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Swinburne Online Education Exploring Stars and the Milky Way
Module :
Life on the Main Sequence
Activity:
From Working
© Swinburne University of Technology
for a living
Summary:
In 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
• some of the nuclear reactions which occur in stars on
the main sequence
Luminosity
too massive
In the last 2 Activities we looked at
• how stars join the main sequence,
• how the time taken depends
on their mass, and
• what happens if they are too massive
or not massive enough
to join the main sequence.
molecular cloud
not massive enough
Temperature
Mass matters
We can actually work out what
is “too massive” and “not
massive 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 onetwelfth of the Sun is not massive
enough.
Our Sun
Too massive
Let’s
talk size
Not massive enough
More fuel
Faster or slower?
If a star is more massive than our Sun, will it stay
on the main sequence for a longer time?
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)
Shorter
Longer
I think that a
I think that a massive
massive star will
star will last longer
not last as long
than the Sun because
as the Sun as its
there is a lot more fuel.
fuel will burn a
lot faster.
Much hotter
Same
I think that there wouldn’t
be much difference: these
effects would sort of
balance each other out.
Unfortunately, Big = fast
I’m sorry: the answer is that the more massive
stars burn out a lot faster.
More mass
More p and T
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.
Faster fusion
Shorter life
OKAY
I’ll try to remember that …
YES! Big = fast
You are right! The more massive stars do
burn out a lot faster.
More mass
More p and T
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.
CONGRATULATIONS!
Thank you!
I do my best, you know...
Faster fusion
Shorter life
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.
Wheee!
YOW!
Ooof!Core of our Sun
er ...
Core of smaller star
How long have we got?
30 million years
to reach ZAMS*
Luminosity
A G2 star such as our Sun
5000 million years
is expected to spend
here so far
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 another 5000 million
years to go
quite a while.
Temperature
* 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).
0.4 solar masses
M class
200,000 million years
1 solar mass
G2 class
10,000 million years
3.3 solar masses
A class
500 million years
40 solar masses
05 class
1 million years
Theory predicts that the time a
star spends on the main
sequence will be inversely
proportional to the cube of the
star’s mass.
That means that if you double
the mass of a star, you get 1/8
of the lifetime. Why?
It’s because
23 = 2x2x2= 8.
If you triple the mass of a star,
you reduce its lifetime to 1/27!
That’s because
33 = 3x3x3 = 27.
Life on main sequence
The mathematical bit
Lifetime depends
on 1/mass3
Mass of star
Hydrostatic whatsit
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 a
while then, eh?
Sure have!
What’s on telly?
How it works
Self-gravity
pulls in
We 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.)
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.
Internal pressure
pushes out
If self-gravity wins,
the shell contracts
If 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.
This is Eta Carinae, where
in at least one shell, on at
least one occasion,
pressure won.
In other stars, self-gravity
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
P-p chain, p-p chain,
Nothin’ all day but
energy (light, heat and so on)
p-p chain …
when hydrogen is fused to
become helium in the core of
the star.
However, when the star is a
little more mature, there are
other options … and they
Remind
depend on temperature.
me about
p-p
Stellar temperature
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.
PE
Surface:
KE
lots of PE
not much KE
PE PE
PE
PE
Core:
not much PE
lots of KE
KE
KE KE
KE
PE
KE
Our Sun, for example
The average kinetic energy of atoms, molecules and other particles has
another name: temperature.
Here is a chart of how the temperature of the Sun varies with distance
from the core (all the way to the edge = 1.0).
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!
Core:
about 15,500,000 K
18
16
14
12
Surface:
about 6,000 K
10
8
6
4
2
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
O
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.
B
A
F
G
K
So, forget about stellar class and surface temperature
for a moment, and let’s consider only core temperature.
M
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:
61H+  4He++ + 21H+ + 2e+ + 2n + 2
Temperature required: at least 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.
p-p cycle
Core: 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
CNO cycle
the CNO cycle to dominate.
Core: 20 million K
p-p cycle
Core: 8 million K
The CNO cycle
Here 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.
e+
e+
14N
+ p+ turns into 15O.
