Core-Collapse Supernovae and Abundances in Extremely Metal-Poor

Keiichi Maeda Dept. of Astronomy, School of Science, Univ. of Tokyo

SN 1998bw () SN 1987A

=

E ~ 30×1051ergs E ~ 1×1051ergs

Explosion Mechanism? Nucleosynthesis? Galactic Chemical Evolution?

1 Contents • Introduction – Stellar evolution & supernovae • Observational properties of hypernovae – Spectra and light curves (Optical) • Evidence of asphericity and formation in hypernova explosions • Jet-induced explosion model – Hydrodynamics of jet propagation – Growth of a central black hole – Nucleosynthesis • Abundances in metal-poor stars and early Galactic chemical evolution – Contribution of hypernovae

SNIa Evolution of Stars

SNII/Ib

2 SNe Ia: Accreting White Dwarfs SD Scenario DD Scenario orbit shrinks

WD GWR WD WD GWR companion accretion disk accretion from thick disk

NS

SNeIa

3 Core-Collapse SNe: Massive Stars

Delayed Neutrino Explosion Model

Marginally Explains Energetic of (Normal) Core-Collapse SNe (1051ergs) e.g., Janka et al. 2002

4 Fate of Massive Stars

• ～１２－２5M~: Core-Collapse Supernovae （Neutron Formation）

• ～２5－１００？M~： Supernovae/Hypernovae （Black Hole Formation?）

• ？－１3０？M~： Direct Collapse to a BH （Black Hole Formation?）

• ～１4０－２７０M~： Pair Instability SNe (PISNe) (No Central Remnant)

• ～３００M~以上: Direct Collapse to a BH? BH + Explosion?

Cycle in the Galaxy/Universe

5 Abundances in Halo-Stars and Galactic Chemical Evolution [X/Y]=log(X/Y) – log(X/Y) [X/Fe]

ISM

Heavy Elements Core-Collapse SNe SNe Ia Stars -1 0 1 0 -1

-4 -2 0 [Fe/H] Supernovae Mass loss Time

More Massive Stars

6 Observational Properties of Hypernovae

Spectra of Supernovae & Hypernovae Ic: no H, no strong He, SiII Ia no strong Si O Ca He Ib Hypernovae： Ic broad features 94I blended lines Hyper 97ef -novae “Large mass at 98bw high velocities”

7 Classification of Supernovae Ia -- Si line -- Exploding WD SNI -- no H Ib -- He lines SN Ic -- no He, Si -- Core-Collapse SNII -- H line

･Evolution of Massive Stars (Mass Loss) C/O Fe Ic

Mass Loss H He Mass Loss C/O Ib H ⇒⇒He PreSN

H He C/O II

Light Curves of Supernovae & Hypernovae

Light Curve Broadness SN1998bw >> SN1994I

Ejected Mass SN1998bw >> SN1994I

Progenitor’s Mass SN1998bw >> SN1994I

8 CO Star Models for SNeIc

Parameters [M , E, M(56Ni)] H-rich ej He Light Curve Spectra ５６Fe 1/2 E ∝ Mej τ ~[τdyn • τdiffusion] C+O 56 1/2 Co R κ Mej ~• M Si VR c C+O 56Ni Fe ∝κ½M ¾E -¼ Collapse ej ５６Ni E ∝ M 3 Mms/M~ MC+O/M~ ej ~40 13.8 ~35 11.0 ~22 5.0

Spectral Fitting: SN1997ef

Model Normal SN

Small Mej

Too Narrow Features

9 Spectral Fitting: SN1997ef

Model Hypernova

Large Mej

Broad Features

Hypernova Candidates × 51 Ekinetic > (5-10) 10 ergs SN 1998bw SNe Ic SNe IIn SN GRB SN GRB 1998bw 980425 1997cy 970514

1997ef 971115 1999E 980910 1999as 1988Z GRB 980425 2002ap 1999eb 991002 1997dq 1998ey 1992ar

10 Progenitors’ Mass – E – M(56Ni)

Evidence of Asphericity and Black Hole Formation in Hypernova explosions

11 2 2 53 Egrav ~ GMREM /RREM ~ G(1.5M) /(10km) ~ 6×10 ergs

Egrav / ESupernova ~ 0.002 ; Marginally attained in simulations.

Egrav / EHypernova ~ 0.02 (NS), 0.002 (BH) ; ???

