Anthony Mezzacappa Department of Physics and Astronomy

University of Tennessee Joint Ins;tute for Computa;onal Sciences

Oak Ridge Na;onal Laboratory

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  Neutrino Heating   Convection   SASI ____________   Nuclear Burning   Rotation   Magnetic Fields

Fundamental Building Blocks

Elements of Neutrino Shock Reheating

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

SASI has axisymmetric and nonaxisymmetric modes that are both linearly unstable!

– Blondin and Mezzacappa, Ap.J. 642, 401 (2006) – Blondin and Shaw, Ap.J. 656, 366 (2007)

Shock wave unstable to non-radial perturbations.

shock

gain radius

!-sphere

neutrinos

matter

Heating

Cooling

SASI

convection

3/7/16 3

4

Neutrino heating depends on neutrino luminosities, spectra, and angular distributions.

Must compute neutrino distribution functions.

f (t, r,θ,φ,E,θ p,φp )

ER (t, r,θ,φ,E) = dθ p∫ dφp f

FRi (t, r,θ,φ,E) = dθ p∫ dφp n

i f

Multifrequency Multiangle

Multifrequency (solve for

lowest-order multifrequency

angular moments: energy and momentum

density/frequency)

3/7/16

Requires a closure prescription: •  MGFLD •  MGVEF/MGVET

€

e−(+) + p(n),A↔ν e (ν e ) + n(p),A'e+ + e− ↔ν e,µ,τ + ν e,µ,τ

v + n, p,A→ v + n, p,A

v + e−,e+ → v + e−,e+

N + N↔ N + N + ν e,µ,τ + ν e,µ,τ

ν e + ν e ↔ν µ,τ + ν µ,τ

¬ 

Reddy, Prakash, and Lattimer, PRD, 58, 013009 (1998) Burrows and Sawyer, PRC, 59, 510 (1999)

•  (Small) Energy is exchanged due to nucleon recoil. •  Many such scatterings.

Hannestadt and Raffelt, Ap.J. 507, 339 (1998) Hanhart, Phillips, and Reddy, Phys. Lett. B, 499, 9 (2001)

•  New source of neutrino-antineutrino pairs.

“Standard” Emissivities/Opacities

¬ 

Bruenn, Ap.J. Suppl. (1985) •  Nucleons in nucleus independent. •  No energy exchange in nucleonic scattering.

Langanke et al. PRL, 90, 241102 (2003) •  Include correlations between nucleons in nuclei.

Janka et al. PRL, 76, 2621 (1996)Buras et al. Ap.J., 587, 320 (2003)

¬ 

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Bruenn, DeNisco, and Mezzacappa, Ap.J. 560, 326 (2001) Liebendoerfer et al. Ap.J. 620, 840 (2005)

25 M Model

15 M Model

€

ds2 = −α 2dt 2 +r'

Γ

%

& '

(

) *

2

da2 + r2 dθ 2 + sin2θdϕ 2( )

1. Geometric Effects 2. Special Rela5vis5c Effects 3. General Rela5vis5c Effects

1.  What equa;ons to use for the neutrino radia;on hydrodynamics is nontrivial. 2.  Discre;za;ons must be chosen to ensure number and energy conserva;on simultaneously.

Spa$al Dimensions

Newtonian or GR

1 2 3 Par$al Weak Interac$ons (Thompson et al. (2003))

Complete Weak Interac$ons

Label

Lentz et al. (2012)

1 GR X X X X GR-­‐Full Op

OC et al. (2008)

2 Newtonian X X

Sumiyoshi and Yamada (2012)

3 Newtonian X X

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Collision Term Conserva;ve treatment presents a significant challenge. •  Liebendoerfer et al. 2004. ApJ Suppl. 150 263 •  Cardall & Mezzacappa 2003 PRD 68 023006 •  Cardall, Endeve, & Mezzacappa 2013 PRD 87 103004 •  Cardall, Endeve, & Mezzacappa 2013 PRD 88 023011

0 20 40 60 80 100 120 140post-bounce time [ms]

0

50

100

150

200

Shoc

k ra

dius

[km

]

GR-FullOpN-FullOpN-ReducOpN-ReducOp-NOC

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

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

3/7/16 8See also B. Mueller et al. 2012. Ap.J. 756, 84 and O’Connor and Couch (2015) for a comparison in the context of 2D models, with similar conclusions.

