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Module :
Activity 1:
From Working for a Living
Module 8: Life on the Main Sequence
Swinburne Online Education Exploring Stars and the Milky Way
© Swinburne University of Technology
SummaryIn this Activity you will learn about • the time a star spends on the main sequence;• how this time depends almost entirely on the mass of the star; and • some of the nuclear reactions which occur in stars on the main sequence.
In the last Module we looked at • how stars join the main sequence,
• how the time taken dependson their mass, and
• what happens if they are too massiveor not massive enough
to join the main sequence.
Temperature
molecular cloudmolecular cloud
too massivetoo massive
Lum
inos
ity
Main Sequence
not massive enoughnot massive enough
Mass matters
We can actually work out what is “too massive” and “notmassive enough” because we can work out the outwards pressure in a hot gas, and the (inwards) gravitational force.
It turns out that anything more massive than 100 Suns is too massive, and anything lighter than one-twelfth of the Sun is not massive enough. Our SunOur Sun
Not massive enoughNot massive enough
Too massiveToo massive
Let’s talk size
Faster or slower?
If a star is more massive than our Sun, will it stay on the main sequence for a longer time?
Longer
I think that a massive star will last longer than the Sun because there is a lot more fuel.
Longer
I think that a massive star will last longer than the Sun because there is a lot more fuel.
Shorter
I think that a massive star will not last as long as the Sun as its fuel will burn a lot faster.
Shorter
I think that a massive star will not last as long as the Sun as its fuel will burn a lot faster.
Same
I think that there wouldn’t be much difference: these effects would sort of balance each other out.
Same
I think that there wouldn’t be much difference: these effects would sort of balance each other out.
More fuelMore fuel
Much hotterMuch hotter
It has a lot more fuel to “burn”.
But on the other hand, that fuel (in the core) will be at a much higher temperature and pressure.
What do YOU think? (click on one red word)
Unfortunately, Big = fastI’m sorry: the answer is that the more massive stars burn out a lot faster.
The more mass there is in a star, the more pressure and temperature there will be in its core and surrounding layers.
That will make the fusion of hydrogen in the core go faster and the star will be lot more luminous.
So the star will run low on hydrogen a lot more quickly.
More massMore mass
More P and TMore P and T
Faster fusionFaster fusion
Shorter lifeShorter life
OKAY
I’ll try to remember that …
OKAY
I’ll try to remember that …
YES! Big = fastYou are right! The more massive stars do burn out a lot faster.
The more mass there is in a star, the more pressure and temperature there will be in its core and surrounding layers.
That will make the fusion of hydrogen in the core go faster and the star will be lot more luminous.
So the star will run low on hydrogen a lot more quickly.
More massMore mass
More P and TMore P and T
Faster fusionFaster fusion
Shorter lifeShorter life
Thank you!
I do my best, you know...
Thank you!
I do my best, you know...
CONGRATULATIONS!
Small = slow
At the other end of the scale, a small new star will not have a very dense, hot core, and the fusion of hydrogen will then go a lot more slowly.
Core of our Sun Core of our Sun
Wheee!YOW!
Ooof!Core of smaller star Core of smaller star
er ...
How long have we got?
A G2 star such as our Sun is expected to spend about 10 billion years altogether on the main sequence.
Since it’s at the 5 billion mark these days there’s nothing to worry about for quite a while.
Temperature
Lum
inos
ity
Main Sequence
30 million yearsto reach ZAMS*30 million yearsto reach ZAMS*
another 5000 millionyears to go
another 5000 millionyears to go
5000 million yearshere so far
5000 million yearshere so far
* ZAMS is the Zero Age Main Sequence.
Other types of stars
Here is a table to show you how the mass of a star can affect the time it spends on the main sequence (1 billion = 1,000 million).
How does ZAMS lifetime scale with mass ?Theory predicts that the time a star spends on the main sequence will be inversely proportional to the cube of the star’s mass.