Jets in the Universe

L1551-IRS5 v4641 Sgr SUBARU/NAO Hjellminget et al. VLA/NRAO

Young Stars Stellar Mass Black Holes

3C175 Centaurs A Bridle NASA/CXC/SAO VLA/NRAO/NSF AURA/NOAO/NSF Galaxies Quasars

12 1) Asphericity in Core-collapse SNe (in general) SN1987A: Asymmetrical, but not spherical, ejecta Optical Polarization in core-collapse SNe > 0.5 % (in SNe Ia < 0.2 - 0.3%)

HST Image of SN1987A Optical Spectropolarimetry of Wang et al. 2002 SNe 1993J, 1996cb, Wang et al. 1999

2) Light Curves of Hypernovae -20 -20 1998bw 1998bw -19 -19 -18 -18 -17 -17 -16 -16 -15 -15 Bol Bol 0 25 50 0 25 50 -14 1997ef -14 1997ef

-12 2002ap -12 2002ap Co -10 -10 0 100 200 300 400 500 0 100 200 300 400 500 Time [day] Time [day] Low Density High (Vacuum) Density

Spherical Hydro Model Maeda et al. 2003, ApJ, submitted

13 3) Late time spectra of SN1998bw Line Width Inversion of Fe and O

[OI] 6300A O FWHM FeII] 5200A Fe Observation

Spherical Expansion Observer Broader Fe lines than O lines in the observations.

[OI] 6300A Interpretation as an FeII] Aspherical explosion 5200A Observation

Spherical 56Fe

15 deg

16O

Aspherical Maeda et al. 2002

14 4) Optical Polarimetry of SN2002ap 6×10–14 (a) February –14 Feb, 2002 4×10 March Flux 2×10–14 <1% at OI7773 0 2 (b) Outer Region Average in February Ca 1 Average in March O

March,2002 % Pol 0 <2% at CaII IR 200 (c) Inner Region 150 100 PA (deg)

–16 1.5×10 (d) 0.0018 × Feb Flux 1×10–16 (redshift = 0.23c) 5×10–17

1)Different flux Pol. asphericity in 0 2 (e) Average in February (cont. sub’d) Average in March different depths. 1 % Pol 0 200 (f) 2)The Polarized flux is 150 100 well fitted by radiation PA (deg) 5000 6000 7000 8000 redshifted by 0.23c. Rest wavelength (Å) Kawabata et al. 2002

A Hypothetical ‘Jet’ Interpretation

F [λ (1 –Vred/c) ] Observer Pjet (λ) = f ＊ F（λ）

Vred = Vjet (1 + cos i) = 0.23 c,

Thus Vjet > 0.115c.

The jet could be a 56Ni-rich blob. High ionization state is expected. vjet i

15 5) BH Formation in a HN explosion

Abundances in Sco [X/H]=log10(X/H)-log10(X/H) 1.5 SN matter 1 BH 0.5 [X/H]

0 NOMgSiSTiFe -0.5

• Enhancement of O,Mg,Si,S,Ti by a factor of 6-10. Israelian et al. 1999

Hypernova model for the formation of the BH in Nova Sco

Abundance in Nova Sco BH mass in the model 1 E51=30 0.8 4.8M at the explosion 0.6 SN

[X/H] 0.4 0.2 0 5.4M now (Post SN) He C O Ne Mg Si S Ca Ti Fe BH

MMS=40, MHe=16, E51=30

MBH at the explosion ~ 5M Black hole formation with Hypernova explosion. Podsiadlowski et al. 2002

16 The properties of hypernova explosions • High velocity material (Fe) • Low velocity & high density material (O) – Contrary to conventional spherical models. • forms a black hole, but explodes with large E51 (>10). – Black hole formation does not always leads to a failed .

Do jet-induced explosions satisfy these conditions?

Jet-induced explosion model

17 Previous Works

Energy Mass cut Yields Input Many Prompt By hand Done 8-300M

Spherical E51=1-100 Nagataki Prompt Byhand Done SN1987A 1998&2000 (No Accretion) Aspherical 20M, E51=1 Maeda et al. Prompt By hand Done SN1998bw 2002 (No Accretion) Aspherical 40M, E51=1-30

Khoklov et Jet induced Hydro No 15M, E51=1 al. 1999 (By hand) (By Accretion) This Work Jet induced Hydro Done 20M,40M (By Accretion) (accretion) E51=1-30

Model: Jet-induced Explosion M 16MHe (MMS=40), Rem0 1.0 – 3.0M 8M He (MMS=25), (Nomoto&Hashimoto 1988)

15o Radiation＋Pairs

Newtonian Gravity

2 Ejet = ε Mc , 0.01

Postprocessing K. Maeda, in preparation 222 isotopes (Tielemann et al.)

