1. Modelling SN Type II: collapse and simple bounce From Woosley et al. (2002) Woosley Lectures 13 and 14

2. Most distant explosion smashes previous record NASA NEWS RELEASE Posted: September 12, 2005 http://www.spaceflightnow.com/news/n0509/12swift/ http://www.spaceflightnow.com/news/n0509/12swift/ This powerful burst was detected September 4. It marks the death of a massive star and the birth of a black hole. It comes from an era soon after stars and galaxies first formed, about 500 million to 1 billion years after the Big Bang. The September 4 burst, named GRB 050904, has a redshift of 6.29, which translates to a distance of about 13 billion light-years from Earth. The Universe is thought to be 13.7 billion years old. The previous most distant gamma-ray burst had a redshift of 4.5. The most distant quasar known is at a redshift of 6.4. This burst was also very long, lasting more than 200 seconds, whereas most bursts last only about 10 seconds. The detection of this burst confirms that massive stars mingled with the oldest quasars.

3. På fredag kommer Troels Haugbølle på besøg fra København. Nogle af jer kender ham sikkert allerede som PhD studerende hos Aake. Han har arbejdet med simuleringer af gamma-ray bursts o.l. I forbindelse med vores "astropartikel" frokostmøde (12-13 i 520-731) holder han et 15-20 minutters foredrag om sine simuleringer, hvis nogle af jer skulle være interesserede. Alle er naturligvis også mere end velkomne til at komme til møderne under alle omstændigheder. De er meget uformelle, og består normalt i, at en eller to medbringer en ny artikel, som de synes ser spændende ud.

10. (Fryer & Kalogera 2001; see also: Burrows 1999)

14. Ejected “metals”

28. 8 – 11 M ¯ : uncertain situation ? M < M 1 ' 8 M ¯ : No C ignition M > M 2 ' 12 M ¯ : Full nondegenerate burning In between: ???? Degenerate off-centre ignition Possibly O-Ne-(Mg?) white dwarfs (after some additional mass loss) With sufficient O-Ne core mass: continued burning and core collapse

29. Pair-instability supernovae He burning collapse and energy release  +  ! e + + e - :  1 < 4/3 Dynamical collapse, bounce, explosive burning (for M < 260 M ¯ ) Dynamical collapse directly to black hole (for M > 260 M ¯ ) Pop. III stars, no mass loss

30. Possibly observed: SN 2006gy Smith et al. (2007; ApJ 666, 1116)

31. Normal core collapse

33. Gravitational Binding Energy of the Presupernova Star This is just the binding energy outside the iron core. Bigger stars are more tightly bound and will be harder to explode. The effect is more pronounced in metal-deficient stars. solar low Z

34. As silicon shells, typically one or at most two, burn out, the iron core grows in discontinuous spurts. It approaches instability. Pressure is predominantly due to relativistic electrons. As they become increasingly relativistic, the structural adiabatic index of the iron core hovers precariously near 4/3. The presence of non- degenerate ions has a stabilizing influence, but the core is rapidly losing entropy to neutrinos making the concept of a Chandrasekhar Mass relevant. In addition to neutrino losses there are also two other important instabilities: Electron capture – since pressure is dominantly from electrons, removing them reduces the pressure. Photodisintegration – which takes energy that might have provided pressure and uses it instead to pay a debt of negative nuclear energy generation.

35. Entropy (S/N A k)

36. Entropy

37. Because of increasing degeneracy the concept of a Chandrasekhar Mass for the iron core is relevant – but it must be generalized.