Mass of starMass of star
Life
on
mai
n se
quen
ceLi
fe o
n m
ain
sequ
ence
Lifetime dependson 1/mass3
Lifetime dependson 1/mass3
That means that if you double the mass of a star, you get 1/8 of the lifetime.
Remember 23 = 2x2x2= 8.
Hydrostatic equilibrium
Our Sun took only 30 million years to reach the main sequence, but now it’s there it’s going to be there for a total of 10,000 million years.
So once on the main sequence, stars hardly change at all: they’re in hydrostatic equilibrium.
Hydro means “fluid”, static means “not changing”, and equilibrium means that there is a balance between two or more opposing effects.
Settled in for awhile then, eh?
Sure have! Give or take another 5,000 million years!
How it worksWe talked a bit about hydrostatic equilibrium early in this course, when studying the Sun. But here’s a reminder for you about how self-gravity and pressure govern whether a star shrinks, expands or stays stable.(Self-gravity is gravity from within, not from something outside. A bit like self-control in astronomy students.)We have to imagine a star consisting of layers or shells, like the skins of an onion, and think about what happens in just one layer.
Self-gravitypulls in
Self-gravitypulls in
Internal pressurepushes out
Internal pressurepushes out
If self-gravity wins,the shell contractsIf self-gravity wins,the shell contracts
If pressure wins,the shell expandsIf pressure wins,the shell expands
Different layers
This picture of a star is useful in that different layers of a star can react in different ways.
For instance, in some stars the core shrinks, making it a lot hotter.
However, this heats up the outer layers, which increases the pressure inside them, and that makes them expand. Whether a star expands or contracts depends on that balance between self-gravity and pressure, and thus on the mass of the star again.
Stable members only
If the balance changes so that pressure and self-gravity no longer balance in the layers of the star, and the layers begin to expand or contract quickly, then the star has left the main sequence. (That topic will be covered in future Activities.)
This is Eta Carinae, where in at least one shell, on at least one occasion, pressure won.
In other stars, self-gravity usually wins.
The fuel tank of a star
A star is formed from many kinds of gas and dust, but as with most things in this Universe it starts off composed mostly of hydrogen.The young star produces energy (light, heat and so on) when hydrogen is fused to become helium in the core of the star.
P-p chain, p-p chain,Nothin’ all day but
p-p chain …
However, when the star is a little more mature, there are other options … and they depend on temperature.
Remind me about
p-p
Stellar temperature Surface: lots of PE
not much KE
Surface: lots of PE
not much KE
Core: not much PE
lots of KE
Core: not much PE
lots of KE
PEPE
PEPE
KEKE
PEPE
PEPE PEPE
KEKE
KEKE
KEKE
KEKE
KEKE
PEPE
When we have mentioned the temperature of a star so far, we have meant the surface temperature.
This is very different to the temperature in the core!
There is always a balance between gravitational potential energy (PE) and kinetic energy (KE).
If a particle moves between the surface of a star and its core, these things both change but their total remains the same. That is, until the particle collides with others and shares its kinetic energy around.
Our Sun, for exampleThe average kinetic energy of atoms, molecules and other particles has another name: temperature.
Here is a chart of how the temperature of the Sun (in million of Kelvin) varies with radius from the core (all the way to the edge = 1).
Just about any star or planet is usually much hotter in the core than on the surface.
This is a left-over effect of core heating during formation, when particles with lots of PE turned it into KE.
The core of our own Earth is still at 5000 K!
0
2
4
6
8
10
12
14
16
18
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Core: about 15,500,000 K
Core: about 15,500,000 K
Surface: about 6,000 K
Surface: about 6,000 K
Core, surface and stellar class
When astronomers talk about a star’s temperature, do we mean the surface temperature, or the core temperature? There is a heck of a difference!
Because it is almost always emission (or absorption) from the atmosphere of stars that we detect on Earth, we use that to classify stars.
So we usually mean the surface temperature.
But surface temperature has little to do with fuelling stars, as the nucleosynthesis - the making of new nuclei - takes place in the core and not on the surface.
