DYNAMICS OF MIXED BINARIES

Transcription

1 DYNAMICS OF MIXED BINARIES Luciano Rezzolla Albert Einstein Institute, Golm, Germany In collaboration with Frank Löffler & Marcus Ansorg [Phys. Rev. D (2006)] SISSA (Trieste, Italy), AEI (Golm, Germany) SFB-TR7, Videoseminar, 20/11/2006

2 Dynamics of Mixed Binaries Mixed binaries Neutron Star (NS)/black hole (BH) binaries Why interesting?

3 Dynamics of Mixed Binaries Mixed binaries Neutron Star (NS)/black hole (BH) binaries Why interesting? Possible candidates for short γ-ray bursts Prime sources of gravitational waves

4 Gamma Ray Bursts Most dramatic, astrophysical events known Size of source: < 100 km 3 relativistic object Two different classes:

5 Gamma Ray Bursts Most dramatic, astrophysical events known Size of source: < 100 km 3 relativistic object Two different classes: Long (> 2s) Afterglow, often visible Produced by core-collapse of massive stars

6 Gamma Ray Bursts Most dramatic, astrophysical events known Size of source: < 100 km 3 relativistic object Two different classes: Long (> 2s) Afterglow, often visible Produced by core-collapse of massive stars Short (< 2s) Energy emitted in < 1 s ergs Short afterglow ( 100 s): difficult to see However, possible (e.g. GRB050509b) Observed event rate > GPc 3 yr 1 Often found in elliptic, non-star-forming galaxies Prime candidates: NSNS or BHNS mergers

7 Gravitational Waves On the importance of NSNS/BHNS mergers: Compact objects: Newtonian and PN approximations may be poor

8 Gravitational Waves On the importance of NSNS/BHNS mergers: Compact objects: Newtonian and PN approximations may be poor Prime source of gravitational waves

9 Gravitational Waves On the importance of NSNS/BHNS mergers: Compact objects: Newtonian and PN approximations may be poor Prime source of gravitational waves Signal correlated to electromagnetic emission? Constraints on EOSs at nuclear densities

10 Gravitational Waves On the importance of NSNS/BHNS mergers: Compact objects: Newtonian and PN approximations may be poor Prime source of gravitational waves Signal correlated to electromagnetic emission? Constraints on EOSs at nuclear densities However, only recently numerical simulations of BHNS systems: Why?

11 Gravitational Waves On the importance of NSNS/BHNS mergers: Compact objects: Newtonian and PN approximations may be poor Prime source of gravitational waves Signal correlated to electromagnetic emission? Constraints on EOSs at nuclear densities However, only recently numerical simulations of BHNS systems: Why? Very complicated task

12 Dynamics of Mixed Binaries Difficulties in numerical simulations of BHs: Numerical stability (Complexity of Einsteins Equations)

13 Dynamics of Mixed Binaries Difficulties in numerical simulations of BHs: Numerical stability (Complexity of Einsteins Equations) Problems with Singularities (e.g. excision)

14 Dynamics of Mixed Binaries Difficulties in numerical simulations of BHs: Numerical stability (Complexity of Einsteins Equations) Problems with Singularities (e.g. excision) Difficulties in simulations of NSs: Additional equations to solve

15 Dynamics of Mixed Binaries Difficulties in numerical simulations of BHs: Numerical stability (Complexity of Einsteins Equations) Problems with Singularities (e.g. excision) Difficulties in simulations of NSs: Additional equations to solve Simulations of mixed binaries have all of those difficulties...

16 Dynamics of Mixed Binaries Difficulties in numerical simulations of BHs: Numerical stability (Complexity of Einsteins Equations) Problems with Singularities (e.g. excision) Difficulties in simulations of NSs: Additional equations to solve Simulations of mixed binaries have all of those difficulties... start simple!...

