Supernovae, Gamma-Ray Bursts and the Origin of the Elements. - a Theorist s Perspective. Stan Woosley Max Planck Institut für Astrophysik

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1 Supernovae, Gamma-Ray Bursts and the Origin of the Elements - a Theorist s Perspective Stan Woosley Max Planck Institut für Astrophysik June 11, 18, 25, 2008 Ludwig F. B. Biermann

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3 NGC Mpc X-ray Optical SN 2008D (Soderberg et al) A supernova is the explosive death of a star. For a few months its luminosity in light can rival that of a galaxy.

4 Supernova Discovery History Asiago Catalog (all supernova types)

5 Supernova Discovery Future Rough predictions and promises Supernova PanStarrs Factory Lick Dark observatory Energy Survey SN search CfA JDEMSN group Carnegie Large Synoptic SN project Survey ESSENCE Telescope (LSST) Supernova Legacy Survey slide from Dan Kasen

6 Outline of Lectures Thermonuclear Supernovae I II Core-Collapse Supernovae III slide adapted from Maryam Modjaz

7 SN Ia SN 1998aq SN 1998dh SN 1998bu SN 1994D HST Among the brightest optical lights in the universe, Type Ia supernovae are also standard candles for cosmology. 30 Vundatons of TNT! 3 x tons peta 15 exa 18 zetta 21 yotta 24 xona 27 weka 30 vunda 33 uda 36

8 But what are they Hoyle and Fowler (1960)

9 Three possibilities double-degenerate (WD merger) scenario burning to O-Ne-Mg WD AIC? slow merger? single-degenerate scenario M Ch models sub-m Ch models

10 Sub-MCh Ia M M yr -1 M WD M

11 Sub-Chandrasekhar models Woosley, Taam, and Weaver (1986) Livne (1990) Woosley & Weaver (1994) Kasen (2008, unpublished) But mechanism robust in 2D and 3D (Fink, Hillebrandt, and Röpke 2007). Ought to happen, but are not the typical Ia s.

12 MERGING WHITE DWARFS High accretion rate leads to compressional ignition of C-burning at edge of WD which leads to the stable conversion of CO to NeOMg, followed by collapse to a neutron star (Saio and Nomoto 1985, 1998 and others) Yoon, Podsiadlowski and Rosswog (2007), SPH calculations. Can avoid edge lit collapse if merger produces subcritical rapidly rotating core and a disk and accretion time scale for the disk is < 10-5 solar masses yr -1. SN 2006gz, lots of unburned carbon at hi v. Luminosity unusually high x erg s -1 at peak. Velocity not unusually high. SN 2003fg is similar. But - magnetic torques in the star and in the disk. Hicken et al. (2007) Howell et al. (2006) The jury is still out

13 CHANDRASEKHAR MASS MODELS Progenitor Arnett (1968, 1969) Nomoto, Sugimoto, & Neo (1976) Ignition occurs as the highly screened carbon fusion reaction begins to generate energy faster than (plasma) neutrino losses can carry it away. At a given temperature, the plasma neutrino losses first rise with density and then decline when p > kt. As 2.5 to gm cm -3 ;T K S nuc ( 12 C+ 12 C) S (plasma); M 1.38 M

14 The ignition conditions depend weakly on the accretion rate. For lower accretion rates the ignition density is higher. Because of the difficulty with neutron-rich nucleosynthesis, lower ignition densities (high accretion rates) are favored. Ignition when nuclear energy generation by (highly screened) carbon fusion balances cooling by neutrino emission. Answer depends somewhat on the accretion rate. nb. This will affect the nucleosynthesis

15 Ignition Conditions Supernova preceded by 100 years of convection throughout most of its interior. Energy goes into raising the temperature of the white dwarf (not expansion, not radiation). Last "good convective model" is when the central temperature has risen to 7 x 10 8 K Pressure scale height: 400 km Convective speed: 50 km s -1 Nuclear time scale: 10 2 s Convective time scale: 10 2 s Binding energy: 4 x erg Density: 3 x 10 9 g cm -3 Burning 0.05 solar masses can cause expansion by a factor of three

16 Convection for 100 years, then formation of a thin flame sheet. Note that at: T 7 x 10 8 K the burning time and convection time become equal. Can t maintain adiabatic gradient anymore 1.1 x 10 9 K, burning goes faster than sound could go a pressure scale height Burning becomes localized S nuc T 26 0 radius

17 A Successful Model Must: Explode violently Produce approximately 0.7 solar masses of 56 Ni (0.1 to 1 M sun ) For the light Produce at least 0.2 solar masses of SiSArCa For the spectrum Not make more than about 0.1 solar masses of 54 Fe and 58 Ni combined Give the observed width-luminosity relation and allow for some diversity For the nucleosynthesis These requirements are at variance with a model that burns only at the laminar speed, < 50 km/s.

