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Supernova Lightcurves

Supernova Lightcurves. From Arnett: Supernovae and nucleosynthesis (1996). Orders of magnitude (I). Energy from core collapse: (3/5) G M ch 2 /R ' 160 foe (but most disappears as neutrinos) Thermonuclear burning 12 C ! 56 Ni: (M ¯ /56 m u ) Q( 56 Ni) = 1.8 foe.

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Supernova Lightcurves

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  1. Supernova Lightcurves From Arnett: Supernovae and nucleosynthesis (1996)

  2. Orders of magnitude (I) • Energy from core collapse: (3/5) G Mch2/R ' 160 foe (but most disappears as neutrinos) • Thermonuclear burning 12C !56Ni: (M¯/56 mu) Q( 56Ni) = 1.8 foe

  3. Orders of magnitude (II) • Release 1 foe as heat by initial explosion (nuclear or neutrino heating after core collapse) • Convert into kinetic energy: v ' 109 cm s-1 [(Esn/1 foe) (M/M¯)-1]1/2 • Cooling by conversion, expansion means lack of thermal energy for radiation • Hence need for radioactive sources

  4. Orders of magnitude (III) • Radioactive decays • 56Ni !56Co 1/2 = 6.1 days Q = 2.1 MeV • 56Co !56Fe 1/2 = 78 days Q = 4.6 MeV • Available energy • 56Ni: 0.07 (M56/M¯) foe • 56Co: 0.16 (M56/M¯) foe

  5. Orders of magnitude (IV) • Initial star: L ' 105 L¯, Teff > 4000 K • ! R0 < 1014 cm • Explosion: L ' 1010 L¯ Teff' 2 Teff, ¯ • ! R ' 0.25 £ 105 R¯' 2 £ 1015 cm • Erad' 0.1 foe • Eke' 1 foe

  6. Orders of magnitude (V) Hydrodynamical time scale: h = 105 s (R0,14/v9) v9 = v/(109 cm/s) For SN 1987a, R0' 2 £ 1012 cm, h = 50 min

  7. Orders of magnitude (VI) |Egrav| ' GM2/R ' M P/' 10-6 foe (M/M¯)2 /R14 R14 = R/(1014 cm) |Egrav|<< Esn! v >> s Supersonic, shocked expansion Clearly plenty of energy to blow the star apart

  8. Orders of magnitude (VII) • ' 3 M/4  R3' 0.5 £ 10-12 m / R153 m = M/M¯ (1 - )/ = a T3 / 3 R Y  = Pg / P Esn' (1/2) a T4 4  R3/3 T ' 6.3 £ 104 K (Esn/R153)1/4Esn in foe (1 - )/' 1.6 £ 104 (R15Esn)1/4/m Radiation dominates thermodynamics A supernova is a ball of light

  9. Different types of supernovae.

  10. Type II, Ib og Ic are Population I stars – new massive stars • - Type Ia are Population II stars – white dwarfs that explode above Mch

  11. Explosive nucleosynthesis • T > 5 £ 109 K for r < 3700 km: NSE on dynamical timescale and hence iron-group elements • T < 4 £ 109 K for r = 5000 km • T < 2 £ 109 K for r = 13 000 km: no reactions beyond helium

  12. Initial phases • Immediate emission of neutrinos (and gravitational waves? • First optical detection at shock breakout (after hours) • Subsequent energy from radiative diffusion of initial thermal energy and energy released from radioactive decay • Initial thermal energy is converted to kinetic energy

  13. Shock breakout

  14. Structure after breakout Photosphere

  15. More detailed analysis From Arnett (1996), Chapter 13 (and Appendix D) Early stages of math anxiety

  16. Expansion model Homologous expansion: d V/d t ' 3 va V/R va = d R/d t ' const R ' R0 + va t

  17. Thermal energy is converted into kinetic energy

  18. Luminosity

  19. Increasing luminosity with • Increasing Esn • Increasing R0 • Decreasing M

  20. Reactions e- + 56Ni !56Co + e 56Co !56Fe + e+ + e Note that radioactive heating is released mainly as gamma rays, which are later thermalized. Hence heating becomes less efficient in the optical etc. when the mean free path of the gamma rays is comparable with the size of the ejecta.

  21. Recombination Recombination reduces opacity and sets radiation free (just as after Big Bang). Also (but generally of lesser significance) releases ionization energy. Opacity dominated by electron scattering, / ne

  22. Opacity

  23. Ionization energy

  24. Recombination wave Concentrate on fast wave

  25. Note: recombination only significant after recombination front is near or below photosphere: Teff4 < 2 Ti4

  26. Overall energy equation

  27. Overall energy equation Together, these can be solved for evolution of supernova and hence luminosity

  28. Final state • Recombination involves all ejecta • Ejecta are optically thin • From superstar to supernebula • Still powered by radioactive decay

  29. Lightcurves for SN type II and fits to Arnett model

  30. Model examples

  31. Mej/M¯ =15 E = 1.5 foe R0 = 3 £ 1012 cm

  32. 1987A, extended lightcurve Suntzeff et al. (1992; ApJ 384, L33)

  33. 1987A, late stages M(56Co)=0.07 M ¯, M(57Co)=3.3×10−3 M ¯, and M(44Ti)=1×10−4 M¯ . 1/2 = 278 d 1/2 = 60 yr Fransson & Kozma (2002; New Astron. Rev. 46, 487)

  34. R0 cm R0 = Mej/M¯ =15 E = 1.5 foe R0 =

  35. E = 1.5 foe R0 = 3 £ 1013 cm

  36. Mej/M¯ =17 E = 1.5 foe R0 = 15 £ 1012 cm

  37. Mej/M¯ =2.2 E = 1.0 foe R0 = 22 £ 1012 cm

  38. Mej/M¯ =3.3 E = 1.7 foe R0 = 0.7 £ 1012 cm (excluding thin H layer)

  39. Discovered 2005/09/27.44 by Lick Observatory Supernova Search • Found in IC 307 • Mag 18.0, Type unknown

  40. Pause… 

  41. Supernovae Light Curves

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