O
B
A
F
G
K
M
O
B
A
F
G
K
M
So, forget about stellar class and surface temperature for a moment, and let’s consider only core temperature.
Low Temperature fuel
During the p-p cycle, hydrogen is converted to helium.
Six protons (hydrogen nuclei) turn into a helium nucleus, spitting out two protons, two positrons, two neutrinos and two gamma rays in the process. It’s written like this:
p-p cycleCore: 8 million K
p-p cycleCore: 8 million K
That’s not low-temperature to us humans, but in terms of stellar cores it’s pretty miserable. It is the absolute minimum temperature at which fusion can drive a star.
Temperature required: at least 8 million K.
Medium temperature fuel
If a star has enough mass, its core pressure and temperature will be enough for another nuclear reaction to happen strongly: the conversion of hydrogen to helium using other elements as catalysts and intermediaries - carbon, nitrogen and oxygen.
This is called the CNO cycle.
Temperature required: over 20 million K for the CNO cycle to dominate.
p-p cycleCore: 8 million K
p-p cycleCore: 8 million K
CNO cycleCore: 20 million K
CNO cycleCore: 20 million K
The CNO cycleHere are the six steps of the carbon-nitrogen-oxygen cycle, in which a friendly carbon nucleus gathers four protons, turns two of them into neutrons, then releases them as a helium nucleus.
12C + p+ turns into 13N
13N sheds a positron to become 13C.
13C + p+ turns into 14N.
14N + p+ turns into 15O.15O sheds a positron to become 15N.
15N + p+ splits into 12C and 4He.
12C12C13N13N
e+e+
13C13C14N14N15O15O
e+e+
15N15N12C12C 4He4He
During many of these steps, energy and/or neutrinos are released.
High temperature fuel
The next important possibility is called the triple-alpha reaction.
Three alpha particles (helium nuclei) fuse to form one carbon nucleus, plus energy, neutrinos and so on.
KAPOW!
Temperature required: at least 100 million K.
12C12C p-p cycleCore: 8 million K
p-p cycleCore: 8 million K
CNO cycleCore: 20 million K
CNO cycleCore: 20 million K
triple-alpha reactionCore: 100 million K
triple-alpha reactionCore: 100 million K
Disgustingly high temperature
If you have really, really high temperature and pressure, then you can have all other kinds of nucleosynthesis.
When carbon and other heavier elements start to “burn” (that is, fuse), the products include elements up to iron (Fe, number 26 in the periodic table of the elements).
p-p cycleCore: 8 million K
p-p cycleCore: 8 million K
CNO cycleCore: 20 million K
CNO cycleCore: 20 million K
triple-alpha reactionCore: 100 million K
triple-alpha reactionCore: 100 million K
carbon burningCore: 600 million K
carbon burningCore: 600 million K
“Periodictable”?
There’s quite a lot of iron around that was formed this way.
Our own Earth has a core of iron nearly 7000 km across!
Temperature required: 600 million K.
Where do the rest come from, then?If the cores of stars can only produce elements up to iron in the periodic table, then where did all the heavier elements come from?
26Fe26Fe
27Co27Co
28Ni28Ni29
Cu29Cu 30
Zn30Zn
31Ga31Ga
32Ge32Ge
33As33As
34Se34Se35
Br35Br
36Kr36Kr
37Rb37Rb 38
Sr38Sr
39Y
39Y
40Zr40Zr
41Nb41Nb
42Mo42Mo
43Tc43Tc
44Ru44Ru
45Rh45Rh
Stop it stop it stop it!How many elements
ARE there?
Stop it stop it stop it!How many elements
ARE there?
The last natural one’s uranium.And we all know howstable THAT is. Not.
The last natural one’s uranium.And we all know howstable THAT is. Not. 92
U92U
The answer will be made clearer later on in this series of activities.
But as you might expect, you need very high temperatures and pressures indeed … such as when a star explodes.
You and ICarl Sagan once said: “We are all star stuff”.
He is absolutely right.
It is only within the cores of stars that any of the elements other than hydrogen are formed.