38. The Chandrasekhar Mass ¯

39. BUT 1)Y e here is not 0.50 (Y e is actually a function of mass) 2) The electrons are not fully relativistic in the outer layers ( g is not 4/3 everywhere) 3) General relativity implies that gravity is stronger than classical and an infinite central density is not allowed (there exists a critical r for stability) 4) The gas is not ideal. Coulomb interactions reduce the pressure at high density 5) Finite temperature (entropy) corrections 6) Surface boundary pressure (if WD is inside a massive star) 7) Rotation Effect on M Ch

40. Relativistic corrections, both special and general, are treated by Shapiro and Teukolsky in Black Holes, White Dwarfs, and Neutron Stars pages 156ff. They find a critical density (entropy = 0). Above this density the white dwarf is unstable to collapse. For Y e = 0.50 this corresponds to a mass ¯

41. Coulomb Corrections Three effects must be summed – electron-electron repulsion, ion-ion repulsion and electron ion attraction. Clayton p. 139 – 153 gives a simplified treatment and finds, over all, a decrement to the pressure (eq. 2-275) Fortunately, the dependence of this correction on n e is the same as relativistic degeneracy pressure. One can then just proceed to use a corrected

42. M¯M¯ M¯M¯ M¯M¯ M¯M¯ ¯

43. Finite Entropy Corrections Chandrasekhar (1938) Fowler & Hoyle (1960) p 573, eq. (17) Baron & Cooperstein, ApJ, 353, 597, (1990)

44. In particular, Baron & Cooperstein (1990) show that

45. And since early on we showed that The entropy of the radiation and ions also affects M Ch, but much less. This finite entropy correction is not important for isolated white dwarfs. They’re too cold. But it is very important for understanding the final evolution of massive stars.

48. But when Si burning in this shell is complete: The Fe core is now ~1.3 M ¯ s e central = 0.4 s e at edge of Fe core = 1.1 hence average s e ' 0.7 M Ch now about 1.34 M ¯ (uncertain to at least a few times 0.01 M ¯ Neutrino losses farther reduce s e. So too do photodisintegration and electron capture as we shall see. And the boundary pressure of the overlying silicon shell is not entirely negligible.

49. Electron

50. The collapse begins on a thermal time scale and accelerates to a dynamic implosion as other instabilities are encountered. Photodisintegration: As the temperate and density rise, the star seeks a new fuel to burn, but instead encounters a phase transition in which the NSE distribution favors a- particles over bound nuclei. In fact, this transition never goes to completion owing to the large statistical weight afforded the excited states of the nuclei. But considerable energy is lost in a partial transformation. not really free neutrons. They stay locked inside bound nuclei that are progressively more neutron rich.

51. What happens? As the density rises, so does the pressure (it never decreases at the middle), but so does gravity. The rise in pressure is not enough to maintain hydrostatic equilibrium, i.e., G < 4/3. The collapse accelerates. Photodisintegration also decreases s e because at constant total entropy (the collapse is almost adiabatic), s i increases since 14 a- particles have more statistical weight than one nucleus. The increase in s i comes at the expense of s e.

52. Electron capture The pressure predominantly comes from electrons but as the density increases, so does the Fermi energy, e F. The rise in e F means more electrons have enough energy to capture on nuclei turning protons to neutrons inside them. This reduces Y e which in turn makes the pressure at a given density smaller. By 2 x 10 10 g cm -3, e F = 10 MeV which is above the capture threshold for all but the most neutron-rich nuclei. There is also briefly a small abundance of free protons (up to 10 -3 by mass) which captures electrons.

53. But the star does not a) photodisintegrate to neutrons and protons; then b) capture electrons on free protons; and c) collapse to nuclear density as a free neutron gas as some texts naively describe. Bound nuclei persist, then finally touch and melt into one gigantic nucleus with 10 57 nucleons – the neutron star. Y e declines to about 0.37 before the core becomes opaque to neutrinos. (Y e for an old cold neutron star is about 0.05; Y e for the neutron star that bounces when a supernova occurs is about 0.29). The effects of a) exceeding the Chandrasekhar mass, b) photodisintegration and c) electron capture operate together, not independently.

54. H He O Fe Si

55. Stars of larger mass have thicker, more massive shells of heavy elements surrounding the iron core when it collapses. Note that the final masses of the 15 and 25 solar mass main sequence stars are nearly the same – owing to mass loss. H He O FeSi

56. Distribution of collapse velocity and Y e (solid line) in the inner 2.5 solar masses of a 15 solar mass presupernova star. A collapse speed of 1000 km/s anywhere in the iron core is a working definition of “presupernova”. The cusp at about 1.0 solar masses is the extent of convective core silicon burning. YeYe v collapse

57. Different weak interaction rates (FFN vs LM) a few years ago gave a smaller value of Y e in essentially the same star.

