Explosions of Massive Starsby	

Jeremiah W. Murphy	

(Florida State University)

A Theory for Core-Collapse Supernova
Explosionsby	

Jeremiah W. Murphy	

(Florida State University)

What is the mechanism of explosion?

Fe	Core

1.4 M!, R ~3000 km
Tdyn ~ 150 ms

Progenitor Stars	

~8 M! < M < ~40-100 M!

R~ 40 km
PNS

Bounce launches	

shock wave

PNS	

r~40km~0.1 to ~10 M!/s

Shock Stalls	

e- cap, ν losses	

Accretion shock	(r ~200 km)
PNS	

r~40kmShock Stalls	

e- cap, ν losses	

Accretion shock	(r ~200 km)
PNS	

Neutrino	

Emission	e- + p → n + νe	

e+ + n → p + νe	

Few x 1052ergs s-1

r~40kmShock Stalls	

e- cap, ν losses	

Accretion shock	(r ~200 km)
PNS	

Neutrino	Emission	

e- + p → n + νe	

e+ + n → p + νe	

Few x 1052ergs s-1
Gain	Radius	(r ~ 100 km)

r~40kmn + νe → e- + p 	p + νe → e+ + n
Gain Region	

~10% for revival

Subsonic below shock	!

Global solution to explosion

1D simulations(Rad-hydro)
Wilson ‘85	

Bethe & Wilson ‘85	

Liebendoerfer et al. ‘01	Rampp & Janka ‘02	

Buras et al. ‘03	Thompson et al. ‘03	

Liebendoer et al. ‘05	Kitaura et al. ‘06	

Burrows et al. ‘07

Neutrino mechanism suggested

No Explosions	(Except lowest masses)

An Important Unsolved
Astrophysical Problem?

Fundamental Question ofCore-Collapse Theory
Steady-State	Accretion

Explosion?

Important Observational Clues

Asymmetry in Ejecta

SiFeCaCas A SN Remnant: Chandra

Pulsar Recoil: A Generic Feature
Guitar Nebula
Pulsar Kicks:	

Pulsar B2224+65	

and Bow Shock	V ≥ 1000 km s-1

Cordes, Romani, Lundgren ‘93

Leonard et al. ’06, NatureAsymmetry in SN 1987A• Early X- and y- ray detection	

Dotani et al. ‘87; Matz et al. ‘88	

• Mixing Pinto & Woosley ‘88 	

• Infrared, gamma-ray, and Hydrogen	lines: Erickson et al. ‘88;	

Barthelmy et al. ‘89; Hoflich ‘88	

• Early Polarization	

Jeffery et al. ‘91 	

• Supernova ejecta

Fundamental Question ofCore-Collapse Theory
Steady-State	Accretion

Explosion?

Relax 1D assumption?

2021Multi-D makes it easier toexplodeNeutrino Mechanism:	

•Neutrino-heated convection	

•Standing Accretion Shock Instability (SASI)	

•Explosions? Maybe	!

Acoustic Mechanism:	

•Explosions but caveats.	

!

Magnetic Jets:	

•Only for very rapid rotations	•Collapsar?

Why is it easier to explode in 2D
compared to 1D?

Two Paths to the Solution• Detailed 3D radiation-hydrodynamic simulations	(“Accurate” energies, NS masses, nucleo., etc.)	

!

• Parameterizations that capture essential physics	

(Tease out fundamental mechanisms)

Burrows & Goshy ‘93	

Steady-state solution (ODE)

Explosions!	

(No Solution)

Lνe
Critical Curve
Steady-state accretion	(Solution).

MIs a critical luminosity relevant inhydrodynamic simulations?
• 1D	

• 2D Convection and SASI?

How do the critical luminosities
differ between 1D and 2D?

Murphy & Burrows ‘08

SASI activity as key to successful neutrino-driven S
3.0

3.0

2.5
15.0-2DLνe [1052 erg/s]

Lνe [1052 erg/s]

15.0-1D
15.0-3D

2.0
11.2-1D
1.5

11.2-2D

2.5
2.0

11.2
1.5

11.2-3D

111.0
0.05

1.0

0.10

0.15

0.20

Ṁ [M⊙/s]

0.25

0.30

0.35

0Fig. 2.— Critical curves for the electron-neutrino luminosity (Lνe ) versus mass accretion rate ( Ṁ)simulations in 1D (black), 2D (blue), and 3D (red) with standard resolution. The accretion rate is mea
explosion sets in. The results of the 11.2 M⊙ models are represented by plus symbols and those of theHanke et al 2011
with standard resolution.
29

1000

1.6

tioned works.

