Evolution Off the Main Sequence: Supernovae
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Evolution off the main sequence: Supernovae March 16, 2020 1 Supernova observations Only a three supernovae have been observed within the Milky way galaxy and five anywhere before the use of telescopes: 1. HB9 was marked on star charts from India about 5000 years ago. 2. SN 185 was viewed by Chinese astronomers in 185 CE 3. On about April 30, 1006 a magnitude −9 star suddenly appeared in the constellation Lupus , bright enough to be seen in daytime and to read by at night. It was reported by astrologers in Europe, the Middle East, and Asia. 4. July 4, 1054, Yang Wei-T’e documented a “guest star” in Taurus, which gradually became invisible after a year. It was also observed in Japan, Korea and Arabia. It was also visible in daylight. This supernova is the source of the Crab nebula (Crab supernova remnant). (Milky Way) 5. Tycho Brahe recorded a supernova in 1572. (Tycho’s supernova) (Milky Way) 6. Johannes Kepler (Tycho Brahe’s student) recorded a supernova in 1604. (Kepler’s supernova) (Milky Way) The closest supernova since Kepler’s supernova occured in the Large Magellenic Cloud in 1987. (SN 1987A) 2 Types of supernovae Supernovae fall into two (or four) distince classes: • Thermal runaway – Thermal runaway happens either when a white dwarf star accumulates enough matter to reignite, or two white dwarf stars collide. In either case, the reignition disrupts the star, leading to a supernova explosion and a collapsed core. • Core collapse – Direct core collapse occurs as the end state of large stars. NASA clip on supernova formation Supernovae are classified by certain distinct spectral characteristics, • Type I: No Hydrogen lines, indicating that the outer layers of the star were stripped before the super- nova 1 – Type Ia: Strong Si II line at 615 nm: found in all galaxies, including those with little new star formation (thermal runaway) – Type Ib: Strong Helium lines: seen only in spiral galaxies, near star forming regions (core collapse) – Type Ic: No strong Helium lines: seen only in spiral galaxies, near star forming regions (core collapse) • Type II: Strong Hydrogen lines (The Crab Nebula and SN 1987A were Type II.) (core collapse) – Type II-P (plateau) (90% of Type II) – Type II-L (linear) (10% of Type II) but a moType Ia supernovae are produced by runaway fusion ignited on degenerate white dwarf progenitors, while the spectrally similar Type Ib/c are produced from massive Wolf–Rayet progenitors by core collapse. Brightness of a Type Ia supernova: MB = −18:4. For comparison, the apparent magnitude of the sun is m = −26:7 and the moon is mmoon = −12:6. (The absolute magnitude of the sun, i.e., its brightness if it were 10 parsecs away, is M = +4:7.) Other Types are1:5 to 2 times dimmer. 2.1 Can the energy release of a supernova be produced by nuclear fusion? The question here is similar to whether the sun’s energy could be provided (for billions of years) by chemical burning, but the power released by a supernova is much greater. Suppose free neutrons and protons were somehow suddenly compressed into iron nucleii. This gives the most energy that could be produced from nuclear fusion. To match the light curve of a supernova, this fusion would have to occur in a matter of days. The energy released by a Type II supernova is on the order of 1046J The release of energy in forming one iron nucleus from free nucleons is the binding energy of iron, 492:26 MeV = 7:9 × 10−11J so the number of iron atoms required is 1046 N = = 1:27 × 1056 7:9 × 10−11 Since one iron nucleus weighs mF e = Z × mp = 56u × 1:66 × 10−27kg=u = 9:3 × 10−26kg the mass of this much iron is 56 −26 Miron = 1:27 × 10 × 9:3 × 10 = 1:18 × 1031 = 5:9 M Forcing six solar masses of iron to fuse in a matter of days seems unlikely; moreover the majority of the star’s mass is already comprised of heavier elements, not free nucleons. We conclude that nuclear fusion is unlikely to be the sole source of the energy of a supernova. 