10/28/13	

Anthony Mezzacappa
University of Tennessee
Oak Ridge National Laboratory1	Neutrino heating depends onneutrino luminosities, spectra,and angular distributions.

➠ Must compute neutrino distribution functions.

f (t, r, θ , φ, E, θ p , φ p )Multifrequency
Multiangle

Multifrequency(solve forlowest-orderdθ p dφ p ... fmultifrequency
angular moments:
energy and momentum
density/frequency)

ER (t, r, θ , φ, E) = ∫ dθ p dφ p f
FR (t, r, θ , φ, E) = ∫10/28/13	

Requires a closure prescription:• MGFLD• MGVEF/MGVET

2	

Mezzacappa et al., PRL, 86, 1935 (2001)

Liebendoerfer et al., PRD, 63, 103004 (2001)

The simulation of core collapse supernovae with fully general relativistic, multi-angle, multi-frequency,
Boltzmann neutrino transport has been achieved for spherically symmetric cases.
ð What’s missing?
• Multi-D Effects•?
See also Lentz et al. 2012. Ap.J. 747, 73.
10/28/13	

3	

shockmatter

gain radius!-sphereconvection
SASI

neutrinos

CoolingHeating

Blondin, Mezzacappa, & DeMarino, Ap.J. 584, 971 (2003)

Shock wave unstable to non-radial perturbations.	

• Near prolate axis:	

• Decreases advection velocity in gain region.	

SASI has axisymmetric and nonaxisymmetric modes• Increases time in the gain region.	

that are both linearly and nonlinearly unstable!
• Increases size of gain region.	

• Blondin and Mezzacappa, Ap.J. 642, 401 (2006)• Moves shock toward silicon/oxygen layer.	

• Blondin and Shaw, Ap.J. 656, 366 (2007)• Blondin and Mezzacappa, Nature 445, 58 (2007) • Opposite effect orthogonal to prolate axis.	

• Seed convection.	

10/28/13	e.g., see Marek and Janka, Ap.J. 694, 664 (2009) 	

4	

Collision	  Term	  1.	  Geometric	  Eﬀects	  2.	  Special	  Rela5vis5c	  Eﬀects	  3.	  General	  Rela5vis5c	  Eﬀects	  E.G.:	  Describes	  increase	  in	  neutrino	  Fermi	  energy	  in	  trapped	  regions	  as	  density	  increases.	  
Spa$al	  Dimensions	  Netwonian	  or	  GR	  1	  2	  3	  Lentz	  et	  al.	  
(2012)	  1	  GR	  X	  X	  X	  OI	  et	  al.	  
(2008)	  2	  Newtonian	  X	  X	  Sumiyoshi	  and	  Yamada	  (2012)	  3	  Newtonian	  X	  X	  10/28/13	

Par$al	  Weak	  Interac$ons	  (Thompson	  et	  al.	  (2003))	  Complete	  Weak	  Interac$ons	  Label	  X	  GR-­‐Full	  Op	  5	

ReducOp	  =	  Bruenn	  (1985)	  –	  NES	  +	  Bremsstrahlung	  (no	  neutrino	  energy	  scaIering,	  IPM	  for	  nuclei)	  500

400

150

Shock Radius [km]Shock radius [km]

200

100
GR-FullOp
N-FullOp
N-ReducOp
N-ReducOp-NOC

50

20

40
60
80
100
post-bounce time [ms]120

Lentz	  et	  al.	  Ap.J.	  747,	  73	  (2012)	  1D2D20010000300

B12-WH07
B15-WH07
B20-WH07
B25-WH07

1400050

100150200

post-bounce time [ms]Bruenn	  et	  al.	  Ap.J.	  Le'.	  767,	  L6	  (2013)	  CHIMERA
10/28/13	

See also B. Mueller et al. 2012. Ap.J. 756, 84 for a comparison in thecontext of 2D models, with similar conclusions.

