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Swinburne Online Education Exploring Stars and the Milky Way Module : Life on the Main Sequence Activity: From Working © Swinburne University of Technology for a living Summary: In this Activity you will learn about • the time a star spends on the main sequence • how this time depends almost entirely on the mass of the star • some of the nuclear reactions which occur in stars on the main sequence Luminosity too massive In the last 2 Activities we looked at • how stars join the main sequence, • how the time taken depends on their mass, and • what happens if they are too massive or not massive enough to join the main sequence. molecular cloud not massive enough Temperature Mass matters We can actually work out what is “too massive” and “not massive enough” because we can work out the outwards pressure in a hot gas, and the (inwards) gravitational force. It turns out that anything more massive than 100 Suns is too massive, and anything lighter than onetwelfth of the Sun is not massive enough. Our Sun Too massive Let’s talk size Not massive enough More fuel Faster or slower? If a star is more massive than our Sun, will it stay on the main sequence for a longer time? It has a lot more fuel to “burn”. But on the other hand, that fuel (in the core) will be at a much higher temperature and pressure. What do YOU think? (click on one red word) Shorter Longer I think that a I think that a massive massive star will star will last longer not last as long than the Sun because as the Sun as its there is a lot more fuel. fuel will burn a lot faster. Much hotter Same I think that there wouldn’t be much difference: these effects would sort of balance each other out. Unfortunately, Big = fast I’m sorry: the answer is that the more massive stars burn out a lot faster. More mass More p and T The more mass there is in a star, the more pressure and temperature there will be in its core and surrounding layers. That will make the fusion of hydrogen in the core go faster and the star will be lot more luminous. So the star will run low on hydrogen a lot more quickly. Faster fusion Shorter life OKAY I’ll try to remember that … YES! Big = fast You are right! The more massive stars do burn out a lot faster. More mass More p and T The more mass there is in a star, the more pressure and temperature there will be in its core and surrounding layers. That will make the fusion of hydrogen in the core go faster and the star will be lot more luminous. So the star will run low on hydrogen a lot more quickly. CONGRATULATIONS! Thank you! I do my best, you know... Faster fusion Shorter life Small = slow At the other end of the scale, a small new star will not have a very dense, hot core, and the fusion of hydrogen will then go a lot more slowly. Wheee! YOW! Ooof!Core of our Sun er ... Core of smaller star How long have we got? 30 million years to reach ZAMS* Luminosity A G2 star such as our Sun 5000 million years is expected to spend here so far about 10 billion years altogether on the main sequence. Since it’s at the 5 billion mark these days there’s nothing to worry about for another 5000 million years to go quite a while. Temperature * ZAMS is the Zero Age Main Sequence. Other types of stars Here is a table to show you how the mass of a star can affect the time it spends on the main sequence (1 billion = 1,000 million). 0.4 solar masses M class 200,000 million years 1 solar mass G2 class 10,000 million years 3.3 solar masses A class 500 million years 40 solar masses 05 class 1 million years Theory predicts that the time a star spends on the main sequence will be inversely proportional to the cube of the star’s mass. That means that if you double the mass of a star, you get 1/8 of the lifetime. Why? It’s because 23 = 2x2x2= 8. If you triple the mass of a star, you reduce its lifetime to 1/27! That’s because 33 = 3x3x3 = 27. Life on main sequence The mathematical bit Lifetime depends on 1/mass3 Mass of star Hydrostatic whatsit Our Sun took only 30 million years to reach the main sequence, but now it’s there it’s going to be there for a total of 10,000 million years. So once on the main sequence, stars hardly change at all: they’re in hydrostatic equilibrium. Hydro means “fluid”, static means “not changing”, and equilibrium means that there is a balance between two or more opposing effects. Settled in for a while then, eh? Sure have! What’s on telly? How it works Self-gravity pulls in We talked a bit about hydrostatic equilibrium early in this course, when studying the Sun. But here’s a reminder for you about how self-gravity and pressure govern whether a star shrinks, expands or stays stable. (Self-gravity is gravity from within, not from something outside.) We have to imagine a star consisting of layers or shells, like the skins of an onion, and think about what happens in just one layer. Internal pressure pushes out If self-gravity wins, the shell contracts If pressure wins, the shell expands Different layers This picture of a star is useful in that different layers of a star can react in different ways. For instance, in some stars the core shrinks, making it a lot hotter. However, this heats up the outer layers, which increases the pressure inside them, and that makes them expand. Whether