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

Termination of Core Hydrogen Fusion 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 Chemical Position on an H-R diagram 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 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 / t E = 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: The 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 while 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 Ordinary gas pressure Ideal gas law Force resisting gravity is directly proportional to temperature Temperature- independent Degenerate electron pressure Pauli exclusion principle Force resisting gravity is independent of temperature The 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 completely independent of temperature

Degenerate Electrons in Ordinary Metal

Star Clusters & Red Giant Evolution The transition to core-He fusion This marks the move into the Red Giant phase The details are determined entirely by mass Analysis of star clusters All the cluster’s stars formed at about the same time Many different masses are represented among those stars High- mass stars evolve very quickly Some leave the main sequence before low-mass stars can form Low- mass stars evolve very slowly The cluster’s H-R diagram depends on the cluster’s age The lower right band slowly approaches the main sequence The upper left band moves away from the main sequence The turn-off gives the cluster’s age

Mass Determines Every Star’s Evolution The 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 A “metal” in this context is 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 Can Affect Close Binaries Critical concepts Binary star systems > 50% of all stars are in binary systems Roche lobes Three-dimensional surfaces marking gravitational domains Inner Lagrangian point The gravitational balance point between binary stars Types of binary star systems Detached Neither star fills its Roche lobe Semi-detached One star fills its Roche lobe Contact Both stars fill their Roche lobes Over-contact Both stars over-fill their Roche lobes

Roche Lobes of Close Binary Stars

Three Kinds of Eclipsing Binary Stars …Semi-detached without mass transfer …with mass transfer Over-contact…

Important Concepts 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