Protostar Æ Star
Stellar Evolution of a Star like the Sun
•
Star collapses further
•
Gets hotter
– On the surface
– In its center
•
Until it is so hot in the center that nuclear reactions can start.
•
This produces even more energy – so much that further gravitational
collapse is halted.
•
•
The star is now “born”
It is a main sequence star.
•
It will remain a main sequence star for the largest fraction of its lifetime.
Thermal Equilibrium
Hydrostatic Equilibrium
• It is a stable star – it
does no longer collapse
(nor expand).
• Star shines at a constant rate
• Energy production in the center equal energy loss
from surface
• The desire to collapse
under its own gravity is
counter balanced by the
pressure exerted by the
“hot” gases.
Energy Source?
Energy Source?
•
What is the Energy Source of a Proto-Star?
•
What is the Energy Source of a Proto-Star?
•
What produces so much energy that the star will no longer collapse?
•
What produces so much energy that the star will no longer collapse?
•
What if a star never gets hot enough to start nuclear fusion?
•
What if a star never gets hot enough to start nuclear fusion?
•
What is the energy source of the Sun?
•
What is the energy source of the Sun?
Coal?
Gravity?
Something else?
Is the Energy Source Coal?
Energy Source and Age of the Sun
•
• The energy per second that a star emits is called
Luminosity. Thus the lifetime of a star is the energy
available divided by the luminosity; or in terms of a
formula:
t age − of − sun
We can measure how much energy is produced when burning coal. It turns out
that one kilo-gram of coal produces 5 ×106 Joules. How much energy would the
entire sun produce if it was made of coal? The sun’s total mass is 2 ×1030 kg, so
the energy available is:
E = 5 × 10 6
•
E
=
L
J
× 2 × 10 30 kg = 10 37 J
kg
How long does this last if the sun emits energy at the present rate? The
Luminosity of the sun is 4 × 1026 W (1Watt = 1 Joule/sec).
•
t age−of − sun =
10 37 J
E
=
= 2.5 × 1010 sec = 800 years
L 4 × 10 26 J
sec
• Why is this important? We know the luminosity of the sun,
and if we could somehow figure out how much energy is
available, we could calculate the sun’s age.
•
So, if the sun received its energy through burning coal, it would radiate for 800
years. Clearly this is a ridiculously short time-scale. In fact an energy source is
needed that provides energy for roughly 10,000,000 times as long a time.
Does the Energy come from Gravitational Collapse?
•
Again, the age of the sun would be given by:
•
t age − of − sun
In the mid 1800’s Kelvin & Helmholz came up with another suggestion. What
if the sun is collapsing, and what if gravitational energy gets transformed into
light energy?
2
E grav
•
3 GM
=−
5 R
•
where M is the total mass of all the particles and R the radius of the sphere.
•
How much of that energy can be transformed into light? As the star collapses,
it turns out that one half of the gravitational energy goes into heating the star,
while the other half is radiated away. This is known as the “Viral Theorem”.
•
•
Thus the total energy reservoir that is available to be radiated away during the
lifetime of the sun would then be:
Elight =
3 GM
10 R
So, if we know the mass, radius and the luminosity of the sun, we ought
to be able to calculate for how long the sun would radiate at its present
rate, if it obtained all of its energy from gravitational energy. Inserting
R¤= 7 x 108 m, M¤= 2 x 1030 kg, L¤= 4 x 1026 W and G = 6.67 x 10-11
m3/(kg sec2)
3 GM 2
3
t=
=
10 RL
10
1
E light = − E grav
2
•
2
• Only in the very center of
the star where
temperatures are hottest.
m3
2
× ( 2 × 10 30 kg )
kg × sec 2
= 9.5 × 1014 sec = 3 × 10 7 years
kg × m 2
7 × 10 8 m × 4 × 10 26
3
sec
6.67 × 10 −11
Kelvin & Helmholz already knew that in the mid 1800’s, but no other
energy source was known. This puzzle was resolved in the 1930’s with
the discovery of the hydrogen bomb.