a star expands or contracts depends on that balance between self-gravity and pressure, and thus on the mass of the star again. Stable members only If the balance changes so that pressure and self-gravity no longer balance in the layers of the star, and the layers begin to expand or contract quickly, then the star has left the main sequence. This is Eta Carinae, where in at least one shell, on at least one occasion, pressure won. In other stars, self-gravity wins. The fuel tank of a star A star is formed from many kinds of gas and dust, but as with most things in this universe it starts off composed mostly of hydrogen. The young star produces P-p chain, p-p chain, Nothin’ all day but energy (light, heat and so on) p-p chain … when hydrogen is fused to become helium in the core of the star. However, when the star is a little more mature, there are other options … and they Remind depend on temperature. me about p-p Stellar temperature When we have mentioned the temperature of a star so far, we have meant the surface temperature. This is very different to the temperature in the core! There is always a balance between gravitational potential energy (PE) and kinetic energy (KE). If a particle moves between the surface of a star and its core, these things both change but their total remains the same. That is, until the particle collides with others and shares its kinetic energy around. PE Surface: KE lots of PE not much KE PE PE PE PE Core: not much PE lots of KE KE KE KE KE PE KE Our Sun, for example The average kinetic energy of atoms, molecules and other particles has another name: temperature. Here is a chart of how the temperature of the Sun varies with distance from the core (all the way to the edge = 1.0). Just about any star or planet is usually much hotter in the core than on the surface. This is a left-over effect of core heating during formation, when particles with lots of PE turned it into KE. The core of our own Earth is still at 5000 K! Core: about 15,500,000 K 18 16 14 12 Surface: about 6,000 K 10 8 6 4 2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 O Core, surface and stellar class When astronomers talk about a star’s temperature, do we mean the surface temperature, or the core temperature? There is a heck of a difference! Because it is almost always emission (or absorption) from the atmosphere of stars that we detect on Earth, we use that to classify stars. So we usually mean the surface temperature. But surface temperature has little to do with fuelling stars, as the nucleosynthesis - the making of new nuclei - takes place in the core and not on the surface. B A F G K So, forget about stellar class and surface temperature for a moment, and let’s consider only core temperature. M Low Temperature fuel During the p-p cycle, hydrogen is converted to helium. Six protons (hydrogen nuclei) turn into a helium nucleus, spitting out two protons, two positrons, two neutrinos and two gamma rays in the process. It’s written like this: 61H+ 4He++ + 21H+ + 2e+ + 2n + 2 Temperature required: at least 8 million K. That’s not low-temperature to us humans, but in terms of stellar cores it’s pretty miserable. It is the absolute minimum temperature at which fusion can drive a star. p-p cycle Core: 8 million K Medium temperature fuel If a star has enough mass, its core pressure and temperature will be enough for another nuclear reaction to happen strongly: the conversion of hydrogen to helium using other elements as catalysts and intermediaries carbon, nitrogen and oxygen. This is called the CNO cycle. Temperature required: over 20 million K for CNO cycle the CNO cycle to dominate. Core: 20 million K p-p cycle Core: 8 million K The CNO cycle Here are the six steps of the carbon-nitrogen-oxygen cycle, in which a friendly carbon nucleus gathers four protons, turns two of them into neutrons, then releases them as a helium nucleus. 12C + p+ turns into 13N 13N sheds a positron to become 13C. 13C + p+ turns into 14N. e+ e+ 14N + p+ turns into 15O. 15O sheds a positron to become 15N. 15N + p+ splits into 12C and 4He. During many of these steps, energy and/or neutrinos are released. 15 13O 14 12 N C 4He High temperature fuel The next important possibility is called the triple-alpha reaction. triple-alpha reaction Three alpha particles (helium nuclei) Core: 100 million K fuse to form one carbon nucleus, plus energy, neutrinos and so on. Temperature required: at least 100 million K. CNO cycle Core: 20 million K KAPOW! 12C p-p cycle Core: 8 million K carbon burning Core: 600 million K Disgustingly high temperature If you have really, really high temperature and pressure, then you can have all other kinds of nucleosynthesis. When carbon and other heavier elements start to “burn” (that is, fuse), the products include elements up to iron (Fe, number 26 in the periodic table of the elements). There’s quite a lot of iron around that was formed this way. Our own Earth has a core of iron nearly 7000 km across! Temperature required: 600 million K. triple-alpha reaction Core: 100 million K “Periodic table”? CNO cycle Core: 20 million K p-p cycle Core: 8 million K Where do the rest come from, then? If the cores of stars can only produce elements up to iron in the periodic table, then where the heck did all the heavier