3/8/16 9

2D Mul5-­‐Frequency (3D)

Models

Newtonian

Ray-­‐by-­‐Ray Transport

Single Flavor

Par5al Weak Physics

Suwa et al. (2016)

Three Flavor

Par5al Weak Physics

Takiwaki et al. (2014), Nakamura

et al. (2014)

2D Transport

Single Flavor

Par5al Weak Physics

Pan et al. (2016)

Three Flavor

Par5al Weak Physics

Dolence et al. (2014)

General Rela5vis5c

Ray by Ray Transport

Three Flavor

Full Weak Physics

Mueller et al. (2012, 2013,

2014)

Bruenn et al. (2013, 2016)

2D Transport without

Rela5vis5c Terms

Three Flavor

Par5al Weak Physics

O’Connor and Couch (2015)

3/8/16 10

3D Mul5-­‐Frequency (4D) Models

Newtonian

Ray-­‐by-­‐Ray Transport

Single Flavor

Par5al Weak Physics

Takiwaki et al. (2012, 2014)

General Rela5vis5c

Ray by Ray Transport

Three Flavor

Full Weak Physics

Hanke et al. (2013), Tamborra et al. (2013, 2014),

Melson et al. (2015)

Lentz et al. (2015)

Progenitor Masses Used •  Takiwaki et al. 11.2 M •  Lentz et al. 15 M •  Hanke, Tamborra, Melson et al. 9.6, 11.2, 20, 27 M

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

Do accre;on hot spots persist? As the angular resolu;on is increased, RbR will approach non-­‐RbR for a central source.

0 200 400 600 800 1000 1200 1400Time after Bounce [ms]

0

5000

10000

15000

20000Sh

ock

Radi

us [k

m]

B12-WH07B15-WH07B20-WH07B25-WH07

0 200 400 600 800 1000 1200 14000

5000

10000

15000

20000

mean shock radiusmaximum shock radiusminimum shock radius

Bruenn et al. 2013. Ap.J. 767, L6. Bruenn et al. 2016. Ap.J. 818, 123.

Time after Bounce [ms]

0

Expl

osio

n En

ergy

[B] B12-WH07

B15-WH07B20-WH07B25-WH07

0 200 400 600 800 1000 1200 1400

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6E+ = Energy sum over positive energy zonesE+

ov = E+ + Overburden

E+ov,rec = E+

ov + Nuclear recombination

0 100Time after bounce [ms]

0

10

20

30

40

50

60

70

B12-WH07B15-WH07B20-WH07B25-WH07

50 150

ν

dimensionless shock stagnation radiusproto-NS radius [km]30 × shock dM/dt [M!s-1]10 × proto-NS mass [M !]

-sphere T [MeV]

0 200 400 600 800Time after bounce [ms]

0

10

20

30

40

50

60

70

L ν [B

(=10

51 er

g) s-1 ],

ε νrms [M

eV]

0.01

0.1

1

10

Mass

Acc

retion

Rate

[M!

s-1 ]

ν luminosityν rms energymass accretion rateνeνe

νμτνμτ

10 15 20 25

ZAMS Progenitor Mass [M]

0

0.5

1

1.5

2

2.5

3

Explo

sion

Ener

gy [B

]

SN 2012aw

SN 2004A

SN 2004dj

SN 2012ecSN 2004et

SN 2009kr

SN 1993J SN 1987A

SN 2004 cs

SN 2004et

10 15 20 25ZAMS Progenitor Mass [M]

0

0.02

0.04

0.06

0.08

0.1

0.12

56Ni

Mas

s [M

]

SN 2012awSN 2004A

SN 2004dj

SN 2004et

SN 1993J

SN 1987A

SN 2004cs

133/10/16

Bruenn et al. 2014. arXiv:1409.5779v1

-600

-500

-400

-300

-200

-100

0

Prot

o-NS

Velo

city [

km s-1

]

-2000

-1000

0

1000

2000

Prot

o-NS

Velo

city [

km s-1

]

GravityMomentumPressure

1

1.2

1.4

1.6

1.8

2Pr

oto-

NS M

ass [

M]