58. Core Collapse Once the collapse is fully underway, the time scale becomes very short. The velocity starts at 10 8 cm s -1 (definition of the presupernova link) and will build up to at least c/10 = 30,000 km s -1 before we are through. Since the iron core only has a radius of 5,000 to 10,000 km, the next second is going to be very interesting.

59. Neutrino Trapping Trapping is chiefly by way of elastic neutral current scattering on heavy nuclei. Freedman, PRD, 9, 1389 (1974) gives the cross section

60. From this point on the neutrinos will not freely stream but must diffuse. Neutrino producing reactions will be inhibited by the filling of neutrino phase space. The total lepton number Y L = Y e +Y n will be conserved, not necessarily the individual terms. At the point where trapping occurs Y L = Y e ~ 0.37. At bounce Y e ~ 0.29; Y n ~ 0.08.

61. Bounce Up until approximately nuclear density the structural adiabatic index of the collapsing star is governed by the leptons – the electrons and neutrinos, both of which are highly relativistic, hence nearly G =4/3. As nuclear density is approached however, the star first experiences the attactive nuclear force and G goes briefly but dramatically below 4/3. At still higher densities, above r nuc, the repulsive hard core nuclear force is encountered and abruptly G >> 4/3.

63. at about point b) on previous slide

64. The collapse of the “iron” core continues until densities near the density of the atomic nucleus are reached. There is a portion of the core called the “homologous core” that collapses subsonically (e.g., Goldreich & Weber, ApJ, 238, 991 (1980); Yahil ApJ, 265, 1047 (1983)). This is also approximately equivalent to the “sonic core”. This part of the core is called homologous because it can be shown that within it, v collapse is proportional to radius. Thus the homologous core collapses in a self similar fashion. Were  = 4/3 for the entire iron core, the entire core would contract homologously, but because  becomes significantly less than 4/3, part of the inner core pulls away from the outer core. As the center of this inner core approaches and exceeds  nuc the resistance of the nuclear force is communicated throughout its volume by sound waves, but not beyond its edge. Thus the outer edge of the homologous core is where the shock is first born. Typically, M HC = 0.6 – 0.8 solar masses. The larger M HC and the smaller the mass of the iron core, the less dissipation the shock will experience on its way out.

65. Factors affecting the mass of the homologous core: Y L – the “lepton number”, the sum of neutrino and electron more numbers after trapping. Larger Y L gives larger M HC and is more conducive to explosion. Less electron capture, less neutrino escape, larger initial Y e could raise Y L. GR – General relativistic effects decrease M HC, presumably by strengthening gravity. In one calculation 0.80 solar masses without GR became 0.67 with GR. This may be harmful for explosion but overall GR produces more energetic bounces and this is helpful. Neutrino transport – how neutrinos diffuse out of the core and how many flavors are carried in the calculation.

66. Relevant Physics To Shock Survival Photodisintegration: As the shock moves through the outer core, the temperature rises to the point where nuclear statistical equilibrium favors neutrons and protons over bound nuclei or even a -particles Neutrino losses Especially as the shock passes to densities below 10 12 g cm -3, neutrino losses from behind the shock can rob it of energy. Since neutrinos of low energy have long mean free paths and escape more easily, reactions that degrade the mean neutrino energy, especially neutrino-electron scattering are quite important. So too is the inclusion of m- and t- flavored neutrinos

67. The Mass of the Presupernova Iron Core Unless the mass of the iron core is unrealistically small (less than about 1.1 solar masses) the prompt shock dies The Equation of State and General Relativity A softer nuclear equation of state is “springier” and gives a larger amplitude bounce and larger energy to the initial shock. General relativity can also help by making the bounce go “deeper”. Stellar Structure and the Mass of the Homologous Core A larger homologous core means that the shock is born farther out with less matter to photodisintegrate and less neutrino losses on its way out.

68. Collapse and bounce in a 13 solar mass supernova. Radial velocity vs. enclosed mass at 0.5 ms, +0.2 ms, and 2.0 ms with respect to bounce. The blip at 1.5 solar masses is due to explosive nuclear burning of oxygen in the infall (Herant and Woosley 1996).

