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Chapter 6: Evolution of Post -main sequence star Stellar Physics PHYS3040 . TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A. 6.1 Overview . Hertzsprun -Russell (HR) Diagram .
Chapter 6: Evolution of Post-main sequence starStellar Physics PHYS3040 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA
6.1 Overview • Hertzsprun-Russell (HR) Diagram • Beside the main sequence, there are several another populations (Giant, supergiant , white dwarfs). • Giant stars are stars in the late stage of the evolution. • White dwarfs are end stage of the low mass star. • After main sequence phase, how do star evolve?
Evolution of 5 star in H-R diagram • We can not observe the evolution of a star. • The numerical study is required to simulate the stellar evolution.
Main-sequence stars; hydrogen burning at the core • After hydrogen is being exhausted, there is no nuclear energy, and hence the core starts to contract. Relativistic degeneracy Non-relativistic degeneracy Radiation pressure Ideal gas
Consider the region of the nuclear processes in diagram. • Energy release rate of the any nuclear processes is described by -a,b and λ are factors depend on the nuclear process. • We write • Index We know the temperature dependency of the energy release rate around the temperature T.
p-p chain ( is ignited at K If q=constant, • CNO cycle ( is ignited at
p-p chain Hydrogen burning CNO cycle
3α process; three helium nuclei are used to produce a carbon ( FeHe Si burning O burning C burning 3α process p-p chain Hydrogen burning CNO cycle • thermal motion of the electrons emit γ-rays, Unstable
13.81 billion years • Slightly older than previously estimated. -13.77 billion by WMAP telescope. -What is the oldest star?
Oldest star • The oldest known star is HD 140283 in Milky way (Howard et al. ApJL 2013) • 13.66 Gyr – 15.26Gyr • 190.1 light-years away Hubble image of HD 140283
Core temperature vs. Core density Relativistic electron degeneracy FeHe Si burning Non-relativistic electron degeneracy O burning C burning 3α process Ideal gas p-p chain Sun CNO cycle Radiation pressure
For low mass star, the central temperature and density are closer to the degeneracy limit • For high mass star, all nuclear processes at the core are occurred under non-degenerate state. Produce difference in evolution of the star
6.2 Evolution of high-mass star • Consider the evolution of star with a mass larger than . • We discuss the evolution of the star in H-R diagram.
6.2.1 Main Sequence stage • As the hydrogen burning proceeds, the fraction of the hydrogen at the core decreases, and the fraction of the helium increases. • Mean molecular weight • for ionized hydrogen and for fully ionized helium • X=0.7 (Solar composition); • X=0.3 ; • As hydrogen burning proceeds, the mean molecular weight increases.
Equation of the ideal gas; • The increase in the mean molecular weight leads the decrease in the pressure. • To keep a constant pressure, the temperature must be increased, which is archived by a slightly contraction of the core. • CNO cycle; increase in the luminosity. • Increase in the luminosity causes • increase of the stellar radius. • decrease in the effective temperature.
Life time of the main-sequence star. • Homology • For star, * For star, yr
6.2.2 Shell hydrogen burning • After hydrogen at the core is nearly exhausted. • There is no nuclear energy • Temperature is constant at the core (isothermal core). • Now the pressure at the core cannot sustain the gravity. • Overall contraction of the star increase luminosity and temperature. Hydrogen burning around the core (shell burning)
6.2.3 Core contraction and evolution to Red Giant. • As hydrogen burning around the core proceeds, the mass of the isothermal core increases. • There is a critical mass, above which the core is unstable and starts to contract. • At the core surface, • pressure exerted by the core • the pressure by the envelope. H H burning He
Pressure exerted by the envelope • Hydrostatic equilibrium, • Integrating from stellar surface (P=0) to the core surface • Temperature and density at the surface of the core • The pressure at the core surface
The pressure exerted by the isothermal core • Hydrostatic equilibrium • Multiplying the volume, and Integrating it • Left hand side • Right hand side ; Mass of core ; Radius of core
Virial theorem • The pressure at the core surface • Maximum pressure
If the core mass exceeds the critical mass, the core is rapidly contracted. • If the degeneracy pressure is taken account into the analysis, there is another radius, at which core can be stable, the rapidly contraction of the core does not happen (low mass star) • For high-mass star, the temperature and density at the core do not close to state of the degeneracy. Sun
Evolution from main sequence stars to Red Giants • For 5 solar mass star, the hydrogen burning in the core continues yr. • After exhausting the hydrogen at the core, the star contracts. • The temperature inside star becomes high enough to star the hydrogen burning around the core. • Shell hydrogen burning increases the mass of the helium core. • The pressure of the helium core rapidly decreases if the mass exceeds • The contraction of the cores. Red Giant Main sequence star
Collapses proceeds on a Kelvin-Helmholtz timescale (, which is • Slow compared to the dynamical timescale (free fall time scale) • Rapid compared to the nuclear burning time scale. Kinetic energy (K) + Gravitational potential energy (U) =constant • Virial theorem 2 K+ U =0
“Mirror principle” • Core shrinks Star expands • Core expands Star shrinks H H burning He core
As contraction proceeds, the envelope expands and the star evolves to the red giant star (or giant star). Evolve to Red giant (yr)
We can estimate the radium of the red giant from the observations. • , For main sequence star, the radius is .
CO (J=3-2) emissions (~1mm). • Spiral structure. • The radius is much bigger than the size of the red giant
Matter injected from Red Giant (Stellar wind) • The velocity can be measure by the Doppler shift. Red Giant • The mass injection started ~1800 years ago
6.2.4 Red Giant Phase and Core Helium Ignition • As the contraction proceeds, the temperature increases accelerate the hydrogen burning • Core; temperature increases • Envelope; temperature decreases • Convection region develop; released energy is transferred by the macroscopic motion of the matter. • Track in H-R diagram is along the Hayashi track
If convection is main process to transfer the energy from core to the surface, the track in H-R diagram is almost vertical. • The luminosity increases due to the energy transfer of the convection. • The surface temperatures tends to decrease due to the expansion of the star . Dredge-up
Horizontal and Asymptotic Giant Branches • When the temperature at the core reaches the helium burning ignites. • Initially, the energy used to expand the core, which accompanies the envelope contraction. Slightly decrease in the luminosity
After reach, hydrostatic equilibrium and thermal equilibrium, the luminosity increases. • Life time Hydrogen burning
The helium at the core is being exhausted (Formation of carbon core). • The luminosity decreases. The stars with the helium burning core are called horizontal branch stars.
If the helium burning at the core is stop, there is an overall contraction of the star. Increase in the temperature inside the star Helium shell burning
As helium shell burning proceeds, the mass of carbon core increases. • If the mass exceeds a critical mass, the core is unstable. • Core contraction • Envelope expansion Asymptotic Giant branch
The low mass stars have central temperatures and densities close to the degeneracy limit. • As the star evolves, the core quickly becomes degenerate state (prevent the contraction of the core)
6.3.1 Hydrogen burning phase • p-p chain process ( • After ～Gyr, the hydrogen burning stops. • Overall contraction of the star. • Ignition of the shell hydrogen burning around the helium core.
Evolution to red giant star • As the shell burning proceeds, the mass of helium core increases. • For a high-mass star, the core becomes unstable, if it’s mass exceeds the critical mass • Core pressure can not sustain the force exerted by envelope. • Rapid contraction of core and expansion of envelope (yr)
For the low mass star, the degenerate pressure changes the situation. • Hydrostatic equilibrium • Left hand side,
Integrating from center to the surface of the core Non-relativistic degenerate Ideal gas