Nuclear fusion in stars. Collapse of primordial density fluctuations into galaxies and stars, nucleosynthesis in stars

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1 Nuclear fusion in stars Collapse of primordial density fluctuations into galaxies and stars, nucleosynthesis in stars

2 The origin of structure in the Universe Until the time of formation of protogalaxies, the Universe contained only the cooling H and He and degraded radiation The only high-density objects present at that time could be black holes (and strings) left over from the original fireball The presence of structure in the 3K background radiation suggests that slight density fluctuations in the expanding H and He gas could develop into galaxies and first stars There would be no further evolution of matter without this environment

3 Basics of cloud collapse Gas cloud collapse occurs, when its gravitational potential energy is greater than the internal thermal energy. Jeans criterion: GmM r c = 3mkT 2 M = 4 3 "r c 3 # r c > c(t /") 1/ 2 A molecule in a cloud larger than r c would have v thermal < v esc. A cloud capable of loosing energy by radiation can collapse! Collapse remains isothermal until the density and opacity become very high As collapse continues, more and more energy is stored in vibrational (3000K) and rotational (300K) states of H. Rotationally excited H will reradiate its energy in far IR as long as opacity is not too high A cloud has to become very dense to start retaining its collapse energy!

4 Cloud fragmentation If a collapsing cloud has mass M=const and radius R, then for a smaller cloud of mass m and radius r, m/m=(r/r) 3, and: r " 2Gm 3kT = 2GM 3kT # % $ r R & ( ' 3 r " # % $ 3kT 2GM & ( ' 1/ 2 R 3 / 2! If R increases by a factor of 4, r does the same by factor of 8. This means that a collapsing cloud can fragment! into smaller collapsing clouds. This process ends with star formation or when rotational speed becomes too high (conservation of angular momentum) Hierarchical collapse can produce many levels of structure from clusters through galaxies down to stellar clusters and stars First generation stars are believed to have formed out of small, high ρ, low angular momentum clouds

5 The scales of collapse size ~ 1 Gpc ~ g cm-3 ~ 1 Mpc ~ 1 mpc ~ 1 µpc ~ 1 kpc ~ 1 pc density ~1 npc ~1 g cm-3

6 Nucleosynthesis in stars Elements production in stars

7 The star formation process - I This process may take some six million years! In an interstellar cloud, gravity acts to collapse it, while thermal motions due to heat try to take it apart Large molecular clouds are generally stable, but they can be broken into smaller, denser, and unstable fragments. Instability is triggered by shock waves Such waves may be caused by supernova explosions, birth events of very hot stars, and density waves due to the spiral structure of our Galaxy

8 Stellar birth and the H-R diagram As part of a cloud begins to collapse under its own gravity, it becomes denser and hotter The cloud heats up, because its contraction converts gravitational energy into heat Fragments of the original cloud produce an association of stars that drifts apart over a few million years As a star s luminosity and temperature change, the star moves in the H-R diagram along an evolutionary track More massive protostars collapse and become stars faster than the less massive ones When collapse is halted by the onset of nuclear reactions in the core, a newborn star reaches the main sequence

9 Energy production in protostars Newly formed stars appear systematically too red for their luminosity Intrinsic reasons for their over-luminosity: (i) large radii (still shrinking), (ii) extra energy source form gravitational potential energy-to-heat conversion, and (iii) deuterium burning: 2 H+ 1 H" 3 He + # Deuterium burning is the energy source for brown dwarfs ( M sun objects) A cloud collapsing from infinity to radius R radiates the amount of its gravitational energy: M "! GM E = # # drdm = $ GM 2 R 2 R 0 0 For the Sun, this gives 4 x ergs, compared to 4 x ergs on MS This difference would double the Sun s L for 3 x 10 7 years, which is enough to observe many! such stars in clusters For a supergiant (say, 100 M sun ), the period of over-brightening would only be ~150 years - too brief to be observed at any given time

10 T Tauri stars and Herbig-Haro objects T Tauri stars appear to be protostars in the process of clearing away the surrounding cocoon of gas and dust Observations show strong outflows of gas in the form of expanding shells and jets (10-7 M sun in 10 6 years) Infrared observations reveal the presence of the remaining dust, sometimes in the form of a disk surrounding the protostar Herbig-Haro objects are often found near T Tauri stars They are small nebulae formed at points, where jets emanating from protostars collide with interstellar clouds, shock-heat them, and make them glow Often, young stars generate two jets emerging in the opposite directions. They are called bipolar flows and appear to be associated with rotating disks of circumstellar matter around these stars

11 The p-p cycle Stars found in elliptical galaxies and globular cluster (Population II stars) are metal-poor compared to Sun-like stars in disks of spiral galaxies (Population I) Pop II stars are very old, originally made of the primordial material (H, He), not enriched in metals (heavier than He) The basic nuclear fusion reaction (proton-proton cycle): 4 p" 4 He + 2e + + 2# e p-p cycle energy rate production:! " = 0.28#X H 2 (T 6 /13) 4.1 Central T~10 7 K is needed to maintain ε ~ 1 erg g -1 s -1!

