Sec$on 7.
Supernova explosions
7.1 Thermonuclear supernova
7.2 Core-collapse supernova

4500
4750
5000
oλ/A
5250

J1257+4220

J0900+2343

5500
5750

Kepler et al. 2019

0.28
0.18
0.33
0.34

Pressure broadening(Stark eﬀect)=> good measureof gravity− 2.46− 1.74− 2.23− 2.01

0.34
0.27
0.39
0.39

total
elogn(He)/n(H)HS 2115+1148

fit
elogn(He)/n(H)NewNew
New
New

New/Known

J0032+1604

log n(He)/n(H)

N VII

He II

Ne X
O VIII
C VI

CVNe X
CVHe II

CVC VIO VIIIHe II
N VII
C VINe IXO VIIIHe IIO VIII
He II

2176

HIHI

Spectra of white dwarf
S. O. Kepler et al.

J1029+2540

C+O and He white dwarfs
758

KALIRAI ET AL.

L = 4πR2 σT4for the helium-core white dwarf, and therefore
g = GM/R!3.5 times slower
than that2 of a carbon-oxygenof similar mass. This is of course offset slightly
if distance is known
mean mass of the helium-core stars is somewh
of normal carbon-oxygenYcore
white dwarfs(clusterorparallax)
C+O

effect in this case). By comparing the observ
minosity function to model luminosity functio
helium cores, pure carbon-oxygen cores, and atwo, Hansen (2005) was able to show that arequires the birthrate fraction of helium-core w~ 0.45cluster to beM
between
50%Msunand 100% of the tot
duction. This is consistent with our findings afor He igni$on

7.6. The Ultraviolet Upturn in Elliptic

Fig. 9.—M-Teff plane for all confirmed NGC 6791 white dwarfs ( filled circles),as well as those that were determined to be 2 ! outliers from cluster membership

The ultraviolet upturn in elliptical galaxie
refers to the sharp, rising flux in the integrat
objects shortward of k ! 2500 8 (Burstein eHe& Renzini 1990; Bressan et al. 1994; O’Con
2004). The phenomenon is found to be extrem
ferent galaxies, and therefore must be very seerties of the sources responsible for the upturn.
main-sequence stellar population of these galacool to constituteKaliraiany
et appreciableal. 2007 fraction of t
the sources must be either young massive stars
formation regions) or more exotic population

Mass distribu$on of WDs (with H)

White dwarfs inKepler et al. 2019
Figure 5. Mass distribution for the 11 129 DAs with S/Ng ≥ 10. This sample

Figure 7. Mass distribution for the 550

Goals of this lecture• Standard proper$es of stars• Stellar structure and proper$es• Stellar evolu$on• Origin of the elements in the Universe• Nucleosynthesis in stars and supernovae• Explosion mechanism of supernovae• Topics in $me-domain astronomy• Radia$on from explosive phenomena• Mul$-messenger astronomy

k and3. Inwithal andty arete thehe na-0.0

2.5

Normalized energy
5.0
7.5
10.0

12.5

15.0

LIGO Hanford
100

10Frequency (Hz)sivelyIts di0.07.
nent isns ande conen theMpc.
maxis remstate,binaryheavy
source2.50–
aviestem.
easurenal rath theeatingences,
1for
act bisuch aophys-

Gravita$onal waves from23 Msun black hole + 2.6 Msun object!

LIGO Livingston
100

10Virgo100

101086420

Time (seconds) from 2019-08-14 21:10:39 UTC
Figure 1. Time–frequency representations (Chatterji et al.
2004) of data containing GW190814, observed by LIGO Hanford (top), LIGO Livingston (middle), and Virgo (bottom).

arXiv: 2006.12611

Is 2.6 Msun object black hole or neutron star?
bsidephot
on

2.5

ALF1
ALF2
AP1-2
AP3
AP4
BSK19
BSK20
BSK21
ENG
GNH3GS1
H4
MPA1
MS1
MS1b
NJL
QMC
SLY
SQM1-3PAL6
WWF1
WWF2WWF3orbitBho lackles

3.0

Mass (M☉)

In

2.0

1.5

1.0

0.5

0.0

618

1012141618

Radius (km)Ozel 2016ent physical assumptions and using a range of computational approaches.

Discovery of the heaviest NS!?
- Large uncertainty in EOS
for NS maGer- But diﬃcult to support 2.6 Msun.

Discovery of lightest black hole!
- Implica:ons tosupernova mechanism

Sec$on 7.
Supernova explosions
7.1 Thermonuclear supernova
7.2 Core-collapse supernova

Binary system

White dwarf
David A. Hardy

Thermonuclear explosion

CSiOFeSupernova!

Mass frac$onExplosion of white dwarf

CenterSurface
Nomoto+84, Timmes+

Pre-explosion

Post-explosion

C+O
0.5

1
1.0

2
0.5

1.4

34

1.0

1.4

*NSE = nuclear sta$s$cal equilibrium (核統計平衡)zoneT (K)Ρ (g cm-3)

1(7-9) x 109

108-9

NSE + e-capture

56Fe, 54Fe, 58Ni

2(5-7) x 109

107-8

NSE56Ni3(4-5) x 109<107

4< 4 x 109<107

Elements

Incomplete Siburning
Incomplete Oburning

28Si, 32S, 40Ca
16O, 24Mg

Thermonuclear supernovae

Normal stars are stable with nuclear burning
Why do white dwarfs explode by nuclear burning?