17 Previous Work - Newtonian Newtonian physics: Zwart et al. (1998), analytical Janka et al. (1999), numerical Lee et al. (1999), numerical Newtonian studies with relativistic modifications (pseudo-newtonian) Rosswog et al. (2005), numerical Overall results: Consistent generic picture is difficult to define: anything from stable mass transfer to complete disruption

18 Previous Work - Newtonian a)t=0 b)t= NS orbiting around BH (mass ratio 3.2), c)t= d) t=100 Newtonian simulation; no waveforms Lee at al. (1999)

19 Previous Work - Relativistic Baumgarte et al. (2004), Taniguchi et al. (2005), numerical quasi-stationary sequence Bishop et al. (2005), numerical, only short-term Miller et al. (2005), analytical Sopuerta et al. (2006), numerical, Full evolution Faber et al. (2006), numerical Shibata & Uryu, numerical astro-ph/ Results: No stable mass transfer Results limited to large BH/NS mass ratio ( 10)

20 Previous Work - Relativistic Computational domain only includes neutron star, BH not included in computational domain, relativistic simulation Baumgarte at al. (2004)

21 Previous Work - Relativistic Large BH/NS mass ratio, BH is included in computational domain, relativistic simulation Sopuerta at al. (2006)

22 Our approximations Chosen Approximations:

23 Our approximations Chosen Approximations: Time-symmetric initial data in particular no initial velocities only head-on mergers possible

24 Our approximations Chosen Approximations: Time-symmetric initial data in particular no initial velocities only head-on mergers possible Neglect magnetic fields, neutrinos, viscosity, heat transfer

25 Our approximations Chosen Approximations: Time-symmetric initial data in particular no initial velocities only head-on mergers possible Neglect magnetic fields, neutrinos, viscosity, heat transfer However: No assumption on mass ratio

26 Our approximations Chosen Approximations: Time-symmetric initial data in particular no initial velocities only head-on mergers possible Neglect magnetic fields, neutrinos, viscosity, heat transfer However: No assumption on mass ratio Black hole included in computational domain

27 Our approximations Chosen Approximations: Time-symmetric initial data in particular no initial velocities only head-on mergers possible Neglect magnetic fields, neutrinos, viscosity, heat transfer However: No assumption on mass ratio Black hole included in computational domain Fully general relativistic evolution

28 Our approximations Chosen Approximations: Time-symmetric initial data in particular no initial velocities only head-on mergers possible Neglect magnetic fields, neutrinos, viscosity, heat transfer However: No assumption on mass ratio Black hole included in computational domain Fully general relativistic evolution Evolution code not restricted to head-on collisions

29 Technical Details Einsteins equations

30 Technical Details Einsteins equations G µν = 8πT µν 3+1 split Conformal traceless formulation, free evolution Ccatie-code (Cactus), mesh refinement Carpet

31 Technical Details Einsteins equations G µν = 8πT µν 3+1 split Conformal traceless formulation, free evolution Ccatie-code (Cactus), mesh refinement Carpet Hydrodynamics equations µ T µν = 0, µ (ρu µ ) = 0 perfect fluid, ideal-gas EOS p = ρε(γ 1) Whisky code High-resolution shock-capturing methods

32 Initial Data Initial data solution in general: Specify sources (NS, BH), separation, masses, spins, velocities ect. Solve four nonlinear, elliptic equations

33 Initial Data Initial data solution in general: Specify sources (NS, BH), separation, masses, spins, velocities ect. Solve four nonlinear, elliptic equations Initial data solution for head-on collisions: As result of simplified scenario (head-on): only one elliptic equation to be solved Solve for Hamiltonian constraint equation using York-Lichnerowicz conformal decomposition

34 Initial Data Elliptic solver: Compactified domain Spectral methods Suitably fitted coordinates Originally written by M. Ansorg for binary BHs Modified to include matter sources

35 Initial Data Elliptic solver: Compactified domain Spectral methods Suitably fitted coordinates Originally written by M. Ansorg for binary BHs Modified to include matter sources Example of the compactified spectral grid

36 Evolution - mesh refinement Cartesian grid for evolution: fixed mesh refinement (Carpet) High resolution near BH: x f inest = M Outer boundary far away from objects: x max 200 M 6 refinement levels: x coarse = 2 x f ine

37 Example System Prototypical system: Spherically symmetric star, polytropic EOS (Γ = 2) M NS 0.86M R NS 12km M BH 5M BH/NS mass ratio 5.8 Separation (surface to horizon) d 70km Zero initial velocities Hereafter: M M, M ADM = 5.78M

