Gravitational waves frombinary neutron star mergers~measuring the equation of state~
Kenta Hotokezaka(Kyoto University)
K. Kyutoku, H. Okawa, M. Shibata, K. Kiuchi, and Y. Sekiguchi(YITP)Ref) K.Hotokezaka, et al. PRD 83. 124008 (2011)
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Outline• Introduction• BNS merger simulations ~dependence on EOS~

• Gravitational waves ~measuring the EOS~
• Summary

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Introduction ~Equation of State~
Several candidates of the real EOS
from nuclear theory(e.g. including hyperon, quark ……)

Mass-Radius relation ofneutron star for each EOSlog PM
TOV equation
One to onelog ρRMeasuring M-R of neutron star simultaneously⇒ we can construct the EOS !!
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Astronomical observation
Integrated EOSe.g.
Moment of inertia

messenger

MassRadius

Isolated Pulsar

××△

radio~γ

Isolated NS(non Pulsar)

△△

×

opt～X

Pulsar-NS/WD◎

×○×radio

LMXB

△~○

△~○

×X

NS-NS/BH merger

◎

○○GW

: Future expected
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Introduction ~Gravitational Wave Astronomy~
Advanced detectors(2015~)

GW

Binary Neutron Star merger(BNS)
Expected event rate
~10 times / yr

Advanced LIGOLCGTAdvanced Virgo

・High energy astrophysics
・Supernuclear-density matter::Need!
precise prediction ofthe gravitational waveform
Numerical Relativity Simulation
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Outline• Introduction• BNS merger simulations ~dependence on EOS~

• Gravitational Waves ~measuring the EOS~
• Summary

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Set up ~Numerical simulations~
Solving Einstein equation & Hydrodynamics (SACRA code)
Equal mass binary neutron star
Adapted EOS :（Piecewise-polytropic EOS. Read et al. 2009）
for systematical study

Fitting 6 nuclear theory based EOSs•

APR4

npe + 3body(Akmal, et al. l 1998)•Slynpe(Douchin and Haensel 2001)•H3, H4npeΛΣ…

(Glendenning and Moszkowski 1991 )•nπPS(Pandharipande and Smith 1975)•ALF2(Alford et al.

npe+quark2005)（ideal gas）

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Numerical Simulation
EOS = Relativistic Mean Field with Hyperon
Total mass =()In cgs8/18

Result: Type of First Remnants
The evolution after the merger strongly depend on the EOS.
Total mass
BH is formed promptlyType of the first remnant of mergers
Type I : prompt BH formation
Black Hole

Type II : Short-lived HMNS
(lifetime < 5 ms)
Hypermassive
TypeNeutron
III : Long-lived
HMNSStar(lifetime > 5 ms)
Neutron Star

EOSs
Large radius
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Outline• Introduction• BNS merger simulations ~dependence on EOS~

• Gravitational Waves ~measuring the EOS~
• Summary

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Gravitational waveform of BNS merger
GWGW

inspiralmerger

Hypermassive
Neutron StarBlack hole +Accretion disk

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Measuring the EOS with BNS merger• Inspiral GW ⇒ Mass( less than 1% forwhen S/N~10 )Cutler & Flanagan (1994)• late inspiral GW ⇒ tidal deformation• HMNS GW ⇒ rotation and oscillation• No HMNS GW ⇒ Cut off frequency
Kiuchi + 2010
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GW spectrum & MR relation
BH is formed promptlyBlack HoleHypermassive
Neutron Star

Neutron Star

The spectral shape is simple

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GW spectrum & MR relation
oscillation
rotation
HMNS is formed

Black HoleHypermassive
Neutron Star

Neutron Star

Short-lived HMNS
⇒ Spectral shape is complicated・ rotation of the HMNS・oscillation of the HMNS
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GW spectrum & MR relation
oscillation
rotation
HMNS is formed

Black HoleHypermassive
Neutron Star

Neutron Star

Long-lived HMNS is form
⇒ Peak width is more narrow

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GW spectrum & MR relation
oscillation
rotation

More compact EOSBlack HoleHypermassive
Neutron Star

Neutron StarSoft EOS⇒peak frequency ↑16/18

Result GW spectrum from HMNSThis peak frequency relates to R of the NS
GWs from a HMNS is useful for constraining on the EOS
See also Bauswein and Janka (2011)17/18

Summary
the dependence of BNS merger on EOS
The first remnants of BNS are classified into 3 types(1) A black hole is promptly formed(2)A short-lived HMNS is formed (lifetime ＜5ms)(3)A long-lived HMNS is formed (lifetime ＞5ms)
A HMNS should be formed in the BNS merger

Gravitational waves
The shape of the GW spectrum ⇒ shape depends on 3 types
The GW spectrum from a HMNS ⇒and the radius of NS18/18

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