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Stellar Evolution of a Star like the Sun Protostar Æ Star • Star collapses further • Gets hotter – On the surface – In its center • Until it is so hot in the center that nuclear reactions can start. • This produces even more energy – so much that further gravitational collapse is halted. • • The star is now “born” It is a main sequence star. • It will remain a main sequence star for the largest fraction of its lifetime. Hydrostatic Equilibrium • It is a stable star – it does no longer collapse (nor expand). • The desire to collapse under its own gravity is counter balanced by the pressure exerted by the “hot” gases. Thermal Equilibrium • Star shines at a constant rate • Energy production in the center equal energy loss from surface Energy Source? • What is the Energy Source of a Proto-Star? • What produces so much energy that the star will no longer collapse? • What if a star never gets hot enough to start nuclear fusion? • What is the energy source of the Sun? Energy Source? • What is the Energy Source of a Proto-Star? • What produces so much energy that the star will no longer collapse? • What if a star never gets hot enough to start nuclear fusion? • What is the energy source of the Sun? Coal? Gravity? Something else? Energy Source and Age of the Sun • The energy per second that a star emits is called Luminosity. Thus the lifetime of a star is the energy available divided by the luminosity; or in terms of a formula: t age − of − sun E = L • Why is this important? We know the luminosity of the sun, and if we could somehow figure out how much energy is available, we could calculate the sun’s age. Is the Energy Source Coal? • We can measure how much energy is produced when burning coal. It turns out that one kilo-gram of coal produces 5 ×106 Joules. How much energy would the entire sun produce if it was made of coal? The sun’s total mass is 2 ×1030 kg, so the energy available is: J E = 5 × 10 × 2 × 10 30 kg = 10 37 J kg 6 • How long does this last if the sun emits energy at the present rate? The Luminosity of the sun is 4 × 1026 W (1Watt = 1 Joule/sec). • t age−of − sun • E 10 37 J = = = 2.5 × 1010 sec = 800 years L 4 × 10 26 J sec So, if the sun received its energy through burning coal, it would radiate for 800 years. Clearly this is a ridiculously short time-scale. In fact an energy source is needed that provides energy for roughly 10,000,000 times as long a time. Does the Energy come from Gravitational Collapse? • In the mid 1800’s Kelvin & Helmholz came up with another suggestion. What if the sun is collapsing, and what if gravitational energy gets transformed into light energy? 2 E grav = − 3 GM 5 R • where M is the total mass of all the particles and R the radius of the sphere. • How much of that energy can be transformed into light? As the star collapses, it turns out that one half of the gravitational energy goes into heating the star, while the other half is radiated away. This is known as the “Viral Theorem”. 1 E light = − E grav 2 • Thus the total energy reservoir that is available to be radiated away during the lifetime of the sun would then be: Elight 3 GM 2 = 10 R • Again, the age of the sun would be given by: t age − of − sun • 3 GM 2 E 10 R 3 GM 2 = = = L L 10 RL So, if we know the mass, radius and the luminosity of the sun, we ought to be able to calculate for how long the sun would radiate at its present rate, if it obtained all of its energy from gravitational energy. Inserting R¤= 7 x 108 m, M¤= 2 x 1030 kg, L¤= 4 x 1026 W and G = 6.67 x 10-11 m3/(kg sec2) m3 2 30 × × × kg 6 67 10 2 10 . ( ) kg × sec 2 3 GM 2 3 = = 9.5 × 1014 sec = 3 × 10 7 years t= 2 10 RL 10 kg × m 7 × 10 8 m × 4 × 10 26 sec 3 −11 • • Kelvin & Helmholz already knew that in the mid 1800’s, but no other energy source was known. This puzzle was resolved in the 1930’s with the discovery of the hydrogen bomb. However, while gravity is not the main energy source of the sun, gravitation is indeed an important energy source. Proto-stars receive all their energy from gravitation!! And proto-stellar lifetimes are much shorter than the main sequence lifetimes. Energy Source? • Nuclear Energy • Only in the very center of the star where temperatures are hottest. Energy Production • Nuclear Fusion • Hydrogen is fused into Helium • Same as an atomic Bomb! • • • How? 4 H atoms from 1 He atom And a lot of Energy. 