NS-NS and BH-NS Merger Simulations Lecture 3 Yuk Tung Liu ( 廖育棟 ) July 26-30, 2010 Asia Pacific Center for Theoretical Physics, Pohang (Korea) 2010 International School on Numerical Relativity and Gravitational Waves
Outline of Lecture 3 History and BHNS parameters Simulation results Gravitational Waves BH + Disk Remnants & SGRB Future Directions
Newtonian/Pazynsky-Wiita Simulations History Lee & Kluzniak (1999); Lee (2000 2001) Janka, Eberl, Ruffert, & Fryer (1999) Rosswog, Speith & Wynn (2004); Rosswog (2005) Ruffert & Janka (2009) Conformal Flat Gravity Faber et al (2006) Full GR Simulations Loffler, Rezzolla & Ansorg (head on collision; 2006) Shibata & collaborators (Kyoto) Shapiro & collaborators (Illinois) Duez & collaborators (Cornell/Caltech/WSU/CITA) Chawla et al (LSU/BYU/LIU/Perimeter)
BSNS Parameters BH mass M BH : 2 10 10 M BH spin NS Mass or Compaction (M NS or C=GM NS /R NS c 2 ) M NS : 1 ~ 2 M NS spin (probably not important) EOS ignorance (cold & hot)
Population Synthesis Result M NS / M BH a spin,init = 0.55 Belczynski, Taam, Rantsiou & van der Sluys, Astrophys. J. 682 (2008) 474
Fates of BHNS Merger ISCO Tidal Disruption NS swallowed by BH No disk Part of NS swallowed by BH Disk? Outflow? Newtonian analysis: Tidal disruption occurs at binary separationdwith M M d R ~ ~ q C d R M BH NS 3 NS 2 NS M BH M q=, C= M R NS NS NS BH 2/3 1 dtr ISCO tidal disruption Tidal disruption likely to occur for small q small C large BH spin (aligned with L orb )
More careful analysis, non-spinning BH Taniguchi, Baumgarte, Faber & Shapiro, PRD 77 (2008) 044003
Outline of Lecture 3 History and BHNS parameters Simulation results Gravitational Waves BH + Disk Remnants & SGRB Future Directions
Effect of Initial Separation Case D 0 / M MΩ A 8.81 0.0333 A-MSep 7.17 0.0441 A-SSep 5.41 0.0623 Etienne, Liu, Shapiro & Baumgarte, PRD 79 (2009) 044024 q=3 a BH / M BH =0 Γ=2 EOS C NS =0.145
Convergence Test q=3 a BH / M BH =0.75 Γ=2 EOS C NS =0.145 Initial sep. D 0 =5.5M Constraint violations ~10-2 Resolution in the innermost refinement box: M/41.5 (LR), M/47.9 (MR), M/64.8 (HR) Etienne, Liu, Shapiro & Baumgarte, PRD 79 (2009) 044024 δe=(m i - M f - E GW )/M i ~ 10-4 δj=(j i - J f - J GW )/J i ~ 10-2
Effect of Mass Ratio on Disk Mass Γ=2 EOS, C NS =0.145, non-spinning BH Shibata, Kyutoku, Yamamoto & Taniguchi, PRD 79 (2009) 044030 Etienne, Liu, Shapiro & Baumgarte, PRD 79 (2009) 044024 Discrepancy in q=3! accuracy degrades as matter crosses AMR refinement boundaries angular momentum spuriously lost (2% Illinois, 5% Kyoto, ~1% Cornell?) need to perform more accuracy simulations Foucart, Duez, Kidder & Teukolsky, arxiv:1007.4203
Effect of NS Compaction on Disk Mass Γ=2 EOS, non-spinning BH Shibata, Kyutoku, Yamamoto & Taniguchi, PRD 79 (2009) 044030
Effect of BH Spin on Disk Mass Γ=2 EOS, C NS =0.145, q=1 4% 15% Etienne, Liu, Shapiro & Baumgarte, PRD 79 (2009) 044024 Foucart, Duez, Kidder & Teukolsky, arxiv:1007.4203
Movie: a/m=0.75 case Credit: S. Shapiro & UIUC REU team (http://research.physics.illinois.edu/cta/irg/movies.html)
Movie: Effect of BH Spin Credit: S. Shapiro & UIUC REU team (http://research.physics.illinois.edu/cta/irg/movies.html)
Effect of BH Spin Orientation i BH 0º 20º 40º 60º 80º i disk 0º 4º 7º 16º 16º Γ=2 EOS, C NS =0.145, a/m = 0.5 Disk mass does not change significantly for i < 40º Population synthesis: Most BHNS system: i < 90º Foucart, Duez, Kidder & Teukolsky, arxiv:1007.4203 ~half of BHNS with i < 40º
