Symposium onQuarks to Universe in Computational Science (QUCS 2012)

Numerical Relativity Simulationsof NS-NS binary merger
Yuichiro Sekiguchi (YITP)
K. Kiuchi, K. Kyutoku, M. Shibata, & Hotokezaka

Why NS-NS mergers are interesting ?
Promising source of gravitational wave (GW)Direct detection of GW within 5-10 years byadv. LIGO(USA), adv. VIRGO (ITA/FRA), KAGRA (JPN)Laboratory for fundamental physics
Verification of GR in strong field regime
 Physics of dense nuclear matter

NS-NS merger as a cosmological colliderTheoretical candidate of gamma-ray bursts (GRB)
Central engine : BH + accretion disk
Energy source : neutrino pair annihilation ?

General relativistic gravity is important
Highly nonlinear and dynamicalNumerical Relativity

Current & up-coming GW detectors

BNS 1.35-1.35Msolar optimal @ 100Mpc
Inspiral charp signal
Post NewtonMerger
HMNS formation
NRWhy NS-NS mergers are interesting ?
Promising source of gravitational wave (GW)Direct detection of GW within 5-10 years byadv. LIGO(USA), adv. VIRGO (ITA/FRA), KAGRA (JPN)

Laboratory for fundamental physics
Verification of GR in strong field regime
 Physics of dense nuclear matter

NS-NS merger as a cosmological collider

Theoretical candidate of gamma-ray bursts (GRB)
Central engine : BH + accretion disk
Energy source : neutrino pair annihilation ?

General relativistic gravity is important
Highly nonlinear and dynamical

Numerical RelativityNS structure ⇔ Theoretical model
For given equation of state, structure of NS is uniquely determined Information of NS structure ⇒ constraining EOS model

F. Weber (2005)

NS structure ⇔ Theoretical model
For given equation of state, structure of NS is uniquely determined Information of NS structure ⇒ constraining EOS model

F. Weber (2005)

Lattimer & Prakash (2007)

NS structure ⇔ Theoretical model
For given equation of state, structure of NS is uniquely determined Information of NS structure ⇒ constraining EOS model

F. Weber (2005)
www.gsi.deLattimer & Prakash (2007)

Open Question
Given the theoretical uncertainty, which one is the right one ?
 Traditional method to constrain the models
Mass-Radius relation :Estimation of mass and radiusobservation of X-ray binary Large systematic errorMaximum mass :byJust find a massive NS

PSR J1614-2230 (NS-WD)
NS of 1.97Msolar
 Mass measurement by
Shapiro time delay Too soft EOSs are excluded

Still we have a number oftheoretical models
Lattimer & Prakash (2007)

Bill Saxton,
NRAO/AUI/NSF

Open Question
Given the theoretical uncertainty, which one is the right one ?
 Traditional method to constrain the models
Mass-Radius relation :Estimation of mass and radiusobservation of X-ray binary Large systematic errorMaximum mass :byJust find a massive NS

PSR J1614-2230 (NS-WD)
NS of 1.97Msolar
 Mass measurement byShapiro time delay Too soft EOSs are excluded

Still we have a number oftheoretical models
Lattimer & Prakash (2007)

Why NS-NS mergers are interesting ?
Promising source of gravitational wave (GW)Direct observation of GW within 5-10 years byadv. LIGO(USA), adv. VIRGO (ITA/FRA), KAGRA (JPN)Laboratory for fundamental physics
Verification of GR in strong field regime
 Physics of dense nuclear matter

NS-NS merger as a cosmological collider

Theoretical candidate of gamma-ray bursts (GRB)
Central engine : BH + accretion disk
Energy source : neutrino pair annihilation ?

