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