Download Document

Chapter 6:
Evolution of Post-main sequence star
Stellar Physics PHYS3040
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 5𝑀⨀ 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
Ideal gas
Radiation
pressure
• Consider the region of the nuclear processes in
log 𝜌𝑐 − log 𝑇𝑐 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 (λ = 1, 𝑏 ≈ 1.13 × 103 ) is ignited at
𝑇𝑐 ~1.5 × 107 K
𝜈~4.
If q=constant,
 CNO cycle (λ = 1, 𝑏 ≈ 1.08 × 103 ) is ignited at
𝑇𝑐 ~3 × 107 K
𝜈~16.
10
9
8
7
6
5
4
3
p-p chain
2
Hydrogen
burning
1
CNO cycle
0
6
7
8
9
10
• 3α process; three helium nuclei are used to
produce a carbon (𝑇𝑐 ~108 𝐾)
10
9
8
7
6
5
4
3
p-p chain
2
1
0
6
Hydrogen
burning
CNO cycle
7
8
9
10
• 𝑇𝑐 > 3 × 109 𝐾, thermal motion of the electrons emit γ-rays,
Unstable
CMB (～2.7K) background
PLANCK telescope
(Europian Space Agency)
• 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
10
9
Relativistic electron
degeneracy
8
7
Non-relativistic electron
degeneracy
6
5
4
3
p-p chain
Sun
Ideal gas
2
CNO cycle
1
Radiation pressure
0
6
7
8
9
10
• 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 𝑀 > 3𝑀⨀ .
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
• 𝜇𝐻 = 1/2 for ionized hydrogen and 𝜇𝐻𝑒 = 4/3 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; 𝑃 =
𝑘𝐵
ρ𝑇
𝜇𝑚𝐻
• 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.
16
• CNO cycle; 𝑞 = 𝑞0 𝜌𝑇 → 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 5𝑀⨀ star,
* For 1𝑀⨀ star, ∼ 1.5 × 109 yr
6.2.2 Shell hydrogen burning
• After ∼ 6 × 107 𝑦𝑟, 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.
• 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
𝑀𝑖𝑐 ; Mass of core
𝑅𝑖𝑐 ; Radius of core
Virial theorem
The pressure at the core surface
Maximum pressure
• The isothermal core has no stable radius,
if 𝑃𝑖𝑐,𝑚𝑎𝑥 < 𝑃𝑒𝑛𝑣
• 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.
10
8
6
4
2
Sun
0
6
7
8
9
10
Evolution from main sequence stars to Red Giants
• For 5 solar mass star, the hydrogen
burning in the core continues ~6 ×
107 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.
Main sequence star
Red Giant
• The pressure of the helium core
rapidly decreases if the mass
exceeds
• The contraction of the cores.
• Collapses proceeds on a Kelvin-Helmholtz timescale
(~106 𝑦𝑟), 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
• Core shrinks  Star expands
• Core expands  Star shrinks
“Mirror principle”
• As contraction proceeds, the envelope expands and the
star evolves to the red giant star (or giant star).
Evolve to Red giant
(~107 yr)
• We can estimate the radium of the red giant
from the observations.
𝐿 ∼ 100𝐿⨀ , 𝑇𝑒𝑓𝑓 ∼ 3000𝐾
2 4
𝐿 = 4𝜋𝜎𝑅 𝑇

For 5𝑀⨀ main sequence star,
the radius is ∼ 4𝑅⨀ .
ALMA (Atacama Large
Millimeter/submm Array)
• CO (J=3-2) emissions
(~1mm).
• Spiral structure.
• The radius is much
bigger than the size of
the red giant
• The velocity can be measure by
the Doppler shift.
Matter injected from
Red Giant (Stellar wind)
• The mass injection started ~1800
years ago
Red Giant
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
(~106 𝑦𝑟)
Horizontal and
Asymptotic Giant Branches
• When the temperature at the
core reaches 𝑇𝑐 ~108 𝐾, 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
6.2 Evolution of low-mass star
White dwarf
 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 (𝑞 ∝ 𝑇 4 )
• 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 (~106 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
Ideal gas
Non-relativistic degenerate
0.1Msun
6.2 Evolution of low-mass star
1, After ～Gyr, the hydrogen burning at
the core stops.
 Overall contraction of the star and
increase in the temperature.
2, The hydrogen shell burning stage and
increase in the mass of the helium core.
• The helium core starts to shrink, if its
mass exceeds ~0.1 solar mass.
Expansion of the envelop (evolution to
the red giant)
 The degeneracy pressure prevents a
rapid contraction of the core (~1Gyr).
(High mass star, ~106 yr.)
3, Convection stage
 The luminosity increases rapidly.
 As increase in the density of the core,
the degenerate helium core is formed.
2, The hydrogen shell burning
stage and increase in the mass of
the helium core.
• The helium core starts to
shrink, if its mass exceeds ~0.1
solar mass.
Expansion of the envelop
(evolution to the red giant)
 The degeneracy pressure
prevents a rapid contraction of
the core (~1Gyr).
(High mass star, ~106 yr.)