6	2D Hydrodynamics
• EoS
• LS
• K=220 MeV• W=29.3 MeV• Cooperstein• 17-Species NSE Solver• GR Corrections• Time Dilation• Effective Gravitational
Potential• Adaptive Radial Grid

1D Neutrino Transport• “RbR-Plus” MGFLD• Complete Weak Interactions• All O(v/c) Observer
Corrections• GR Corrections• Time Dilation• Red Shift• Aberration (in flux limiter)+150	  Isotope	  Network	  2D Self Gravity• Newtonian Multipole with GRMonopole

Nuclear Network• Alpha Network• 14 Alpha Nuclei between Heand Zn

CHIMERA2D and 3D models include
the same physics.
10/28/13	

7	

Solve a number of sphericallysymmetric problems.
In spherical symmetry, RbR
is exact.

10/28/13	

8	

Mean, Minimum, and Maximum Shock Radii vs Post Bounce Time12, 15, 20, and 25 Solar Mass W-H Progenitors; GR; Full Physics
20000

Shock Radius [km]mean shock radiusmaximum shock radiusminimum shock radius
15000
12 Msolar
15 Msolar
20 Msolar
25 Msolar

10000

5000

00200400

600

800

1000

1200

1400

Post Bounce Time [ms]10/28/13	

10	Explosion Energy vs Post-Bounce TimeComparison of 12, 15, 20, and 25 Msolar W-H Progenitors, GR, Full Physics
1.6+

E = Energy sum over positive energy zones++

E ov = E + Overburden

1.4++

Explosion Energy [B]E ov, rec = E ov + Nuclear recombination

1.2
12 Msolar
15 Msolar

120 Msolar
25 Msolar

0.8
0.6
0.4
0.2
00200

400

600

800

1000

1200

1400

Post-Bounce Time [ms]10/28/13	

11	

Proto-Neutron Star: Mass vs Time12 - 25 W-H Progenitors
21.9	  1.8	  Mass [Msolar]

1.8

1.67	  1.61.47	  1.412 Msolar
15 Msolar
20 Msolar
25 Msolar

1.2

10200

400

600

800

1000

1200

1400

Time from Bounce [ms]10/28/13	

12	

Nomoto,	  Tominaga,	  …	  2006	  Lattimer and Prakash (2010)10/28/13	

13	

2000
Entropy

B15-WH0730
22.5

Radius (km)

1500

15
7.5
01000

500

02000
01000

01000

2000Radius (km)

500

1000

1500

0.3 s after bounce

B20-WH07

2000

10/28/13	

14	

10/28/13	

15	

Entropy

15 M WH (2007)
512 X 45 X 90

10/28/13	

Lentz	  et	  al.,	  in	  prepara5on	  17	Will require ~ 65 million proc-hrs.

Entropy

15 M WH (2007)
512 X 90 X 180
400 X 88 X 176 (MPA)
10/28/13	

Lentz	  et	  al.,	  in	  prepara5on	  18	

10/28/13	

19	

Electron Fraction

15 M WH (2007)
512 X 90 X 180

10/28/13	

Lentz	  et	  al.,	  in	  prepara5on	  20	

SASI	  induced	  shear	  layer	  in	  3D	  induces	  turbulence	  via	  secondary	  instabili5es	  (e.g.,	  Kelvin-­‐Helmholtz).	  	  Phys. Scr. T155 (2013) 014022

E Endeve et al

Figure 3. Evolution of Fourier spectra during SASI development in the strong-field simulation. Left panel: compensated spectral specificHigh-resolution
3Dê studies
suggestthatdensitytheê . energy
kinetic energy density⇥ k . Right panel:
Spectral enstrophy
In both panels, dashed lines represent time averaged spectra(averaged over the time period extending from t = 1000 ms to t = 1100 ms). The dotted vertical reference lines denote spatial scalesof long-wavelengthmodes
may be sappedcorresponding to 300 km,SASI
20 1l and 101l.
by short-wavelength modes via turbulence.
u

5/3

turbulence (this number, of course, depends on the valueT
adopted for k T in the definition of E kin, but we consider k T =0.1 to be somewhat conservative, and the turbulent kinetic
energy is possibly even larger;
p cf figure 3). Moreover, the1T
turbulent rms velocity u Trms = 2E kin/MSh is about 5000 km sduring the saturated state (MSh is the mass within VSh ).
Additional, quantitative insight into the development ofturbulence from the SASI is gained by inspecting the Fourier
spectra of select quantities from the simulations. From the10/28/13	

Fourier transform of a vector field f ,Z1!

of turbulence, and subsequent SASI saturation. The
compensated spectral specific kinetic energy density(i.e. êu ⇥ k 5/3 ) is plotted versus wavenumber k for select timestates in the left panel in figure 3. (Enstrophy spectra ê! forthe same time states are plotted in the right panel in figure 3.)
The figure shows the time evolution of the spectra from theearly, linear phase of the SASI (t = 600 ms; cf left panel infigure 1), the transition to the nonlinear phase, and well into
the nonlinear, saturated state.
Our simulations suggest that the SASI saturates in thenonlinear regime due to the development of post-shock— Endeve et al. 2012. Ap.J. 751, 26.