B12-WH07B15-WH07B20-WH07B25-WH07

0 200 400 600 800 1000 1200 1400

Time After Bounce [ms]

a

b

c

143/10/16

NS62CH19-Lattimer ARI 18 September 2012 8:10

X-ray/opticalbinaries

Double–neutron starbinaries

White dwarf–neutron starbinaries

Main sequence–neutron starbinaries

Black widow pulsar

Hulse–Taylor binary

In M15

Double pulsar

In NGC 6544

In NGC 6539

In Ter 5

2.95 ms pulsarIn 47 Tuc

In NGC 1851In M5

In NGC 6440In NGC 6441

In NGC 6752

4U1700-37 (32)Vela X-1 (33)Cyg X-2 (34)4U 1538-52 (33)SMC X-1 (33)LMC X-4 (33)Cen X-3 (33)Her X-1 (33)XTE J2123-058 (35)2S 0921-630 (36)4U 1822-371 (37)EXO 1722-363 (38)B1957+20 (39)IGR J18027-2016 (40) J1829+2456 (42)J1829+2456 comp. (42)J1811-1736 (43)J1811-1736 comp. (43)J1906+0746 (44)J1906+0746 comp. (44)J1518+4904 (27)J1518+4904 comp. (27)B1534+12 (45)B1534+12 comp. (45)B1913+16 (46)B1913+16 comp. (46)B2127+11C (47)B2127+11C comp. (47)J0737-3039A (48)J0737-3039B (48)J1756-2251 (49)J1756-2251 comp. (49)J1807-2500B (29)J1807-2500B comp. ? (29)B2303+46 (31)J1012+5307 (50)J1713+0747 (51)B1802-07 (31)B1855+09 (52)J0621+1002 (53)J0751+1807 (53)J0437-4715 (54)J1141-6545 (55)J1748-2446I (56)J1748-2446J (56)J1909-3744 (57)J0024-7204H (56)B1802-2124 (58)J051-4002A (56)B1516+02B (59)J1748-2021B (60)J1750-37A (60)J1738+0333 (61)B1911-5958A (62)J1614-2230 (63)J2043+1711 (64)J1910+1256 (28)J2106+1948 (28)J1853+1303 (28)J1045-4509 (31)J1804-2718 (31)J2019+2425 (65)J0045-7319 (31)J1903+0327 (66)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Neutron star mass (M)

Figure 7Measured neutron star masses with 1-σ errors. References in parentheses following source names are identified in Table 1.

www.annualreviews.org • Nuclear EOS and Neutron Star Masses 497

Ann

u. R

ev. N

ucl.

Part.

Sci

. 201

2.62

:485

-515

. Dow

nloa

ded

from

ww

w.a

nnua

lrevi

ews.o

rgby

Oak

Rid

ge N

atio

nal L

ab o

n 06

/12/

14. F

or p

erso

nal u

se o

nly.

Laamer, ARNPS 62 485 (2012) Bruenn et al. 2014. arXiv:1409.5779v1

153/7/16

The Astrophysical Journal, 766:43 (21pp), 2013 March 20 Muller, Janka, & Marek

Table 1Model Setup

Model Progenitor Neutrino Treatment of Simulated Angular Explosion Time of EOSOpacities Relativity Post-bounce Time Resolution Obtained Explosiona

G8.1 u8.1 Full set GR hydro + xCFC 325 ms 1.4 Yes 175 ms LS180G9.6 z9.6 Full set GR hydro + xCFC 735 ms 1.4 Yes 125 ms LS220G11.2 s11.2 Full set GR hydro + xCFC 950 ms 2.8 Yes 213 ms LS180G15 s15s7b2 Full set GR hydro + xCFC 775 ms 2.8 Yes 569 ms LS180S15 s15s7b2 Reduced set GR hydro + xCFC 474 ms 2.8 No . . . LS180M15 s15s7b2 Full set Newtonian + modified potential 517 ms 2.8 No . . . LS180N15 s15s7b2 Full set Newtonian (purely) 525 ms 1.4 No . . . LS180G25 s25.0 Full set GR hydro + xCFC 440 ms 1.4 No . . . LS220G27 s27.0 Full set GR hydro + xCFC 765 ms 1.4 Yes 209 ms LS220

Note. a Defined as the point in time when the average shock radius ⟨rsh⟩ reaches 400 km.

explode rather early and exhibit convective activity only on amoderate level after the onset of the explosion. The 11.2 M⊙model G11.2 shows a much slower expansion of the shock andseveral violent shock oscillations before the explosion takesoff. Model G15 develops a very asymmetric explosion as late as∼450 ms. The more massive 25 M⊙ and 27 M⊙ models G25 andG27 differ from the other models by more clearly discernibleSASI activity, visible as strong periodic sloshing motions ofthe shock in Figure 1, which lead to an explosion in the caseof G27. We note that no explosion develops in the simulationswithout general relativity and/or the full neutrino rates (M15,N15, S15).

