Download Main Sequence Lifetime

Our Place in the
Cosmos
Lecture 12
Stellar Evolution
Stellar Evolution
• We saw in the last lecture that all main
sequence stars generate their energy by fusing
hydrogen into helium in their cores
• The Sun, a typical main sequence star, fuses
over 4 billion kg of hydrogen to helium each
second
• Eventually (in about 5 billion years time) that
hydrogen will be exhausted, and the Sun will
evolve off the main sequence
• The same will happen to all main sequence
stars
Stellar Evolution
• Just as mass determines the other properties of
a main sequence star (luminosity, size,
temperature), the eventual fate of a star is also
pre-ordained by its mass, which is locked in
place when the star forms
• Chemical composition also plays a secondary
role in a star’s properties and fate
• Each star is thus unique - minor differences in
mass and composition can result in significant
differences in fate
• Low and high mass stars evolve differently
Main Sequence Lifetime
• If one were to add mass to the Sun, the extra
weight of material pushing down would
compress its core, driving up temperature and
density
• Nuclear reaction rate would increase as nuclei
collide more frequently and with higher energy
• A modest increase in pressure can lead to a
dramatic increase in energy production and
hence luminosity
Main Sequence Lifetime
• This is why main sequence is primarily a
sequence of masses
• More mass  stronger gravity  higher
temperature and pressure  faster
nuclear reaction rates  higher luminosity
• Hence more massive stars lie further up
and to the left on the main sequence
Main Sequence Lifetime
• The length of time a star can continue fusing
hydrogen to helium, its main sequence lifetime,
depends on
• The amount of hydrogen available
• The rate at which hydrogen is fused into helium
• More massive stars contain more fuel, but the
rate at which the fuel is used up, as measured
by the luminosity, is also higher
Main Sequence Lifetime
• The main sequence lifetime is equal to the
amount of fuel available (proportional to mass)
divided by rate at which fuel is used
(proportional to luminosity)
• The Sun has an estimated MS lifetime of ten
billion years
• For other MS stars, lifetime is given by
Main Sequence Lifetime
• Luminosity increases very
rapidly with mass
• The most massive stars (about 60 times more
massive than the Sun) have luminosities
794,000 times greater and lifetimes below 1
million years
• In general, more massive stars are shorter-lived
than less massive stars
Main Sequence Evolution
• As the hydrogen within a main sequence star is fused
into helium, its composition gradually changes and it
evolves slowly up the main sequence, gaining in
luminosity
• The Sun’s luminosity will roughly double between first
joining and leaving the main sequence
• Helium cannot be fused into heavier nuclei in a main
sequence star due to four times stronger electrostatic
repulsion between helium nuclei compared with
hydrogen nuclei
• Helium simply accumulates within the core of a star, like
the ash in a fireplace
Helium “ash”
accumulates most rapidly
in the centre of a star
where reaction rates are
highest
Sun was initially 30%
helium throughout
Today, the Sun’s centre
consists of 65% helium,
35% hydrogen
In about 5 billion years
time no hydrogen will
remain at the centre
Farewell Main Sequence
• Once all hydrogen is exhausted in the core of a
star, no more energy is generated and the star is
no longer in equilibrium and is no longer on the
main sequence
• How a star subsequently evolves depends on its
mass
• The rest of this lecture will discuss the evolution
of low mass stars, those less massive than
about 3 M
• The evolution of massive stars will be discussed
in the next lecture
Degenerate Helium Core
• No hydrogen burning  lower pressure 
gravity wins
• Core becomes extremely dense until it becomes
electron degenerate (around 1000 kg per cubic
centimetre)
• Although core is “dead”, hydrogen can still burn
in a shell around the core - shell burning
• As shell deposits more helium “ash” on the core
the core shrinks due to extra weight of material
Post-Main Sequence
Evolution
• Just outside helium core the gravitational
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acceleration is given by gcore = G Mcore/r2core
As more helium “ash” is deposited onto core it
both increases in mass Mcore and decreases in
radius rcore
Both cause gravity at core’s surface to increase
Stronger gravity increases pressure within
hydrogen-burning shell thus increasing shell
burning rate and hence luminosity of star
As a star runs out of nuclear fuel it becomes
more luminous!
Subgiant Stage
• As the degenerate core grows and the shellburning rate increases, the surrounding layers of
the star are heated and expand
• As the star’s surface expands it becomes more
luminous but also cooler
• The star becomes a subgiant - luminous but red
in colour
• The star moves above and to the right of the
main sequence on the H-R diagram until its
surface temperature has dropped by about
1000K
Red Giant
• At this point the formation of H- ions (hydrogen
atoms with 2 electrons) regulates how much
radiation can escape - just as greenhouse gases
in the Earth’s atmosphere trap in heat
• The star is now a red giant - it can no longer
cool and moves almost vertically up the red
giant branch on the H-R diagram as it grows
larger and more luminous but remains at the
same surface temperature
Giant Evolution
• It takes around 200 million years for a star like
the Sun to evolve from the main sequence to the
top of the red giant branch, starting slowly, then
evolving at a rapidly increasing rate
• In the first 100 million years the star’s luminosity
increases to about 10 L to become a subgiant
• In the remaining 100 million years the luminosity
skyrockets to almost 1000 L
• As mass accumulates on core hydrogen shell
burning rate increases (positive feedback)
As core gains mass and shrinks,
shell burning increases and the
outer parts of the star swell up
Helium Burning
• As core shrinks it becomes hotter
• Eventually the helium nuclei are moving
energetically enough to combine together to
form carbon
Helium Flash
• The degenerate core behaves more like a solid than a
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gas so heat from helium burning rapidly spreads through
core with no accompanying expansion
Rapidly rising temperature within core leads to a chain
reaction known as the helium flash
Within just a few seconds the core explodes
The energy released lifts the outer layers and core is no
longer degenerate
The expanded core now has a much weaker surface
gravity  lower pressure  slower nuclear reactions 
lower luminosity
Horizontal Branch Star
• The star is now stably burning helium to carbon
in a non-degenerate core and burning hydrogen
to helium in a surrounding shell
• Stars in this phase have a narrow range of
luminosities, about one hundredth of their
luminosity at the time of the helium flash, but still
much more luminous than their main sequence
stage
• They are know as horizontal branch stars from
their locations on the H-R diagram, where they
remain for about 50 million years
Asymptotic Giant Branch Star
• As helium is depleted in the core, gravity again
wins over pressure and degenerate carbon core
is surrounded by helium and hydrogen burning
shells
• As before, star grows larger and redder,
following a path close to the red giant branch
known as the asymptotic giant branch (AGB)
• Core temperatures are too low for carbon fusion
and AGB star starts to lose outer envelope
• This is heated by hot degenerate core and glows
as a spectacular planetary nebula
Planetary nebulae are
so-called because they
look like planets when
seen through small
telescopes
HST reveals their
beautiful structure