3, Convection stage
 The luminosity increases
rapidly.
 As increase in the density of
the core, the degenerate helium
core is formed.
Helium core temperature reaches
~108 K, and helium burning is started.
 For low mass star, the helium core
burning is explosively. A large
amount energy is released within
short time scale.
(For high mass star, the helium core
burning is silent. )
6.3.2 Helium flash
• Eventually, the temperature of the “degenerate”
helium core reaches 𝑇𝑐 ~108 K, and the helium burning
ignites.
• The initial stage of the helium burning is explosively
(Helium flash).
• Equation of the degenerate electrons,
• Although the temperature increases, the pressure and
density do not change
The core does not expand to cool.
• The increase in the temperature leads a further
increase in the rate of the release energy.
Equation of temperature
Heat capacity (how much released energy can
be used to increase the temperature)
Energy release rate
• Increase in the temperature
 a rapid increase in the energy release
rate
 a rapid increase In the temperature
Density
Initial temperature
After several days, the temperature and the
energy release rate rapidly increases (flash).
10
Relativistic
degeneracy
9
8
7
Helium flash
6 Non-relativistic
degeneracy
5
4
Ideal
gas
3
2
Radiation
pressure
1
0
6
7
8
9
10
• Increase in
temperature under
the constant density
removes the
degeneracy.
• The helium flush will
stop, when equation
of state is described
by the ideal gas
condition.
6.3.3 Evolution to White dwarf
• After helium flash stops, the
core will expand to stabilize.
the envelope is contracted
(mirror principle)
Increases in effective
temperature.
• After helium burning is
stabilized, the luminosity
increases.
• During this phase, the
carbon core develops
 Decrease of the pressure
of the core (molecular weight
increases).
Expanding of the envelope
Evolution to Asymptotic
Giant Branch.
• The star with a mass
lower than ~3𝑀⨀ will
not proceed further
nuclear processes.
• During the evolution of
the AGB stars, the mass
loss from the star reduces
the mass and radius of the
star.
• They move leftward with
a constant luminosity.
• If the mass becomes
lower than Chandrasekhar
mass limit  White dwarf.
6.3.4 Mass loss from the AGB stars
6.3.4 Mass loss from the AGB stars
• As the envelop expands, the gravity at
exerting to particles at the surface decreases.
Surface temperature ∼ 5 × 103 K.
Thermal energy of the surface particles
The thermal energy exceeds gravitational
energy when the radius becomes
• Mass loss rate
the momentum of the stellar wind
=momentum of the radiation
Planetary nebulae
• The induced matter from the AGB stars shine
because of irradiation of the AGB stars.
6.4 Ends of the stellar evolution
• 𝑀 < 0.1𝑀⨀
No hydrogen burning. During the contraction
of the protostar, the electrons becomes
degenerate state.
The degenerate pressure prevents further
contraction and temperature can not reach
𝑇𝑐 ∼ 106−7 K.
This kind of failed stars are called brown
dwarfs.
Core temperature vs. Core density
10
9
Relativistic electron
degeneracy
8
7
Non-relativistic electron
degeneracy
6
5
4
3
p-p chain
Ideal gas
2
CNO cycle
1
Radiation pressure
0
6
7
8
9
10
6.4 Ends of the stellar evolution
• 𝑀 < 0.1𝑀⨀
No hydrogen burning. During the contraction
of the protostar, the electrons becomes
degenerate state.
The degenerate pressure prevents further
contraction and temperature can not reach
𝑇𝑐 ∼ 106−7 K.
This kind of failed stars are called brown
dwarfs.
• 0.1𝑀⨀ < 𝑀 < 0.5𝑀⨀
 Hydrogen burning occurs at
the core
 Helium core becomes
degenerate state
 Helium is never ignited.
 Helium whit dwarfs.
• 0.5𝑀⨀ < 𝑀 < 1 − 2𝑀⨀
Helium burning is ignited (helium
flash).
White dwarf with the carbon core.
No mass loss
• 1 − 2𝑀⨀ < 𝑀 < 8𝑀⨀
 After helium flash, the helium
burning is stabilized.
 In the late stage of evolution,
the stellar wind is formed and
the mass is decreased below
Chandrasekhar mass.
 White dwarf with carbon
degenerate core.
• 𝑀 > 8𝑀⨀
10
9
Relativistic electron
degeneracy
8
7
Non-relativistic
electron degeneracy
6
5
4
3
p-p chain
Ideal gas
2
CNO cycle
1
0
6
7
8
9
10
Thermal radiation of the electrons produces
gamma-rays.
Iron photodisintegration breaks the iron nuclei
into helium atoms.
The core is unstable and rapid contraction of
core.
𝑀 < ~30𝑀⨀ , supernova explosion leaves a
neutron star.
𝑀 > ~30𝑀⨀ , black hole.
• This lecture provided very basic idea of the
stellar evolution.
-Theoretical astrophysics (Volume II: Stars and
Stellar systems)- T. Padmanabhan
-Stellar evolution and nucleosynthesis/Sean G.
Ryan and Andrew J.