The Frequencies and Timescales Associated With Gravitational Wave - - PowerPoint PPT Presentation

The Frequencies and Timescales Associated With Gravitational Wave Radiation From Compact Stars

Joel E. Tohline Louisiana State University

Forget That!!

I’d rather present a summary report from …

Structure, Stability & Dynamical Behavior

• f Compact Astrophysical Objects

A Discussion Meeting

Sponsored by

Center for Gravitational Wave Phenomenology Penn State University 23 - 27 October 2002

Structure, Stability & Dynamical Behavior

• f Compact Astrophysical Objects

Discussion Group’s Primary Participants:

• Nils Andersson
• Beverly Berger
• John Friedman
• James Imamura
• Ian Jones
• Kostas Kokkotas
• Norman Lebovitz
• Ben Owen
• Nick Stergioulas
• Joel Tohline
• Anna Watts

Instability Mechanisms Discussed

• Purely Hydrodynamical, in the presence of Newtonian

gravity

– Dynamical f-mode (bar-mode) – Instabilities in “ellipsoidal” figures

• Driven by Gravitational Radiation-Reaction Forces

– r-mode – Secular f-mode (Dedekind-like)

Issues Discussed in the Context of Each Instability Mechanism

• Mode Identification

– Pattern Frequencies ( f ) – Growth rates ( τgrow )

• Damping Mechanisms ( τdamp )
• NOTE: α = δq/q ∝ e-t/τ , where τ−1 = [τdamp ]−1 - [τgrow ]−1
• Expected maximum amplitude & duration
• Effects of GR on mode character & damping mechanisms
• Likelihood of producing a detectable GW signal

Dynamical f-mode (pt. 1) f ≈ 1 kHz (ρ/ρnuc)1/2

Behavior depends on NS’s angular momentum distribution!

• For most (relatively shallow) j(ϖ) distributions:

– Instability encountered only if T/|W| > 0.27. – τ ≈ τgrow ≈ 1 ms (ρ/ρnuc)-1/2 – Once encountered, almost certainly will grow to nonlinear amplitude. – Newtonian simulations suggest nonlinear bar will persist for many (>10-100) oscillation periods. – Presently unclear how GR (or shocks or viscosity) will affect duration of signal. – Unclear whether NSs will ever reach this state.

Dynamical f-mode (pt. 2) f ≈ 1 kHz (ρ/ρnuc)1/2

• For steep j(ϖ) distributions [Shibata, Karino & Eriguchi 2002]:

– Instability encountered for T/|W| at least as small as 0.03. – τgrow » 1 ms (ρ/ρnuc)-1/2 – Newtonian simulations show small limiting amplitude. – Duration presently uncertain. – Results need to be confirmed. – Damping effects not yet examined. – Effects of GR not known. – Unclear whether NSs will ever reach this state.

r-mode

• f ≈ Ωrot --- 0 < f < ΩK ≈ 1 kHz (ρ/ρnuc)1/2
• τgrow » 1 ms (ρ/ρnuc)-1/2
• Inviscid simulations driven by exaggerated FRR show growth to

nonlinear amplitude, then burst.

• More than one likely source of damping

– Mode-mode coupling (suggested by both “analytical” and simulation work). – Viscosity due to “funny” particles. – Magneto-viscous and/or shear instabilities (particularly relevant to LMXBs?)

• Looks like high-order modes disappear when GR effects taken into

account.

• May survive at low limiting amplitudes (e.g., LMXBs)

Secular f-mode

• 0 < f < 1 kHz (ρ/ρnuc)1/2
• τgrow » 1 ms (ρ/ρnuc)-1/2
• Instability with reasonable growth rate encountered only

when T/|W| relatively large.

• Nonlinear simulations of this instability not yet available.
• What about likely source of damping?

– Mode-mode coupling not yet examined – Viscosity likely to suppress growth in many systems, but there may well be a regime where τdamp >> τgrow.

• Work underway to characterize these modes in full GR.

Elliptical Instability

• “New” instability not previously discussed in context of

compact stars [Lebovitz & Lifschitz 1996, ApJ, 458, 699]

• Virtually all ellipsoidal flows will be dynamically unstable

to a multitude of long- and short-wavelength velocity and/or shape distortions.

• Not discussed as source of gravitational-wave radiation;

rather, it may serve as a hydrodynamical mechanism that severely limits amplitude of other (f- and r-) modes.

• Not yet examined in compressible systems.
• Nonlinear development not known.

Other (related) Issues

• Fizzlers

– If they exist, enhances likelihood of unstable f-modes (both secular and dynamical) – But existence sensitive to angular momentum distribution of pre- collapse core.

• Effects of shear on discrete modes in both Newtonian and

GR systems.

• May need to pursue two-fluid and superfluid simulations.
• Need to construct steady-state “triaxial” configurations

– Effect of FRR on evolution – Linear and nonlinear examination of “elliptical” instabilities

• How do we perform “slow” evolutions?

Likely Sources of Detectable GW Signals?

• Dynamical f-mode

– Pessimistic: Unlikely T/|W| ever going to be high enough

Likely Sources of Detectable GW Signals?

• Dynamical f-mode

– Pessimistic: Unlikely T/|W| ever going to be high enough

• Secular f-mode

– More pessimistic: Unlikely T/|W| going to be high enough and some sources of damping already identified

Likely Sources of Detectable GW Signals?

• Dynamical f-mode

– Pessimistic: Unlikely T/|W| ever going to be high enough

• Secular f-mode

– More pessimistic: Unlikely T/|W| going to be high enough and some sources of damping already identified

• r-mode

– Most pessimistic: Damping mechanisms in abundance amplitude never gets very large