18 The ashes are less dense than the fuel, hence Rayleigh-Taylor unstable ~ 20% g eff ~10 9 cm s -2 RT Shear, turbulence Zingale et al. (2005) Roepke and Hillebrandt (2007)

19 As a result of the RT instability, the overall burning front progresses roughly at a speed given by the Sharp-Wheeler model (1984). v flame ~ 0.1 g eff t >> S laminar GM (r) g eff = r cm s -2 This accelerates the flame to a fraction of the sound speed in a second as is necessary to explain the observations - very roughly. In fact, the SW model alone fails to give adequate intermediate mass elements and is a poor description of the flame on any but the largest scales. Any proper treatment must include the effect of turbulence, both on and below the grid (Damköhler 1940; Niemeyer and Hillebrandt 1995) v flame (grid scale) u turb at the grid scale

20 Pure Symmetric Deflagration - MPA 1600 points within 180 km Röpke et al (2007) t=10.0s t=3.0s t=0.0s t=0.6s

21 Pure Symmetric Deflagration Deflagration model Successes good subgrid flame physics reasonable agreement with observed properties of weaker SNe Ia Shortcomings artificial starting conditions low 56 Ni mass (~0.4 M ) do not reproduce brighter SNe Ia composition of outer layers in disagreement with those expected for brighter SNe Ia

22 Symmetrically Ignited Delayed Detonations Röpke & Niemeyer (2007) Mazzali et al. (2007) See also previous work by Khokhlov (1991) Höflich (1995) Gamezo et al (2003) Woosley & Weaver (1994) Niemeyer and Woosley (1997)

23 Symmetrically Ignited Delayed Detonations Not so good: Ignition points still artificially distributed Detonation initiated ad hoc Good: Now accounts for bright SN Ia (faint ones would be when DDT fails). Agreement with energies, light curves and spectra likely to be good A sea change for Niemeyer et al.

24 Gravitationally Confined Detonation Chicago FLASH - UCSC - MPA Munich/Santa Cruz results agree with Chicago in 2D, but show weaker collisions in 3D that do not, in general, detonate

25 Chicago GCD Model Jordan et al (2008) White dwarf expands less than in the Röpke et al. model, so the collision on the far side occurs at higher density and less geometrical dilution. The temperature is sufficient to ignite a detonation that consumes the rest of the star. Will always make a bright supernova. The answer depends on the subgrid model

26 Asymmetric Delayed Detonation PPM based code Use level set for flame tracking subgrid model for turbulence (Pocheau 1994; Schmidt et al 2006ab) Roepke, Woosley, and Hillebrandt (2007) For models whose ignition kernels extend even slightly to the far side of the star, sufficient burning occurs on the first try to completely unbind the star (about 2/3 of the star burns). But the explosion is weak. Something else is needed.

27 Parameterized simulations Röpke, Kasen, Woosley (2008) Currently carrying out a survey of 2D models in which ignition location and the conditions for transitioning to detonation are parameters. For some, but not all models, the light curve and decline rate depend on viewing angle. This model made 0.7 solar masses of 56 Ni and had an explosion energy of 1.2 x erg.

28 The stronger the deflagration phase > the more pre-expansion > the lower the densities at detonation > the less 56 Ni produced M Ni = 0.5 M sun E K = 1.2 x ergs

29 Off-center Detonation Roepke, Kasen, Woosley M Ni = 1.0 M sun E K = 1.3 x ergs An alternative to super-chandra SNe? Howell et al, 2006 Hillebrandt, Sim, Roepke 2007

30 So the answer depends on how the white dwarf is ignited and whether and where there is a transition to detonation. great..

31 IGNITION Roepke et al. (2006) Roepke, Woosley, and Hillebrandt (2007) multi-point off-center single point off-center Origin of Diversity? Displacement 1st Explosion 50 km 2.31 x erg single point central Plewa (2007) (2D survey)

32 Chandraskhar (1961) Kuhlen, Woosley, and Glatzmaier (2006) Central T 7 x 10 8 K (just before runaway) spectral grid - 3D anelastic 241(n) x 42(m) x 85(l)

33 Central T 7 x 10 8 K (just before runaway) Cartesian non-rotating Ma et al (2008)

34 t = 0.2 s t = 0.5 s t = 1.0 s 3D Cartesian, anelastic hydrodynamics 384x384x384 zones. Resolution ~10 km. Ra ~ 5 x 10 6, Re ~ 1000 Barely turbulent No flame model In the SN Ra ~ Re ~ Ignition continued ~100 km off center for ~ 1 second

35 = 0 Ro ~ 0.01 Re ~ x D calculation of high Re convection between two rotating cylinders in a gravitational field that goes as 1/r. (Glatzmaier 2007)

36 128 3 Cartesian = 0.8 rad/sec 2% Keplerian at the surface 0.8 rad s-1 Ro = 0.06

37 = 0 = 0.8radians/sec xy - non-rotating case xy - rotating case

38 Dependence on Rotation Ignition radius (rad/s) (km) If ignition farther off center correlates with greater Ni production in the detonation, as seems likely, then the brightness of a SN Ia will correlate with its rotation rate.