18 Log (Density[g cm-3]) Hydrodynamics Radial Velocity/c

Collimated jets (Z) + Bow shock (All direction) R/1010cm M Lateral expansion

Density Hydrodynamics (Center) Radial Velocity

Accretion from the side R/1010cm

Continue to accrete, MBH

19 56 E51=11, MBH(final)=5.9M, M( Ni)=0.11M Outflow

Inflow

0.7 s

1.5 s

R/1010cm

Density Distribution

High density core at the central region Jet (R) High velocity material along z Sph (E51=1)

Sph (E51=10)

Jet (z)

(E51=11)

20 Growth of a central remnant

MBH

8 Inefficient Jet MREM can be ~ 5 – 10M, starting from 1.5 – 3M. efficient Still a strong explosion 4 Jet

follows (E51>10).

0 20 40 Time A hypernova with a stellar mass black hole (sec) (X-ray Novasco; Large Si,S with black hole formation).

Final Remnants’ masses and Kinetic Energies

11 6.9 5.9

51 1.9 E51=E/10 ergs MBH(M)

• A more massive star makes a more energetic explosion (As seen in ‘Hypernova Branch’).

21 Fe, O Distribution 51 E51（=E/10 ergs）=10, Vz (/109cm s-1) MRem=6M8, 6 56 M( Ni)=0.18

4

2 High Velocity Fe Low Velocity O 0 9 246

0.5 0.1 56Ni(56Fe) 16O 0.01

56 Relation in MREM and M( Ni) Optical L ) (M

40M

20M

Efficient (M) inefficient GW: ν GW: ν e.g., rotation

22 Jet-Driven Explosion Model • High velocity material (Fe) • Low velocity & high density material (O) – Contrary to conventional spherical models.

• forms a black hole, but explodes with large E51 (>10). – Black hole formation does not always leads to a failed supernova.

These conditions can be satisfied. Nucleosynthesis features?

Abundances in Extremely Metal-Poor stars and Early Galactic Chemical Evolution

23 Abundances in Halo-Stars and Galactic Chemical Evolution [X/Y]=log(X/Y) – log(X/Y) [X/Fe]

ISM

Heavy Elements Core-Collapse SNe SNe Ia Stars -1 0 1 0 -1

-4 -2 0 [Fe/H] Supernovae Mass loss Time

More Massive Stars

24 Abundances in Extremely Metal-Poor Stars as Relics of SN Explosions in the Early Galactic Evolution Only one explosion likely PopII Star Ｓｈｏｃｋ Ｗａｖｅ produced metal- poor stars Formation with [Fe/H]= –4 ~ –2.5

☆ [X/Fe]=log(X/Fe)-log(X/Fe)~ ☆ （Ryan et al. 1996, Shigeyama & Tsujimoto 1998, Nakamura, Umeda, Nomoto, Thielemann, Burrows ☆ 1999) PopIII ＳＮ The abundance of these stars are determined by the ☆ nucleosynthesis in individual ☆ Core-Collapse SNe. ☆ Star Formation The SNe should be massive because of their short lifetime.

25 [X/Fe]=log(X/Fe) - log(X/Fe)~ Co Cr

trend Individual SNe Time [Fe/H] [Fe/H]

More Massive Star? Mn

Zn

More Massive Star Smaller [Fe/H]

Fe/H= Fe ejected by individual Core-Collapse SN/ H swept up by the Shock wave ∝ ～M(Fe)/E （Ryan et al 1996; Shigeyama & Tsujimoto 1998）

Fe: depends on the mass cut

Mg: Independent from the mass cut Observations: [Mg/Fe]~0.5, almost constant

26 Explosive Nucleosynthesis in SNe

Before the Explosion After the Explosion

Explosive Nucleosynthesis in SNe

• Explosion ⇒Shock heating⇒Explosive Nucleosynthesis

•Tpeak (peak temperature after the shock passage) –Tpeak > 5･109K -- Complete Si burning • (Products: e.g., 56Ni, Zn, Co) –4･109K < Tpeak < 5･109K -- Incomplete Si burning • (Products: e.g., 56Ni, Mn, Cr) • the matter outside the “Mass-Cut” is ejected. – The location of Mass-cut is somewhere in the explosive Si- burning region, but uncertain (because of the uncertainty in the explosion mechanism). – The location of Mass-cut may be constrained by observations of 56Ni mass and Zn, Co, Mn, Cr abundance.

