Download - 07 Nov 2003Gravitational Wave Phenomenology Workshop1 Numerical Relativity Deirdre ShoemakerCornell University The role of numerical relativity in gravitational-wave.

07 Nov 2003 Gravitational Wave Phenomenology Workshop 1

Numerical Relativity

Deirdre Shoemaker Cornell University

The role of numerical relativity in gravitational-wave astrophysics

Status of Binary Black Hole (BBH) simulations

In the absence of a complete solution to the BBH problem, what can we do today?– Introduce approximations

• Sequences of quasi-circular orbits • Lazarus approach to BBH mergers

– Extract info from single BH evolutions• The spectrum of highly distorted black-holes

Open Questions


Numerical Relativity: Modeling gravitational wave sources

Full NR:• Compact object binaries• Supernovae ?

Less NR:• Extreme mass ratio binaries• NS oscillations


Today’s black-hole source simulations

1. Single BH evolutions:

• Static

• Boosted

• Wobbling

• Distorted

2. BBH Mergers

3. BBH < 30% orbit


Quasi-equilibrium orbits

BHb MME 2

0,

BHMJb

l

E

Binding Energy:

• We have the numerical infrastructure to solve elliptic equations (i.e. initial data)

• Quasi-adiabatic phase of the BBH system ~ sequences of quasi-circular initial data orbits

• Identification of the “innermost stable circular orbit”

Effective Potential Method(Cook & Baumgarte)

bE


Thin-Sandwich Method (Meudon)

Data Satisfy: Circular orbits found from:

0

0

K

g

t

ijt KomarADM MM


• Goal: to resurrect a death non-linear calculation

• How: On the 3rd day, match it to a perturbative calculation

• Lazarus Project:

• Start with ISCO data, merger takes place before code dies, continue with Teukolsky evolution.

• This approach is a natural extension of close limit approximation (Price & Pullin)

Non-linear matching to perturbative regime




Lazarus

Equal mass spinning black holes (~2.25%) Baker et al (2003)


Generating modes in black-hole spacetimes

What modes are generated if you hit a black hole hard enough?

• Study highly distorted black-holes

• End result of the merger of two black holes

• Prediction of mode content impacts data analysis algorithms

• In the linear regime, the modes are well known

• In the non-linear regime, it is possible to study mode coupling

• Allen et. al (1998)

• Papadopoulos (2002)

• Zlochower et. al (2003)

• DS et. al (2003)


Distorted black holes

Using Characteristic codes: mode-mode coupling for Schwarzschild DBHs.

• Papadopoulos(2002)

• Zlochower et. al (2003)


Distorted black holes in Cauchy formulism

MrAH 2 Mr 15 MrO 25

D. Shoemaker, H. Pfeiffer, L. Kidder, and S. Teukolsky

log(A) vs evolution time FFT(A) vs period

Amplitude of the l=2,m=0 mode for A(t=0) = 0.01 and A(t=0) = 0.1


Numerical Relativity

• We need more approaches that involve approximations.

• Lower dimension calculations (i.e. axisymmetry)

• Impact of numerical accuracy on data analysis tools.

• More astrophysical input in initial data

• And of course the usual