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Supernova Lightcurves From Arnett: Supernovae and nucleosynthesis (1996) 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 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 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 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 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 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 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)1/4 Esn in foe (1 - )/ ' 1.6 £ 104 (R15 Esn)1/4/m Radiation dominates thermodynamics A supernova is a ball of light Different types of supernovae. Observeret hyppighed 2,3 ~1 5,0 - Type II, Ib og Ic are Population I stars – new massive stars - Type Ia are Population II stars – white dwarfs that explode above Mch 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 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 Shock breakout Structure after breakout Photosphere More detailed analysis From Arnett (1996), Chapter 13 (and Appendix D) Early stages of math anxiety Expansion model Homologous expansion: d V/d t ' 3 va V/R R ' R0 + va t va = d R/d t ' const Thermal energy is converted into kinetic energy Luminosity • Increasing luminosity with • Increasing Esn • Increasing R0 • Decreasing M 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. 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 Opacity Ionization energy Recombination wave Concentrate on fast wave Note: recombination only significant after recombination front is near or below photosphere: Teff4 < 2 Ti4 Overall energy equation Overall energy equation Together, these can be solved for evolution of supernova and hence luminosity Final state • • • • Recombination involves all ejecta Ejecta are optically thin From superstar to supernebula Still powered by radioactive decay Lightcurves for SN type II and fits to Arnett model Model examples Mej/M¯ =15 E = 1.5 foe R0 = 3 £ 1012 cm 1987A, extended lightcurve Suntzeff et al. (1992; ApJ 384, L33) 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) R0 = R0 cm Mej/M¯ =15 R0 = E = 1.5 foe E = 1.5 foe R0 = 3 £ 1013 cm Mej/M¯ =17 E = 1.5 foe R0 = 15 £ 1012 cm Mej/M¯ =2.2 E = 1.0 foe R0 = 22 £ 1012 cm Mej/M¯ =3.3 E = 1.7 foe R0 = 0.7 £ 1012 cm (excluding thin H layer) • Discovered 2005/09/27.44 by Lick Observatory Supernova Search – Found in IC 307 – Mag 18.0, Type unknown Pause… Supernovae Light Curves Supernovae Light Curves • SN type II – L&P – SN 1987A – SN 1993J • SN type I – Ib & Ic – Ia • Archaeology Type II • • • • Iron core collapse Rapid rise in luminosity Maximum light about Mbol = -18 Decreases about 6-8 magnitudes / year Light curves • Radioactive decay – 56Ni ½ = 6.1 days – 57Co ½ = 271 days – 22Na ½ = 2.6 yr – 44Ti ½ = 47 yr – This can cause the slope of the light curve to change. Type II-L • L - Linear Doggett and Branch, Astron. J., 90, 2303, 1985 Type II-P • P - Plateau – A plateau - 30 – 80 days after maximum light – Decay energy is deposited in an optical thick shell Doggett and Branch, Astron. J., 90, 2303, 1985 SN 1987A SN 1987A SN 1987A • Sanduleak -69202 • Unusual – Slow rise - 80 days to maximum light – Maximum Mbol = -15.5 – Blue supergiant - B3 I SN 1987A • Deeper potential – More energy to lift the envelope – Time scale for the energy to radiate away >>6.1 days • Bump in the light curve Suntzeff et al., 1992, ApJ, 384, L33 Suntzeff et al., 1992, ApJ, 384, L33 SN 1987A • Red supergiant to Blue supergiant – Stellar mass (can`t be much more than 20Msun) – Composition (low Z) – Mass loss (low) SN 1987A Arnett et al., Annu. Rev. Astron. Astrophys., 27, 629, 1989 SN 1987A Hubble Space Telescope`s WF/PC2 SN 1987A Arnett et al., Annu. Rev. Astron. Astrophys., 27, 629, 1989 SN 1993J • SN type II in M81 – Weak hydrogen lines • But the H-lines weakened and SN1993J turned in to a type Ib • MHS = 15Msun • Mass loss: All but 0.1-0.6Msun of the H – By Roche lobe overflow SN type I Doggett and Branch, Astron. J., 90, 2303, 1985 SN type Ib & Ic • In spiral galaxies only – HII regions • Fainter then II & Ia by 1.5-2mB – More massive stars produce less 56Ni • Light curve decline 0.065±0.007mag / day at 20 days after max • Decline 0.010mag / day after 50 days (the half-life of 56Co – 77.7days) SN type Ia • Nuclear energy generation (white dwarf) • Seen in all types of galaxies • Light curve decline 0.065±0.007mag / day at 20 days after max • Decline 0.015mag / day after 50 days – 50% faster than type Ib & Ic • At maximum light MB = -19.6 ± 0.2 SN type Ia • Spectra of Type Ia supernovae at the time of B-band maximum (taken from a paper on SN 1999aa, astro-ph/0404393, by Garavini et al.) SN type Ia Cadonau 1987 SN type Ia Phillips, AJ, 413, L105, 1993 SN type Ia Krisciunas et al, AJ, 125 , 166, 2003 SN type Ia SN type Ia Goldhaber et al. ApJ 558, 359, 2001 SN type Ia Perlmutter et al. ApJ 517, 565, 1999 SN type Ia Perlmutter et al. ApJ 517, 565, 1999 Archaeology Doggett and Branch, Astron. J., 90, 2303, 1985 Summary • Energy production • Optical thickness • Radioactive decay