12 Hydrogen fusion - II Another way to fuse helium from hydrogen is to use carbon in series of reactions called the CNO cycle Since the Coulomb barrier for carbon is six times that of hydrogen, much higher temperatures are needed for this reaction to work. The CNO cycle is important in stars with masses larger than 1.1 M (core temperatures higher than 16 million K) At even higher temperatures, carbon fusion leads to synthesis of numerous heavy atoms

13 Post-main sequence evolution of a solarmass star Accumulation of a pure He core takes ~10 10 years for a solar-mass star (its L increases 10-20% over that period) When T~10 8 K and the star s mass > 0.8 M sun, He ignition occurs. The star becomes a giant or supergiant and He synthesizes C in the triplealpha reaction: Stars with masses M sun never go beyond the He burning and eventually become white dwarfs after shedding much of their mass! 4 He+ 4 He" 8 Be 8 Be+ 4 He" 12 C + # Pop II stars in clusters are billion years old

14 Nuclear fusion in massive stars Massive star do not end their lives as white dwarfs. They evolve much faster than sun-like stars and destroy themselves in supernova explosions Massive stars fuse hydrogen, then helium and develop carbon-oxygen cores. At ~1 billion K, they are able to ignite carbon, then oxygen, neon and magnesium fuse to make silicon, which finally fuses to make iron Because more and more protons are used up to make heavier and heavier atoms and progressively less energy is released, fusion proceeds and a higher and higher rate A 25M star needs 7 million years to fuse its hydrogen and just one day to fuse silicon

15 Carbon burning in the core Core temperatures of stars with initial masses > 8M sun exceed 10 9 K, at which point carbon begins to fuse: Hydrogen fuses immediately through reactions like:! 4 He+ 12 C" 16 O + # 12 C+ 12 C" 20 Ne+ 4 He 12 C+ 12 C" 23 Na + p 12 C+ 12 C" 23 Mg + n 16 O+ 16 O" 28 Si+ 4 He 12 C + p" 13 N + # 13 N" 13 C + e + + $ 13 C+ 4 He" 16 O + n Succesive reactions leading up to 56 Fe produce energy (exothermic). Beyond iron they require energy input to occur (endothermic).! Exothermic reactions produce feedback conditions, in which higher T caused by them leads to even higher T and increases reaction rate

16 Supernova explosions When a stellar core gets converted to iron, there are no more fusion reactions that could synthesize heavier elements and release energy Electrons of the degenerate core and gamma-ray photons are captured by iron atoms. This causes cooling and rapid collapse of the core in less than 0.1 seconds When this collapse is halted by pressure of free neutrons, energy carried away by neutrinos and huge convection currents make the outer layers of a star explode and get ejected into space What is left of a star is either a neutron star or a black hole, depending on the mass of the core

17 Conditions in the core The iron core has T~ 4 x 10 9 K and density > kg m -3. Pressure in a 1 M sun core of density 5 x kg m -3 would be: P = GM 2 In such conditions, photon-photon interactions produce e - -e + pairs and neutrinos, which carry away core energy cooling it in a runaway process leading up to core collapse Heat pulse caused! by the core bounce cause detonation of successive shells of the star and a catastrophic nucleosynthesis, such as explosive silicon burning: Explosive burning in successive shells produces all the remaining elements above 56 Fe! R 4 28 Si+ 4 He" 32 S+ 4 He" 36 Ar+ 4 He" 40 Ca 40 Ca+ 4 He" 44 Ti+ 4 He" 47 V + p 42 Ca+ 4 He" 45 Ti + n

18 Post main sequence stellar evolution

19 B I G B A N G H, He, CNO soot Element recycling scheme H, He Interstellar medium 100K <10K H, He, CNO, Si,Mg,S, Fe explosion ejecta explosion ejecta explosion ejecta Stellar generations Planets, brown dwarfs, white dwarfs, neutron stars, black holes Pop. II stars H+He planets Pop. I, 2 nd generation stars, H+He+CNO--> soot & ice planets Pop. I, 3 rd generation stars, H+He+CNO+rock --> terrestrial planets

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