elements come from? As you might expect, you need very high temperatures and pressures indeed … such as when a star explodes. Heavier elements are created in supernovae, the violent, explosive end of many medium-mass stars. Stop it stop it stop it! How many elements ARE there? The last natural one’s uranium. And we all know how 92 stable THAT is. Not. U 36 Kr 45 Rh 44 Ru 43 Tc 37 Rb 38 42 Mo Sr 26 Fe 27 Co 29 Cu 34 35 Se Br 39 41 Y Nb 40 Zr 28 Ni 30 Zn 33 As 32 Ge 31 Ga You and I Carl Sagan once said: “We are all star stuff”. He is absolutely right. It is only within stars that any of the elements other than hydrogen and helium are formed. Everything (other than hydrogen) in your body (and the whole planet) was nucleosynthesised in the core of stars and in exploding stars. Since the dust in molecular clouds must have also come from older stars, everything in your body may have actually been in a number of different stars at different times. You are made of star stuff, and your atoms are very well-travelled indeed. No problem :-) Hey, thanks for the carbon and oxygen and nitrogen and ... This Activity This Activity has shown you how stars of different masses continue to evolve very slowly after joining the Zero-Age Main Sequence. The evolution of the star will be controlled mostly by its mass, because it is the mass which decides how, and if, there can be hydrostatic equilibrium within each layer of the star. Image Credits The Trapezium region in Orion: Michael Bessell (MSSSO). Copyright, reproduced with permission. Eta Carinae: Credit J. Morse (U. Colorado), K. Davidson (U. Minnesota) et al., WFPC2, HST, NASA http://antwrp.gsfc.nasa.gov/apod/ap980816.html Hit the Esc key (escape) to return to the Index Page The mass of an object will depend on its three dimensions: height, width and thickness. These are multiplied (sometimes with a number thrown in) to give the volume of the object. If you double the diameter of something like a star, you actually double it in all three directions. So the object has 2x2x2 = 8 times the volume, and therefore 8 times the mass. (We are assuming, just for now, that the stars have the same composition. This isn’t the case: a more massive star will have a denser core, for a start.) Twice as high A note on scale Twice as wide Small change … in diameter only This kind of thinking will tell you that, for 100 solar masses, you need a star with between roughly 4 to 5 times the diameter of the Sun. To get 1/12 of a solar mass, you need a star with between 1/3 and 1/2 of the diameter of the Sun. So relatively small differences in diameter can correspond to relatively large differences in mass! Our Sun 4 times the diameter = 4x4x4 = 64 times the volume 5 times the diameter = 5x5x5 = 125 times the volume Back to Mass Matters Back to Mass Matters Another type of “nuclear” There are actually a number of different kinds of “nuclear” reaction, involving different forces, particles and energies. While fission occurs when nuclei split up into smaller particles, there is a type of nuclear interaction where the reverse happens. This type of nuclear interaction is called fusion. Fusion 1 It is very difficult under Earth conditions to make fusion occur: the particles being fused often have the same electrostatic charge (positive, in the case of nuclei) and therefore repel each other very strongly. So a cloud of gas has to be very compressed (or collapse a great deal under its own weight) before the high pressure and temperature can overcome this repulsion, and fusion can begin. Electrostatic repulsion stops impact … but high pressure and temperature encourage impact Fusion 2 When fusion does occur, it not only involves the formation of a new atom from several old ones, but there is also the release of some energy in the form of electromagnetic radiation (heat, light, x-rays and so on) and perhaps particles such as neutrinos, electrons etc. particle new nucleus electromagnetic radiation electromagnetic radiation particle Fusion 3 Ninety percent of the time, fusion in the Sun involves hydrogen nuclei being fused to make helium: Start with 4 protons under enormous pressure and temperature End up with a “normal” helium nucleus, two gamma rays, two positrons and two neutrinos Fusion 4 Here is that process broken into its three steps: 1. Two protons fuse to make deuterium, releasing a positron and a neutrino 2. The deuterium fuses with another proton to make a light helium nucleus and a gamma ray 3. Two light helium nuclei fuse to make “normal” helium, plus two protons proton neutron positron neutrino gamma ray hydrogen nucleus one positive charge like a proton but with no charge “positive electron” one positive charge no charge and no mass e.g. light, heat, radio wave, xray or similar Fusion 5 Here are the symbols and equations used by physicists to show how the various particles and so on “add up” for this reaction: 1H+ + 1H+ 2H+ + e+ + n 1H+ + 2H+ 3He++ + 3He++ + 3He++ 4He++ + 1H+ + 1H+ Two Two A hydrogen hydrogen helium-3 nucleus nuclei nuclei combines combine totomake a “heavy” one combinewith make a “heavy” hydrogen hydrogen nucleus nucleus to helium-4 nucleus. (also produce called helium-3. deuterium). Two hydrogen nuclei AA positron gamma ray andisa emitted. neutrino are emitted. are emitted. Fusion 6 This reaction starts with protons (bare hydrogen nuclei) and so is called the proton-proton chain. If you combine all of the equations for the entire chain, you find that six protons end up producing a helium nucleus, two positrons, two gamma rays and two neutrinos, with two left-over protons which fly off to start p-p fusion over again elsewhere. 