CCSN E NEUTRINO MECHANISM
3.0

LS220
LS180
STOS
1D
2D

2.5

L e (1052 erg s 1 )L e (1052 erg s 1 )

3.0

2.0

1.5

2.5

2.0

1.5

0.15

0.20

0.25
Ṁ (M s 1 )

0.30

0.35

0.0Figure 4. Neutrino luminosity versus
mass2012
accretion rate at time of explosion (left panel)
Couchwork. Results from both 1D (dashed lines) and 2D (solid lines) are shown. For30each EO
Swesty EOS result in easier explosions in both 1D and 2D than the Shen et al. EOS.

2D & 3D critical luminosity
lower than 1D
Turbulence plays an importantrole!

A Theoretical Framework for
Successful Explosions

+Lν.

M

Turbulence	

Model
Murphy & Meakin 2011

A Theoretical Framework for
Successful Explosions+Lν

Turbulence	

Model.

M
Calibrate with 3D	

SimulationsMurphy et al. 2013, in prep

A Theoretical Framework for
Successful Explosions+Lν.

MTurbulence	

Model

A Theoretical Framework for
Successful Explosions+Lν

Turbulence	

Model.

M
1D Rad-hydro simulations	

Realistic and quantitative explosions	

Systematic exploration

What dominates the turbulence?	

Convection, SASI... both?

36

Neutrino-driven Convection	

(Buoyancy)37

Neutrino-driven Convection	

(Buoyancy)
Shock Stalls	

e- cap, ν losses	

Accretion shock	(r ~200 km)
PNS	

Neutrino	Emission	

e- + p → n + νe	e+ + n → p + νe	

Few x 1052ergs s-1
Gain	

Radius	(r ~ 100 km)

r~40kmn + νe → e- + p 	

p + νe → e+ + n
Gain Region	

~10% for revivalNeutrino-driven Convection	

(Long Recognized)

Bethe ’90	

Herant et al. ’92	Benz et al. ’94	Burrows et al. ’95	Janka & Mueller ’96	...	

Murphy & Meakin 2012	

Murphy et al. 201239

Standing Accretion Shock Instability	(SASI)

40

postshock turbulence in standing accretion shocks.
Also shown in Figure 5 is a similar simulation but with diﬀerent inner boundary conditions:a reflecting wall plus a thin cooling layer. The initial radial solution is nearly identical to theadiabatic solution except close to the inner boundary, where the cooling becomes strong and thegas quickly settles Blondin
into a thinon top of the hard surface. As shown in Figure 5, the evolution
et layer
al. ’03is qualitatively the same as in the adiabatic model with a leaky boundary. This comparison verifies– 14 –
the independence of these results from the details of the boundary conditions.

Standing Accretion Shock Instability	

(SASI)

adily. The intermediate epoch is characterized by large oscillations in the postshock flow thatd to an aspect ratio for the accretion shock that varies between one and two. The volume of
cked gas exhibits a growing oscillation, reminiscent of a breathing mode. This phase of theution is dominated by the l = 1 mode; i.e., is distinctly oscillatory. Beyond a time of 170, thew takes on a strikingly self-similar form dominated by the l = 2 mode; i.e., is distinctly bipolar.
e aspect ratio becomes remarkably constant at a value ∼ 2 (2.3 to be precise), but the scale ofaspherical shock grows roughly linearly with time. From t = 165 to t = 225, the angle-averaged
ck radius increases from 5 to 15. This corresponds to an expansion velocity of order 50% theape velocity at the shock. This self-similar expansion is illustrated in Figure 10, where we plot
ges of the gas entropy at three diﬀerent times chosen such that the shock has roughly doubled
ize in each interval. When scaled to the same size, the images look qualitatively similar.

Fig. 6.— Images of the gas entropy (red is higher than the equilibrium value, blue is lower) illustrate
the instability of a spherical standing accretion shock. This model has γ = 4/3 and is perturbed byplacing over-dense rings into the infalling preshock gas. Note that with the scaling for a realistic
supernova model, the last image on the right corresponds to ∼ 300 ms. These simulations areaxisymmetric, forcing a reflection symmetry about the vertical axis.