A summary of all nine models considered in this paper isgiven in Table 1. For a detailed discussion of models G11.2 andG15, see Muller et al. (2012b), and for details on G8.1 and G27,see Muller et al. (2012a).

3. GRAVITATIONAL WAVE EXTRACTION

The xCFC approximation used in Vertex-CoCoNuT doesnot allow for a direct calculation of GWs as the correspond-ing degrees of freedom in the metric are missing. We thereforeneed to extract GWs in a post-processing step with the helpof some variant of the Einstein quadrupole formula (Einstein1918). Modified versions of the Newtonian quadrupole for-mula (exploiting ambiguities concerning the identification ofNewtonian and relativistic hydrodynamical variables) have beenfound to be reasonably accurate even in the strong-field regime(Shibata & Sekiguchi 2003; Nagar et al. 2007; Cordero-Carrionet al. 2012). For the gauge used in Vertex-CoCoNuT and thetypical conditions in a supernova core, it is possible to derive amodified version of the time-integrated Newtonian quadrupoleformula (Finn 1989; Finn & Evans 1990; Blanchet et al. 1990)directly from the field equations (see Appendix A). Assumingaxisymmetry, we obtain the quadrupole amplitude AE2

20 in non-geometrized units for spherical polar coordinates as

AE220 = 32π3/2G√

15c4

∫dθ drφ6r3 sin θ

×

∂

∂t[Sr (3 cos2 θ − 1) + 3r−1Sθ sin θ cos θ ]

− [Sr,ν, (3 cos2 θ − 1) + 3r−1Sθ,ν sin θ cos θ ]. (1)

Here φ is the (dimensionless) conformal factor for the three-metric in the CFC spacetime, and Si denotes the covariant

components of the relativistic three-momentum density (in non-geometrical units, i.e., Sr is given in g cm−2 s−1 and Sθ ing cm−1 s−1) in the 3 + 1 formalism, which is given in termsof the rest-mass density ρ, the specific internal energy ϵ, thepressure P, the Lorentz factor W, and the covariant three-velocitycomponents vi as

Si = ρ(1 + ϵ/c2 + P/ρc2)W 2vi. (2)

Si,ν denotes the momentum source term for Si due to neu-trino interactions (which must be subtracted from ∂Si/∂t asexplained in Appendix A). In practice, these neutrino sourceterms do not yield a significant contribution to the integral inEquation (1).

AE220 determines the dimensionless strain measured by an

observer at a distance R and at an inclination angle Θ withrespect to the z-axis (see, e.g., Muller 1998),

h = 18

√15π

sin2 ΘAE2

20

R. (3)

In the following, we will always assume the most optimistic caseof an observer located in the equatorial plane, i.e., sin2 Θ = 1. Inaddition to the GW signal from the matter, we compute the GWsignal due to anisotropic neutrino emission using the Epsteinformula (Epstein 1978; Muller & Janka 1997) for the GWstrain hν ,

hν = 2G

c4R

∫ t

0Lν(t ′)αν(t ′) dt ′. (4)

Here Lν is the total angle-integrated neutrino energy flux, andthe anisotropy parameter αν can be obtained as

αν = 1Lν

∫π sin θ (2| cos θ | − 1)

dLν

dΩdΩ (5)

in axisymmetry (Kotake et al. 2007). hν can be converted intoan amplitude AE2

20,ν by inverting Equation (3).The energy EGW radiated in GWs can be computed from

AE220,ν as follows (see, e.g., Muller 1998):

EGW = c3

32πG

∫ (dAE2

20,ν

dt

)2

dt. (6)

4

SUBMITTED TO APJ ON 2015 NOVEMBER 23 O’CONNOR & COUCH

Table 1

Reference Gravity EOS Grid Treatment s12 s15 s20 s25Exp? texp [s] Exp? texp [s] Exp? texp [s] Exp? texp [s]

Bruenn et al. (2013) GREP LS220 Spherical MGFLD RxR+ Yes 0.236 Yes 0.233 Yes 0.208 Yes 0.212Hanke (2014) GREP LS220 Spherical VEF RxR+ Yes 0.79 Yes 0.62 Yes 0.32 Yes 0.40this work GREP LS220 Cylindrical MG M1 No – Yes 0.737 Yes 0.396 Yes 0.350Dolence et al. (2015) NW H. Shen Cylindrical MGFLD No – No – No – No –Suwa et al. (2014) NW LS220 Spherical IDSA RxR Yes 0.425 No – No – N/A N/Athis work NW LS220 Cylindrical MG M1 No – No – No – No –