27 Incomplete Si-burning

Mass Cut

星の Remnant Ejecta 星の 内側 外側

Mn

Abundance Ratio: Post Explosion/Pre Explosion

28 Low energy High energy

For the same Mass-cut, mass fraction of complete Si- burning region becomes larger.

Low Energy ｖｓ High Energy Explosion

28Si 28Si 56 16 56Ni 16O Ni O

29 Low Energy

(Si, S, Ar, Ca, Ti) /(Mg, O) & Zi/Fe

Larger

High Energy

Hypernova Nuclosynthesis

zM(Complete Si-burning) Zn,Co/Fe Mn,Cr/Fe O,Si/Fe (If Mass-cut is deep enough) zMore α-rich High Entropy Zn/Fe 64Ge Ti/Fe zMore O burns Si,S,Ca/O

30 Zn production

• is not successful in Observed range in very the ALL previous low metal [Fe/H]<-3 Halo-stars models • is important because, for Damped Lyman-α system abundance, [Zn/Fe]=0 has been often assumed.

Zn production

• Large Explosion Energetic Energy is required to get [Zn/Fe]>0.3 • We claim Zn is mainly produced in Hypernova explosive nucleosynthesis for low [Fe/H]

Hypernova models

31 Low energy – Larger explosion Ｅｎｅｒｇｅｔｉｃ energy ⇒Higher entropy (T3/ρ) ⇒ Low energy more α-rich ⇒ more 64Ge ⇒ decay to 64Zn – Zn abundance is maximum for Ye =0.5 because 64Ge is a symmetric species （Ye: electron mole fraction) Ｙｅ＝０．５ Ｅｎｅｒｇｅｔｉｃ

[O,Mg/Fe] Mixing in SNe?

[Co,Zn/Fe] 56Fe 16O 1 28 Si 16 4He 56 12C O 16O Fe 20Ne 32S 4 24 28Si 40 44Ti 0.1 He Mg 48Cr Ca 52Fe 55Co 56Ni 58Ni 59Cu 58 64Ge 0.01 Ni 55 24Mg Mn 40Ca 48 59Co Ti 0.001 64 32 Zn S 1e-04 Mass 1.5 1.7 1.9 2.1 Complete No burning Si burning O,Mg Co, Zn

32 Mixing ＆ Fall-Back Model (1D) Mixing Region Fall Back Ｏ Ｓｉ

Ｆｅ

Initial Mcut Final Mcut Ejected 56Ni mass can (should) be smaller without changing the Zn,Co/Fe ratio

Matter Mixing by Rayleigh-Taylor Instability

Kifonidis et al. 1999

33 Maeda et al (2002)

Asymmetric Explosion 16O 一種のBeaming 効果 56Ni

Mass Cut

Comparison with Extremely Metal-Poor Stars Umeda & Nomoto 2002

• Typical (Averaged) Abundance (Norris, Ryan, Beers 2001) – [Fe/H] ~ -3.7 • C,N rich – Extremely Metal-Poor Stars • CS 22949-037 – [Fe/H]= - 4.0, [C/Fe]=+1.1 • CS 29498-043 – [Fe/H]= - 3.8, [C/Fe]=+1.9 • CS 22957-027 – [Fe/H]= - 3.1, [C/Fe]=+2.4

34 Typical (Averaged) Abundance （NRB01）

25M~, E51=1, Mcut=2.20M~ (Normal energy model)

Mg, Al ⇒ Mcut Co, Zn ⇒ Mcut

Mcut の違いでは解決しない ⇒ E 大

Typical (Averaged) Abundance: [Fe/H]~ -3.7

25M~, E51=20, Mixing =2.35 - 4.88M~ (High energy model)

Mcut(I)=2.35, Mcut(f)=4.88, 放出率 f=0.1 --- Mixing & Fallback

Mg, Al, Zn – O.K. (Large + Mixing Effect) Sc, Co, Ti – Not enough ⇒ Another Effect (e.g., Jet)? Mn -- Low energy? Ye?

35 C,N rich – Extremely Metal-Poor Stars

CS 22949-037, [Fe/H]~ -4.0 (NRB01; Depagne et al. 2002)

30M~, E51=10, Mixing=2.46 - 6.69M~ , f= 0.005

Little Fe（５６Ni) ⇒C,N,O/Fe

これ以上Eが大きいと Mg/Si (Si )が合わない Ca,Sc,Ti, Co,Zn: Not enough ⇒Another Effect?