3D multi-physics simulations will be needed to determine how this plays out.
• Resolution will remain a serious challenge.
21	• Necessary Realism: Multifrequency neutrino transport with relativistic effects and astate-of-the-art weak interaction set, and general relativity.
150400100

Entropy [kB-1]
220406080
100
post-bounce time [ms]12022150 ms
26 30

000

8 12.5 17200

GR-FullOp
N-FullOp
N-ReducOp
N-ReducOp-NOC

50140• We have obtained explosions in ab initio 2D simulations withprogenitors from 12 to 25 M, with most outcomes consistentwith observations.
• A three-dimensional counterpart simulation is underway,
for the 15 M progenitor, and has already reached >100 ms
post-bounce.

Distance from symmetry axis [km]Shock radius [km]200200
Radial velocity [km s-1]

400-30000

0-400

30000

-2000200400

300 ms1000
5000500
1000-1500 -1000-5000500

1000

1500

600 ms

4000
2000
02000
4000-6000 -4000 -2000

02000

4000

6000

Distance along symmetry axis [km]10/28/13	

22	Comparative quantitative analyses of 2D models*	  Suwa et al. 2010. PASJ 62, L49.
Mueller, Janka, and Marek 2012. Ap.J. 756, 84.
Mueller, Janka, and Heger 2012. Ap.J. 761, 72.
Bruenn et al. 2013. Ap.J. Lett. 767, L6.

Takiwaki et al. 2012. Ap.J. 749, 98.
Hanke et al. 2013. Ap.J. 770, 66.
Lentz et al. 2014. In preparation.

should be performed, ala’ Liebendoerfer, Rampp,Janka, and Mezzacappa Ap.J. 620, 840 (2005)
and Mezzacappa and Bruenn Ap.J. 410, 740 (1993).

* Included physics and treatments of thephysics are comparable.

10/28/13	

2D Models of
1990s: Herant etal. 1992, 1994,etc. Explosions
acrossprogenitors andsupernovagroups.
Parameterized.

Final Frontier:
3D
Current 2DModels:Explosions
acrossprogenitors andgroups. First
principles.

23	Burrows, Dolence, and Murphy, Ap.J. 759, 5 (2012)
Dolence, Burrows, Murphy, and Nordhaus, Ap.J. 765, 110 (2013)
Murphy, Dolence, and Burrows, Ap.J. 771, 52 (2013)
Couch, Ap.J. 775, 35 (2013)
Couch and O’Connor (2013), arXiV: 1310.5728v1
Fernandez, Mueller, Foglizzo, and Janka (2013), arXiV:1310.0469v1
Difficult to fully assess the (relative) roles of neutrino-driven convection and the SASI outside ofself-consistent explosion models.
The latter tell us:••••

Either can dominate in different models.
Either can dominate in different epochs within a given model.
They may act in tandem/concert in a given model.
We now have clear examples of this in self-consistent 2D and 3D models.
o Mueller et al. Ap.J. 761, 72 (2012), Hanke et al., Ap.J. 770, 66 (2013),
Fernandez, Mueller, Foglizzo, and Janka (2013), arXiV:1310.0469v1

Independent of dimension, the key role of the SASI is to induce the large-scale entropy
perturbations that spawn the formation of a large-scale high-entropy bubble(s) required
for explosion.
10/28/13	

➠ Fernandez, Mueller, Foglizzo, and Janka (2013), arXiV:1310.0469v124	

Blondin
MauneyChertkow
EndeveHarris
Hix
Lentz
MesserMezzacappa
Parete-Koon
Yakunin10/28/13	

Funded by
BruennMarronetti

25