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Current status of numerical relativity Gravitational waves from coalescing compact binaries

Current status of numerical relativity Gravitational waves from coalescing compact binaries. Masaru Shibata (Yukawa Institute, Kyoto University). GW spectrum from compact binaries. Initial LIGO. Chirp. h=h ( f ) f. Merge. Prediction only by

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Current status of numerical relativity Gravitational waves from coalescing compact binaries

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  1. Current status of numerical relativityGravitational waves fromcoalescing compact binaries Masaru Shibata (Yukawa Institute, Kyoto University)

  2. GW spectrum from compact binaries Initial LIGO Chirp h=h(f)f Merge Prediction only by Num. Rela Adv LIGO, LCGT… Assume BH=10Msun NS=1.4Msun Frequency f (Hz)

  3. Needed implementations 1. Einstein’s evolution equations solver 2. GR Hydrodynamic equations solver 3. Gauge conditions (coordinate conditions) 4. Realistic initial conditions 5. Gravitational wave extraction techniques 6. Apparent horizon (Event horizon) finder 7. Special techniques for handling BHs 8. Micro physics (EOS, neutrino processes, B-field, radiation transfer …) 9. Powerful supercomputers or AMR

  4. Present status ○ ○ ○ ○ ○ ○ ○ △ ○ 1. Einstein’s evolution equations solver 2. GR Hydrodynamic equations solver 3. Gauge conditions (coordinate conditions) 4. Realistic initial conditions 5. Gravitational wave extraction techniques 6. Apparent horizon (Event horizon) finder 7. Special techniques for handling BHs 8. Micro physics (EOS, neutrino processes, B-field, radiation transfer …) 9. Powerful supercomputers or AMR Not yet

  5. Summary of current status • Simulation for BH spacetime (BH-BH, BH-NS, collapse to BH) is now feasible. • Simulation for NS-NS with a variety of equations of state is in progress. • Adaptive mesh refinement (AMR) enables to perform a longterm simulation for inspiral. • MHD effects, finite temperature EOS, neutrino cooling, etc, start being incorporated⇒Application to relativistic astrophysics (but still in a primitive manner)

  6. §BH-BH: Status • Simulation from late inspiral through merger phases is feasible: Evolve ~10 orbits accurately by several groups • For nonspining BHs, an excellent analytical modeling (i.e. Taylor-T4 formula) has been found for orbital evolution and gravitational waveforms • For the spinning BH-BH, several works exist, but still a large parameter space is left; good modeling has not been done yet.

  7. Gravitational waves from BBH merger QNM BH ringing Inspiral waveform By F. Pretorius

  8. Universal Fourier spectrum Buonanno, Cook, & Pretorius, PRD75 (2007) (15+15Msun) f-2/3 merger h(f) e-aw ringdown f -7/6 inspiral

  9. 1st LIGO Current level h=h(f)f Larger mass Assume BH=10 Msun Detection is possible now advLIGO, LCGT Frequency (Hz)

  10. High-precision computation by Cornell-Caltech group Nonspining Equal-mass 15 orbits

  11. Excellent agreement with Taylor T4 formula

  12. §NS-NS: Status • Late inspiral phase by AMR: It is possible to follow >~5 orbits before merger with nuclear-theory based EOS  Will clarify the dependence of GWs on EOSs at the onset of merger • Merger phase: It is feasible to follow evolution to a stationary state of BH/NS. BUT, still, with simple EOS/microphysics More detailed modeling is left for the future work

  13. 1.4Msun 1.4Msun 1.5Msun 1.5Msun Merger to BH Merger to NS Akmal-Pandharipande-Ravenhall EOS Kiuchi et al. (2009)

  14. Gravitational waveform for black-hole formation case Ring down Inspiral Merger

  15. Universal spectrum for BH formation Bump Inspiral heff ~ f n n~-1/6 BH QNM Damp Damp Merger Different from BBH

  16. Gravitational waveform for hyper-massive NS formation case QPO Inspiral Merger

  17. Spectrum for two EOSs EOS-dependence of fcut advLIGO

  18. §Status of BH-NS • It is possible to follow several orbits. • Significant difference between tidal-disruption and no-disruption waveforms Merger waveforms depend significantly on the neutron star radius • Still in an early stage; simulations have been performed with simple EOSs  Next task: Survey for waveforms using a wide variety of EOSs (on going)

  19. Inspiral: (M/R)NS=0.145, G=2 polytrope MBH/MNS=2 MBH/MNS=5 ~5 orbits ~7.5 orbits

  20. (M/R)NS=0.145, MBH/MNS=2

  21. (M/R)NS=0.145, MBH/MNS=4 (& >4) No disk

  22. Gravitational waveforms Dotted curve = 3 PN fit inspiral disruption Quick shutdown (M/R)NS=0.145, MBH/MNS=2

  23. Gravitational waveforms Dotted curve = 3 PN fit ringdown (M/R)NS=0.145, MBH/MNS=5

  24. (M/R)NS=0.178 MBH/MNS=3(M/R)NS=0.145 No disruption Clear ringdown Mass shedding Not very clear

  25. Typical spectrum Hz BH-QNM Inspiral Damp ∝ exp[-(f/fcut)n] (M/R)NS=0.145, MBH/MNS=3

  26. No-disruption • Spectrum extends to high-frequency Spectrum Inspiral Damp Ringdown frequency (M/R)NS=0.145, 0.160, 0.178, MBH/MNS=3

  27. Relation between Compactness (C) and mass ratio (Q) QNM frequency For small mass ratio, strong dependence of fcut on NS compactness C

  28. Summary • Accurate GR simulation can be performed. • Many simulations are ongoing for many groups not only for BH-BH, but also for NS-NS and BH-NS. • In 3—5 years, a variety of theoretical waveforms will be derived. These may be used for deciding design for next-generation detectors

  29. With spin: Q=2, C=0.145, 0.160, 0.178 a=0.5 Cyan = with spin S>0 shifts lower f

  30. Relation between Compactness (C) and mass ratio (Q) spin C

  31. Spectrum • No-disruption • Spectrum extends to high-frequency Ringdown ∝ exp[-(f/fcut)n] (M/R)NS=0.145, MBH/MNS=2–5

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