C,N rich – Extremely Metal-Poor Stars

CS 29498-037, [Fe/H]~ -3.8 (Aoki et al. 2002)

25M~, E51=10, Mixing=2.09 - 4.95M~ , f= 0.004

Little Fe（５６Ni) ⇒C,N,O/Fe

36 C,N rich – Extremely Metal-Poor Stars

CS 22957-027, [Fe/H]~ -3.1 (Aoki et al. 2002)

25M~, E51=1, Mixing=2.16 - 4.84M~ , f= 0.003

Little Fe（５６Ni) ⇒C,N,O/Fe

C/Mg ⇒E 、Mcut(f)

質量がより大きく、Eも大きいものでも合う

M=50~, E51=10

37 [O/Fe] Mixing in SNe Jet-Driven SNe?

[Co/Fe] 56Fe 16O 1 28 Si 16 4He 56 12C O 16O Fe 20Ne 32S 4 24 28Si 40 44Ti 0.1 He Mg 48Cr Ca 52Fe 55Co 56Ni 58Ni 59Cu 58 64Ge 0.01 Ni 55 24Mg Mn 40Ca 48 59Co Ti 0.001 64 32 Zn S 1e-04 Mass 1.5 1.7 1.9 2.1 Complete No burning Si burning O,Mg Co, Zn

T/109K Peak Temperature & Density Z Z 8 Ejected

4 R Accreted 0 R He 0.1 0.01

Spherical 0 • High T + Low ρ Material are Ejected Accreted preferentially

4 6 8 ejected. Log(Density[g cm-3])

38 Velocity Inversion of isotopes

Fe Zn

O Mn

V(Fe) > V(O), V(Zn) > V(Mn) Prediction Ejection of Spherical; Zn Fe Mn O heavier isotopes T , Inner (smaller V) with higher V

Fe He He O Si 0.01 0.01 Mn Zn Si

Ca O 0.0001 0.0001 Jet (Z) Jet (R) 1 2 3 1 2 3 Velocity [10000 km/s] O Velocity [10000 km/s] Fe and heavier

He O Fe He Fe O Si Si Zn 0.01 0.01 Ca Ca

Zn 0.0001 0.0001 Mn Mn Spherical Jet (all direction) 1 2 3 1 2 3 Velocity [10000 km/s] Velocity [10000 km/s]

39 Abundances in the whole ejecta Spherical, 1052ergs, 0.1M Ni

Mn O, Mg

Co，Zn

Jet-Driven，1052ergs, 0.1M Ni

Fe-Peak Elements

44Ti(44Ca) 64Ge(64Zn) M/M M/M 10-3 Jet Models

10-4

Spherical Models without mixing

-5 10 Mcut 0.1 0.5 1 56 Jet = Large E Effect M( Fe)/M

40 [Co/Fe] Co, Zn

Jet Fe

Cr, Sph Mn -0.5 0 0.5 -0.5 0 0.5 25M 40M Obs 0 0.5 1 0 0.5 1 [Mg/Fe] [Zn/Fe] Jet = Mixing Effect

Sph Mcut -0.5 0 0.5

[Cr/Fe] Co, Zn Sph Fe

Cr, Mn Jet 40M 25M -0.5 0 0.5 -0.5 0 0.5 Obs [Mg/Fe] 0 0.5 1 0 0.5 1 [Mn/Fe] Jet = Mixing Effect Sph Mcut -0.5 0 0.5

40M 25M

41 Fe-Peak Elements in the Jet Model compared with Metal-Poor Stars Jet = Large E + Mixing Effect [X/Y] = log(X/Y) – log(X/Y)

20M,Asp, E51=7 40M,Sph, E51=1 40M,Asp, E51=10 40M,Asp, 20M,Sph, E51=10 E51=1 20M,Sph, E51=1 20M,Asp, Past E51=7

40M,Sph, E51=1

Jet model: [Zn/Fe] ,[Mn/Fe] Agrees with the abundances in old stars.