Everything (other than hydrogen) in your body (and the whole planet) was nucleosynthesised in the core of stars and in exploding stars.
Since the dust in molecular clouds must have also come from older stars, everything in your body may have actually been in a number of different stars at different times.
You are made of star stuff, and your atoms are very well-travelled indeed.
Hey, thanks for thecarbon and oxygenand nitrogen and ...
Hey, thanks for thecarbon and oxygenand nitrogen and ...
No problem :-) No problem :-)
Summary
This Activity has shown you how stars of different masses continue to evolve very slowly after joining the Zero Age Main Sequence.
The evolution of the star will be controlled mostly by its mass, because it is the mass which decides how, and if, there can be hydrostatic equilibrium within each layer of the star.
Image Credits
The Trapezium region in Orion: Michael Bessell (MSSSO). Copyright, reproduced with permission.
Eta Carinae: http://antwrp.gsfc.nasa.gov/apod/image/etacarinae_hst2.gif
RCW 38:
http://antwrp.gsfc.nasa.gov/apod/image/9812/RCW38_vlt_big.jpg
Now return to the Module home page, and read more about the lives of stars on the main
sequence in the Textbook Readings.
Hit the Esc key (escape) to return to the Module 8 Home Page
A note on scale
The mass of an object will depend on its three dimensions: height, width and thickness. These are multiplied (sometimes with a number thrown in) to give the volume of the object.
If you double the diameter of something like a star, you actually double it in all three directions.
Twice
as
thick
Twice
as
thick
Twice as wideTwice as wide
Tw
ice
as h
igh
Tw
ice
as h
igh
So the object has 2x2x2 = 8 times the volume, and therefore 8 times the mass. (We are assuming, just for now, that the stars have the same composition. This isn’t the case: a more massive star will have a denser core, for a start.)
Small change … in diameter onlyThis kind of thinking will tell you that, for 100 solar masses, you need a star with between roughly 4 to 5 times the diameter of the Sun.
Our SunOur Sun
4 times the diameter = 4x4x4 = 64 times
the volume
4 times the diameter = 4x4x4 = 64 times
the volume
5 times the diameter = 5x5x5 = 125 times
the volume
5 times the diameter = 5x5x5 = 125 times
the volume
To get 1/12 of a solar mass, you need a star with between 1/3 and 1/2 of the diameter of the Sun.
So relatively small differences in diameter can correspond to relatively large differences in mass!
Back to Activity
While fission occurs when nuclei split up into smaller particles, there is a type of nuclear interaction where the reverse happens.
Another type of “nuclear”
There are actually a number of different kinds of “nuclear” reaction, involving different forces, particles and energies.
This type of nuclear interaction is called
fusion.
Fusion
It is very difficult under Earth conditions to make fusion occur: the particles being fused often have the same electrostatic charge (positive, in the case of nuclei) and therefore repel each other very strongly.
So a cloud of gas has to be very compressed (or collapse a great deal under its own weight) before the high pressure and temperature can overcome this repulsion, and fusion can begin.
Electrostatic repulsion stops impact
… but high pressure and temperature
encourage impact
Fusion
When fusion does occur, it not only involves the formation of a new atom from several old ones, but there is also the release of some energy in the form of electromagnetic radiation (heat, light, x-rays and so on) and perhaps particles such as neutrinos, electrons etc.
electromagnetic radiation
electromagnetic radiation
particle
new nucleus
particle
FusionNinety percent of the time, fusion in the Sun involves hydrogen nuclei being fused to make helium:
Start with 4 protons under enormous
pressure and temperature
End up with a “normal” helium nucleus,
two gamma rays, two positrons and
two neutrinos
FusionHere is that process broken into its three steps:
1. Two protons fuse to make deuterium, releasing a positron
and a neutrino
2. The deuterium fuses with another proton to make
a light helium nucleusand a gamma ray
3. Two light helium nuclei fuse to make “normal”
helium, plus two protons
positron “positive electron”one positive charge
neutronlike a proton
but with no charge
gamma rayenergetic photon of
light, eg an Xray
neutrinono charge
and no mass
protonhydrogen nucleus
one positive charge
FusionHere are the symbols and equations used by physicists to show how the various particles and so on “add up” for this reaction:
Two hydrogen nuclei combine to make one
“heavy” hydrogen nucleus (also called deuterium).