Movie: Tilted BH Spin Credit: http://www.black-holes.org/explore2.html
Precession of Disk Different precession rate at different radii Fragile et al [Astrophys. J. 691 (2009) 482]: should precess at a constant rate as a solid body after ~4s Timescale much longer than expected lifetime of BHNS disk remnant (~100ms)
Effects of NS EOS Duez et al, Class. Quantum Grav. 27 (2010) 114104 Simulations with Γ=2, Γ=2.75 and Shen EOS Need to evolve electron fraction Y e in Shen EOS i ( gρy ) + ( gρy v ) = s t e i e s : set by weak interaction and neutrino radiation Two limiting cases: - weak interaction timescale p merger timescale, set s=0 - weak interaction timescale ` merger timescale, enforce β- equilibrium: µ n = µ p+ µ e
Effects of NS EOS: Results For a fixed NS compaction, disk mass, GW waveforms are insensitive to NS EOS. Higher compaction, lower disk mass. Similar density and temperature in disk Different disk composition between Shen- Adv and Shen-βEOS (more electron-rich in Shen-β EOS) Larger tidal tail for stiff EOSs No outflow in all GR simulations
Magnetized BHNS Simulation Chawla et al, arxiv:1006.2839
Outline of Lecture 3 History and BHNS parameters Simulation results Gravitational Waves BH + Disk Remnants & SGRB Future Directions
Gravitational Radiation M BH / M NS = 3 Γ=2 EOS, C NS =0.145 a BH = 0 Solid lines: h +, dash lines: h r ex = 30M 80M Initial MΩ = 0.033 Etienne, Liu, Shapiro & Baumgarte, PRD 79 (2009) 044024
Γ=2 EOS, C NS =0.145, non-spinning BH GW Power Spectrum Duez et al, Class. Quantum Grav. 27 (2010) 114104 Γ=2 EOS, non-spinning BH Etienne, Liu, Shapiro & Baumgarte, PRD 79 (2009) 044024 Shibata et al, PRD 79 (2009) 044030
Outline of Lecture 3 History and BHNS parameters Simulation results Gravitational Waves BH + Disk Remnants & SGRB Future Directions
NSNS BH + Disk Remnant BHNS Rezzolla et al, Class. Quantum Grav. 27 (2010)114105 Etienne, Liu, Shapiro & Baumgarte, PRD 79 (2009) 044024
Temperature Estimate (for Hybrid EOS) Hybrid EOS: P(ρ, ε )= P cold (ρ )+(Γ th -1)ρε th, ε = ε cold + ε th ε cold 1 ρ = Pcold d Initially, P = P cold Estimate temperature by (c.f. Popham, Woosley, & Fryer 1999) ε th 4 3kT at _ = + f f depends on # of species (γ, e m ρ ±, υ i, υ i ) 2 n Post-merger disks: ρ ~ 10 11 10 12 g cm -3, T ~ 10 10 10 11 K (kt ~ 1 10 Mev)
Hyperaccreting BH & SGRB Possible SGRB central engine if M disk t 0.01M, 1 Mɺ 1 10 M s, τ 0.01 0.1 s acc Neutrino Dominated Advection Flow (NDAF) Popham, Woosley, & Fryer 99, Chen & Beloborodov 06 Di Matteo, Perna, & Narayan 02, Setiawan, Ruffert, & Janka 06 Lee, Ramirez-Ruiz, and Page 04, Shibata, Sekiguchi, & Takahashi 07 _ May produce a total γ-ray energy E ~ 10 47 10 50 erg from υυ annihilation Angular frequency Ω decreases with increasing radius MRI MHD turbulence ultra-relativistic jets?
Outline of Lecture 3 History and BHNS parameters Simulation results Gravitational Waves BH + Disk Remnants & SGRB Future Directions
Future Directions More simulations Longer inspiral orbits (better matching to PN waveform) More accurate initial data (lower eccentricity, less spurious GW) More accurate simulations Cover more parameters: masses, spins, NS EOSs Long term evolution of merged remnants (HMNS, BH+disk) Magnetic fields Neutrino transport Improve Software Better AMR technique Implicit scheme?