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

1. Goal: To understand the lifetime of a star and how the mass of a star determines its lifetime Objectives: To learn what defines a Main sequence star To understand why Energy is important for a star To examine the Cores or stars To understand what determines the Lifetime of a star To see when the Beginning of the end is going to occur During break: Why does fusion create energy?

2. 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”

3. 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).

4. 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?

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

6. 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?

7. 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

8. 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!

9. 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….

10. 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.

11. 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!

12. 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!

13. 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.

14. 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.

15. 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).

16. 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.

17. 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.

18. 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

19. 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!!!

20. 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).

21. 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).

22. 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.

23. 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.

24. 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.

25. 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

26. 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.

27. 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.

28. 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.

29. 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.

30. 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?

31. 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.

32. 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.