Note. — GREP gravity is used to denote Newtonian hydrodynamic simulations with an effective, spherically symmetric, GR potential instead of the Newtonianmonopole term. NW gravity is pure Newtonian gravity. The LS220 EOS is the Lattimer & Swesty (1991) K0 = 220MeV EOS while H. Shen is the EOS fromShen et al. (2011). The neutrino treatment in Bruenn et al. (2013) is multigroup flux-limited diffusion (MGFLD) and in Hanke (2014) is a two moment schemewith the closure solved by a model Boltzmann equation. Both of these transport schemes use the the ray-by-ray+ (RxR+) approximation for the multidimensionaltransport treatment where the transport is solved only in the radial direction (along rays). The ‘+’ refers to the addition of advection of neutrinos in the lateraldirection in optically thick regions. Dolence et al. (2015) use MGFLD as well, but solve the multidimensional transport directly. Suwa et al. (2014) employthe isotropic diffusion source approximation, akin to MGFLD, and use the ray-by-ray approximation. Bruenn et al. (2013) defines the explosion time as thepostbounce time when the shock reaches 500 km. We use this definition for extracting the explosion time from Suwa et al. (2014). Hanke (2014) only showsshock radius data to 400 km, therefore we use the postbounce time when the shock reaches this radius. However, this makes no qualitative difference since theshock expansion is quite rapid at this time. We also show the results of this work. We use the abbreviation MG M1 to denote multigroup M1 neutrino transport.

moment evolution equations (i.e. ↵ = 1;@i = 0). Finally,, a, and s are the neutrino emissivity, absorption opacity,and scattering opacity, respectively, which depend on the lo-cal density, temperature, and electron fraction as well as theneutrino species and energy. For the remainder of this sec-tion we describe the numerical techniques used to solve theseequations and the microphysics used to compute the neutrinointeraction coefficients.

Closure: To close the hierarchy of moment evolution equa-tions after the first two moments, we must specify a closurerelation for the Eddington tensor Pi j in terms of the two lowermoments E and Fi. We choose the common M1 closure. Inregions where the radiation is isotropic, Pi j Pi j

thick = i jE/3and in regions far from the source, Pi j Pi j

thin = E(FiF j/F2).Therefore, for our Eddington tensor, we choose a commoninterpolation between these two limiting regimes,

Pi j =3(1 -)

2Pi j

thick + 3- 12

Pi jthin , (12)

or, using the expressions mentioned above,

Pi j =

3(1 -)2

i j

3+ 3- 1

2FiF j

F2

E . (13)

In these equations is taken to be

=13

+ 215

(3 f 2 - f 3 + 3 f 4) , (14)

where f (FiFi/E2)1/2 is the flux factor. f is equal to 0 if theradiation is isotropic, which gives a = 1/3 and Pi j = Pi j

thick. fis 1 if the radiation is fully forward peaked in some direction.For this case, = 1 and Pi j = Pi j

thin.Explicit Fluxes: For computing the spatial flux terms on the

left hand side of Eq. 7-Eq. 11, we use finite differencing,

@x[↵rmFx] =(↵rm)(k+1/2)F(k+1/2) - (↵rm)(k-1/2)F(k-1/2)

x, (15)

and

@x[↵rmPxi] =(↵rm)(k+1/2)P i

(k+1/2) - (↵rm)(k-1/2)P i(k-1/2)

x, (16)

where m is either 0,1,2. To obtain the interface fluxes F(k+1/2)and P i

(k+1/2), we use the standard HLLE Riemann solver for

hyperbolic equations. For the flux evaluation at an interface(k +1/2), we reconstruct E and Fi/E to both sides of the zoneinterfaces using 2nd-order TVD (total variation diminishing)interpolation. On both sides of the interface we recomputethe closure via Eq. (13) to obtain the cell interface values ofPi j. The characteristic speeds for the Riemann solver are cal-culated in a similar way as the closure in that we interpolatebetween the optically thick and optically thin limits. First,for each interface (characterized here by the direction k), wedetermine the minimum and maximum speeds on each sideof the interface in both the optically thin and optically thicklimits. For the optically thick limit the choice is clear,

(k)thick,min = - 1p

3;(k)

thick,max = + 1p3. (17)