2 2.2 Can the energy of a supernova be produced by gravitational collapse? Consider a different possibility. As the core of the star reaches nuclear density, the electrons, protons and neutrons of the atoms are in close proximity. If the electrons and protons were to combine into neutrons, the volume of the star would decrease substantially, releasing gravitational energy. Can this happen energetically? Can it provide enough energy (on the order of 1046J) to drive a supernova? Consider a 20 M star. There are three things to examine: 1. Free neutrons decay, giving off :782 MeV . Reversing this requires neutrons to form from electrons and protons, and the reaction must provide this much energy for each neutron formed. A 20 M star contains about 1057 protons so collapse will require about :782 × 1057 = 7:82 × 1056MeV J = 7:82 × 1056MeV × 1:6 × 10−13 MeV = 1:25 × 1044J to be lost into the neutrons. 2. The volume change in going from a white dwarf or the core of a large star (say, 5000 km, roughly the size of Earth) to a degenerate neutron gas. The degenerate neutron gas will have at least nuclear density, 2:3 × 1017kg=m3, so the volume of a 4 × 1031kg star will be Mstar Vstar = ρnuclear 4 × 1031 = m3 2:3 × 1017 = 1:74 × 1014m3 4πR3 and therefore, setting V = 3 , the radius after collapse will be 3 1=3 R = V 4π 3 1=3 = × 1:74 × 1014 4π = 3:46 × 104m = 34:6 km or less. 3. Now we find the gravitational energy released. The total contribution to gravitational potential energy of a constant density shell of mass dm = 4πρr2dr dropped from infinity onto a sphere of the same material of radius r is GM dm dE = − r r G 4πρr3 = − 4πρr2dr r 3 16π2Gρ2 = − r4dr 3 Integrating as r grows from zero to the final radius R of the star, 16π2Gρ2R5 E = − 15 3 4πρR3 4πρR3 9G = − 3 3 15R 3GM 2 = − 5R This is the binding energy of a star of mass M and radius R. The energy change of a star of mass 20 M as the radius changes from 5000 km to 34:6 km is 3GM 2 3GM 2 ∆E = − − − 5R5000 5R50 3GM 2 1 1 = − − 5 R5000 R50 3 × 6:67 × 10−11 × 400 × 4 × 1060 1 1 = − − 5 5000 36:4 = 1:75 × 1051 If only a small fraction of this energy ultimately drives the supernova explosion, there is more than enough gravitational energy. 2.3 Fusion processes in massive stars For stars above eight solar masses 8 M , the early evolution is similar to that of low mass stars. Looking at the evolution on the Hertzsprung-Russell diagram (see tiff) the main difference is the amount of time spent burning helium. The difference begins at the centers of large stars, which become hot and dense enough to enable further fusion. 4 Adding alpha particles 2He to various fusion products, we find 12 4 16 6 C + 2He ) 8 O + γ 16 4 20 8 O + 2He ) 10Ne + γ 20 4 24 23 + 10Ne + 2He ) 12Mg + γ ) 11Na + e + ν 24 1 23 + 12Mg + 0p ) 12Mg + e + ν Adding another alpha particle to magnesium, we reach silicon, 24 4 28 12Mg + +2He ) 14Si + γ At this point, the core temperature reaches about 3 × 109K (yes, billion!) and the reactions take on a different character because the ambient energy is so high. While it is energetically favorable for Si to continue to absorb further alpha particles to yield sulfur, argon and other elements up to iron, the abundance of high energy photons makes it possible for these reactions to go in the other direction as well (,), creating an equilibrium mixture of many elements, 28 4 32 14Si + +2He () 16S + γ 32 4 36 16S + +2He () 18Ar + γ . 52 4 56 24Cr + +2He () 26Ni + γ 56 54 56 56 These equilibrium reactions can include elements above iron 26F e as well, with 26F e; 26F e and 28Ni most abundant. As with hydrogen, helium and carbon, the heavier elements migrate toward the core and the lighter elements at larger radii in layers. The dominant layers outside the iron core are silicon, oxygen, carbon, helium and hydrogen. The bottom of each of these layers is hot and dense enough to continue fusion. 4 2.4 Collapse In addition to the reversal of the fusion reactions, it is also possible for the high photon enegies to break down nuclei through other photodisintegration reactions, 56 4 26F e + γ ) 132He + 4n 4 + 2He + γ ) 2p + 2n Photodisintegration happens in a short period of time once the core becomes hot enough, undoing the long fusion process. A great deal of energy is required for the process, but as we have seen, the energy difference between iron and free nucleons is of order 1:25 × 1044J, much less than the energy released by gravitational collapse. The two processes drive one another. Energy loss though photodisintegration lowers the central pressure, allowing the core to collapse. The collapse releases gravitational energy, driving further photodisintegration. Core masses at this stage vary from one to a few solar masses. When the temperature and density (for a 15 M star) reach about 9 Tcore ∼ 8 × 10 K kg ρ ∼ 1013 core m3 electron capture by protons occurs, + − p + e ! n + νe As we have seen, this also requires energy.