A positron and a neutrino are emitted.
A hydrogen nucleus combines with a “heavy”
hydrogen nucleus to produce helium-3.
A gamma ray is emitted.
Two helium-3 nuclei
combine to make a
helium-4 nucleus.
Two hydrogen nuclei
are emitted.
FusionThis reaction starts with protons (bare hydrogen nuclei) and so is called the proton-proton chain.
61H+ 4He++ + 21H+ + 2e+ + 2 + 2
If you combine all of the equations for the entire chain, you find that six protons end up producing a helium nucleus, two positrons, two gamma rays and two neutrinos, with two left-over protons which fly off to start p-p fusion over again elsewhere.
[By the way, the positrons don’t just sit there. They fly off and combine with electrons,
but that’s another story.]
FusionHere it is in one diagram:
Energy productionNow, just for a moment remember why astronomers need to know about fusion and fission and nuclear reactions:
it is to work out how stars produce so much energy.
It turns out that if you compare the mass that you start with and the mass you end up with there is a difference …
Although there is an exchange of energy in most of the steps, it is the step where a gamma ray is emitted that is of most interest.
Energy production
… and that difference is exactly accounted for by one of the most widely-known and least-understood equations in physics:
E = mc2
According to this equation, energy (E) and mass (m) may be interchangeable: for example, in fission reactions and in fusion reactions like the proton-proton chain.
c is the speed of light in a vacuum: 3 x 108 ms-1.
Energy productionHere is that equation at work with respect to the proton-proton chain:
BEFORE: four protons
AFTER:helium nucleus
plus two positrons plus two neutrinos
… and two gamma rays
Initial total mass = 6.693 x 10-27 kg
Final total mass = 6.645 x 10-27 kg
Difference = 0.048 x 10-27 kg
… and according to E = mc2 this is equivalent to ...
Energy = 0.43 x 10-11 joules
… which is just the energy observed in the two gamma rays
Back to Activity
Periodic table of the elementsA scientist called Mendeleev found quite a while back that you could arrange elements according to their numbers of protons into a table so that certain properties were common on one side, and others on the other side.
1H1H
2He2
He
3Li3Li
4Be4
Be5B5B
6C6C
7N7N
8O8O
9F9F
10Ne10Ne
11Na11Na
12Mg12Mg
13Al13Al
14Si14Si
15P
15P
16S
16S
17Cl17Cl
18Ar18Ar
19K19K
20Ca20Ca
21Sc21Sc 22
Ti22Ti 23
V23V 24
Cr24Cr 25
Mn25Mn 26
Fe26Fe 27
Co27Co 28
Ni28Ni 29
Cu29Cu 30
Zn30Zn 31
Ga31Ga
Atomic number (number of protons)Atomic number (number of protons)
Symbol used for the elementSymbol used for the elementHey! Where are
you going?Hey! Where are
you going?
Look, it gets messy,and this isn’t a
chemistry lesson,so just accept thatthere are patterns,
okay?
Look, it gets messy,and this isn’t a
chemistry lesson,so just accept thatthere are patterns,
okay?
StabilityIt turns out that electrons, protons and so on are more stable if they are in pairs. They also like to be in groups of twice a perfect square.
The first few perfect squares are 1, 4 and 9 (that is, 12, 22 and 32).
Doubling these gives 2, 8, and 18.
That is why there are two elements in the first row and eight in each of the next two rows, with the row after that having 18 elements.
1H1H
2He2
He 22To be frank, I couldn’t
face lining up18 little squares ...
To be frank, I couldn’tface lining up
18 little squares ...
Fair enough!Fair enough!
