Gravitational Waves from NS tidal disruption in NSNS and NSBH - - PowerPoint PPT Presentation

Michele Vallisneri

Jet Propulsion Laboratory, Caltech Oct 28, 2002

Gravitational Waves from NS tidal disruption in NS–NS and NS–BH binaries

• M. Vallisneri, Oct 28 2002

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Knowledge of m(R) provides information about the NS equation of state

Relativistic, nonrotating NS

models are described by the Oppenheimer–Volkoff equation

p = p(ρ) ρ(0) = ρc

mT(ρc) R(ρc)

mT(R)

With a few experimental points on the mT(R) curve, we can

invert the OV map and obtain p(ρ) as a piecewise-linear law [Lindblom ’92]

Even one point might be very significant, characterizing the

effective adiabatic index Γ in the NS core

OV

Modern NS equations of state (EOSs) for NSs are still

constrained poorly by experiment and observation. To improve this situation it is especially promising to exploit the correspondence between the EOS and the NS mass-radius curve.

• M. Vallisneri, Oct 28 2002

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How to measure the NS radius/EOS?

ELECTROMAGNETIC OBSERVATIONS: error » factor two

• Direct thermal radii of isolated NS (problems: non–black-body emission,

absorption in the stellar atmosphere)

• X-ray burst oscillations (m/R through gravitational light bending)
• Absorption lines in the photosphere (m/R and m/R2 through

gravitational redshift and pressure broadening; problem: no lines found) GRAVITY-WAVE OBSERVATIONS: advanced interferometers

• “Of particular interest are robust characteristics, such as spectral breaks

and features that should be measurable without needing detailed models of the phasing” [Hughes ’02]

• Merger waveforms in NS–NS binaries: frequencies too high but:

hydrodynamical effects on the orbital evolution [Faber et al. ’02]

• NS tidal disruption in NS–BH binaries: only with small or spinning BHs
• Form factors in the GW spectrum [Saijio & Nakamura ’00]

• M. Vallisneri, Oct 28 2002

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NS tidal disruption in NS–BH binaries as a probe of the NS EOS [MV, PRL 84 (2000)]

For small or rapidly rotating BHs, the BH tidal

field tears apart the NS on dynamical timescales before it plunges into the BH

Tidal locking is unlikely [Bildsten & Cutler ’92] Only the last GW cycles are affected;

disruption is rapid and violent

For given BH (M and a) and NS parameters

(m and R), we set the tidal-disruption freq. ftd at the end of the sequence of the relativistic Roche–Riemann ellipsoids that orbit the BH

• n circular, equatorial geodesics

We find that ftd depends strongly on R, and that the waveforms lie

in the band of good interferometer sensitivity (300–1000 Hz)

Thus, mature interferometers should be able to measure the NS R

[and therefore m(R)] to 15%, out to 1 event/yr distances

• M. Vallisneri, Oct 28 2002

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GW ftd (@ tidal disruption) vs. NS radius R

m=1.4 M¯; dots give minimum a/M to disrupt NS before plunge

• M. Vallisneri, Oct 28 2002

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Thus, observations of NS tidal disruption in NS–BH binaries should

be possible with advanced interferometers, and should provide useful information about the NS EOS

However, we need better theoretical and numerical studies of NS

tidal disruption to compute the effect of the EOS on the waveforms, and devise template families for data analysis. A few simulations are already available:

Numerical studies of NS tidal disruption in NS–BH binaries

Lee & Kluzniak [1998–2001]:

SPH Newtonian simulation;

polytropic NS

BH is M/r2 + absorbing

membrane; mass ratio » a few

RR force computed from motion

• f center of mass

tidally locked and irrotational

configurations

Janka, Eberl, Ruffert, Fryer [1999]:

Eulerian PPM (nested grids);

physical NS EOS

BH is M/r2 + absorbing

membrane; mass ratio » a few

RR force computed from motion of

center of mass

tidally locked, irrotational and

counterrotating configurations

• M. Vallisneri, Oct 28 2002

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Expected features of NS tidal disruption

• RR decreases separation until Roche overflow occurs; then a mass-transfer

stream forms and there is a rapid accretion episode (possibly incomplete)

• Hydrodynamical effects are important at small separations: the location and
• utcome of coalescence depends on the stiffness of the EOS
• The simulations support a sudden-shutoff model for the GW signal

always in irrotational binaries never tidal tails (r-processes) always always for higher mass ratios (small BH) accretion (» 0.2 M¯) sudden shutoff complete soft sudden shutoff almost complete stiff lower-amplitude inspiral signal from remnant incomplete; light remnant

• n ellipt. orbit

very stiff

• grav. waveforms

after disruption tidal disruption NS EOS

• M. Vallisneri, Oct 28 2002

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Zhuge, Centrella & McMillan (1994, 1996; Newt. SPH) + many others

Numerical studies of NS disruption in NS–NS binaries

Evolution in the LIGO band:

Starts out in the point-mass

regime (RR governs inspiral)

Once the stars are close enough,

dynamical effects (tidal torquing) dominate, leading to accelerated inspiral, merger, and coalescence

Merger and coalescence take

place within several orbits of initial contact; the stars form a temporary barlike structure

Spiral arms form; angular

momentum is transported

• utwards; the arms merge

For stiffer EOS, the core

remains nonaxisymmetric

• M. Vallisneri, Oct 28 2002

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NS disruption in NS–NS binaries: EOS-dependent features of GWs

point-like inspiral dip: onset of dynamical instability

GW dE/df for two m=1.4 M¯, R=10 km NSs

peak: metastable bar-like structure secondary peak: transient oscillations LIGO

• M. Vallisneri, Oct 28 2002

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Relativistic effects anticipate the dip in the GW spectrum [Faber et al, astro-ph/0204397]

100%, 90%, 75%, 50%

• f Newtonian GW power;

intersects show break freqs irrotational 3PN point-like binary

GW dE/df for sequence of quasiequilibrium NS–NS (conformal GR)

LIGO

• M. Vallisneri, Oct 28 2002

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Direct measurement of R from the GW spectrum in NS–BH mergers [Saijio & Nakamura ’00]

• Use BH perturbation theory to

compute the spectrum of GW emitted by a disk of dust inspiraling into a BH

• When the disk radius R is larger than

the wavelength of the Kerr QNM, form factor effects become apparent: the spectrum has several peaks, and their separation / R-1, irrespective of M and a

• Conjecture: the spectrum of GW

signals from NS–BH binaries will tell us the NS R directly

• Problems: geodesic motion; NS

internal dynamics; interferometer sensitivity

Some remarks:

• emphasis on robust techniques
• n the other hand...
• tidal-disruption measurements possible on high-S/N signals (LIGO-II)
• mass-spin parameters already known from adiabatic inspiral
• possibility of ad hoc simulations
• rough constraints on NS radius/EOS already useful; e-m observations

can help

Gravitational Waves from NS tidal disruption in NS–NS and NS–BH binaries