For the thin limit, and our choice of closure, the maximumand minimum characteristic speeds are (Shibata et al. 2011)

(k)thin,min/max = min/max

±Fk

pFiFi

,EFk

FiFi

. (18)

Next, to determine the maximum and minimum speed on eachside of the interface we interpolate between the optically thick((k)

thick) and free streaming ((k)thin) regimes via,

(k)min/max =

3(1 -)2

(k)thick,min/max + 3- 1

2(k)

thin,min/max . (19)

The final step to determine the minimum and maxi-mum speeds for the Riemann solver is to take (k),+ =max((k),(R)

max ,(k),(L)max ) and (k),- = min((k),(R)

min ,(k),(L)min ). Where

(R) and (L) denote the right and left side of the interface, re-spectively.

With the reconstructed moments and minimum and maxi-mum characteristic speeds in hand, the HLLE Riemann solu-tion for the fluxes at the interface is then,

F(k+1/2),HLLE =(k),+Fk,(L) -(k),-Fk,(R) +(k),+(k),-(E (R) - E (L))

(k),+ -(k),-(20)

and

P j(k+1/2),HLLE =

(k),+P(L)k j -(k),-P(R)

k j +(k),+(k),-(F (R)j - F (L)

j )(k),+ -(k),-

(21)

4

0 50 100 150 200 250 300 350 400 450Time [ms]

050

100150200250300350400450500550600650700750800

C15-2D

Minimum/maximum

C15-1D

C15-3D

Mean shock radius

Shoc

k ra

dius

[km

]

0 50 100 150 200 250 300 350 400 450Time [ms]

0

10

20

30

40

50

60

70

Lum

inos

ity [B

s-1]

C15-3DC15-2D

νeνμτ ,νμτ

νe−−

b)

100 150 200 250 300 350 400 450Time [ms]

0

0.1

0.2

0.3

0.4

Dia

gnos

tic e

nerg

y [B

]

C15-3DC15-2D

a)

0 50 100 150 200 250 300 350 400 450Time [ms]

0

0.5

1

1.5

2

2.5

Acc

retio

n ra

te [M

s-1

]

C15-3D

at shockat gain surface

C15-2Dd)

Lentz et al. 2015. Ap.J. LeW. 807, L31.

183/7/16

15 M LS (220)

Simula5on Stats •  64,800 cores •  35 weeks/postbounce second •  100 M processor-­‐hours/postbounce second

Lentz et al. 2015. Ap.J. LeW. 807, L31.

4 Hix˙Piaski2015 printed on February 18, 2016

0 100 200 300 4000

100

200

300

400

500

600

700

Time after Bounce (milliseconds)

Mea

n Sh

ock

Rad

ius

(km

)

Melson (2015) 3DsMelson (2015) 2DsMelson (2015) 3DnMelson (2015) 2DnLentz (2015) 3DLentz (2015) 2DLentz (2015) 1D

Fig. 1. Comparison of the mean supernova shock radius after bounce for 3D models(solid lines) from leading neutrino transport codes using 15 M [27] and 20 M[28] solar metallicity progenitor stars. Results of 2D (dashed lines) and 1D (dottedlines) models are also shown.

the neutrino luminosity. A simplier approach is the lightbulb approximation[10], where the neutrino transport calculation within the proto-neutron staris replaced by a prescribed neutrino luminosity at the PNS surface.

The question of how well axisymmetric 2D models reflect the 3D realityof CCSNe has been examined in a series of simulations using variations onthese simplified schemes. Nordhaus et al. [29] found 3D simulations to bemore favorable than 2D, producing explosions at lower neutrino luminosi-ties, a view supported, though tempered, by Burrows et al. [30] and Dolenceet al. [31]. In contrast, Hanke et al. [32], Couch [33] and Couch & Ott [7]find 3D to be, at best, neutral compared to 2D, and likely pessimistic. How-ever, “light-bulb” and leakage schemes do not include the complete feedbackprovided by self-consistent transport methods.

Takiwaki et al. [34, 35] have shown that 3D models using the isotropicdi↵usion source approximation (IDSA) scheme for spectral neutrino trans-

20 M

15 M

Similari;es in the qualita;ve behavior of 2D models, and 3D models, obtained by the MPA and Oak Ridge groups is evident in the above graph.

3/7/16 20

Replace 1D RbR Transport with 3D (Lowest Angular Moments) Transport

Will require ~3 days @ 1 PF sustained. Strong scaling essential.