3Li3Li
4Be4
Be5B5B
6C6C
7N7N
8O8O
9F9F
10Ne10Ne 88
11Na11Na
12Mg12Mg
13Al13Al
14Si14Si
15P
15P
16S
16S
17Cl17Cl
18Ar18Ar 88
19K19K
20Ca20Ca
21Sc21Sc
22Ti22Ti
23V
23V
24Cr24Cr
25Mn25Mn
26Fe26Fe
27Co27Co
28Ni28Ni
29Cu29Cu
30Zn30Zn
31Ga31Ga
Etc….Etc…. 1818
In the nucleusWhile chemistry is concerned with what electrons do in atoms, nuclear physics is concerned with what nuclei do. However protons and neutrons in the nucleus follow the same kinds of laws as the electrons in their shells outside. So you can use the periodic table in nuclear physics as well.
That’s a relief. I don’t want to have tomake up a NEW one!
That’s a relief. I don’t want to have tomake up a NEW one!
Stop complaining!Stop complaining!
1H1H
2He2
He 22
3Li3Li
4Be4
Be5B5B
6C6C
7N7N
8O8O
9F9F
10Ne10Ne 88
11Na11Na
12Mg12Mg
13Al13Al
14Si14Si
15P
15P
16S
16S
17Cl17Cl
18Ar18Ar 88
19K19K
20Ca20Ca
21Sc21Sc
22Ti22Ti
23V
23V
24Cr24Cr
25Mn25Mn
26Fe26Fe
27Co27Co
28Ni28Ni
29Cu29Cu
30Zn30Zn
31Ga31Ga
Etc….Etc…. 1818
Square dancingIn the nucleus, the main work of the neutrons is to stop the protons from squabbling amongst themselves because of their electrostatic repulsion.
It turns out that protons and neutrons are happiest when they are in bunches of four: two protons and two neutrons.Hey, would you like
to have a go at Helium?Hey, would you like
to have a go at Helium?
Why, that wouldbe lovely!
Why, that wouldbe lovely!
IsotopesNow, neutrons aren’t charged and don’t repel each other.
So you can get variable numbers of them in a nucleus and still have the same element.
For example, carbon (with 6 protons) can have 6 neutrons (12C), 7 neutrons (13C) or 8 neutrons (14C).
12C6 protons
6 neutrons
12C6 protons
6 neutrons
13C6 protons
7 neutrons
13C6 protons
7 neutrons
14C6 protons
8 neutrons
14C6 protons
8 neutrons
Shhhhh! Thisisn’t a nuclear
physics course!
Shhhhh! Thisisn’t a nuclear
physics course!
Which do you think would be the most stable of these?
12C, of course, becauseit’s like four heliums.
Which is the least stable?
12C, of course, becauseit’s like four heliums.
Which is the least stable?
StabilityThis is one of the reasons why iron (Fe) ends up at the end of a lot of nucleosynthesis.
Its protons form very happy groups in the 2, 8, 8, 8 pattern and most isotopes of iron have enough neutrons to stop them squabbling too much electrostatically.
6C6C
14Si14Si
22Ti22Ti
2He2
He
10Ne10Ne
18Ar18Ar
26Fe26Fe
4Be4
Be8O8O
12Mg12Mg
16S
16S
20Ca20Ca
24Cr24Cr
28Ni28Ni
1H1H
3Li3Li
5B5B
7N7N
9F9F
11Na11Na
13Al13Al
15P
15P
17Cl17Cl
19K19K
21Sc21Sc
23V
23V
25Mn25Mn
27Co27Co
29Cu29Cu
30Zn30Zn
31Ga31Ga
Etc….Etc….
22
88
88
Very comfy nucleusVery comfy nucleusQuite comfyQuite comfy
Sort of comfySort of comfy
But other elements are not so lucky … What about the rest?What about the rest?
Um … it gets awfullycomplicated …
Let’s not take thisany further right now?
PLEASE?
Um … it gets awfullycomplicated …
Let’s not take thisany further right now?
PLEASE?
Fine by me.Fine by me.
Back to Activity
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