However, while gravity is not the main energy source of the sun,
gravitation is indeed an important energy source. Proto-stars
receive all their energy from gravitation!! And proto-stellar
lifetimes are much shorter than the main sequence lifetimes.
Energy Production
Energy Source?
• Nuclear Energy
3 GM 2
E 10 R
3 GM 2
= =
=
L
L
10 RL
•
Nuclear Fusion
•
Hydrogen is fused into
Helium
•
Same as an atomic Bomb!
•
•
•
How?
4 H atoms from 1 He atom
And a lot of Energy.
Why does this only happen at high temperatures?
Protons are positively charged
Æ Need to overcome the repulsion
How?
1
H + H → H + e +ν
1
2
+
1
1
H + H → He + γ
1
3
Bash together the protons
Protons need to have high velocities
Under which conditions do you get
high velocities?
H
High Temperature
T >15 million Kelvin
Where do you get those high temperatures?
P-p chain
3
Center of the star – in the “core”
He+ 3He→ 4He+1H +1H
Energy Production in high mass stars
Energy Production in low mass stars
P-P Chain
(short for proton-proton chain)
CNO cycle
Involves Carbon, Nitrogen, Oxygen
These are only used as a catalyst.
4 H → 1He + Energy
1
Four protons are added to C, N, & O,
He is produced
And C, N, & O are restored
H +1H → 2H + e + + ν
2
H +1H →3He + γ
3
He+ 3He→ 4He+1H +1H
The CNO cycle needs higher initial
temperatures to get started, however,
once it is going, it is a faster method of
burning H to He than the pp-chain.
How does this nuclear reaction produce so much Energy?
How much mass has gotten “lost”?
It turns out that four hydrogen atoms have more
mass than one helium atom.
Since we know the mass of the hydrogen and the helium atoms, we can calculate how much mass has been lost, and how
much energy was produced during this process. The mass of one hydrogen atom is 1.673 × 10-27 kg and that of one helium
atom is 6.645 × 10-27 kg.
So where did the extra mass go?
The mass somehow got converted into energy.
4 × mhydrogen = 6.693 × 10 −27 kg
1 × mhelium = 6.645 × 10 − 27 kg
Einstein?
Difference = 0.048 × 10 − 27 kg
This means that Energy and Mass are
“different faces of the same thing”, and that
one can be transformed into the other.
E = mc
2
fractionlost − mass =
0.048 ×10 −27 kg
= 0.007
6.693 ×10 − 27 kg
Energy Transport
How much Energy is that?
E = mc 2 = 0.048 × 10 −27 kg × (3 × 108 m / sec) 2
E = 4.3 × 10 −12 Joules
•
•
•
Convection
Radiative Diffusion
Conduction
One kilo-gram of hydrogen then produces:
E = mc 2 = 0.007 kg × (3 × 108 m / sec) 2
E = 6.3 × 1014 Joules
How much energy is that? As a reference, to get the same amount of energy, you would have to burn 20,000 tons of coal; and 20,000 tons
corresponds to roughly 4×1011kg of coal. This is quite a lot of coal! So you can do quite a lot of damage with only one kilo-gram of hydrogen…
Energy Transport by Radiative Diffusion
Convection
Granulation on the surface of the sun
HRD on
Blackboard
Follow what
happens at
individual steps,
i.e. from 1 to 2 to
3 etc….
Life as a main sequence star:
star Stage 1 to 2
Stage 1:
• The star has just become a main sequence star
(onset of nuclear fusion)
• The hot (T > 15 mil K) region is called the
“core”.