15O sheds a positron to become 15N.
15N
+ p+ splits into 12C and 4He.
During many of these steps, energy and/or
neutrinos are released.
15
13O
14
12
N
C
4He
High temperature fuel
The next important possibility is called
the triple-alpha reaction.
triple-alpha reaction
Three alpha particles (helium nuclei)
Core: 100 million K
fuse to form one carbon nucleus, plus
energy, neutrinos and so on.
Temperature required: at least 100 million K.
CNO cycle
Core: 20 million K
KAPOW!
12C
p-p cycle
Core: 8 million K
carbon burning
Core: 600 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).
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.
triple-alpha reaction
Core: 100 million K
“Periodic
table”?
CNO cycle
Core: 20 million K
p-p cycle
Core: 8 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 the heck did all
the heavier elements come from?
As you might expect, you need very high
temperatures and pressures indeed … such as when
a star explodes. Heavier elements are created in
supernovae, the violent, explosive end of many
medium-mass stars.
Stop it stop it stop it!
How many elements
ARE there?
The last natural one’s uranium.
And we all know how
92
stable THAT is. Not.
U
36
Kr
45
Rh
44
Ru
43
Tc
37
Rb 38
42
Mo
Sr
26
Fe
27
Co
29
Cu
34
35 Se
Br
39
41
Y
Nb 40
Zr
28
Ni
30
Zn
33
As
32
Ge
31
Ga
You and I
Carl Sagan once said: “We are all star stuff”.
He is absolutely right.
It is only within stars that any of the elements
other than hydrogen and helium 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.
No problem :-)
Hey, thanks for the
carbon and oxygen
and nitrogen and ...
This Activity
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: Credit J. Morse (U. Colorado), K. Davidson (U.
Minnesota) et al., WFPC2, HST, NASA
http://antwrp.gsfc.nasa.gov/apod/ap980816.html
Hit the Esc key (escape)
to return to the Index Page
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.
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.)
Twice as high
A note on scale
Twice as wide
Small change … in diameter only
This 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.
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!
Our Sun
4 times the diameter =
4x4x4 = 64 times
the volume
5 times the diameter =
5x5x5 = 125 times
the volume
Back to
Mass
Matters
Back to
Mass
Matters
Another type of “nuclear”
There are actually a number of different kinds of
“nuclear” reaction, involving different forces, particles
and energies.
While fission occurs when nuclei split up into smaller
particles, there is a type of nuclear interaction where the
reverse happens.
This type of nuclear
interaction is called
fusion.
Fusion 1
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 2
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.
particle
new
nucleus
electromagnetic
radiation
electromagnetic
radiation
particle
Fusion 3
Ninety 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
Fusion 4
Here 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 nucleus
and a gamma ray
3. Two light helium nuclei
fuse to make “normal”
helium, plus two protons
proton
neutron
positron
neutrino
gamma ray
hydrogen nucleus
one positive charge
like a proton
but with no charge
“positive electron”
one positive charge
no charge
and no mass
e.g. light, heat, radio
wave, xray or similar
Fusion 5
Here are the symbols and equations used
by physicists to show how the various
particles and so on “add up” for this
reaction:
1H+
+ 1H+  2H+ + e+ + n
1H+
+ 2H+  3He++ + 
3He++
+ 3He++  4He++ + 1H+ + 1H+
Two
Two
A hydrogen
hydrogen
helium-3
nucleus
nuclei
nuclei
combines
combine
totomake
a “heavy”
one
combinewith
make
a
“heavy”
hydrogen
hydrogen
nucleus
nucleus
to
helium-4
nucleus.
(also
produce
called helium-3.
deuterium).
Two hydrogen nuclei
AA positron
gamma ray
andisa emitted.
neutrino
are
emitted.
are emitted.
Fusion 6
This reaction starts with protons (bare hydrogen nuclei)
and so is called the proton-proton chain.
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.
61H+  4He++ + 21H+ + 2e+ + 2 + 2n
[By the way, the positrons don’t just sit there.
They fly off and combine with electrons,
but that’s another story.]