69. It is now generally agreed (despite what you may read in old astronomy text books), that the so called “prompt shock mechanism” – worked on extensively by Bethe, Brown, Baron, Cooperstein, and colleagues in the 1980’s – does not work. The shock fails and becomes in a short time (< 10 ms) an accretion shock. It will turn to neutrinos to actually blow up the star. But the success of the neutrino model will depend, in part, upon the conditions set up in the star by the failure of the first shock. How far out did it form? What is the neutrino luminosity? Does convection occur beneath the neutrinosphere? So all the factors listed on the previous pages are still important.

70. Colgate and White, (1966), ApJ, 143, 626 see also Arnett, (1966), Canadian J Phys, 44, 2553 Wilson, (1971), ApJ, 163, 209 The explosion is mediated by neutrino energy transport....

72. Myra and Burrows, (1990), ApJ, 364, 222 Woosley et al. (1994), ApJ,, 433, 229 Neutrino luminosities of order 10 52.5 are maintained for several seconds after an initial burst from shock break out. At late times the luminosities in each flavor are comparable though the m - and t - neutrinos are hotter than the electron neutrinos. Wilson 20 M-sun

73. K II 2140 tons H 2 O IMB 6400 tons “ Cerenkov radiation from  (p,n)e + - dominates (e -,e - ) - relativistic e all flavors

74. Hirata et al. (1987; Phys. Rev. Lett. 58, 1490)

75. Time scale Very approximate Neutrino Burst Properties:

77. Temperature:

79.  bounce = 5.5 x 10 14 g cm -3 Explosion energy at 3.6 s 3 x 10 50 erg 20 Solar Masses Mayle and Wilson (1988)

80. Infall Accretion Shock radius Velocity gain radius Neutrinosphere Inside the shock, matter is in approximate hydrostatic equilibrium. Inside the gain radius there is net energy loss to neutrinos. Outside there is net energy gain from neutrino deposition. At any one time there is about 0.1 solar masses in the gain region absorbing a few percent of the neutrino luminosity. Energy deposition here drives convection Bethe, (1990), RMP, 62, 801 (see also Burrows, Arnett, Wilson, Epstein,...)

81. Colgate (1989; Nature 341, 489)

82. Burrows (2005)

83. Beneficial Aspects of Convection Increased luminosity from beneath the neutrinosphere Cooling of the gain radius and increased neutrino absorption Transport of energy to regions far from the neutrinosphere (i.e., to where the shock is) Also Helpful Decline in the accretion rate and accompanying ram pressure as time passes A shock that stalls at a large radius Accretion sustaining a high neutrino luminosity as time passes (able to continue at some angles in multi-D calculations even as the explosion develops).

84. Challenges Tough physics – nuclear EOS, neutrino opacities Tough problem computationally – must be 3D (convection is important). 6 flavors of neutrinos out of thermal equilibrium (thick to thin region crucial). Must be followed with multi-energy group and multi-angles Magnetic fields and rotation may be important If a black hole forms, problem must be done using relativistic (magnto-)hydrodynamics (general relativity, special relativity, magnetohydrodynamics)

85. When Massive Stars Die, How Do They Explode? Neutron Star + Neutrinos Neutron Star + Rotation Black Hole + Rotation Colgate and White (1966) Arnett Wilson Bethe Janka Herant Burrows Fryer Mezzacappa etc. Hoyle (1946) Fowler and Hoyle (1964) LeBlanc and Wilson (1970) Ostriker and Gunn (1971) Bisnovatyi-Kogan (1971) Meier Wheeler Usov Thompson etc Bodenheimer and Woosley (1983) Woosley (1993) MacFadyen and Woosley (1999) Narayan (2004) All of the above? 10 20 35

86. Gravitational Binding Energy of the Presupernova Star This is just the binding energy outside the iron core. Bigger stars are more tightly bound and will be harder to explode. The effect is more pronounced in metal-deficient stars. solar low Z

87. ; mass cut at Fe-core (after fall back)