39 Rayleigh-Benard convection between two plates Ra = 2 x Rogers, Glatzmaier, and Woosley (2002) unpublished Kraichnan (1962) regime?? see also Lohse and Toschii, PRC, 90, (2003) Kadanoff, Physics Today, 54, 34 (2001)

40 Transition to Detonation

41 Transition to Distributed Burning 1.5 x 10 7 g cm x 10 7 g cm x 10 7 g cm -3 RT instability only; no external turbulence; 2D (Bell et al. 2004, ApJ, 608, 883)

42 3D fully resolved studies Aspden et al (2008) ApJ, submitted For typical SN Ia turbulence parameters u = 100 km/s L = 10 km

43 7 = 8 Ka = = 4 Ka = = 3 Ka = 0.97 Low Mach Number code SNe. Adaptive mesh. Background Kolmogorov turbulence u = 10 7 cm s -1 L = 10 km Aspden, Bell, Day, Woosley and Zingale (2008), ApJ, submitted 3D 1000 x 1000 x 250 zones ~ 2 M hr ATLAS LLNL 7 = 2.35 Ka = = 1 Ka = 230

44 X( 12 C) T 7 = 8 Ka = = 4 Ka = = 3 Ka = D simulations by Aspden et al (2008) u = 10 7 cm s -1 L = 10 km 7 = 2.35 Ka = 3 7 = 1 Ka = 230

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46 The Linear Eddy Model (LEM) is a 1D stochastic simulation of 3D turbulence Kerstein (1988, 1989, 1990) Assume background of isotropic Kolmogorov turbulence Turbulent advection represented by randomly sampled eddy events on a1d grid Each event is an instantaneous rearrangement of property profiles: triplet map

47 The triplet map is a 1D procedure TRIPLET MAP that emulates 3D eddy kinematics Kerstein (1988, 1989, 1990) c(x) The triplet map captures compressive strain and rotational folding effects, and causes no property discontinuities The triplet map is implemented numerically as a permutation of fluid cells c(x) c(x) x x This procedure emulates the effect of a 3D eddy on property profiles along a line of sight

48 Woosley, Kerstein, Sankaraan, & Röpke (2008 in preparation) 5 x laminar LEM results; 7 = 1 Agrees on speed and flame width with the 3D study

49 Keep turbulent energy density, u 3 /L, constant and vary L L = 120 cm L = 960 cm Varying the characteristic length scale of the turbulence one sees self similar profiles. Turbulence is dominating the transport but the turbulent turnover time on the integral scale is staying much shorter than the nuclear time. The flame looks just like a laminar one, but D ~ u 'L not D = D rad Speed ~ D t / nuc u'l L 2/3 Speed < u' for L < Width D t nuc L 2/3 Width < L for L < Width/L L -1/3

50 7 = 1, X 12 = 0.5 X 12 nuc T 9 4 snapshots from the same run L = 76.8 m ~

51 What is this thing called? 3 = nuc Kol = f (, ) Kol = u'3 L e.g. u' = 100 km/s L = 10 km = turbulent energy density =10 15 erg gm -1 s -1 = 10 7 g cm -3, ~ 500 m When =L, the mixture burns on a time scale equal to the turnover time on the largest turbulent scale. nuc = u'/ L Related to the Damkohler Number Da = eddy (L) nuc = L nuc u' = L 2/3 when Da = 1, =L

52 Distributed Reaction Zone c s /5 Da = 1 Da = 2 c s /10 Stirred Reactor n-flames Ka = 10 Flamelet Regime

53 = 3.2 m v' = 6.85 km s -1 x = 0.1 cm

54 12 km

55 12 km Elapsed time 2 ms

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58 Conclusions Understanding how a Type Ia supernova explodes takes us to the frontiers of both fluid mechanics and combustion theory. It is not only a multi-scale problem but a multi-physics problem. Today (but maybe not tomorrow), the most reasonable model seems to be one that ignites in a lopsided way, though perhaps not in the simple way I showed. It then detonates at a density very close to 10 7 g cm -3. Models of this sort are being explored and show good promise for agreeing with observations

59 Interesting issue (e.g., Filippenko 1989; Sullivan et al (2006):

60 Possible explanations: Metallicity in ellipticals is higher, hence a larger ratio of 54 Fe and 58 Ni to 56 Ni and, for the same iron group content, a fainter supernova. (Timmes et al 2003 but see Gallagher et al astroph , age more important than metallicity) Higher ignition density due to lower accretion rate in older systems - larger leverage on 54 Fe than Z Two kinds of models Different DDT density for different carbon mass fractions in outer layers. Lower DDT density makes less 56 Ni, X( 12 C) may vary with white dwarf mass Umeda et al (1999) and Woosley (2007) reach opposite conclusions. Rotation and ignition conditions