1 H +1H →1H + e + + ν 2 1 H +1H →3He + γ H P-p chain 3 He+ 3He→ 4He+1H +1H Why does this only happen at high temperatures? Protons are positively charged Æ Need to overcome the repulsion How? Bash together the protons Protons need to have high velocities Under which conditions do you get high velocities? High Temperature T >15 million Kelvin Where do you get those high temperatures? Center of the star – in the “core” Energy Production in low mass stars P-P Chain (short for proton-proton chain) 4 H → 1He + Energy 1 H +1H → 2H + e + + ν 2 H +1H →3He + γ 3 He+ 3He→ 4He+1H +1H Energy Production in high mass stars CNO cycle Involves Carbon, Nitrogen, Oxygen These are only used as a catalyst. Four protons are added to C, N, & O, He is produced And C, N, & O are restored The CNO cycle needs higher initial temperatures to get started, however, once it is going, it is a faster method of burning H to He than the pp-chain. How does this nuclear reaction produce so much Energy? It turns out that four hydrogen atoms have more mass than one helium atom. So where did the extra mass go? The mass somehow got converted into energy. Einstein? This means that Energy and Mass are “different faces of the same thing”, and that one can be transformed into the other. E = mc 2 How much mass has gotten “lost”? Since we know the mass of the hydrogen and the helium atoms, we can calculate how much mass has been lost, and how much energy was produced during this process. The mass of one hydrogen atom is 1.673 × 10-27 kg and that of one helium atom is 6.645 × 10-27 kg. 4 × mhydrogen = 6.693 × 10 −27 kg 1 × mhelium = 6.645 × 10 − 27 kg Difference = 0.048 × 10 − 27 kg fractionlost − mass 0.048 ×10 −27 kg = = 0.007 − 27 6.693 ×10 kg How much Energy is that? E = mc 2 = 0.048 × 10 −27 kg × (3 × 108 m / sec) 2 E = 4.3 × 10 −12 Joules One kilo-gram of hydrogen then produces: E = mc 2 = 0.007 kg × (3 × 108 m / sec) 2 E = 6.3 × 1014 Joules How much energy is that? As a reference, to get the same amount of energy, you would have to burn 20,000 tons of coal; and 20,000 tons corresponds to roughly 4×1011kg of coal. This is quite a lot of coal! So you can do quite a lot of damage with only one kilo-gram of hydrogen… Energy Transport • • • Convection Radiative Diffusion Conduction Energy Transport by Radiative Diffusion Convection Granulation on the surface of the sun HRD on Blackboard Follow what happens at individual steps, i.e. from 1 to 2 to 3 etc…. Life as a main sequence star: star Stage 1 to 2 Stage 1: • The star has just become a main sequence star (onset of nuclear fusion) • The hot (T > 15 mil K) region is called the “core”. • Energy source: pp-process (H Æ He; 4 protons turning into one He-ion) • Star is in Hydrostatic Equilibrium Stage 1 Æ 2: • In the core the fraction of helium increases gradually • Luminosity and Radius increase gradually • Energy transport in core: radiative diffusion Life as a main sequence star: Stage 1 to 2 Stage 2 Æ 3: • Hydrogen in the core gets used up • Get a core of helium • Hydrogen burning to helium continues in a “shell” surrounding this core • Energy transport in core: radiative diffusion • Energy transport in envelope: radiative diffusion On the way to a red giant Stage 3 Æ 4: Æ as more H Æ He; He mass of core increases (to roughly 0.5 the total mass of star) Æ one He atoms occupies less space than four H atoms Æ core contracts slowly Æ Viral theorem applies; ½ of energy gets radiated away; ½ goes into heating core Æ central temperature increases, reaction rates increase Æ more energy gets produced in the center of the star (see below) Æ this energy has to be carried from the center to the surface of the star Æ energy transport via radiation is no longer efficient enough Æ the envelope turns convective Æ energy can then be transported more efficiently to the surface Æ luminosity increases Æ envelope expands (radius increases) Æ surface temperature decreases (color gets redder) Æ star moves to the top right hand side of the HRD (The Sun has now become a red giant and Mercury and Venus will be part of the sun, and maybe the Earth too. In any case we will be fried, if we have not yet died…) Comparing main sequence stars to Red Giants (but giant is much bigger ~ 100X) Becoming a Red Giant Degeneracy • • • Energy transport in Core is by radiative diffusion Get more and more Helium until the core turns degenerate. Different Laws of Physics apply for degenerate gasses Normal gasses: density, pressure and temperature are counterbalanced by each other. The normal gas laws do not apply any more. What is degeneracy? The electrons are packed as closely together as possible. Cannot fit any more electrons into the space – more accurately, cannot fit more than two electrons into a “phase space” Comparison Maximum number of chairs; If the classroom is full have no more spaces; Lets be inventive. Can have one person sit on the Lap of the other. If classroom totally full the “gas of students” has turned degenerate. The core explosion – the He-flash At Stage 4: • Sudden onset of Helium to Carbon fusion (Tripple Alpha process, “3α”) • He-flash = Core explosion (invisible) How did a He-flash happen? As H Æ He, Æ core shrinks Æ the central temperature keeps on rising Core gets degenerate: “electrons as close as possible” Perfect gas law does not apply to degenerate gases Æ Æ Æ Æ Æ Æ Æ As temperature increases, the pressure does no longer balance it out Temp can increase further reaction rates speed up until He fusion starts this reaction is even more energetic (energy generation rate is proportional to T40) faster reaction Æ more energy output Æ higher temp “run-away” process “core explosion” - “Helium Flash” HeÆCarbon or the “Tripple Alpha Reaction” 4 He → 1C + Energy 4 2 He+ He→ Be + γ 4 2 4 2 8 4 He+ 48Be→126C + γ This reaction requires a higher initial Temperature than the pp-chain, but it produces more energy. Before it was known what He nuclei were, they were called “alpha particles”. Since this process involves three He-nuclei, I.e., three alpha particles, this set of reactions in known as the “tripple alpha process”. Stage 5: Horizontal branch phase After the He-flash in the core, the star is temporarily unstable and changes its radius, energy output and temperature. Pretty soon after the He-flash, the star will have different properties, i.e. a lower luminosity and a higher temperature. It is now a yellow star. Energy Source: HeÆC (3α) and HÆHe Helium core burning Hydrogen shell burning Stage 6: A brief Variable star phase Stage 6: A brief Variable star phase (only in certain place of HRD) over-expansion of envelope followed by collapse of envelope Æ Æ Æ Æ Æ Æ Æ Æ Æ too much collapse rebounce expansion too much expansion etc radius increases and decreases surface temperature increases and decreases luminosity increases and decrease Period-Luminosity Relationship The Asymptotic Giant Branch… Stage 6Æ7: On the way to a Giant/Supergiant As the central temperature, the temperature gets so high that another nuclear reaction is initiated: C Æ O 12 6 C + He→ O + Energy 4 2 16 8 Energy Source: A small fraction of C Æ O in core Remaining fraction remains carbon ash He Æ C (3α) in a shell H Æ He in another shell Surrounded by an envelope The Asymptotic Giant Branch… Stage 6Æ7: On the way to a Giant/Supergiant • • • Carbon/Oxygen core Helium shell burning Hydrogen shell burning Stages 1Æ 4 repeat themselves (only faster) Æ Carbon mass of core increases Æ core contracts slowly Æ central temperature increases Æ reaction rates increase Æ envelope expands (radius increases) Æ surface temperature decreases Æ color gets redder Æ luminosity increases Æ star moves to top RHS of HRD Æ Red Super Giant Size of Giant Star The Sun has now become a red giant and Mercury and Venus will be part of the sun, and the Earth too… and Mars…. Almost… In any case we will be fried, if we have not yet died…:) Planetary Nebula Phase… Stage 7Æ8 as the radius increases Æ outer shells get dispersed Æ He burning shell gets exposed to the surface Æ get tripple alpha reactions on the surface Æ these are rather explosive Æ material is expelled in shells Æ see a planetary nebula but the central star appears to be hotter Æ hotter means a bluer color Æ star moves towards blue in HRD Æ Star becomes a White Dwarf White Dwarfs and Planetary Nebulae White Dwarf • Carbon Ash in core, He & H burning shells • Remaining material gets expelled Æ Left behind “Small Carbon Star” Planetary Nebula • as the star grows in size, outer layers are only loosely bound • outer shells get dispersed • He burning shell gets exposed to the surface • get Tripple Alpha reactions on the surface of the star • These “He-flashes” rather explosive • Material is expelled in shells Æ see a planetary nebula Ring Nebula (M57) – picture taken at CUNY - CSI Nearest Planetary Nebula Size 0.5o (same as sun!) Greenish middle: Oxygen Outer Red: Hydrogen, some Nitrogen. Size: 150 AU Distance: 400 lyr Helix Nebula -- or Sun Flower Nebula Making color photos with HST observe with different Filters, then combine pictures… Nitrogen Oxygen (doubly ionized) Helium Colors roughly right Blue: helium (close to central star) Green: Ionized oxygen Red: ionized nitrogen (coolest gas - furthest away) All gases are heated from the central star. Helix Nebula Movie Helix Nebula Shows HST insert HST Helix nebula Spoke-like globules Each gaceous head is twice the size of the solar system Helix Detail The gaseous knots may be the result of the collision between gases. Hot gases that are ejected from the surface of the star collide with the cooler gases that were ejected some 10,000 years prior to the last ejection.This crash fragments the cloud into