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VI. Main sequence stars h"p://sgoodwin.staff.shef.ac.uk/phy111.html 0. The main sequence We saw that most stars lie on the main sequence, and there is a mass-luminosity relationship but there are also giants and white dwarfs… Why are most stars on the MS, but some not? Why are there giants and white dwarfs? What is happening in a star on the main sequence? 1. Energy generation We can age the Earth to about 4.5 Gyr from radiometric dating – so the Sun must be at least this old as well. The only process that could keep the Sun producing 3.8 x 1026 J s-1 for 4.5 Gyr (that’s 5x1041 J so far!) is nuclear fusion. We convert mass to energy from E=mc2 – and c is big, so a small amount of mass turns into a very large amount of energy. We saw the Sun is about 75% H and 25% He – the easiest way to make energy with this mixture is fusing H to He. 1. Energy generation To fuse H to He we need very high temperatures (T) and pressures (P). High T means the nuclei move very fast, and high P means they meet each other often. The higher the T and P, the more reactions there are and the more energy is generated. The central T and P depend on stellar mass – the more massive a star the higher the T and P. If the mass is less than about 0.1M, the central T and P never get high enough to fuse H. 1. The pp-chain The way most stars fuse H to He is via the pp-chain. The first step is to make deuterium (a proton+neutron) 1H + 1H 2H + e+ + ν + energy where e+ is a positron and ν is a neutrino (the positron annihilates with an electron and makes energy). Then another 1H is added to make 3He 2H + 1H 3He + energy Then two 3He meet to make 4He and 2 protons 3He + 3He 4He + 21H + energy 1. The pp-chain There are slightly different ways of doing this, but this is the most common in the Sun. In massive (ie. hotter) stars there is the CNO cycle that involves C, N and O in the fusion process – but we’ll ignore that. The final 4He nucleus has 0.7% less mass than the 4 1H nuclei – this is released as energy: about 4x10-12 J. So to make the ~4x1026 J the Sun releases every second needs about 1038 reactions per second! 1. Solar neutrinos We are confident this is what is happening in the Sun because we can estimate the number of neutrinos that must be being produced every second (1038-ish). Neutrinos hardly interact with anything – most pass right through the Sun and Earth and never notice them. But a tiny fraction do interact with large underground detectors in exactly the right numbers. [You might read about the Solar Neutrino Problem – we see only 1/3rd of the neutrinos we first expected, this is because neutrinos ‘change flavour’ as they travel – it isn’t a problem anymore.] 2. Lifetimes of stars We can estimate the length of time the Sun can continue producing energy this way. The core where reactions happen is about 10% of the mass of the Sun = (0.1)x(2x1030 kg). We can convert about 0.7% of this mass into energy which from E=mc2 is 1x1044 J = (0.007 x 2x1029 kg)(3x108 m s-1)2 Divide by the luminosity 4x1026 W and we get a main sequence lifetime of 4x1017 s, or about 10 billion years (10Gyr). 2. Lifetimes of stars More massive stars have more fuel, but burn it much more rapidly. Low-mass stars burn at a very slow rate. A 10 M star has L=3000 L – so 10x more fuel, but burnt 3000x faster lifetime of about 50 Myr. A 0.1 M star has L=3x10-4 L – 10x less fuel, but burnt 3000x slower lifetime of 30 trillion years (30 000 Gyr). So main sequence lifetimes are a very strong function of mass. 3. Stellar structure Stars have the particular radii they do because they are in ‘hydrostatic equilibrium’. Gravity attempts to make a star smaller, pressure attempts to make it larger. The vast majority of the time these two forces are in equilibrium and the star remains stable. Pressure is mainly due to the thermal energy of the gas/ plasma (there can be radiation pressure as well). [Because of something called the virial theorem the balance is always such that the kinetic energy in the pressure is exactly half the potential energy due to gravity.] 3. Stellar structure The structure of stars is dominated by having an energy source at their centres. Stars must radiate away energy at the rate they produce it (otherwise they would shrink or grow as their thermal energy changed). So the energy from the core must pass through the star in one of two ways: Radiation Convection 3. Stellar structure How energy is transported depends on the opacity of the gas – a measure of how easily radiation can pass through something: Glass and air have very low opacity. Wood and steel have very high opacity. It does depend on wavelength – our atmospheric windows depend on the opacity of the atmosphere – it doesn’t let much UV or sub-mm through, but lots of visible or radio. 3. Stellar structure What sets opacity can be horribly complicated, but stars can generally be divided into two zones – the core and envelope. How heat is transported depends on mass (it depends a lot on the rate of energy generation) 3. Stellar structure A star like the Sun has a radiative core and a convective envelope – we see the convection cells on the surface of the Sun. Sunspots are cooler regions where magnetic fields inhibit the convection and don’t allow the cooled material to fall back down. Summary Main sequence stars generate their energy through HHe fusion in their cores. For most stars this is via the pp-‐chain. Stellar lifeCmes are a strong funcCon of mass (because luminosity is). Massive stars live only Myr, Solar-‐type stars about 10 Gyr, and low-‐mass stars for trillions of years. The structure of stars is set by a balance between (thermal) pressure and gravity, and how the star is able to transport energy (radiaCve or convecCve). Key points To describe the basics of nuclear fusion and the pp-‐chain. To be able to esCmate the lifeCme of a star of a given mass. Understand that structure depends on energy generaCon and energy transport. Quickies What is the main sequence lifeCme of a 5Msun star? Roughly what fracCon of a star’s mass is turned into energy on the main sequence? Very simply, what is the structure of a Solar mass star? Very simply, what is opacity? What fracCon of the mass is lost in going from 4 protons to a 4He nucleus? Notes Opacity is very important, but in reality really quite complex. Opacity depends on composiCon, temperature, and density and will change with the wavelength of the light trying to pass through the material. It turns-‐out that opacity is a very strong funcCon of temperature. At low temperatures everything is neutral (or even molecular) and the main source of opacity are heavy elements (more electrons, more energy levels, and so more absorpCon). As the temperature increases, heavy elements are ionised and create free electrons. These electrons can bind with H to make H-‐ ions which have a very high opacity (you destroy them with a photon and then they recombine) – the more H-‐ the higher the opacity and opacity increases roughly as T4. But at about 50000K H-‐ starts being destroyed and so the opacity rapidly decreases with increasing temperature (about T-‐4). Thus a mix of thermodynamics and radiaCon transport together with ionisaCon and quantum mechanics determine what happens at different layers in a star – high opacity=convecCon, and low opacity=radiaCon.