General relativistic gravity is important
Highly nonlinear and dynamical

Numerical Relativity

What is Numerical Relativity ?
 Solving Einstein eq. and source field eqs. to clarify dynamical

phenomena in the universe where strong gravity plays a role
8GGab c4Tab aT ab  0 (T ab  (TFluid  TEM  T  ...) ab )
 a J a  0 ( J a ~ (nbaryon, nlepton (ne , n , ...) , ... )u a ) All four known interactions play important roles
 Gravity : GR, BH formation, ISCO, etc
 Strong : EOS (equation of state) of dense nuclear/hadronic matter EM: MHD phenomena, EOS of dense matter Weak : Electron capture, Neutrino production, neutrino pair annihilation
 99% gravitational binding energy released is carried away by neutrinos in SNe

NR simulations with a physical modeling isnow possible !
 Einstein’s equations: Shibata-Nakamura (BSSN) formalism
 4th order finite difference in space, 4th order Runge-Kutta time evolution
 Gauge conditions : 1+log slicing, dynamical shift GR Hydrodynamics with neutrinos (Sekiguchi 2010)
Nuclear-theory-based finite temperature EOS tablea(leak)
T


Qa bb
 EOM of Neutrinos (leakage scheme, moment scheme)
 Lepton Conservations
 aTba ( ,stream)  Qb(leak) Weak Interactionsa



e± captures, pair annihilation,
plasmon decay, Bremsstrahlung

A detailed neutrino opacitiesHigh-resolution-shock-capturing scheme

BH excision technique (Fixed) Mesh refinement technique a ( Yeu )   e cap   e cap a ( Ye u a )   e cap   pair   plasmon   Brems    eleak a ( Y e u a )   e cap   pair   plasmon   Brems    eleak a ( Y   u a )   pair   plasmon   Brems    leak

Sekiguchi (2010) Progress of Theoretical Physics 124, 331

Neutrino transfer : a preliminary result
Solving Boltzmann equation (6+1 dims. !) is not feasible at current status
 Approximate solution by Thorne’s Moment scheme with a closure relation
 Neutrino heating (absorption on proton/neutron) can be treated But some (approximate) treatment is required for νannihilation
Evolution of NS-NS Binary

Shibata et al. 2005,2006

tidal deformationr  Mr ~ several M

M total  M crit  2.9  3.2 M sun
Hyper Massive NS(HMNS)

M total  M NS, max

M total  M critGWs,neutrinos

M total  M NS, max

Imre Bartos, GECo, Columbia University(Bartos et al. 2013, in prep.) with permission

Evolution of NS-NS Binary

Shibata et al. 2005,2006

tidal deformation
Lattimer & Prakash (2007)r  Mr ~ several M

M total  M crit  2.9  3.2 M sun

MCanonicaltotal  Mmass
crit= 1.35-1.4Msolar

Hyper Massive NS(HMNS)

M total  M NS, max

GWs,neutrinos

M total  M NS, max

Imre Bartos, GECo, Columbia University(Bartos et al. 2013, in prep.) with permission

Sekiguchi et al. PRL (2011a, 2011b)
Kiuchi et al. PRL (2010); Hotokezaka et al. (2011); (2012)

GW from NS-NS (long lived HMNS)
NS(1.2Msolar)-NS(1.5Msolar) binary (APR EOS)
log10 [g/cm ]3TidalInspiral
deformation
Charp signalMerger
HMNSDensity Contour
Gravitational Waveform

Animation by Hotokezaka

Exploring Dense matter physics by GW
Inspiral phase Point particle approximation
 Information of orbits,
neutron star mass etc.

Tidal
deformation
 Finite size effect Deviation fromcharp ⇒ NS radius

Merger and oscillationof HMNS BH or NS ⇒ maximum mass
 GW from rotating HMNS
⇒ NS radius (and EOS)

kmLog density[g/cm3]

Amplitude

Density contour

TimeKiuchi et al. PRL (2010)

Prompt BH formation
GW spectra : deviation from point particle
GW spectra for prompt BH formation
Point particle
approximation

Deviation due tofinite size effects

f cut

Kiuchi, YS et al. (2010) PRL 104 141101

Kiuchi et al. PRL (2010)

fcut may be used to estimate RNS

Kiuchi, YS et al. (2010) PRL 104 141101

Exploring Dense matter physics by GW
Inspiral phase Point particle approximation
 Information of orbits,neutron star mass etc.

