Goal: To understand the lifetime of a star and how the mass of a star determines its lifetime Objectives: 1)To learn what defines a Main sequence star 2)To understand why Energy is important for a star 3)To examine the Cores or stars 4)To understand what determines the Lifetime of a star 5)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.