19. main-sequence stars & later
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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
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