Replace GR Monopole Correction with “Full” GR

Replace 3D Moments Transport with 3D Boltzmann Transport

Will require ~12 days @ 1 EF sustained. ~4000X more computationally intensive. Will there be enough memory?

Replace 3D Boltzmann Transport with 3D Quantum Kinetics

?

What’s Next?

Cooling

Accre5on

CC

NC

≈“Shock Revival”

3D CORE-COLLAPSE SUPERNOVA SIMULATION 3

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Figure 3. a) Net neutrino heating in the gain region. b) νe (solid), νe (dashed), and νµτ (dash-dotted) total luminosities at 1000 km. c) Neutrino heatingefficiencies. d) (inward) Accretion rates at gain radius (solid) and shock (dash-dotted). e) Advection–heating time scale ratio, τadv/τheat. f) Turbulent kineticenergy. Data for C15-2D is averaged with a 25-point boxcar (∼8 ms). Plotted using colors of Figure 1.

indicating earlier shock revival and explosion. The shockfor C15-1D, which lacks multi-dimensional flows, reaches amaximum radius of ≈180 km at ≈80 ms and recedes there-after, typical of 1D CCSN simulations.

The shock in C15-2D expands rapidly from ≈230 ms on-ward (Figure 1), with the diagnostic energy10 E+ (Figure 2a)simultaneously becoming positive. E+ surpasses 0.01 B by250 ms and grows rapidly thereafter. For C15-3D, the first ev-idence of potential explosion begins with an increased growth

10 following B2014, E+ is defined as the integral of the total energy (ther-mal, kinetic, and gravitational) in all zones of the cavity where locally posi-tive.

of Rshock at ≈280 ms, accelerating after ≈350 ms, as thelargest buoyant plume expands, leading to a small, but grow-ing E+.

The explosion is clearly more energetic in C15-2D at alltimes (Figure 2a). We evaluate the growth of E+ over a com-mon period beginning when Rshock exceeds 500 km and end-ing 45 ms later. For C15-3D, Rshock passes 500 km at 393 mswhen E+ is 0.034 B, which grows to 0.067 B at 438 ms whenRshock is 735 km. For C15-2D, Rshock exceeds 500 km at278 ms when E+ is 0.041 B, which grows to 0.147 B at323 ms when Rshock reaches 900 km. Over this 45 ms com-parison period, the E+ growth rate is 0.73 B s−1 for C15-3D

What are the amplitudes, varia;ons, and ;me scales of the accre;on signatures?

What are the explosion ;me scales -­‐ i.e., when does the cooling phase begin for each progenitor?

What are the late-­‐;me neutrino signatures -­‐ i.e., the signature at O(10) s?

What is the impact of neutrino mixing on all of the above?

o  The absolute flux from the neutroniza;on burst.

•  Will allow us to discriminate between different EOS.

o  The ms-­‐scale structure of the emission from the accre;on phase (convec;on vs. SASI).

•  We need at least 1 ms ;ming resolu;on to discern the feature that precedes the neutroniza;on burst, which depends on the symmetry energy, as well as the neutroniza;on peak. •  We need 1 ms ;ming to resolve well the O(10 ms) SASI cycle ;me.

o  10% energy resolu;on is sufficient. o  Need SnowGlobes to handle neutrino energies above 100 MeV.

We can provide

o  raw luminosity spectra as a func;on of ;me,

o  our output from SnowGlobes,

o  our alpha fit (2-­‐alpha fit as a func;on of ;me).

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rapid shock expansion -­‐ Si-­‐Si/O

accre5on-­‐powered evolu5on

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C15-­‐2D, angle-­‐averaged, SNOwGLoBES Ar17kt, 10 kpc

Messer, Devo5e, et al. In prepara5on.

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Figure 3.13: Total Count vs. Time (Argon & Lead Interactions in 3D - NH)

37

Mixing washes out details of shock revival and dynamics. Reconstruc;on of raw signature will be necessary.

Messer, Devo5e, et al. In prepara5on.

Oak Ridge group evolves both the neutrino and the an;neutrino distribu;ons for all 3 flavors.

Messer, Devo5e, et al. In prepara5on.

