The Russell-Vogt Theorem
Stellar old age
! 10.1 – Evolution off the main sequence
" Low mass stars
" High mass stars
! 10.2 – Cepheid Variables
" Variable stars
" Cepheid mechanism
" Period-luminosity relation
! 10.3 – Planetary nebulae
! 10.4 – White dwarfs
" Electron degeneracy
" Properties of white dwarfs
" Relativistic effects
Eta Carina, a young massive star.
Chapter 10
Physics 216 – Introduction to Astrophysics
! The Russell-Vogt Theorem states:
“The structure of a star is uniquely determined by
its mass and its chemical composition.”
! Put another way, the position of star in the Hertzsprung-Russell
(HR) diagram is uniquely determined by its mass and chemical
composition.
2
The Main Sequence
Chapter 10
Evolution on the Main Sequence
! Recall that the zero-age main sequence (ZAMS) is the position of
stars in an HR diagram when they first begin hydrogen burning.
From this moment on, stars are locked in a losing battle with
gravity. A star’s life is entirely driven by this struggle.
!
Thermonuclear reactions in the core begin when gravity compresses the
core to sufficiently high density and temperature.
!
The thermal energy released by fusing
hydrogen to helium heats the gas and
maintains the core temperature high
enough to resist the force of gravity.
!
! For a star like the Sun (i.e., an
intermediate-age, metal-rich star
belonging to the Galactic disk), the
initial composition (by mass) is:
Hydrogen
Helium
Heavy Elements
Physics 216 – Introduction to Astrophysics
! As thermonuclear reactions alters the
chemical composition of the core, the
star must move in the H-R diagram.
4
Leaving the Main Sequence
Pressure! density " temperature
! To compensate for the decreased
pressure, the core contracts, thereby
increasing the temperature.
This in turn increases the rate of
thermonuclear reactions. As a result,
the star slowly brightens and moves
away from the ZAMS.
Physics 216 – Introduction to Astrophysics
Chapter 10
Physics 216 – Introduction to Astrophysics
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Ascent to the Red Giant Branch
! As hydrogen is converted to helium, the
pressure decreases because the number
of particles per unit volume decreases
(four H atoms fuse to one He nucleus).
Recall that the ideal gas law gives
Chapter 10
! 72%
! 26%
! 2%
! But as hydrogen burning proceeds, the
helium fraction in the core increases.
As hydrogen is exhausted in the core, the
response to gravity drives the star to high
luminosity, and, in some cases, to a
spectacular end as a supernova. Stellar
corpses are white dwarfs, neutron stars,
and the ultimate compression, a black hole.
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! When hydrogen is entirely depleted, the core contracts, and the
conversion of gravitational potential energy to thermal energy
replaces thermonuclear burning as the source of energy. The
temperature rises until hydrogen begins to burn in a shell
around the core.
! As the hydrogen burns, the mass of the helium core increases.
The core continues to contract and grow hotter, increasing the
rate of hydrogen burning in the shell. As the core contracts,
eventually reaching a size 1/10 that of the original core, the
atmosphere expands and cools.
! The star’s surface temperature decreases, but at the same time,
its radius increases so dramatically that its luminosity also
increases. The star is now situated on the red giant branch.
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Physics 216 – Introduction to Astrophysics
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The “Helium Flash”
Hydrogen Shell Burning and Red Giants
The Sun is getting old :
# Age: 10 Gyr... moves off
of the main sequence
$ Age: 10.2 Gyr... As the
star ascends the red
giant branch, the inert
helium core grows in
mass and temperature.
% Age: 10.5 Gyr... At
a certain critical
temperature, helium
burning becomes
possible: helium flash
in the core.
Helium Core (Hot,
inert, contracting, and
increasingly massive).
Red giant envelope
(mostly hydrogen).
Hydrogen burning shell.
!
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Physics 216 – Introduction to Astrophysics
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Physics 216 – Introduction to Astrophysics
Life on the Horizontal Branch
The Sun in 5 Billion Years
! When the Sun becomes a red giant, it will swell to a diameter of ~1 AU,
and the surface temperature will drop to T ~ 3500 K.
! The start of core He burning (marked by the He Flash) via triplealpha process causes the core to expand and the star’s internal
structure changes yet again.
! The outer parts of the star
shrink, and the surface
temperature increases. The
star’s luminosity drops. The star
becomes a yellow giant residing
on the Horizontal Branch in
the H-R diagram.
! The luminosity will
increase by a factor
of 2000, boiling away
the Earth’s
atmosphere and
oceans, and even
much of the mantle.
! The name “Horizontal Branch”
comes from the fact that all
stars on it have roughly the
same luminosity.
Luminosity "
Chapter 10
In low-mass stars like the Sun,
the helium in the core burns
suddenly and explosively in an
event called the Helium Flash.
Horizontal
Branch
Red Giants
Turnoff
Point
Main Sequence
! These stars are burning helium
in their cores.
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Physics 216 – Introduction to Astrophysics
!
Core He burning, and H burning in a
thin surrounding shell, will continue
for a while, until the star ascends the
Asymptotic Giant Branch. As it
brightens and cools, the star loses
mass through strong stellar winds.
The star becomes unstable, and begins
to pulsate. Eventually, it releases as
much as 10% of its mass into space.
Chapter 10
Luminosity "
!
When helium in the core is exhausted,
the core (which is now composed mostly
of carbon and oxygen) will begin to
contract. In stars like the Sun, the core
temperature will never get high enough
for carbon/oxygen burning to begin.
AGB
Physics 216 – Introduction to Astrophysics
RGB
!
The evolutionary sequence described to this point applies to stars that
have roughly the same mass as the Sun.
!
Recall that the Sun will spend about 10 billion years on the main sequence;
once it leaves the main sequence, only ~100 million years will elapse before
it becomes a white dwarf.
!
A star’s main sequence lifetime depends very sensitively on its mass:
lifetime "
# Surface Temperature
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The Evolution of High- (and Low-) Mass Stars
Subsequent Evolution
!
Chapter 10
# Surface Temperature (K)
13
1
M3
!
This means that an O star (with a mass of ~ 10M&) will leave the main
sequence just 10 million years after first settling on it!
!
It also means that it will take low-mass stars (i.e., those with masses below
~ 0.8M&) ~ 14!
billion years to leave the main sequence. But that’s the age of
the universe! In other words, every low-mass star that ever arrived on the
main sequence since the Big Bang is still there!
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Physics 216 – Introduction to Astrophysics
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The Evolution of High- (and Low-) Mass Stars
! For stars more massive than
roughly 2.5M&, helium burning
begins smoothly (i.e., there is
no sudden “flash” as the core
is not degenerate).
! For stars more massive than
roughly 8M&, the core
temperatures are high enough
that fusion of Carbon and
Oxygen is possible.
! We will have more to say about
these stars when we talk about
stellar explosions.
(See Fig 10.2)
Physics 216 – Introduction to Astrophysics
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Evolution of Low/High Mass Stars
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Evidence of Stellar Evolution
Luminosity "
! Star clusters contain stars with a range of masses. But the mass
(and chemical composition) of a star determine how it evolves.
! We use H-R diagrams for star clusters to measure their age.
AGB
RGB
# Surface Temperature
Evolution of a low-mass (<5 M&) stars.
Chapter 10
Flow chart of stellar evolution by mass.
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Overlaid H-R diagrams of young clusters.
Chapter 10
H-R diagram of a typical old cluster. White dwarfs
are missing but should be included.
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