素核宇融合による計算基礎物理学の進展－ミクロとマクロのかけ橋の構築－

2011年12月3-5日

合歓の郷

Effects of Hyperon in Binary NeutronStar Merger
Yuichiro Sekiguchi (YITP) with HPCI collaboration
K. Kuchi, K. Kyutoku, M. Shibata, K. HotokezakaReferences Sekiguchi , Kiuchi, Kyutoku, Shibata

Physical Review Letters 107, 051102 (2011) Nucleonic EOS
 Sekiguchi , Kiuchi, Kyutoku, Shibata

Physical Review Letters 107, 211101 (2011) Hyperonic EOSIntroduction
 Coalescence of binary neutron star (BNS)

Promising source of GWs
 Theoretical candidate of Short GRBs
 Laboratory for dense nuclear matter physics
 Overview of BNS merger

Binary separation gradually shrinks due to GW emission
 Mcrit : if the total mass is larger than this, BH will be formed

Mcrit depends of EOS : Mcrit = 1.2—1.7Mmax,sph.cold.NS
 Hotokezaka et al. 2011GWemission

M total < M crit
HMNSM total > M crit

BH

Properties of dense matter Still poorly understood There may be exotic phases at high densities (Pauli principle)
Meson cond., Quarks, Hyperons, …

 How to constrain equation of state (EOS) of neutron star (NS)matter

12/5 talks by

Kyutoku (久徳)Hotokezaka (仏坂)Properties of dense matter Popular method

Mass-Radius relation
 Maximum mass of NS

Mmax = 1.97 Msun

 Strong impact by

PSR J1614-2230
 Too soft EOS are ruled out However, existence of

exotic phases remains
unconstrained

Lattimer & Prakash 2007

Lattimer & Prakash 2011
Bednarek+ 2011
Weissenborn+ 2011

M max ( f S ) = M max (0) − 6 f S
f S ( M max ) < 0.17in solar mass unit

for M max > 2 M solar( f S :# of strange quark / baryon)

Numerical Studies Exploring Exotic Phases
 Stellar Core CollapseQuarks (Nakazato+ 2008,2010; Sagert+ 2009; Fischer+ 2011)
 Hyperons (Sumiyoshi+ 2009; Nakazato+ 2011) Binary Neutron Star (BNS) Merger

Not yet studied in detail Parametric Study (Hotokezaka+ 2011), Bauswein+ 2011 This Study

The first full GR simulations for BNS merger incorporating afinite temperature hyperonic EOS

 Key Question:
Is it possible to tell the existence of hyperons by observationsof Neutrino and Gravitational-Wave (GW) signals ?

Equation of State (EOS) S-EOS: ‘normal’ nucleonic matter EOSShen, Toki, Oyamatsu, Sumiyoshi, NPA 637, 435 (1998)

 H-EOS: EOS with Λ hyperonsShen, Toki, Oyamatsu, Sumiyoshi, ApJ 197, 20 (2011)

 We only consider contribution of Λ hyperons becauseΛ hyperons are believed to appear first because they are lightest
and feel an attractive potential (e.g. Ishizuka et al. 2008) Σ hyperons have comparable mass but feel a repulsive potential ,and will not appear at lower densities (Noumi et al. 2002)Equation of State (EOS) At T = 0, Λ hyperons appear at ρ ~ a few ρnuc, and XΛ increases

as density and temperature increase Due to the appearance of Λ hyperons, EOS becomes softer andthe maximum mass of the cold spherical NS is decreased to beMmax,sph.cold.NS ~ 1.8 Msolar

Set up of BNS
 S-EOS (nucleonic EOS) :Equal mass BNS with individual mass of 1.35, 1.5, and 1.6 Msolar
 Referred to as S135, S15, and S16
 H-EOS (hyperonic EOS) :Equal mass BNS with individual mass of 1.35 and 1.5 Msolar
 Referred to as H135 and H15Nucleonic EOS

Merger Dynamics (S135)
Hyper massive NS (HMNS) is formed and lives a long time characterized
by neutrino cooling timescale ~ Eth/Lν ~ 2-3 sec (Lν: discuss later)
 GW emissivity declines to be low because the HMNS becomes only
weakly spheroidal and relaxes to a quasi-stationary state at a later timeDensity [ log10 g/cc]

Temperature [ MeV ]Merger Dynamics (S135)
Hyper massive NS (HMNS) is formed and lives a long time characterized
by neutrino cooling timescale ~ Eth/Lν ~ 2-3 sec (Lν: discuss later)
 GW emissivity declines to be low because the HMNS becomes only
weakly spheroidal and relaxes to a quasi-stationary state at a later timeDensity [ log10 g/cc]

Temperature [ MeV ]Merger Dynamics (S16) HMNS which is supported by thermal pressure as well as

centrifugal force is first formed and eventually collapses to a BH
because the angular momentum is carried away by GW
Density [ log10 g/cc]

