numerical relativity & gravitational waves
DESCRIPTION
Numerical Relativity & Gravitational waves. M. Shibata (U. Tokyo). Introduction Status Latest results Summary. I. Introduction. Detection of gravitational waves is done by matched filtering (in general) Theoretical templates are necessary - PowerPoint PPT PresentationTRANSCRIPT
Numerical Relativity&
Gravitational waves
I. Introduction
II. Status
III. Latest results
IV. Summary
M. Shibata (U. Tokyo)
I. Introduction• Detection of gravitational waves is done by
matched filtering (in general) Theoretical templates are necessary
• For coalescing binaries & pulsars We have post-Newtonian analytic solutions BUT, for most of other sources (SN, Merger of 2NS, 2BH, etc), it is not possible to compute gravitational waveforms in analytical manner Numerical simulation in full GR is the most promising approach
Goal of our work
• To understand dynamics of general relativistic dynamical phenomena (merger, collapse)
• To predict gravitational waveforms carrying out fully GR hydrodynamic simulations
• In particular, we are interested in * Merger of binary neutron stars (3D) * Instability of rapidly rotating neutron stars (3D) * Stellar collapse to a NS/BH (axisymmetric) * Accretion induced collapse of a NS to a BH (axisymmetric)
II. Necessary elements for GR simulations
• Einstein evolution equations solver• Gauge conditions (coordinate condition)• GR Hydrodynamic equations solvers• Realistic initial conditions in GR• Horizon finder• Gravitational wave extraction techniques• Powerful supercomputer• Special techniques for handling BHs.
Status
OK
OK
OK
OK
OK
~OK
To be developed
Simulations are feasible for merger of 2NS to BH, stellar collapse to NS/BH
• Einstein evolution equations solver• Gauge conditions (coordinate condition)• GR Hydrodynamic equations solvers• Realistic initial conditions in GR• Horizon finder• Gravitational wave extraction techniques• Powerful supercomputer NAOJ, VPP5000• Special techniques for handling BHs.
III. Latest Results: Merger of binary neutron stars
• Adiabatic EOS with various adiabatic constants
P (extensible for other EOSs)
• Initial conditions with realistic irrotational velocity fields (by Uryu, Gourgoulhon, Taniguchi)
• Arbitrary mass ratios (we choose 1:1 & 1:0.9)
• Typical grid numbers (500, 500, 250) with which
L ~ gravitational wavelength &
Grid spacing ~ 0.2M
Setting at present
Low mass merger : Massive Neutron star is formed
Elliptical object.
Evolve as a result of gravitationalwave emissionsubsequently.
Lifetime ~ 1sec
Kepler angular Velocity for Rigidly rotating case
Formed Massive NS is differentially rotating
Angularvelocity
Disk mass for equal mass merger
r = 6M.Mass for r > 6M~ 0%
Negligible for merger of equal mass.
Mass for r > 3M~ 0.1%
Apparent horizon
Disk mass for unequal mass merger
r = 6M.Mass for r > 6M~ 6%
Merger of unequal mass; Mass ratio is ~ 0.9.
r = 3M.Mass of r > 3M~ 7.5%
Disk mass ~ 0.1 Solar_mass
AlmostBH
Products of mergers
Equal – mass cases ・ Low mass cases Formation of short-lived massive neutron stars of non-axisymmetric oscillation. (Lifetime would be ~1 sec due to GW by quasi-stationary oscillations of NS; talk later) ・ High mass cases Direct formation of Black holes with negligible disk mass
Unequal – mass cases (mass ratio ~ 90%) ・ Likely to form disk of mass ~ several percents ==> BH(NS) + Disk
BH-QNM would appear
BH-QNM would appear
GW associatedwith normal modesof formed NS
crash
crash
~ 2 msec
Gravitational waveforms along z axis
• Axisymmetric simulations in the Cartesian coordinate system are feasible (no coordinate singularities)
=> Longterm, stable and accurate simulations are feasible• Arbitrary EOS (parametric EOS by Mueller) • Initial conditions with arbitrary rotational law• Typical grid numbers (2500, 2500)• High-resolution shock-capturing hydro code
IIIB Axisymmetric simulations:Collapses to BH & NS
Example
• Parametric EOS (Following Mueller et al., K. Sato…)
Initial condition: Rotating stars with =4/3 & ~ 1.e10 g/cc
Polytrope Thermal
Thermal Thermal Thermal
11 Nuc
Polytrope2
2 Nuc
Thermal Polytrope
1 2 Thermal
1
4 ~ 2 1.5
3
P P P
P
KP
K
Collapse of a rigidly rotating star with central density ~ 1e10 g/cc to NS
At t = 0, T/W = 9.e-3(r=0) = 1.e10M = 1.49 SolarJ/M^2 = 1.14
Animationis started here.
Densityat r = 0
Lapseat r = 0
Qualitatively the same as Type I of Dimmelmeier et al (02).
Gravitational waveforms
2sin
h
Time
Characteristic frequency = several 100Hz
Due to quasiradialoscillation ofprotoneutron stars
IV Summary• Hydrodynamic simulations in GR are feasible
for a wide variety of problems both in 3D and 2D (many simulations are the first ones in the world)
• Next a couple of years : Continue simulations for many parameters in
particular for merger of binary neutron stars and stellar collapse to a NS/BH.
To make Catalogue for gravitational waveforms• More computers produce more outputs (2D) Appreciate very much for providing Grant ! Hopefully, we would like to get for next a
couple of years
Review of the cartoon method
X
Y
・ Use Cartesian coordinates : No coordinate singularity・ Impose axisymmetric boundary condition at y=+,-y・ Total grid number = N * 3 * N for (x, y, z)
Needless
The same point In axisymmetric space.
3 po
ints
Solve equations only at y = 0