61H+ 4He++ + 21H+ + 2e+ + 2 + 2n [By the way, the positrons don’t just sit there. They fly off and combine with electrons, but that’s another story.] Fusion 7 Here it is in one diagram: 61H+ 4He++ + 2e+ + 2n + 2 + 21H+ Energy production 1 Now, just for a moment remember why astronomers need to know about fusion and fission and nuclear reactions: it is to work out how stars produce so much energy. Although there is an exchange of energy in most of the steps, it is the step where a gamma ray is emitted that is of most interest. It turns out that if you compare the mass that you start with and the mass you end up with there is a difference … Energy production 2 … and that difference is exactly accounted for by one of the most widely-known and least-understood equations in physics: E= 2 mc According to this equation, energy (E) and mass (m) may be interchangeable: for example, in fission reactions and in fusion reactions like the proton-proton chain. c is the speed of light in a vacuum: 3 x 108 ms-1. Energy production 3 Here is that equation at work with respect to the protonproton chain: BEFORE: four protons Initial total mass = 6.693 x 10-27 kg Final total mass = 6.645 x 10-27 kg AFTER: helium nucleus plus two positrons plus two neutrinos Difference = 0.048 x 10-27 kg … and according to E = mc2 this is equivalent to ... … and two gamma rays Energy = 0.43 x 10-11 joules Back to the Fuel Tank … which is just the energy observed in the two gamma rays Back to the Fuel Tank Periodic table of the elements A bloke called Mendeleev found quite a while back that you could arrange elements according to their numbers of protons into a table so that certain properties were common on one side, and others on the other side. 1 H 2 Atomic number (number of protons) Symbol used for the element He 3 Li 4 Be 5 B 6 C 7 N 8 O 9 F 10 Ne 11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 19 K 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn Hey! Where are you going? Look, it gets messy, and this isn’t a chemistry lesson, so just accept that there are patterns, okay? 26 Fe 27 Co 28 Ni 29 30 Stability It turns out that electrons, protons and so on are more stable if they are in pairs. They also like to be in groups of twice a perfect square. The first few perfect squares are 1, 4 and 9 (that is, 12, 22 and 32). Doubling these gives 2, 8, and 18. That is why there are two elements in the first row and eight in each of the next two rows, with the row after that having 18 elements. 1 H 2 He 2 8 3 Li 4 Be 5 B 6 C 7 N 8 O 9 F 10 Ne 11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 8 19 K 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co To be frank, I couldn’t face lining up 18 little squares ... Fair enough! 28 Ni 29 Cu 30 Zn 31 Ga Etc …. 18 In the nucleus While chemistry is concerned with what electrons do in atoms, nuclear physics is concerned with what nuclei do. However protons and neutrons in the nucleus follow the same kinds of laws as the electrons in their shells outside. So you can use the periodic table in nuclear physics as well. 1 H 2 He 2 8 3 Li 4 Be 5 B 6 C 7 N 8 O 9 F 10 Ne 11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 8 19 K 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co That’s a relief. I don’t want to have to make up a NEW one! Stop complaining! 28 Ni 29 Cu 30 Zn 31 Ga Etc …. 18 Square dancing In the nucleus, the main work of the neutrons is to stop the protons from squabbling amongst themselves because of their electrostatic repulsion. Hey, would you It turns out that protons and neutrons arelike happiest when they are in to have a go at neutrons. Helium? bunches of four: two protons and two Why, that would be lovely! Isotopes Now, neutrons aren’t charged and don’t repel each other. So you can get variable numbers of them in a nucleus and still have the same element. 12C, of course, For example, carbon (with 6 protons) can have 6 neutrons (12C),because 7 it’s like four heliums. neutrons (13C) or 8 neutrons (14C). Which is the least stable? Which do you think would be the most stable of these? 12C 13C 6 protons 6 neutrons 6 protons 7 neutrons Shhhhh! This 6 protons isn’t a nuclear 8 neutrons physics course! 14C Stability This is one of the reasons why iron (Fe) ends up at the end of a lot of nucleosynthesis. Its protons form very happy groups in the 2, 8, 8, 8 pattern and most isotopes of iron have enough neutrons to stop them squabbling too much electrostatically. What about the rest? But other elements are not so lucky … Quite comfy 1 H 2 He 2 3 Li 4 Be 5 B 6 C 7 N 8 O 9 F 10 Ne 8 11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 8 19 K 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co Very comfy nucleus Um … it gets awfully complicated … Let’s not take this any further right now? Sort of comfy PLEASE? 28 Ni 29 30 31 Etc Fine by me. Cu Zn Ga ….Back to disgustingly high T Back to disgustingly high T