SHIBATA2

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Merger of Black hole-Neutron star binary: Simulation in full GR: 

Merger of Black hole-Neutron star binary: Simulation in full GR M. Shibata (Univ. Tokyo) Introduction: Why study for BH-NS is important. 2 Status of numerical relativity 3 Latest work of BH-NS merger

I Introduction: 

I Introduction Merger of BH-NS binary One of the promising sources of gravitational wave detectors Possible origin of short GRBs  Deserves detailed study

Gravitational wave amplitude: 

Initial LIGO Advanced LIGO,      LCGT, … BH=10 solar mass, NS=1.4 solar mass Effective Amplitude Gravitational wave amplitude frequency

Frequency of GW at last orbits: 

Frequency of GW at last orbits GWs at last orbits will be detected by advanced detectors  Observe strong GR fields

Slide5: 

One of candidates of GRBs

Two fates of BH-NS: 

Two fates of BH-NS NS falls into BH with no disruption (for high mass BH) Tidal disruption (low mass BH) Later is important because GWs may carry information on radius of NS 2 Disk will be formed  Short GRB?

Condition of tidal disruption: 

Condition of tidal disruption BH’s tidal force > NS’s self gravity r R MBH Tidal disruption is likely for low-mass BH, but full GR study is necessary.

What to do ?: 

What to do ? Study for quasiequilibrium before merger  Determine the condition for tidal disruption Effort (still in early stage) by Illinois Meudon, & Japan groups indicates that tidal disruption is slightly less subject in GR (due to strong gravity of NS) GR simulation for merger  Clarify the fate after tidal disruption and compute GW ◎

Slide9: 

Time Space Black Hole Horizon Gravitational waves Hydrodynamics Collapse II What is numerical relativity gij , Kij r, u, P

Specifically, we need to: 

Specifically, we need to Solve Einstein’s evolution equations Solve GR Hydrodynamic equations Impose appropriate coordinate conditions Extract gravitational waves Find horizon (apparent / event horizon) Handling BHs …..(EOS, B-fields, microphysics …)

Status 3 yrs ago: 

Status 3 yrs ago Solve Einstein’s evolution equations Solve GR Hydrodynamic equations Impose appropriate coordinate conditions Extract gravitational wave Find horizon (apparent / event horizon) Handling BHs ….. ○ ○ ○ ○ ○ × Longterm evolution of BH was not feasible

Status since 2005: 

Status since 2005 Solve Einstein’s evolution equations Solve GR Hydrodynamic equations Impose appropriate coordinate conditions Extract gravitational wave Find horizon (apparent / event horizon) Handling BHs ….. ○ ○ ○ ○ ○ ◎

Significant progress in the last two yrs: 

Significant progress in the last two yrs Simulation for BH-BH is feasible Frans Pretorius first suceeeded Excision surfaces Apparent horizon Caltech-Cornell group have developed an extremely robust tool (06); 15 orbits !! But, highly technical; one cannot follow easily

Results by Pretorius: Lapse: 

Results by Pretorius: Lapse From his homepage

Moving Puncture method: handy !: 

Moving Puncture method: handy ! Two Einstein-Rosen bridge (Brill-Lindquist (63) for P=0 Brandt-Bruegmann (97) for moving) No singularity but coordinate singularities No Excision Coordinate singularities

Coordinate singularity can be handled: Change a variable.: 

Coordinate singularity can be handled: Change a variable. Campanelli et al. PRL 96, 111101 (2006)

Appropriate choice of gauge is needed: 

Appropriate choice of gauge is needed a=0 is required at puncture: Solution Dynamical gauge (Alcubierre -Bruegmann 02) since c is not singular, but still irregular. But, it always couples to lapse a. Many groups have succeeded in BH-BH merger. Rochester, NASA, Jena, Penn-State, AEI-LSU, myself, …

III First numerical results of BH-NS: 

III First numerical results of BH-NS Moving puncture for BH Quasiequilibrium initial condition BH mass = 3.2 Msun             NS mass = 1.3 Msun (baryon mass=1.4)                     NS radius= 13.8 km              EOS = G-law EOS (G=2): P=(G-1)re MW ~ 0.052 (r/M~7): close to ISCO Corotation velocity field ⇒ more subject to tidal disruption  Upper limit of disk mass

Slide19: 

BH NS Density in the equatorial plane

Baryon mass outside BH & area of AH: 

Baryon mass outside BH & area of AH Baryon mass outside BH Area of apparent horizon

Gravitational waveforms: 

Gravitational waveforms Amplitude damps quickly

Summary of results: 

Summary of results Low-mass BH (M~3--4 Msun) tidally disrupts NS of mass ~ 1.3 Msun and radius ~ 13 km Disk mass is ~ 0.2 Msun for MBH = 3.2 Msun ~ 0.1 Msun for MBH = 3.9 Msun large enough for short-GRB Amplitude of GW quickly damps after tidal disruption

Prospect: 

Prospect Simulation for BH-NS is now feasible  Next step: Many simulations changing mass of BH/NS and EOSs of NS. Goal: To make a catalog of GW To clarify the outcome (disk mass, disk temp & density, BH spin) for Short-GRB study

Density contours in equatorial plane: 

Density contours in equatorial plane

convergence: 

convergence Hamiltonian constraint

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