Post on 16-Dec-2015
Current status of numerical relativity
Gravitational waves fromcoalescing compact binaries
Masaru Shibata
(Yukawa Institute, Kyoto University)
Initial LIGO
Adv LIGO, LCGT…
Prediction only byNum. Rela
h=h(f)f Merge
Frequency f (Hz)
GW spectrum from compact binaries
AssumeBH=10Msun
NS=1.4Msun
Chirp
Needed implementations1. 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
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
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)
§ 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.
Gravitational waves from BBH merger
By F. Pretorius
QNMBH ringingInspiral waveform
Universal Fourier spectrum
f 7/6
inspiral
f 2/3
merger
Buonanno,Cook, & Pretorius,PRD75 (2007)
e
ringdown
h(f)
(15+15Msun)
advLIGO, LCGT
1st LIGO
Frequency (Hz)
Currentlevel
AssumeBH=10 Msun
h=h(f)f Larger mass
Detectionis possible now
High-precision computation byCornell-Caltech group
NonspiningEqual-mass15 orbits
Excellentagreement with Taylor T4 formula
§ 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
1.5Msun 1.5Msun
Merger to BH
Akmal-Pandharipande-Ravenhall EOS
Kiuchi et al. (2009)
1.4Msun 1.4Msun
Merger to NS
Gravitational waveform for black-hole formation case
Inspiral
Merger
Ringdown
Universal spectrum for BH formation
Inspiralheff ~ f n
n~-1/6Damp BH QNM
Merger
Different from BBH
Bump
Damp
Gravitational waveform for hyper-massive NS formation case
Inspiral Merger QPO
Spectrum for two EOSs
advLIGO EOS-dependence of fcut
§ 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)
Inspiral: (M/R)NS=0.145, =2 polytrope
MBH/MNS=2 MBH/MNS=5
~5 orbits ~7.5 orbits
(M/R)NS=0.145, MBH/MNS=2
(M/R)NS=0.145, MBH/MNS=4 (& >4)
No disk
Gravitational waveforms
(M/R)NS=0.145, MBH/MNS=2
Dotted curve = 3 PN fit
inspiral disruption
Quickshutdown
Gravitational waveforms
(M/R)NS=0.145, MBH/MNS=5
Dotted curve = 3 PN fitringdown
(M/R)NS=0.178
MBH/MNS=3
(M/R)NS=0.145
Clear ringdown
Not very clear
No disruption
Mass shedding
Typical spectrum
(M/R)NS=0.145, MBH/MNS=3
Inspiral
Damp
∝ exp[-(f/fcut)n]
BH-QNM
Hz
Spectrum
(M/R)NS=0.145, 0.160, 0.178, MBH/MNS=3
No-disruptionSpectrum extends to high-frequency
Ringdownfrequency
Inspiral
Damp
Relation between Compactness (C) and mass ratio (Q)
C
For smallmass ratio, strong dependence offcut on NS compactness
QNMfrequency
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
With spin: Q=2, C=0.145, 0.160, 0.178
S>0shifts lower f
Cyan = with spina=0.5
Relation between Compactness (C) and mass ratio (Q)
C
spin
Spectrum
(M/R)NS=0.145, MBH/MNS=2–5
No-disruptionSpectrum extends to high-frequency
∝ exp[-(f/fcut)n]
Ringdown