Module : Activity: From Working for a living Life on the Main Sequence Swinburne Online Education...

Module :

Activity:

From Working for a living

Life on the Main Sequence

Swinburne Online Education Exploring Stars and the Milky Way

© Swinburne University of Technology

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

In the last 2 Activities 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).

The mathematical bitTheory 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. Why?

It’s because23 = 2x2x2= 8.

If you triple the mass of a star, you reduce its lifetime to 1/27! That’s because33 = 3x3x3 = 27.

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 awhile then, eh?

Sure have!What’s on telly?

How it works

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.

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.

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 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 varies with distance from the core (all the way to the edge = 1.0).

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

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

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

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:

61H+ 4He++ + 21H+ + 2e+ + 2 + 2Temperature required: at least 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.

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.



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




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).







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 the heck 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

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.

You and ICarl 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.

Hey, thanks for thecarbon and oxygenand nitrogen and ...

Hey, thanks for thecarbon and oxygenand nitrogen and ...

No problem :-) No problem :-)

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

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.

Back to Mass Matters

Our SunOur Sun

4 times the diameter = 4x4x4 = 64 times

the volume


the volume


the volume


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 Mass Matters

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 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.

electromagnetic radiation

electromagnetic radiation

particle

new nucleus

particle

Fusion 3Ninety 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 4Here 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 raye.g. light, heat, radio wave, xray or similar

neutrinono charge

and no mass

protonhydrogen nucleus

one positive charge

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:

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.

1H+ + 1H+ 2H+ + e+ +

1H+ + 2H+ 3He++ +

3He++ + 3He++ 4He++ + 1H+ + 1H+

Fusion 6This 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.]

Fusion 7Here it is in one diagram:

61H+ 4He++ + 2e+ + 2 + 2 + 21H+

Energy production 1Now, 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 2

… 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 production 3Here 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 the Fuel

Tank

Back to the Fuel

Tank

Periodic table of the elementsA 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.

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 todisgustingly

high T

Back todisgustingly

high T

Module : Activity: From Working for a living Life on the Main Sequence Swinburne Online Education...

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