Type Ia
SNSun0.0 sec

1,000 km

0.6 sec

2,000 km

3.0 sec
20,000 km

Roepke 2007

1.0 sec
70,000 km

How to trigger explosion (progenitor scenarios)
Accre$on fromnon degenerate star

C: David Hardy

single degenerate

Merger of two white dwarfs

C: NASAdouble degenerate

Which is correct or dominant? Not yet understoodSummary: Thermonuclear supernovae• Explosion of white dwarf close to Mch• Nuclear burning => runaway under degenerate condi:on• Explosive nucleosynthesis•

About 0.8 Msun of Fe-group elements (56Ni & 56Fe, 54Fe, 58Ni)> Core-collapse SNe•

About 0.4 Msun of intermediate mass elements (28Si, 32S, 40Ca)• Progenitor scenario• Single degenerate or double degenerate• Not yet solved

Sec$on 7.
Supernova explosions
7.1 Thermonuclear supernova
7.2 Core-collapse supernova

1. Massive stars
軽い星

赤色巨星

惑星状星雲
M > 10 Msun

~ 10 Myr

図の大きさは天体の大きさと一致していません(C: Essay Web)

白色矮星

H

He

Fe

Si

C+O

Ne + Mg

Images are not to scale20 Msun star（~16 Msun before the collapse)

Mass(Msun)

R(Rsun)Free-fall $me(s)1610003x 107(1yr)

60.5

300

542
1.5

0.2

50
20
10.1

H
He
C/OO/Mg
Si0.080.005
0.003

FeRsun = 7 x 1010 cm
R(Fe core) ~ 0.003 x 7 x 1010 cm~ 2 x 108 cm ~ 2,000 km

HHe

1000

0.5

Rho-T diagram

degenerat
ee

lec

tro

ns

relativistic electrons

textbook by Pols

hen the temperature in the contracting C-O core reaches 5 − 8 × 108 K (depending on the mascore), carbon is the first nuclear fuel to be ignited. The reactions involved in carbon burningfornuclearburningstagestherTimescales
nuclear burning
cycleswere treatedin Sec.
6.4.3. In the following sections we briefly rev
se and discuss the consequences for the structure and evolution of the star. A typical example
interior evolution is shown in Fig. 12.7 for a 15 M⊙ star, and the corresponding stellar proper
given in Table 12.1.

Table 12.1. Properties of nuclear burning stages in a 15 M⊙ star (from Woosley et al. 2002).
burning stage

T (109 K)

ρ (g/cm3 )fuelmain products

timescalehydrogenheliumcarbonneon
oxygensilicon

0.035
0.18
0.83
1.6
1.9
3.3

5.8
1.4 × 103
2.4 × 105
7.2 × 106
6.7 × 106
4.3 × 107

HHeCNeO, Mg
Si, SHe
C, OO, NeO, Mg
Si, SFe, Ni

1.1 × 107 yr
2.0 × 106 yr
2.0 × 103 yr
0.7 yr
2.6 yr
18 d182

Collapse(< 1 sec)

Neutron star
orBlack holeSupernova!

Core-collapse supernovae

What happens to massive stars at the end of lives?
Where does huge energy come from?

Assignment 3 / レポート課題 3
Consider gas consis$ng of- non-rela$vis$c (NR) par$cles (e.g., NR ideal gas, NR degenerate gas) and- extremely-rela$vis$c (ER) par$cles (e.g., ER degenerate gas, photons)
非相対論的(NR)/超相対論的(ER)粒子からなるガスを考える(3a) Show the following rela$ons
between pressure (P) and energy density (ε)
圧力 (P) とエネルギー密度 (ε) の間に、以下の関係が成り立つことを示せ* P = (2/3) ε for NR par$cles* P = (1/3) ε for ER par$cles(3b) Show adiaba$c index (γ) are following
Adiaba$c index (γ) が以下のようになることを示せ* γ = 5/3 for NR par$cles* γ = 4/3 for ER par$cles

ν(1)

(2)

Neutrino trapping

Core-collapseν

eFeν
ν νν

Fe coreννν	ShockSN neutrinoν"νν ννν ννν ννν ννν(3)Core bounce
図 1.4ν(4)(5)Supernova

Neutron star(C) 原子核から読み解く超新星爆発の世界

重力崩壊型超新星の爆発メカニズムの概要．重い星の中心部にある鉄住吉光介さん著 (Kosuke Sumiyoshi)
コアの重力崩壊から始まり，密度・温度が高まる中で発生したニューSummary: Core-collapse supernovae• Stability of star
• Dynamically unstable if adiaba:c index γ < 4/3• Degenerate Fe core => unstable• What trigger the core-collapse?
• Energy source• Gravita:onal energy• Collapse of the core (~1 Msun) to ~10 km size=> 1053 erg