Sc & Ti: Failed in Sph. Models Produced in the jet models (along the z-axis) [Sc/Fe]

Jet 0 0

Sph

-2 -1 40M 25M -2 -1 [Mg/Fe] [Ti/Fe]0 0.5 1 0 0.5 1

Sph

-0.5 0 Mcut -0.5 0

42 [S/Si] 56Ni

Sph

Jet -1 -0.5 0 -1 -0.5 0 25M 40M Accretion MBH/M [Si/O] 0 5 10 0 1 2 3

Accretion [S/Si],[Si/O] -0.6 -0.4 -0.2 0 -0.6 -0.4 -0.6 -0.4 -0.2 0 -0.6 -0.4 S Si O

[Mg/O] Accretion 0.2 0.4 [Mg/O] ,[C/O] 0.2 0.4

40M Accretion 25M -0.2 0 -0.2 0 MBH/M 0 5 10 0 1 2 3 [C/O]

Jet

Sph O,Mg C -1.4 -1.2 -1 -0.8 -1.4 -1.2 -1.4 -1.2 -1 -0.8 -1.4 -1.2

43 C,N rich – Extremely Metal-Poor Stars

CS 22957-027, [Fe/H]~ -3.1 (Aoki et al. 2002)

25M~, E51=1, Mixing=2.16 - 4.84M~ , f= 0.003

Little Fe（５６Ni) ⇒C,N,O/Fe

C/Mg ⇒E 、Mcut(f)

Fe-deficient Hypernovae?

MBH

M(Fe) = 1.6E-4M

8 E51= 8.5

MBH=10.5M

4 Prediction: [S/Si], [O/C]

0 20 40 Time (sec)

44 Most Fe-deficient Star

How to satisfy this Umeda & Nomoto, 2003 extreme condition?

Fe-deficient Jet model

Summary (1) • The studies on hypernovae indicate; – Velocity inversion of Fe and O – Dense core – Black hole formation • Jet-induced explosions satisfy the above condition! – Blow up heavy isotopes (e.g., Fe, Zn) to the surface. – A black hole grows, with an energetic explosion

–MBH efficiency of the jets (e.g., rotation?)

–MBH ( inefficient Jets) LOpt

–MBH Abundances (e.g., MBH [S/Si], [O/C] )

45 Summary (2) • Extremely Metal-Poor Stars – Large [Zn,Co/Fe] • Large E and/or Jet – Small [Mg, O, Mn, Cr/Fe] • Mixing and Fallback Effect – Trends in Fe-peak Elements • More massive star for lower [Fe/H] – Most-Fe deficient Star -5 • Very small Fe ejected (~10 M), significant mixing • Effect of Jet – Large [Zn, Co/Fe] (high T along the jet axis) – Similar effect to mixing and fallback: [Zn,Co,Mg,O/Fe] – Large [Sc, Ti/Fe]

46 本田、他２００１ すばるHDS、 preliminary

本田、他２００１ すばるHDS

47 48 2) Light Curves of Hypernovae Radioactivities in SN ejecta

Decay τ Ee+ (keV) % Eγ (keV) % 56Ni > 56Co 8.8 ------158 99 days 750 50 812 87 56Co > 56Fe 111.3 660 19 847 100 days 1238 68 2598 17 57Co > 57Fe 391.0 ------14 89 Days 122 89 136 11 44Ti > 44Ca 69.2 597 94 68 100 years 78 100 1156 100

Optical output as a result of γ ray transfer in SN ejecta

γ rays 56Co > 56Fe Loptical ~Lγ (1-exp(-τγ)) + L e+ + e -2 τγ = κγρR = τ0 (t/1day) 2 τ0 ∝ M /E Expansion Optical

Non-thermal e- Radiative deex. Excitations γ rays 0.01 – 1 MeV Recombinations Ionizations hν ~ 1 MeV Secondary e- Coll. Excitations Heating 1 – 30 eV hν ~ 1 – 10 eV

49 -20 Optical Light Curves of -19 ‘Original’ models -18 Spherical Hydro -17 -16 Model curves fainter than -15

observed after ~ 50 days. Bol 0 25 50 -14 Needs to increase τγ = κγρR. But must not in the outer layers -12 (V>10000km/s). Co Larger ρ in the central region. -10 0 100 200 300 400 500

56 SN Mej E51 M ( Ni) Time [day] 1997ef 9.5 21 0.11 1998bw 10.2 45 0.5 2002ap 2.4 5.4 0.07

Models with -20 -19 Inner Dense Cores -18 Observations fitted well!! -17 -16 High Density -15

Bol 0 25 50 SN ejecta -14

-12 Spherical Hydro Required in L.C Modeling -10 K. Maeda, in preparation 0 100 200 300 400 500 56 56 SN Vin (km/s) Min Niin Niout Time [day] 1997ef 3500 5.0 0.084 0.050 1998bw 5000 3.9 0.12 0.44 2002ap 3000 1.1 0.014 0.065

50