• Energy source: pp-process (H Æ He; 4
protons turning into one He-ion)
• Star is in Hydrostatic Equilibrium
Life as a main sequence star:
Stage 1 to 2
Stage 1 Æ 2:
• In the core the fraction of helium increases
gradually
• Luminosity and Radius increase gradually
• Energy transport in core: radiative diffusion
On the way to a red giant
Stage 2 Æ 3:
• Hydrogen in the core gets
used up
• Get a core of helium
• Hydrogen burning to
helium continues in a
“shell” surrounding this
core
• Energy transport in core:
radiative diffusion
• Energy transport in
envelope:
radiative diffusion
Stage 3 Æ 4:
Æ as more H Æ He; He mass of core increases (to roughly 0.5 the total mass of star)
Æ one He atoms occupies less space than four H atoms
Æ core contracts slowly
Æ Viral theorem applies; ½ of energy gets radiated away; ½ goes into heating core
Æ central temperature increases, reaction rates increase
Æ more energy gets produced in the center of the star (see below)
Æ this energy has to be carried from the center to the surface of the star
Æ energy transport via radiation is no longer efficient enough
Æ the envelope turns convective
Æ energy can then be transported more efficiently to the surface
Æ luminosity increases
Æ envelope expands (radius increases)
Æ surface temperature decreases (color gets redder)
Æ star moves to the top right hand side of the HRD
(The Sun has now become a red giant and Mercury and Venus will be part of the sun,
and maybe the Earth too. In any case we will be fried, if we have not yet died…)
Comparing main sequence stars to Red Giants
(but giant is much bigger ~ 100X)
Becoming a Red Giant
Degeneracy
Comparison
•
•
•
Energy transport in Core is by radiative diffusion
Get more and more Helium until the core turns
degenerate.
Different Laws of Physics apply for degenerate gasses
Normal gasses: density, pressure and temperature are
counterbalanced by each other. The normal gas laws do
not apply any more.
What is degeneracy?
The electrons are packed as closely
together as possible.
Cannot fit any more electrons into the
space – more accurately, cannot fit
more than two electrons into a “phase
space”
Maximum number
of chairs;
If the classroom is
full have no
more spaces;
Lets be inventive.
Can have one
person sit on
the Lap of the
other.
If classroom totally
full the “gas of
students” has
turned
degenerate.
The core explosion – the He-flash
HeÆCarbon or the “Tripple Alpha Reaction”
At Stage 4:
•
Sudden onset of Helium to Carbon fusion (Tripple Alpha process, “3α”)
•
He-flash = Core explosion (invisible)
4 He → 1C + Energy
How did a He-flash happen?
As H Æ He, Æ core shrinks Æ the central temperature keeps on rising
Core gets degenerate: “electrons as close as possible”
Perfect gas law does not apply to degenerate gases
Æ
Æ
Æ
Æ
Æ
Æ
Æ
4
2
4
2
As temperature increases, the pressure does no longer balance it out
Temp can increase further
reaction rates speed up until He fusion starts
this reaction is even more energetic
(energy generation rate is proportional to T40)
faster reaction Æ more energy output Æ higher temp
“run-away” process
“core explosion” - “Helium Flash”
Pretty soon after the He-flash, the
star will have different properties,
i.e. a lower luminosity and a higher
temperature. It is now a yellow star.
Energy Source:
HeÆC (3α) and HÆHe
Helium core burning
Hydrogen shell burning
He+ 48Be→126C + γ
This reaction requires a higher initial Temperature than the pp-chain, but it
produces more energy.
Before it was known what He nuclei were, they were called “alpha particles”.
Since this process involves three He-nuclei, I.e., three alpha particles, this set of
reactions in known as the “tripple alpha process”.
Stage 5: Horizontal branch phase
After the He-flash in the core, the
star is temporarily unstable and
changes its radius, energy output and
temperature.
