Goal: To understand the lifetime of a star and how the mass of a

star determines its lifetimeObjectives:

1) To learn what defines a Main sequence star2) To understand why Energy is important for a star

3) To examine the Cores or stars4) To understand what determines the Lifetime of a

star5) To see when the Beginning of the end is going to

occur

During break: Why does fusion create energy?

To prevent collapse

• Remember when we looked at the core of the sun that we saw that the sun held itself up with a combination of gas pressure and radiation pressure (light has energy)

• This was called “Hydrostatic Equilibrium”

Proton – Proton Chain

• Short answer: method by which a star converts protons (Hydrogen nuclei) to Helium nuclei (the electrons in the core of a star fly around on their own).

Proton – Proton Chain

• However it is a lot more complicated that I have made it seem.

• After all, how do we take 4 protons and make a helium atom when a helium atom has 2 protons and 2 neutrons?

Why don’t the atoms in this room fuse together?

Repulsion

• In the cores of stars all the nuclei have + charges.

• + charges repel other + charges.

• So, they won’t attract and fuse by accident.

• So, what do we need to be able to do it?

Energy

• It takes energy to overcome this repulsive force.

• Much like it takes energy to get up the stairs.

• The energy they have is measured by their temperature

Step one

• We take 2 protons in the core to the sun and try to slam them together.

• They get closer and closer.

• Here come the fireworks!

• And!

Step one

• We take 2 protons in the core to the sun and try to slam them together.

• They get closer and closer.

• Here come the fireworks!

• Nothing happens….

Quantum Mechanics!

• No, I will not do a lecture on Quantum.

• Just 1 basic principal: there is uncertainty in the position of each proton.

• In laymen’s terms that means that a proton is not just in a specific position, but has a small probability at being in a nearby position.

So,

• When 2 protons start to get close, there is a small probability they will actually be in the same spot.

• This is called quantum tunneling – basically tunneling through the repulsive barrier.

• This allows us to have fusion!

However,

• The probability of this tunneling is very small, and it depends very highly on how close they get.

• This means that how rapidly you fuse protons depends very highly on the temperature (and also on the density squared).

• Fusion in the proton – proton chain (sometimes call p-p chain) relies on temperature to the FORTH power!

Step 1 concluded

• So, eventually we get 2 protons to collide.• What do we get?• No, we don’t get a Helium atom with 2 protons

and no neutrons. Those don’t exist.• Another difficulty in the fusion process is that

you turn 2 protons into deuterium (which is hydrogen with a neutron in it) + stuff.

• So, that means a proton has to convert to a neutron. That is hard to do.

Step 2

• It would be easy to say 2 deuterium go to 1 helium.

• It would give you 2 protons and 2 neutrons.

• But, sadly, it does not work that way.

• Reason, there just is not enough deuterium.

Instead

• Deuterium fuses with what is the most common thing around, a proton.

• This creates Helium 3 (Helium which has a weight of 3; 2 from the 2 protons and the last from 1 neutron).

Step 3a

• 3a occurs 69% of the time in our sun.

• In time you will get some amount of Helium 3.

• If 2 of these fuse, then you get a Helium 4 and 2 protons.

Step 3b

• 31% step 3b occurs instead.

• In this case a Helium 3 fuses with a Helium 4 creating Beryllium 7.

• The Beryllium 7 combines with an electron (converts a proton into a neutron) to create Lithium 7.

• The Lithium 7 fuses with a proton to create 2 Helium 4 atoms.

Carbon – Nitrogen – Oxygen Cycle

• While the sun utilizes the p-p chain. Other stars use this (called hereafter the CNO cycle).

• Instead of fusing protons and protons we now fuse protons to carbon.

• Larger atom to fuse makes it a LOT harder

Charges

• Protons have 1 atomic charge.

• Carbon has 6 (6 protons).

• Therefore, it takes more energy, which means higher temperatures.

• This method depends on temperature to the 20TH power!!!

Why does fusion create energy?

• 4 protons have more mass than 1 Helium atom.

• So, when you fuse protons into helium, you loose mass.

• Mass is a form of energy.

• Once again, energy is always conserved!

• So, you gain energy (in forms of photons and neutrinos).

Other than the stuff our sun does now

• Stars on the main sequence slowly burn their fuel.

• While the do get a little brighter with time (10-50% over their lifetime), their outer temperature, radius, and brightness all stay approximately the same (well within a small range anyway).

Core

• Now lets examine different sizes of stars.

• Stars come in all sizes from 200 times the mass of our sun to 1% the mass of our sun.

Smallest stars

• The smallest stars are called Brown Dwarfs.

• These stars are between 1-8% of the mass of our sun and about the size of Jupiter.

• These stars are too small to fuse Hydrogen.

• Instead they fuse Deuterium into Helium.

Red Dwarfs

• Next up the stellar ladder are Red Dwarfs.• Red dwarfs are 8-40% the mass of the

sun.• Unlike the sun, the Red Dwarfs do not

have a Radiative Zone (a zone where matter does not move through).

• In fact, the entire star is convective (like a boiling pan of water).

• So, eventually, it will burn all the Hydrogen in the star to Helium.

continued

• Red Dwarfs are very dim compared to the sun.

• What does that tell you about the energy generated at the core of a Red Dwarf?

• A) there is less of it• B) it takes longer to get to the surface• C) the energy has a harder time escaping

from the star• D) tells you nothing

What does this tell you about the expected lifetime of a Red Dwarf?

• A) It is longer than our sun

• B) It is the same as our sun

• C) It is shorter than our sun

• D) Tells us nothing about its expected lifetime.

Yellow/Orange Dwarfs

• This is just a silly way of saying stars like our sun.

• So, starts like our sun.• They have Radiative Zones which

separate the core from the rest of the star (much like our Stratosphere keeps clouds in the Troposphere).

• The core is about 10% of the mass of the sun.

Larger Main Sequence Stars

• Here we have Blue stars.• Blue stars are always big. • They are very hot.• Their cores are very hot.• That means that even though they are bigger,

they use up their fuel a lot faster.• So, they don’t live very long.• A star stays on the main sequence for about:

10 Billion years / (its Mass in solar masses)2

• So, a star 10 time the mass of our sun will only be on the main sequence for 100 million years – they don’t live long.

Properties of stars

• Temperature: bigger star means higher temps both on surface and in the core.

• Lifetimes: Bigger stars have shorter lives.• Color: Big main sequence stars are blue.

Medium ones yellow/orange/white. Small ones are red.

• Brightness: Bigger means much brighter (Mass cubed).

• Size: More massive stars have bigger sizes (by factor of mass).

• Density: Oddly, bigger stars have LOWER densities! The biggest stars have an average density of our air.

Concept question

• If a star is fusing Helium into something else in its core then is it considered a Main Sequence Star?

• Suppose a star uses up all its Hydrogen in its core so only does fusion of Hydrogen to Helium in a shell outside of the core. Is it considered a Main Sequence Star?

However

• No matter what the size of star, with the exception of the Brown Dwarf, all fuse hydrogen into helium in the core (using either p-p chain or CNO cycle).

• Eventually each of them will run out of fuel.

• What happens next? Well, stay tuned. It all depends on the size of the star.

Conclusion

• Fusion is really hard even in the cores of stars• Fusion depends on Quantum Mechanics (or

Quantum tunneling) and very highly dependant on temperature

• Stars don’t change much on the main sequence over the course of their lifetime.

• Stars come in a wide range of masses (0.01 to 200 solar masses).

• Different massed stars have slightly different attributes, but all do the same thing – fuse protons into Helium.