Frontiers of GW predictions from CCSN Model

• Takami Kuroda (Basel Univ.)Kei Kotake(Fukuoka Univ.), Tomoya Takiwaki(NAOJ),

Ko Nakamura (Waseda Univ.), Kazuhiro Hayama(Osaka-city Univ.)

Asymmetries in CCSNe

Tanaka+,’12 Milisavljevic & Fesen, ‘13

3D mapping of optically emitting ejecta (Cas A)

From many observationsCCSNe are asymmetric explosions!

Asymmetries in CCSNe

From many numerical simulations suggestInitiation of CCSNe is asymmetric!

Takiwaki+, ‘12 Scheidegger+, ‘10

Suwa+, ‘10 Marek&Janka, ‘09

All of thesesimulations are within the innermostregion of star(R/Rstar<10-3~-5)

optical observationis impossible

Asymmetries in CCSNe

TimeT < 〜１ sec

Milisavljevic & Fesen, ‘13

Spatial Scale

T > １ day 〜 1yr

R < 〜１03km

R > 〜１ 06-13km

Too wide dynamical range !!!

Hammer+,’10

~108km

Gravitational wavesDirect observation by

R=0kmNeutrinosR 〜

20km

Kotake,’11, "Gravitational Waves (from detectors to astrophysics)"

Diversity of Gravitational Waveforms

2)MHD explosionExplosion Mechanisms

1)ν-driven explosion

“Round” explosion “Oriented” explosion

Buras+,’06 Takiwaki+,’11

Suwa+,’10 Marek&Janka,’09 Takiwaki+,’08 (2D)

Scheidegger+,’10 (3D)

rotation is not necessary rotation is necessary

Obergaulinger+,’06 (2D)

Rotation Explosion Morphology GWs

GW Emissions from Rotating CoreHow does rapid rotation affectson the observed GW emissions?

Type I signal (Dimmelmeier+,’02)

GW Emissions from Rotating CoreHow does rapid rotation affects

on the observed GW amplitude?

Obergaulinger+,’06

GW Emissions from Rotating CoreType I signal appears irrespective

of dimensionality of explosion.

3DDimmelmeier+,’08

Scheidegger+,’10 (3D)

Microphysical EOS2D

Microphysical EOSNu-cooling3D-MHD

GW Emissions from Rotating Core

Dimmelmeier+,’08

Type I signal --->Linear correlation between |h|max and T/|W|b(=βb)

In modern stellar evolution,βi<~0.1% (Heger+,’05, Yoon&Langer,’08) βb<~1%

GW Emissions from Rotating CoreHow does rapid rotation affectson the observed GW emissions?

① 　 Dynamical instability (|T/W|>0.27) …… Rampp + ’98 ② 　 Secular instability (|T/W|>0.13) …… Chandrasekhar ’70 ③ 　 Low |T/W| instability (|T/W|>0.01) …… Watts +’05

Rotational instabilities

GW Emissions from Rotating CoreHow does rapid rotation affectson the observed GW emissions?

3DGR + Γ-law EOS (Ott+,’05)

Low-T/Winstability

GW Emissions from Rotating Core

3DNMHD + Microphysics (Scheidegger+,’10)

m=1

m=2

GW Emissions from Rotating CoreBecause the low-T/W instability

occurs in the vicinity of PNS,• FGW~kHz• hGW~10-20~-19 @D=10kpc

Ott+,’07 Scheidegger+,’10

AdvLIGO

GW Emissions from Rotating Core

Blondin&Mezzacappa,’07 Fernandez,’10

GW emissions from one-armed spiral wave

one-armed spiral wave (Rshock>R>RPNS)

Scheidegger+,’10

Tpb~27ms

•Full spatial domain• Without excising inner boundary• 0<φ<2π (for m=1 mode)

•Neutrino cooling (for Rshock)

GW Emissions from Rotating Core

GW emissions from one-armed spiral wave3DGR + Neutrino radiation (leakage for cooling term)

15Msun with (KT, Takiwaki & Kotake, arXiv:1304.4372)

EquatorPolar

Consistent with Ott+,’12

GW Emissions from Rotating Core

Time evolution of “h=A/10kpc” spectrum

S/N(=h/N)=1 (for KAGRA)

log(

h)

GW Emissions from Rotating Core

€

ψ ij ≡d

dt

Strong emission fromone-armed spiral wave

Scheidegger+,’10

Tpb~27ms

€

ψ ≡ (2ψ xy )2 +(ψ xx −ψ yy )2

Angular frequency of “Acoustic+Rotational” mode

Ωrot

Ωrot+Ωaco

X (cm)

GW Emissions from Rotating Core

One armed spiral waves produce GW emission at F~FDoppler.FDoppler(~200Hz) represents “Acoustic+Rotational” frequency.