To further illustrate this early evolution we show a time series of the two-dimensional flow inFigure 6. We use the gas entropy to visualize the flow because a steady, spherical shock would
produce a postshock region of constant entropy. Thus, any deviation from a spherical shock shows
up as a change in the postshock entropy. Aside from the overall trend of growing perturbations in41
10.— The
self-similar
growthentropy,of the asymmetricaccretionillustrates
shock is illustrated
these entropy of low-order modes. This is a generic
thepostshock
this figure
the indominanceges from three diﬀerent times in our simulation. The postshock volume grows with time, butStanding Accretion Shock Instability	

(An Advective Acoustic Cycle)
Foglizzo et al. 201242

What dominates the turbulence?	

Convection, SASI... both?

43Compare nonlinear theories for convectionand SASI with post shock flow

SASI nonlinear theory?
44Compare nonlinear theories for convectionand SASI with post shock flow

A Nonlinear Theory for Convection	

!
Murphy & Meakin 2012	

Murphy, Dolence, Burrows 201345

Compare nonlinear theories for convectionand SASI with post shock flow

A Nonlinear Theory for Convection	

!
Murphy & Meakin 2012	

Murphy, Dolence, Burrows 2013

We can test this fledgling theory with 3Dsimulations
4647

4849Nonlinear Convection is Consistent with
Post Shock Flow
1. Consistent buoyancy flux profile	2. Consistent Reynolds stresses	

3. Buoyant driving balances dissipation	

4. Analytic scaling between buoyant flux and neutrino driving

Nonlinear Convection is Consistent with
Post Shock Flow

But what about the SASI?

A theory for neutrino-driven explosions

A turbulence model for CCSNe
Post shock flow is consistent withnonlinear convection theory

Constrain Giant Eruptions fromMassive Stars

Kinematics!
!
!
!

Stellar Structure of Massive Stars

Stellar Evolution(Successes)

HR-diagram, Mass
Nucleosynthesis

Skeletons in the Closet?

60

Skeletons in the Closet
Mass Loss
Convection
Rotation(not mere details)

61

Mass Loss

Credit: Alex Heger62

Episodic Mass Loss
SN IIn	Evidence of episodic mass loss	

before explosion63Episodic Mass Loss
SN Impostors	

Some SN Impostors occur just before SN64

Episodic Mass LossText

65Episodic Mass Loss

LBV Dust Shells	Represent a giant eruption	

Massive amounts of mass loss?

66

Is episodic mass loss a dominantmode of mass loss?

67

What causes Giant Eruptions?

68

We don’t know what’s going oninside!
Stellar Structure?	

Evolutionary State?

69

The Data(Kochanek 2011 & Kochanek 2012)104
log 10(vImpostor ) =2.7 ± 0.3
log 10(vLBV ) =1.7 ± 0.3

LBV Dust Shells
SN Impostors

vshell (km/s)

103

102

101

10−4

10−3

10−210−1
Mshell (M⊙)

10010170

A Natural Energy Scale

71

101
100

Energy [1050 erg]

10−1M-50-C
M-50-C-nw
K-19-CC
K-50-HeLBV Dust Shells
SN Impostors∗|Eg | ≈ GMR∗ m

10−210−3Blue Supergiant
10−4Red Supergiant

10−510−6 −51010−410−310−210−1m [M⊙ ]100101
72

6.5
LBV dust shells(Giant Eruptions)6.0log10 (L/L⊙ )

80 M⊙
5.5

50 M⊙

5.025 M⊙

SN Impostors

4.5

4.0
5.0

4.8

12 M⊙
4.6
4.4
4.2
4.0log10 (Teﬀ /K)]

3.8

3.6

3.4

73

107

106

103

0

10−2

1857
6H
R
Car
AGCar
W
ra
75
1H
en351
9H
D
1686
25
G
79.2
9+0SN .46
2011ht
SN2006jcSN1994
W
SN
20
10mc

Cy
g

10IR
A
S

P

Age (Years)
108

H
He

105

104

C

102

101

O

10−1

Si

74

Kinematics!
!
!
!

Stellar Structure and Evolutionary
State of Massive Stars