Tidaldeformation
 Finite size effect Deviation fromcharp ⇒ NS radius

Merger and oscillationof HMNS BH or NS ⇒ maximum mass
 GW from rotating HMNS
⇒ NS radius (and EOS)

kmLog density[g/cm3]

Amplitude

Density contourTime

Hotokezaka et al. (2011); (2012)

GWs from HMNS (1.3-1.4 Msolar Merger)
Soft EOS
More compact
structuref HMNS ~ 3.2kHz

f HMNS ~ 2.9kHz
Stiff EOS
Less compact

f HMNS ~ 2.5kHz

f HMNS ~ 2.0kHz

Hotokezaka et al. (2011); (2012)

GW spectra (1.35-1.35 Msolar)
GW spectra show characteristic
peak frequency fpeakfpeak’s are different for different
EOS ⇒ constraining EOS

Relation between fpeak and NS structure The peak GW frequency depends strongly on EOS
 The frequency has correlation with NS radius and stiffness of

EOS
Bauswein et al. (2012)

Bauswein & Janka. 2011
 Bauswein et al. 2012
 Hotokezaka et al. 2012

Stiffer EOS
Radius of 1.6Msolar NS

Relation between fpeak and NS structure The peak GW frequency depends strongly on EOS
 The frequency has correlation with NS radius and stiffness of

EOS
Bauswein et al. (2012)

Bauswein & Janka. 2011
 Bauswein et al. 2012
 Hotokezaka et al. 2012

Stiffer EOS
Radius of 1.6Msolar NS

Relation between fpeak and NS structure The peak GW frequency depends strongly on EOS
 The frequency has correlation with NS radius and stiffness ofEOS
Bauswein et al. (2012)

Bauswein & Janka. 2011
 Bauswein et al. 2012
 Hotokezaka et al. 2012preliminary

Stiffer EOS
Radius of 1.6Msolar NS

fpeak vs. NS radius

Sekiguchi et al. PRL (2011)

Emergence of Hyperon is putted in GW ?
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 Might providing potential way to tell existence of hyperons (exotic particles)
Hyperon Fraction

NucleonicHyperonicSekiguchi et al. PRL (2011)

Neutrino signal (w. and w.o. hyperons)
There is no difference except for the duration until the BH formationDifficult to tell the existence of hyperons using the neutrino signals alone Copious neutrinos are emitted from disk around BH


NS-NS merger as a progenitor of short GRBs ?

ν emissivity [log erg/s/cc ]Possible EM counterpartExpected electromagnetic (EM) wave emission from the merger

Detection of EM counterpart enhances reliability and detectability of GW

Ejecta Sweeping inter stellar matter ⇒ shock ⇒ Synchrotron rad.
Nakar & Piran (2011) Nature ∼ 90μJy (E0/1050erg)(n0/1cm-3)0.9(v/0.3c)-2.8 (D/200Mpc)-2 (νobs/1.4 GHz) -0.75
Neutron rich ejecta ⇒ R-process ⇒ radioactive decay (talk by Wanajo san)Li & Paczynski (1998)
 Lpeak ∼ 2.6
1042 erg/s (f/3

10-6) (v/0.3c)1/2 (Meje/10-2 M )1/2

These transient event could be detected with upcoming radio or
optical detectors

Hotokezaka et al. (2012)

Mass ejection depends strongly on EOS
 More compact NS results in more massive ejecta

For mass ratio close to unity (q~1) and more compact NS, massejection is driven by shocks. Tidal effects are relatively less important For larger mass ratio and less compact NS, tidal effect is also important Coupled observations of GW and EM will be important !