Fusion 7
Here it is in one diagram:
61H+  4He++ + 2e+ + 2n + 2 + 21H+
Energy production 1
Now, 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.
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.
It turns out that if you compare the mass that you start with
and the mass you end up with there is a difference …
Energy production 2
… and that difference is exactly accounted for by one of
the most widely-known and least-understood equations in
physics:
E=
2
mc
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 production 3
Here is that equation at work with respect to the protonproton chain:
BEFORE:
four protons
Initial total mass = 6.693 x 10-27 kg
Final total mass = 6.645 x 10-27 kg
AFTER:
helium nucleus
plus two positrons
plus two neutrinos
Difference = 0.048 x 10-27 kg
… and according to E = mc2
this is equivalent to ...
… and two gamma rays
Energy = 0.43 x 10-11 joules
Back to
the Fuel
Tank
… which is just the energy observed
in the two gamma rays
Back to
the Fuel
Tank
Periodic table of the elements
A bloke 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.
1
H
2
Atomic number (number of protons)
Symbol used for the element He
3
Li
4
Be
5
B
6
C
7
N
8
O
9
F
10
Ne
11
Na
12
Mg
13
Al
14
Si
15
P
16
S
17
Cl
18
Ar
19
K
20
Ca
21
Sc
22
Ti
23
V
24
Cr
25
Mn
Hey! Where are
you going?
Look, it gets messy,
and this isn’t a
chemistry lesson,
so just accept that
there are patterns,
okay?
26
Fe
27
Co
28
Ni
29
30
Stability
It 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.
1
H
2
He
2
8
3
Li
4
Be
5
B
6
C
7
N
8
O
9
F
10
Ne
11
Na
12
Mg
13
Al
14
Si
15
P
16
S
17
Cl
18
Ar
8
19
K
20
Ca
21
Sc
22
Ti
23
V
24
Cr
25
Mn
26
Fe
27
Co
To be frank, I couldn’t
face lining up
18 little squares ...
Fair enough!
28
Ni
29
Cu
30
Zn
31
Ga
Etc
….
18
In the nucleus
While 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.
1
H
2
He
2
8
3
Li
4
Be
5
B
6
C
7
N
8
O
9
F
10
Ne
11
Na
12
Mg
13
Al
14
Si
15
P
16
S
17
Cl
18
Ar
8
19
K
20
Ca
21
Sc
22
Ti
23
V
24
Cr
25
Mn
26
Fe
27
Co
That’s a relief.
I don’t want to have to
make up a NEW one!
Stop complaining!
28
Ni
29
Cu
30
Zn
31
Ga
Etc
….
18
Square dancing
In the nucleus, the main work of the neutrons is to stop the protons
from squabbling amongst themselves because of their electrostatic
repulsion.
Hey,
would you
It turns out that protons and
neutrons
arelike
happiest when they are in
to have
a go
at neutrons.
Helium?
bunches of four: two protons
and
two
Why, that would
be lovely!
Isotopes
Now, 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.
12C, of course,
For example, carbon (with 6 protons) can have 6 neutrons
(12C),because
7
it’s like four heliums.
neutrons (13C) or 8 neutrons (14C).
Which is the least stable?
Which do you think would be the most stable of these?
12C
13C
6 protons
6 neutrons
6 protons
7 neutrons
Shhhhh! This
6 protons isn’t a nuclear
8 neutrons physics course!
14C
Stability
This 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.
What about the rest?
But other elements are not so lucky …
Quite comfy
1
H
2
He
2
3
Li
4
Be
5
B
6
C
7
N
8
O
9
F
10
Ne
8
11
Na
12
Mg
13
Al
14
Si
15
P
16
S
17
Cl
18
Ar
8
19
K
20
Ca
21
Sc
22
Ti
23
V
24
Cr
25
Mn
26
Fe
27
Co
Very comfy nucleus
Um … it gets awfully
complicated …
Let’s not take this
any further right now?
Sort of comfy
PLEASE?
28
Ni
29
30
31 Etc
Fine
by
me.
Cu Zn Ga ….Back to
disgustingly
high T
Back to
disgustingly
high T