He+ 24He→ 48Be + γ
Stage 6: A brief Variable star phase
Stage 6: A brief Variable star phase
(only in certain place of HRD)
over-expansion of envelope
followed by collapse of envelope
Æ
Æ
Æ
Æ
Æ
Æ
Æ
Æ
Æ
too much collapse
rebounce
expansion
too much expansion
etc
radius increases and decreases
surface temperature increases and
decreases
luminosity increases and decrease
Period-Luminosity Relationship
The Asymptotic Giant Branch…
Stage 6Æ7: On the way to a Giant/Supergiant
The Asymptotic Giant Branch…
Stage 6Æ7: On the way to a Giant/Supergiant
As the central temperature, the temperature gets so high that another
nuclear reaction is initiated: C Æ O
12
6
C + 24He→168O + Energy
Energy Source:
A small fraction of C Æ O in core
Remaining fraction remains carbon ash
He Æ C (3α) in a shell
H Æ He in another shell
Surrounded by an envelope
Size of Giant Star
The Sun has now become a red giant and Mercury and Venus will be
part of the sun, and the Earth too… and Mars…. Almost…
In any case we will be fried, if we have not yet died…:)
•
•
•
Carbon/Oxygen core
Helium shell burning
Hydrogen shell burning
Stages 1Æ 4 repeat themselves
(only faster)
Æ Carbon mass of core increases
Æ core contracts slowly
Æ central temperature increases
Æ reaction rates increase
Æ envelope expands (radius increases)
Æ surface temperature decreases
Æ color gets redder
Æ luminosity increases
Æ star moves to top RHS of HRD
Æ Red Super Giant
Planetary Nebula Phase…
Stage 7Æ8
as the radius increases
Æ outer shells get dispersed
Æ He burning shell gets exposed to the
surface
Æ get tripple alpha reactions on the surface
Æ these are rather explosive
Æ material is expelled in shells
Æ see a planetary nebula
but the central star appears to be hotter
Æ hotter means a bluer color
Æ star moves towards blue in HRD
Æ Star becomes a White Dwarf
White Dwarfs and Planetary Nebulae
White Dwarf
• Carbon Ash in core, He & H burning shells
• Remaining material gets expelled
Æ Left behind “Small Carbon Star”
Planetary Nebula
• as the star grows in size, outer layers are only loosely bound
• outer shells get dispersed
• He burning shell gets exposed to the surface
• get Tripple Alpha reactions on the surface of the star
• These “He-flashes” rather explosive
• Material is expelled in shells
Æ see a planetary nebula
Ring Nebula (M57) – picture taken at CUNY - CSI
Making color photos with HST
observe with different Filters, then combine pictures…
Nearest Planetary
Nebula
Size 0.5o
(same as sun!)
Greenish middle:
Oxygen
Nitrogen
Outer Red:
Hydrogen, some
Nitrogen.
Size: 150 AU
Distance: 400 lyr
Helix Nebula -- or Sun Flower Nebula
Oxygen
(doubly ionized)
Colors roughly right
Blue: helium
(close to central star)
Helix Nebula Movie
Green: Ionized oxygen
Red: ionized nitrogen
(coolest gas - furthest
away)
All gases are heated from
the central star.
HST
Helix Nebula
Shows HST
insert
Helix
nebula
Spoke-like
globules
Each gaceous
head is twice
the size of
the solar
system
Helium
Helix Detail
The gaseous knots may be
the result of the collision
between gases. Hot gases
that are ejected from the
surface of the star collide
with the cooler gases that
were ejected some 10,000
years prior to the last
ejection.This crash
fragments the cloud into
finger-like droplets
NGC 7027
Ground Based
Image
Binary Star Evolution
with a White Dwarf and a Red Giant
NGC 6543
Color coded to
show detail
Hourglass
Nebula
Becoming a White Dwarf
Spectacular Stellar Deaths
Stage 9 and beyond:
planetary nebula disappears
star has no nuclear fuel
star looses energy (radiates it away)
(radiates thermal energy)
ÆStar gets dimmer
Æ star cools, temperature decreases
Æ Cooler means redder
Æ star moves towards bottom right
in HRD
star now is a white dwarf
eventually it will cool more and more and
become an even dimmer red dwarf…
White Dwarfs
Material?
Size?
Mass?
Density?