38 Evolution - slide show I Diagonal metric component in x-y-plane γ xx t = 0M = 0.00ms x y 40

39 Evolution - slide show I Diagonal metric component in x-y-plane γ xx t = 50M = 0.25ms x y 40

40 Evolution - slide show I Diagonal metric component in x-y-plane γ xx t = 100M = 0.49ms x y 40

41 Evolution - slide show I Diagonal metric component in x-y-plane γ xx t = 150M = 0.74ms x y 40

42 Evolution - slide show I Diagonal metric component in x-y-plane γ xx t = 200M = 0.99ms x y 40

43 Evolution - slide show I Diagonal metric component in x-y-plane γ xx t = 250M = 1.23ms x y 40

44 Evolution - slide show I Diagonal metric component in x-y-plane γ xx t = 300M = 1.48ms x y 40

45 Evolution - slide show I Diagonal metric component in x-y-plane γ xx t = 350M = 1.72ms x y 40

46 Evolution - slide show II Density isocontours + apparent horizon radius + excision y t = 0M = 0.00ms x

47 Evolution - slide show II Density isocontours + apparent horizon radius + excision y t = 50M = 0.25ms x

48 Evolution - slide show II Density isocontours + apparent horizon radius + excision y t = 100M = 0.49ms x

49 Evolution - slide show II Density isocontours + apparent horizon radius + excision y t = 150M = 0.74ms x

50 Evolution - slide show II Density isocontours + apparent horizon radius + excision y t = 200M = 0.99ms x

51 Evolution - slide show II Density isocontours + apparent horizon radius + excision y t = 250M = 1.23ms x

52 Evolution - slide show II Density isocontours + apparent horizon radius + excision 10 t = 265M = 1.31ms y x

53 Evolution - slide show II Density isocontours + apparent horizon radius + excision 10 t = 275M = 1.35ms y x

54 Evolution - slide show II Density isocontours + apparent horizon radius + excision 10 t = 285M = 1.40ms y x

55 Evolution - slide show II Density isocontours + apparent horizon radius + excision 10 t = 295M = 1.45ms y x

56 Evolution - slide show II Density isocontours + apparent horizon radius + excision t = 305M = 1.50ms 5 y x

57 Evolution - slide show II Density isocontours + apparent horizon radius + excision t = 315M = 1.55ms 5 y x

58 Evolution - slide show II Density isocontours + apparent horizon radius + excision t = 325M = 1.60ms 5 y x

59 Evolution - slide show II Density isocontours + apparent horizon radius + excision t = 335M = 1.65ms 5 y x

60 Evolution - Animation Animation of dynamics. Neutron star density isosurfaces on the left Black hole horizon and excision sphere on the right Refinement boxes indicated

61 Evolution - AH mass Capturing the mass accretion Apparent horizon mass increase during merger at t = 300M

62 Physics before merger Capturing the physics of the neutron star Oscillations of the density maximum compared to the fundamental mode frequency, as found by perturbative methods ( f F 1.28kHz)

63 Physics after merger Capturing the physics of the black hole Oscillations of the circumference ratio of the black hole horizon, compared to the fundamental mode, as found by perturbative methods ( f F 2.06kHz)

64 Gravitational waves First GWs from merger of a mixed binary system of comparable mass Clearly visible ringdown of the final black hole Emitted energy M Less than for Newtonian, orbiting systems; expected

65 Conclusions First relativistic simulations of a BH-NS merger with comparable mass (head-on configurations only) Long-term stable evolutions, good matching with perturbative studies Ability to extract gravitational waves Emitted energy in GWs: M

66 Conclusions First relativistic simulations of a BH-NS merger with comparable mass (head-on configurations only) Long-term stable evolutions, good matching with perturbative studies Ability to extract gravitational waves Emitted energy in GWs: M Work in progress: consider non-zero angular momentum ID use more realistic EOS abandon excision for punctures include magnetic fields: large differences possible

67 Einsteins equations Evolution equations: 12 first order PDEs for γ ab and K ab Constraint equations: (1+3=)4 elliptic equations: In York-Lichnerowicz: R+K 2 K i j K i j = 16πρ ADM j ( K i j γ i j K ) = 8πi i. γ i j = ψ 4 γ i j K i j = ψ 10 à i j ψ 4 γ i j K à i j = ( LV) i j + M i j j ( LV) i j 2 3 ψ6 i K = j M i j + 8πψ 10 j i 2 ψ 1 8 ψ R 1 12 ψ5 K ψ 7 à i j à i j = 2πψ 5 ρ ADM.

68 Evolution - Convergence Convergence of the evolution Second order convergence of Hamiltonian constraint during evolution (t = 100M)

69 Spacetime diagram Worldlines of surface and maximum density at x-axis: t/ms distance/m

70 Quadrupole waveforms Lee et al. (1999)