goal: to understand the lifetime of a star and how the mass of a star determines its lifetime...
TRANSCRIPT
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.