Carbon “ash”, maybe Carbon/Oxygen mixture
Size of Earth
Roughly 80% of main sequence mass
Material is very dense
White Dwarfs
As big as the Earth
As big as the Earth,
but MUCH denser
Æ 100,000 x surface
gravity
Material is packed as closely as possible
Electrons form a Degenerate “gas”
Limiting Mass for White Dwarfs
Sirius A & B
Paradoxically
more massive
W.D.’s tend to
be smaller
White Dwarfs in M4
The Evolution of Massive Stars
Eta Carina – A Massive Star
Massive Stars
Differences to lower mass stars like the sun
1. Main Sequence lifetime is faster.
2. Hydrogen burning Mechanism is not the pp-chain, it is via the
CNO cycle
3. Central temperature can rise higher, so energy in the core is
transported via convection. Degeneracy will not occur, so will
NOT have s He-flash.
4. Central temperature can rise higher, so can burn heavier metals.
5. Strong Mass Loss up to a few solar masses during m.s. life.
1. Main Sequence lifetime
HRD for low mass stars – HRD for high mass stars
1. Main Sequence lifetime is faster. Proto-stellar Evolution is
also faster (more gravitational energy Æ faster collapse)
Life expectancies of main sequence stars scale with mass
2. Hydrogen Burning
T∝
Energy Production in low mass stars
P-P Chain
(short for proton-proton chain)
Overall 4 protons Æ 1 He atom.
4 H → 1He + Energy
1
In low mass stars via the p-p chain
In high mass stars via the CNO cycle
Energy Production in high mass stars
CNO cycle
Involves Carbon, Nitrogen, Oxygen
These are only used as a catalyst.
Four protons are added to C, N, & O,
He is produced
And C, N, & O are restored
The CNO cycle needs higher initial
temperatures to get started, however,
once it is going, it is a faster method
of burning H to He than the pp-chain.
1
M 2.5
H +1H → 2H + e + + ν
2
H +1H →3He + γ
3
He+ 3He→ 4He+1H +1H
3. Energy Transport and the Helium Flash
4. Heavier Metals
Convective core; NO He-flash
•
•
•
•
•
•
•
•
High mass stars burn hydrogen via the CNO cycle
Since this produces relatively more energy (the temperature gradient is steeper)
The Energy Transport Mechanism is Convection in the core.
Convection results in the mixing of the core.
Some hydrogen from the hydrogen burning shell is mixed into the core.
You will not get an inert He-core,
Thus the core (the electrons in the core) will not become degenerate
Thus no He-flash will occur.
• The He-flash (the explosive onset of He burning) only happens in low mass stars
like the sun, and for stars that are 3 times as massive as the sun.
Massive stars have more gravitational Energy that can be used to heat the
central core. The central temperature need to be hotter and hotter each time
a new nuclear fuel is used. Burning H to He requires tens of millions of
degrees Kelvin. Burning Helium requires a higher temperature because the
repulsion between the He-nuclei is larger (twice as much) than that of the Hnuclei. Burning Carbon requires yet higher temperatures.
In low mass stars core temperatures in excess of about 100 million degrees
Kelvin are never obtained. This is because lower mass stars do not have
enough gravitational energy for the central temperatures to rise this high.
Thus low star masses finish their nuclear reactions after having produced
Carbon and a little Oxygen.
Higher mass stars can burn Carbon, then burn Oxygen, then Silicon, etc…
but only up to Iron.
The Onion Skin Model
Burning heavier elements up to Iron
Time scales in each element burning stage in 25 MSun Star
Why only up to Iron?
Abundances of
Elements
To make elements lighter than
Iron from even lighter elements
will release a lot of energy
The heavier the element
the less abundant it is.
Making elements heavier than
Iron requires energy
(individual protons and neutrons
cannot hold onto each other any
more…)
Secondary Peak at
Iron… why?
Fusion
Fission
Think of a water-drop that gets
bigger and bigger, and then
eventually drops.
What are we made of?
Large drop in Boron,
Lithium and Beryllium –
these elements get
destroyed in stellar
interiors and are made
into heavier elements
Evolution in
HRD
Read chapter 16
of Silk’s Big Bang
Globular cluster HRD