Hotokezaka et al. (2012)

Homologous mass ejection for q~1

Hotokezaka et al. (2012)

Tidal effects play role for q<1 and stiff EOS

Hotokezaka et al. (2012)

Mass ejection depends strongly on EOS
 More compact NS results in more massive ejecta

For mass ratio close to unity (q~1) and more compact NS, massejection is driven by shocks. Tidal effects are relatively less important For larger mass ratio and less compact NS, tidal effect is also important Coupled observations of GW and EM will be important !

Hotokezaka et al. (2012)

Mass ejection depends strongly on EOS
 More compact NS results in more massive ejecta

For mass ratio close to unity (q~1) and more compact NS, massejection is driven by shocks. Tidal effects are relatively less important For larger mass ratio and less compact NS, tidal effect is also important Coupled observations of GW and EM will be important !

Summary
 Numerical Relativity is the unique tool to study dynamical

phenomena such as NS-NS merger where strong gravity playsa role

Recent developments enable us to perform simulations in physicalmodeling NS-NS merger is interesting both in physics and astrophysics

Promising sources of ground-based GW detectors
 As laboratory for exploring physics of dense matterCentral engine of SGRB

It may be possible to constrain EOS by GW from the merger
A large number of neutrinos are emitted from the hot disk

Exploring EM counterpart will be also important

Sekiguchi et al. (2012) Progress of Theoretical & Experimental Physics
Sekiguchi & Shibata ApJ (2011)

BH+Disk formation in stellar core collapse (2D)
100Msolar model by Umeda & Nomoto (2008) + rotation
 Torus-structured shock : accumulation of matter to the proto-NS
 Time varying, large (~1052 erg/s) neutrino luminosity after BH formation
x-z plane
After the core bounce
Standing shock wave isformed

Sekiguchi et al. (2012) Progress of Theoretical & Experimental Physics
Sekiguchi & Shibata ApJ (2011)

BH+Disk formation in stellar core collapse (2D)
100Msolar model by Umeda & Nomoto (2008) + rotation (< ms NS)
 Torus-structured shock : accumulation of matter to the proto-NS
 Time varying, large (~1052 erg/s) neutrino luminosity after BH formationeeLν [1053 erg/s]  Density [ log10 g/cc]

km

e
e

Lν [1053 erg/s]

Entropy/baryon [kB]kmImportance of Rotation: Oblique Shock Torus-structured shock Infalling materials areaccumulated into the PNS
due to the oblique shock Thermal energy is efficiently
stored in the pole of PNS
 Ram pressure ↓ ⇒Outflow
 Flows hit central PNS
 NS oscillation ⇒ PdV work , Lν ↑

Importance of High Entropy/Rotation :Energy balance Compact core / Oblique shock ⇒ high mass accretion rate Energy balance may not be satisfied ……

Rotation decreases |Qadv| & |Qν| (dense disk) Additional ‘cooling’ sources requiredQ acc Q adv
 Q
 Q   Q   Q   Q acc

adv


Qoutflow/ expansion
convection

Strong dependence of Qν (ν-cooling) on T (and ρ)⇒ slight change of configuration leads to dynamically large change


Torus is partially supported by the (thermal) pressure gradient Smaller amount of heavy nuclei ⇒ more energetic SNe ?
Dissociation of 0.1 Msolar Fe costs ~ 1051 erg

Higher temperature : Less Pauli blocking in neutrino pair annihilation

Importance of Rotation: BH spin
Energy conversion efficiency can change two orders of magnitude
 Disk properties to neutrinos strongly depend on BH spin

Slow rot. BH ⇒ ISCO (disk edge) located far ⇒ low density / opacity ⇒Efficient cooling ⇒ the local valance satisfied ⇒ weak/no time variability
trappeda = 0Chen & Beloborodov (2007)

a = 0.95

Similarities to ordinary SN
 Same components: ‘stalled’ shock + neutrino sphere/torus

SASI-like activities are likely to occur ?
 The gain (neutrino-heated) regions do exist (Sumiyoshi+ 2012) Only topology is different

How will this system evolvein the presence of ν-heating The next study using
GR-νRad-Hydro Code(recently developed)

Sumiyoshi+ 2012

gain region