Transcript Power-point slides for Lecture 7

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