Messer, Devo5e, et al. In prepara5on.

inside the PNS. The low-frequency component arises fromthe modulations in the shock radius as the SASI developsand evolves. The high-frequency component is generatedwhen the SASI-induced accretion flows strike the PNSsurface (Fig. 3). It is clear from the analysis of thecontributions to the strain from r < 50 km and r >50 km that the PNS convection, deceleration of theaccreting matter at the PNS surface, and neutrino-drivenconvection in the gain region contribute significantly.The shock modulations affect the kinetic energy of the

accretion flows and, consequently, the amplitude of theGWs generated when these flows hit the PNS surface.The signal structure during the strong signal phase in bothB12-WH07 and B15-WH07 is similar to that in thecorresponding A-series models. However, this is not thecase for B25-WH07 and A25-WH07. The beginning ofthe strong signal phase in A25-WH07 is ∼50 ms behindthat in B25-WH07, which indicates an earlier developmentof neutrino-driven convection and SASI activity in the lattermodel. The peak amplitude in B25-WH07 is twice as largeas it is in A25-WH07.

The peak frequency of the signal grows almost linearlyfrom 100 Hz up to 1000 Hz during the strong signal phase(right panels of Fig. 1). We see the same trend in frequencyevolution, with a similar slope, in the M15 model fromMüller et al. [8], which is the closest to our B15-WH07 model.

D. Explosion phase

All of our GW signals end with a slowly increasing tail,which reflects the (linear) gravitational memory associatedwith accelerations at the prolate outgoing shock. Thenoticeable decrease of the high-frequency component ofthe amplitude during the explosion phase (most pro-nounced for model B12-WH07 at 520 ms) is due to thecessation of active accretion onto the PNS surface (Fig. 4).The time of the cessation coincides, within a width of theSTFTwindow, with the time when the frequency reaches itsmaximum value, for all of our models except B20-WH07(Fig. 1). B20-WH07 has a different explosion morphology.A single downstream is formed in all of our models exceptB20-WH07 in the early SASI phase. This downstreamproduces the local large amplitude spikes in the GW strainby its deceleration at the PNS surface. The downflow alsoinduces the l=2 mode of the mass distribution deep in thePNS, which enables high-frequency PNS convection tocontribute to the GW signal. Thus, PNS convection isresponsible for the high-frequency component of the GWwaveform. Termination of the single accretion stream leadsto a significant decrease in both the frequency and theamplitude of the GW signal. In B20-WH07, multipledownstreams are formed during the SASI phase. Thisprevents the establishment of a more precise correlationbetween the changes of the accretion flow and the asso-ciated changes of the waveform amplitude and peakfrequency. The typical frequency in B20-WH07 starts todecrease when the first accretion downflow detaches fromthe surface of the PNS (∼500 ms) while other downstreamscontinue to perturb the PNS and thus support the high-frequency and the amplitude of the B20-WH07 signal(Fig. 5), until the moment when the last accretion downflowbecomes detached from the PNS surface (∼630 ms). Afterthe cessation of accretion, the GW signal in all of ourmodels is essentially generated by the shock only. The tailscontinue to rise until they reach their saturation values at700–1000 ms, depending on the model and its prolateness.The total emitted GW energy is shown in Fig. 6. The

values of the GW energy emitted in the B-series modelspresented here are very close to what we predicted in the A-series models presented in Ref. [45]. Due to the “anoma-lous” evolution of model B20-WH07, we do not observe asimple correlation between the progenitor mass and thetotal energy emitted in gravitational waves. The GWenergyemitted is a function of the complex explosion dynamics—in particular, the number and characteristics of the accretionstreams that form during the preexplosion and explosion

FIG. 3 (color online). Top: The entropy distribution for theB15-WH07 model inside the PNS at 228 ms after bounce.Downflows onto and convective activity inside the high-densityregion produce the strongest GW signal. Bottom: The GWwaveforms, Dhþ vs time, showing the contributions of threeregions: r < 50 km, r > 50 km and r > 500 km. The latterregion shows the contribution due to shock expansion.

GRAVITATIONAL WAVE SIGNATURES OF PHYSICAL REVIEW D 92, 084040 (2015)

084040-7

Gravita5onal wave signal is dominated by the SASI and the SASI-­‐induced accre5on flows impinging on the PNS surface.

•  Evidence of the SASI.

Explosion is imprinted in the signal as well. •  Explosion 5me scale. •  Progenitor.

Yakunin et al. 2015. Phys. Rev. D 92, 084040

Bruenn Marronetti

Blondin

Endeve Harris

Hix Landfield

Lentz Lingerfelt Messer

Mezzacappa Yakunin

Funded by

293/7/16