finger-like droplets NGC 7027 Ground Based Image Binary Star Evolution with a White Dwarf and a Red Giant NGC 6543 Color coded to show detail Hourglass Nebula Spectacular Stellar Deaths Becoming a White Dwarf Stage 9 and beyond: planetary nebula disappears star has no nuclear fuel star looses energy (radiates it away) (radiates thermal energy) ÆStar gets dimmer Æ star cools, temperature decreases Æ Cooler means redder Æ star moves towards bottom right in HRD star now is a white dwarf eventually it will cool more and more and become an even dimmer red dwarf… White Dwarfs Material? Size? Mass? Density? Carbon “ash”, maybe Carbon/Oxygen mixture Size of Earth Roughly 80% of main sequence mass Material is very dense As big as the Earth, but MUCH denser Æ 100,000 x surface gravity Material is packed as closely as possible Electrons form a Degenerate “gas” White Dwarfs As big as the Earth Paradoxically more massive W.D.’s tend to be smaller Limiting Mass for White Dwarfs Sirius A & B White Dwarfs in M4 The Evolution of Massive Stars Eta Carina – A Massive Star Massive Stars Differences to lower mass stars like the sun 1. Main Sequence lifetime is faster. 2. Hydrogen burning Mechanism is not the pp-chain, it is via the CNO cycle 3. Central temperature can rise higher, so energy in the core is transported via convection. Degeneracy will not occur, so will NOT have s He-flash. 4. Central temperature can rise higher, so can burn heavier metals. 5. Strong Mass Loss up to a few solar masses during m.s. life. HRD for low mass stars – HRD for high mass stars 1. Main Sequence lifetime 1. Main Sequence lifetime is faster. Proto-stellar Evolution is also faster (more gravitational energy Æ faster collapse) Life expectancies of main sequence stars scale with mass T∝ 1 M 2.5 2. Hydrogen Burning Overall 4 protons Æ 1 He atom. In low mass stars via the p-p chain In high mass stars via the CNO cycle Energy Production in low mass stars P-P Chain (short for proton-proton chain) 4 H → 1He + Energy 1 H +1H → 2H + e + + ν 2 H +1H →3He + γ 3 He+ 3He→ 4He+1H +1H Energy Production in high mass stars CNO cycle Involves Carbon, Nitrogen, Oxygen These are only used as a catalyst. Four protons are added to C, N, & O, He is produced And C, N, & O are restored The CNO cycle needs higher initial temperatures to get started, however, once it is going, it is a faster method of burning H to He than the pp-chain. 3. Energy Transport and the Helium Flash Convective core; NO He-flash • • • • • • • • High mass stars burn hydrogen via the CNO cycle Since this produces relatively more energy (the temperature gradient is steeper) The Energy Transport Mechanism is Convection in the core. Convection results in the mixing of the core. Some hydrogen from the hydrogen burning shell is mixed into the core. You will not get an inert He-core, Thus the core (the electrons in the core) will not become degenerate Thus no He-flash will occur. • The He-flash (the explosive onset of He burning) only happens in low mass stars like the sun, and for stars that are 3 times as massive as the sun. 4. Heavier Metals Massive stars have more gravitational Energy that can be used to heat the central core. The central temperature need to be hotter and hotter each time a new nuclear fuel is used. Burning H to He requires tens of millions of degrees Kelvin. Burning Helium requires a higher temperature because the repulsion between the He-nuclei is larger (twice as much) than that of the Hnuclei. Burning Carbon requires yet higher temperatures. In low mass stars core temperatures in excess of about 100 million degrees Kelvin are never obtained. This is because lower mass stars do not have enough gravitational energy for the central temperatures to rise this high. Thus low star masses finish their nuclear reactions after having produced Carbon and a little Oxygen. Higher mass stars can burn Carbon, then burn Oxygen, then Silicon, etc… but only up to Iron. The Onion Skin Model Burning heavier elements up to Iron Time scales in each element burning stage in 25 MSun Star Why only up to Iron? To make elements lighter than Iron from even lighter elements will release a lot of energy Making elements heavier than Iron requires energy (individual protons and neutrons cannot hold onto each other any more…) Think of a water-drop that gets bigger and bigger, and then eventually drops. Fusion Fission Abundances of Elements The heavier the element the less abundant it is. Secondary Peak at Iron… why? Large drop in Boron, Lithium and Beryllium – these elements get destroyed in stellar interiors and are made into heavier elements What are we made of? Read chapter 16 of Silk’s Big Bang Evolution in HRD Globular cluster HRD