Gravitational Waves from NS tidal disruption in NS–NS and NS–BH binaries Michele Vallisneri Jet Propulsion Laboratory, Caltech Oct 28, 2002
Knowledge of m(R) provides information about the NS equation of state � 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. � Relativistic, nonrotating NS models are described by the Oppenheimer–Volkoff equation m T ( ρ c ) p = p( ρ ) OV m T (R) R( ρ c ) ρ (0) = ρ c � With a few experimental points on the m T (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 M. Vallisneri, Oct 28 2002 2
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/R 2 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 3
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. f td at the end of the sequence of the relativistic Roche–Riemann ellipsoids that orbit the BH on circular, equatorial geodesics � We find that f td 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 4
GW f td (@ 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 5
Numerical studies of NS tidal disruption in NS–BH binaries � 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: � Lee & Kluzniak [1998–2001]: � Janka, Eberl, Ruffert, Fryer [1999]: � SPH Newtonian simulation; � Eulerian PPM (nested grids); polytropic NS physical NS EOS � BH is M/r 2 + absorbing � BH is M/r 2 + absorbing membrane; mass ratio » a few membrane; mass ratio » a few � RR force computed from motion � RR force computed from motion of of center of mass center of mass � tidally locked and irrotational � tidally locked, irrotational and configurations counterrotating configurations M. Vallisneri, Oct 28 2002 6
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 outcome of coalescence depends on the stiffness of the EOS • The simulations support a sudden-shutoff model for the GW signal NS tidal accretion � tidal tails grav. waveforms ( » 0.2 M ¯ ) EOS disruption (r-processes) after disruption very incomplete; for higher never lower-amplitude stiff light remnant mass ratios inspiral signal on ellipt. orbit (small BH) from remnant stiff almost always in irrotational sudden shutoff complete binaries soft complete always always sudden shutoff M. Vallisneri, Oct 28 2002 7
Numerical studies of NS disruption in NS–NS binaries � Zhuge, Centrella & McMillan (1994, 1996; Newt. SPH) + many others � 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 outwards; the arms merge � For stiffer EOS, the core remains nonaxisymmetric M. Vallisneri, Oct 28 2002 8
NS disruption in NS–NS binaries: EOS-dependent features of GWs GW dE/df for two m=1.4 M ¯ , R=10 km NSs dip: onset of dynamical instability peak: metastable point-like inspiral bar-like structure secondary peak: transient oscillations LIGO M. Vallisneri, Oct 28 2002 9
Relativistic effects anticipate the dip in the GW spectrum [Faber et al, astro-ph/0204397] GW dE/df for sequence of quasiequilibrium NS–NS (conformal GR) 100%, 90%, 75%, 50% of Newtonian GW power; intersects show break freqs LIGO irrotational 3PN point-like binary M. Vallisneri, Oct 28 2002 10
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 M. Vallisneri, Oct 28 2002 11
Gravitational Waves from NS tidal disruption in NS–NS and NS–BH binaries Some remarks: • emphasis on robust techniques on 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
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