t

– Combining the two…L . t = f . M . c2

t µ M / L– Considering the mass-luminosity relationship…

L µ M+3.5

t µ M–2.5

Lifetimes of Main-Sequence Stars

Red Giant: Sun In 5 Billion Years

Changes As Core H Is Exhausted• Basic physical processes

– Core temperature drops as H fusion ends• Core pressure decreases

– Gravity again dominates• Core diameter decreases

– H just outside the old core compresses & heats• H-shell fusion begins• No core-He fusion as yet

– He core eventually reaches ~ 100,000,000 K• He fusion into C & O begins & H-shell fusion continues

• Differences due to mass– High- mass stars

• He fusion begins gradually– Low- mass stars

• He fusion begins in a flash

Three Evolutionary Stages for Stars

The Pauli Exclusion Principle• Two different kinds of pressure

– Temperature- dependent pressure• Ordinary gas pressure Ideal gas law• Force resisting gravity isproportional to temperature

– Temperature- independent pressure• Degenerate electron pressure Pauli exclusion

principle• Force resisting gravity isindependent of temperature

• Pauli exclusion principle– One expression of quantum mechanics– Only effective when core gases become ionized

• Some electrons roam freely• Such electrons may not get extremely close to each other

– Quantum exclusion keeps these electrons apart• This exclusion is independent of temperature

Degenerate Electrons in Ordinary Metal

Star Clusters & Red Giant Evolution• The transition to core He fusion

– Marks the move into the Red Giant phase– Details are determined entirely by mass

• Analysis of star clusters– All a cluster’s stars formed at about the same

time– All a cluster’s stars have different masses

• High- mass stars evolve very quickly– Some leave the main sequence before low-mass stars can form

• Low- mass stars evolve very slowly– A cluster’s H-R diagram depends on cluster age

• Lower right band slowly approaches the main sequence• Upper left band moves away from the main sequence

– The turn-off gives the cluster’s age

Mass Determines Every Star’s EvolutionThe main

sequence is a band

Main Sequence Turn-Off Points

Two Distinct Star Populations• Remnants of the Big Bang

– Very few atoms heavier than H & He formed• Noticeable deficiency of “metals”

– The oldest stars contain little metal• These are Population II stars

• Remnants of supernovae explosions– Relative abundance of “metals”

• Some even as heavy as Uranium

– The newest stars contain abundant metal• These are Population I stars

Metal-Poor & Metal-Rich Stars

Metal-poor Population II stars

Metal-rich Population I stars

“Metal” means any element heavier than helium

Many Mature Stars Pulsate• Critical differences

– Main sequence stars• Characterized by hydrostatic & thermal equilibrium

– No significant change in diameter– Pulsating stars

• Distinct lack of hydrostatic & thermal equilibrium– Cyclical change in diameter

• Some examples of pulsating stars– Long-period variables

• Cool red giants that vary in luminosity by a factor of ~ 100– Cepheid variables

• Vary over periods of ~ 1 to ~ 100 days– RR Lyrae variables

• Vary over periods of < 1 day

Cepheid Variables As Standard Candles• Two types of Cepheid variables

– Type I Metal-rich Population I stars• More luminous than Type II Cepheids

– Type II Metal-poor Population II stars• Less luminous than Type I Cepheids

• Standard candles– Basic properties

• Very bright objects of known luminosity• Relatively abundant throughout galaxies

– Cepheids• Luminosity is sufficient to be visible at millions of

parsecs• Luminosity is directly proportional to period

Variable Stars On An H-R Diagram

d Cephei: A Pulsating Star

Mass Transfer Affects Close Binaries• Critical concepts

– Binary star systems• > 50% of all stars are in binary systems

– Roche lobes• Three-dimensional surfaces mark gravitational domains

– Inner Lagrangian point• The gravitational balance point between binary stars

• Types of binary star systems– Detached Neither star fills Roche

lobe– Semi-detached One star fills Roche

lobe– Contact Both stars fill Roche

lobes– Over-contact Both stars over-fill Roche

lobes

Roche Lobes of Close Binary Stars

…Semi-detachedwithoutmass transfer

…withmasstransfer

Over-contact…

3 Kinds of Eclipsing Binary Stars

• Termination of core hydrogen fusion– Zero-age main-sequence stars– Main-sequence lifetime of stars

• Proportional to M2.5

– Progressive increase in luminosity• Number of atoms in core decreases• 4 H atoms become 1 He atom• Core contracts & heats

• Three evolutionary stages of stars– Start of core-H fusion into He

• Birth of a ZAMS star– End of core-H fusion into He

• Start of shell-H fusion– Start of core-He fusion into C & O

• ~ 30% as long as core-H fusion• Two kinds of pressure

– Ordinary gas pressure– Degenerate e– pressure

• Does not depend on temperature

• Star cluster analysis– Same birthday but different masses– H-R turn-off gives cluster age

• Two distinct star populations– Metal-poor Population II stars

• Formed soon after the Big Bang– Metal-rich Population I stars

• Formed long after the Big Bang• Variable stars

– Long-period variables– Cepheid variables

• Used as standard candles– RR Lyrae variables

• Binary star systems– Detached– Semi-detached– Contact– Over-contact Mass

transfer

Important Concepts