Entropy per baryon

Entropy per baryon is ~ 2-3 kB
which effect increases themaximum mass by 20-30%

Gravitational Waveforms
inspiral

HMNS becomes
Merger and oscillation
spheroidal and GW
emissivityS135
gets small

S15

S16

BH formation due toangular momentum
loss by GW emission

Gravitational Wave Spectra
Prominent peakassociated withHMNS oscillation

EOS information frompeak frequency(Hotokezaka+ 2012
Bauswein + 2011)
S135
S15
S16

Events within 20Mpc
can be detectedNeutrino Luminosity

Events within 5Mpc can bedetected by Hyper Kamiokande

S135

S15

S16

Anti-electron neutrinos are
dominantly emitted via
n+e+ → p+aν because oflarge neutron fraction andlarge e+ fraction due to hightemperature

Huge neutrino luminosityof ~ 1053 erg/s even after
the BH formation

Neutrino is dominantly emitted from thepole-region of HMNS
 x-z plane contours of density and neutrino emissivity
 Shock waves are formed as the materials which expand

hit the pole (low density) of HMNS ⇒ high emissivity
Density [ log10 g/cc]

ν emissivity [ log10 erg/cc/s]

Hyperonic EOS

Merger Dynamics (H135) hyperonic EOSHyper massive NS (HMNS) first forms and eventually collapses to BHAs HMSN shrinks, density and temperature increase and consequently more
hyperons appear, making EOS more softer

After the BH formation, a massive accretion disk (~0.08 Msolar) is formed⇒ short GRBs ?
Density [ log10 g/cc]

Temperature [ MeV ]Merger Dynamics (H135) hyperonic EOSHyper massive NS (HMNS) first forms and eventually collapses to BHAs HMSN shrinks, density and temperature increase and consequently morehyperons appear, making EOS more softer

After the BH formation, a massive accretion disk (~0.08 Msolar) is formed⇒ short GRBs ?
Density [ log10 g/cc]

Temperature [ MeV ]Gravitational Waveforms : Hyperonic
GWs from inspiral phaseagree well because only
few hyperons exist
BH is formed in a shortertime and GWs damp
steeply there

Nucleonic / Hyperonic

Characteristic GW
frequency for hyperonic
EOS increases with time :This potentially marks
the existence of hyperons

Nucleonic / Hyperonic

Nucleonic

Frequency Shift due to HyperonDynamics of HMNS formed after the merger
Nucleonic：HMNS shrinks by angular momentum loss in a long GW timescale Hyperonic：GW emission ⇒ HMNS shrinks ⇒ More Hyperons appear ⇒EOS becomes softer ⇒ HMNS shrinks more ⇒ ….
 As a result, the characteristic frequency of GW increases with time Providing potential way to tell existence of hyperons (exotic particles)
Hyperon Fraction

Hyperonic

Gravitational Wave Spectra
Nucleonic EOS

Hyperonic EOS
Peak is weakened and broadened
reflecting the short lifetime ofHMNS and the frequency shift

Neutrino Luminosity

There is no difference except for the duration until the BH formationEffects of hyperons are significant in the central region where neutrino
diffusion time is very long, and swallowed into BH

Difficult to tell the existence of hyperons using the neutrino signals alone

ν emissivity [log erg/s/cc ]Summary We performed the first numerical-relativity simulations ofBNS merger incorporating a finite temperature EOS withhyperons Existence of hyperons are imprinted in GWs

The characteristic GW frequency increases in time which stems from Nucleonic-to-Hyperonic Transition
 Providing potential way to tell existence of hyperons by GWobs.


It is difficult to constrain EOS by neutrino signals only

Effects of hyperons are significant in the central high density
region which is swallowed into BH

Future prospect Gravitational Waves from Hadron-to-Quark Transition
Second order phase transition ⇒ Frequency shift (as in hyperon case)First order transition ⇒ Double peaked GW spectrum is expected:

One associated with NS and the other with Quark starPP

Second orderHadronHadronQuarkρ N→QFirst orderρ

Quark

ρNρQ

ρ

Exploring EOS by GWs from BNS
Inspiral phase

Tidaldeformation

Merger and oscillation

 Point particle approximation

 Finite size effect Maximum mass, oscillation

 Information of orbits,
neutron star mass etc.

 Information ofequation of state Information of equationof state

kmLog density[g/cm3]

Amplitude

Density contour

Typical WaveformTimeWhy GWs from Binary Neutron Star
Merger ?
One of most promising source of GWs





Tidal deformation (radius) : relatively low density
Maximum mass : most high densityOscillation :Radius is sensitive torelatively low density parts
Δ ~ 10%Less uncertain parameters

By contrast with static, isolated neutron starMultiple information of equation of stateVery small cross section with matter

Dynamical response of dense matter

Δ ~ 10%Unique window to ‘see’ inside dense matters

Next generation interferometer can see ~ 350Mpc
Expected event rate : more than 10/yr

Inspiral waveform provides information of mass
Mass should be determined in isolated neutron starOzel & Psaltis
2009

Simple in a complementary sense

Essentially quadrupole formula
By contrast with optical observation

Maximum mass depends onmost dense parts