How is this “~200Hz” determined?

GW Emissions from Rotating CoreImportance of neutrino-cooling

Importance of neutrino-cooling

GW Emissions from Rotating Core

w/o coolingw/ cooling

Unstable region (Rns<R<Rshock) becomes more compact

due to ν-cooling

Non-axisymmetricstructure

Rns

Rshock

Importance of neutrino-cooling

GW Emissions from Rotating Core

Unstable region (Rns<R<Rshock) becomes more compact

due to ν-cooling

Non-axisymmetricstructure

Scheidegger+,’10

w/o cooling

w/ cooling

~10 timesstronger GWs

Fully general relativistic 3D-Rad-Hydro!!

GW Emissions from Rotating CoreIn addition, if there is strong magnetic field…….

Obergaulinger+,’06

R<60km

Total

w/ B

Type I signal (Dimmelmeier+,’02)

w/o B

Offset

GW Emissions from Rotating CoreIn addition, if there is strong magnetic field…….

2D 3D

Takiwaki+,’08(2D) Scheidegger+,’10 (3D)

Slowly varying positive offsetoriginated from MHD jet

GW Emissions from Rotating Core

If the star rotates sufficiently fast (T/W|b > a few % T/W|i > a few ‰)

Strong Type I signalLow frequency Emission from MHD jet

Low T/W instability (F~kHz, τdecay~10ms, from PNS)One armed spiral wave (F~ a few 100Hz, τdecay~τexplo (?) , above PNS)

GW Emissions from Non-Rotating Core

Neutrino

Matter

When rotation is negligible,(Neutrino Explosion occurs)GW waveforms are characterized as

1) Early (Linear) SASI motion2) Hot Bubble Convection & SASI3) Explosion Phase

Z(km

)

Muller B.+,’13

Freq

uenc

y (H

z)

Neutrino

Matter

Advective mode

Acoustic mode

Blondin+, ‘03

GW Emissions from Non-Rotating Core

Local contributionto GW emissions Matter acceleration

Muller B.+,’13

Tpb=22ms

Coherent Stripe Pattern(not stochastic convective one)

GW Emissions from Non-Rotating Core

SASI (L 〜 1,2….) Convection (higher order L)

or

Hanke+,’13

Muller B.+,’13

From Brunt-Vaisalla frequency,Muller+,’13 derived following relation

GW Emissions from Non-Rotating Core

Brunt-Vaisallafrequency

gravitationalforce at NS surfaceNS surface

temperatureCompact parameter

Uni- (or Bi-) polar explosion• positive GW amplitude• low frequency (<100Hz)

GW Emissions from Non-Rotating Core

Murphy+,’09

Information on explosion morphology is imprinted in GW waveforms

GW Emissions from Non-Rotating Core

Up to now, there is no GW analysis studyusing successful ν-explosion model in full-3D

Iwakami+, ‘08

GW Emissions from Non-Rotating Core

Equipartition of energy

Hanke+,’13

Light-bulb method in 3D

Kotake+,’11

GW Emissions from Non-Rotating Core

3DGR + ν-Radiation (Gray M1+Leakage for cooling)Progenitor: 11.2, 15.0, 27.0 & 40.0 Msun (WW95)　　　　　　　　 ~0.3, 1.05, 1.85 & 2.10 Xi(1.5Msun)1283cells * 9 Level nested structure (dxmin~450m)Long term simulations (Tpb=200-250ms)

GW emissions and mass dependence

KT, Takiwaki & Kotake, in preparation

We can investigate• Progenitor dependence• SASI evolution without excising inner boundary• Correlation between GW & Lnu

S27.0

S15.0

Convective Initiation of SASI (?)

SASI SASI

S11.2

S27.0

S15.0

S40.0

Lack of data

SASI feature ?

GW Emissions from Non-Rotating Core

Egw ↑Mprogenitor ↑

How about observations?

Equatorial

Polar

S11.2

S40.0

S15.0_Rot

Hayama+

S15.0_Rot_Ext

•Source is located at optimal direction•SNR is only for “KAGRA”

Lack of data

€

Lν e

€

Lν e

€

Lν e

€

Lν e

Summary

•We may be able to link future GW observations and core rotational profile.•anti-νe energy & Fpeak evolution will tell us, e.g., M/R.•Confirmed SASI (27&40Msun) in 3DGR for the first time•Their GW frequency appears ~100Hz•They can be detected up to ~20kpc•There is oscillation in anti-e neutrino luminosity