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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
From many observations
CCSNe are asymmetric explosions!
3D mapping of optically emitting ejecta (Cas A)
Milisavljevic & Fesen, ‘13
Tanaka+,’12
Asymmetries in CCSNe
From many numerical simulations suggest
Initiation of CCSNe is asymmetric!
Takiwaki+, ‘12
Scheidegger+, ‘10
All of these
simulations are within
the innermost
region of star
(R/Rstar<10-3~-5)
optical observation
is impossible
Suwa+, ‘10
Marek&Janka, ‘09
Asymmetries in CCSNe
T < 〜１sec
Too wide dynamical
range !!!
R < 〜１03km
~108km
Direct observation by
Hammer+,’10
Gravitational
waves
R=0km
R〜20km
Neutrinos
T > １day〜1yr
Time
R > 〜１06-13km
Spatial
Scale
Milisavljevic & Fesen, ‘13
Diversity of Gravitational Waveforms
Kotake,’11, "Gravitational Waves (from detectors to astrophysics)"
Explosion Mechanisms
1)ν-driven explosion
Buras+,’06
Suwa+,’10
Takiwaki+,’11
Marek&Janka,’09
“Round” explosion
rotation is not necessary
2)MHD explosion
Scheidegger+,’10 (3D)
Obergaulinger+,’06 (2D)
Takiwaki+,’08 (2D)
“Oriented” explosion
rotation is necessary
Rotation  Explosion Morphology  GWs
GW Emissions from Rotating Core
How does rapid rotation affects
on the observed GW emissions?
GW Emissions from Rotating Core
How does rapid rotation affects
on the observed GW amplitude?
Type I signal (Dimmelmeier+,’02)
Obergaulinger+,’06
GW Emissions from Rotating Core
Type I signal appears irrespective
of dimensionality of explosion.
Microphysical EOS
Nu-cooling
3D-MHD
Microphysical EOS
2D
Dimmelmeier+,’08
3D
Scheidegger+,’10 (3D)
GW Emissions from Rotating Core
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%
Dimmelmeier+,’08
GW Emissions from Rotating Core
How does rapid rotation affects
on the observed GW emissions?
Rotational instabilities
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
GW Emissions from Rotating Core
How does rapid rotation affects
on the observed GW emissions?
Low-T/W
instability
3DGR + Γ-law EOS (Ott+,’05)
GW Emissions from Rotating Core
m=1
m=2
3DNMHD + Microphysics
(Scheidegger+,’10)
GW Emissions from Rotating Core
Because the low-T/W instability
occurs in the vicinity of PNS,
•FGW~kHz
•hGW~10-20~-19 @D=10kpc
AdvLIGO
Ott+,’07
Scheidegger+,’10
GW Emissions from Rotating Core
GW emissions from one-armed spiral wave
Scheidegger+,’10
Blondin&Mezzacappa,’07
•Full
spatial domain
Fernandez,’10
•Without excising inner boundary
•0<φ<2π (for m=1 mode)
•Neutrino cooling (for Rshock)
Tpb~27ms
one-armed spiral wave (Rshock>R>RPNS)
GW Emissions from Rotating Core
GW emissions from one-armed spiral wave
3DGR + Neutrino radiation (leakage for cooling term)
15Msun with
(KT, Takiwaki & Kotake, arXiv:1304.4372)
Polar
Equator
Consistent with Ott+,’12
GW Emissions from Rotating Core
log(h)
Time evolution of “h=A/10kpc” spectrum
S/N(=h/N)=1 (for KAGRA)
GW Emissions from Rotating Core
  (2 xy )2  ( xx   yy )2
Scheidegger+,’10
d
 
dt
ij
Tpb~27ms
Strong emission from
one-armed spiral wave
GW Emissions from Rotating Core
How is this “~200Hz”
determined?
Angular frequency of
“Acoustic+Rotational” mode
Ωrot+Ωaco
Ωrot
X (cm)
One armed spiral waves produce GW emission at F~FDoppler.
FDoppler(~200Hz) represents “Acoustic+Rotational” frequency.
GW Emissions from Rotating Core
Importance of neutrino-cooling
GW Emissions from Rotating Core
Importance of neutrino-cooling
w/o cooling
Rshock
w/ cooling
Rns
Unstable region (Rns<R<Rshock)
becomes more compact
due to ν-cooling
Non-axisymmetric
structure
GW Emissions from Rotating Core
Importance of neutrino-cooling
~10 times
stronger GWs
w/o cooling
w/ cooling
Fully general relativistic 3D-Rad-Hydro!!
Scheidegger+,’10
Unstable region (Rns<R<Rshock)
becomes more compact
due to ν-cooling
Non-axisymmetric
structure
GW Emissions from Rotating Core
In addition, if there is
strong magnetic field…….
Total
Offset
R<60km
w/o B
w/ B
Type I signal (Dimmelmeier+,’02)
Obergaulinger+,’06
GW Emissions from Rotating Core
In addition, if there is
strong magnetic field…….
Slowly varying positive offset
originated from MHD jet
2D
Takiwaki+,’08(2D)
3D
Scheidegger+,’10 (3D)
GW Emissions from Rotating Core
If the star rotates sufficiently fast
(T/W|b > a few %
T/W|i > a few ‰)
Low T/W instability (F~kHz, τdecay~10ms, from PNS)
One armed spiral wave (F~ a few 100Hz, τdecay~τexplo (?)
, above PNS)
Strong Type I signal
Low frequency Emission from
MHD jet
GW Emissions from Non-Rotating Core
Z(km)
When rotation is negligible,
(Neutrino Explosion occurs)
GW waveforms are characterized as
1) Early (Linear) SASI motion
2) Hot Bubble Convection & SASI
3) Explosion Phase
Frequency (Hz)
Neutrino
Matter
Muller B.+,’13
GW Emissions from Non-Rotating Core
Advective mode
Neutrino
Acoustic mode
Matter
Blondin+, ‘03
GW Emissions from Non-Rotating Core
Local contribution
to GW emissions
Matter acceleration
Tpb=22ms
Coherent Stripe Pattern
(not stochastic convective one)
Muller B.+,’13
GW Emissions from Non-Rotating Core
From Brunt-Vaisalla frequency,
Muller+,’13 derived following relation
Muller B.+,’13
gravitational
NS surface
force at NS surface
Compact parameter
temperature
Convection (higher order L)
SASI (L〜1,2….)
or
Brunt-Vaisalla
frequency
Hanke+,’13
GW Emissions from Non-Rotating Core
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 study
using successful ν-explosion model in full-3D
Equipartition of energy
Iwakami+, ‘08
Hanke+,’13
GW Emissions from Non-Rotating Core
Light-bulb method in 3D
Kotake+,’11
GW emissions and mass dependence
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)
KT, Takiwaki & Kotake, in preparation
We can investigate
•Progenitor dependence
•SASI evolution without excising inner boundary
•Correlation between GW & Lnu
S15.0
S27.0
Convective
Initiation of SASI (?)
S11.2
S15.0
SASI
S27.0
SASI
S40.0
Lack of
data
SASI feature ?
GW Emissions from Non-Rotating Core
Egw ↑
Mprogenitor ↑
How about observations?
Hayama+
Polar
Equatorial
•Source is located at optimal direction
•SNR is only for “KAGRA”
Le

Le

Le

Lack of
data
L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