GR Simulations of Neutron Star-Neutron Star & Black Hole-Neutron Star Binaries

Transcription

1 GR Simulations of Neutron Star-Neutron Star & Black Hole-Neutron Star Binaries Masaru Shibata Yukawa Institute for Theoretical Physics, Kyoto University

2 Introduction: Why NS-NS/BH-NS simulations are important? 1. One of the most promising sources of gravitational waves 2. Huge laboratory of nuclear physics Information for high-density nuclear matter could be extracted 3. High-energy phenomena: Possible progenitor of short GRBs Numerical relativity is probably the unique approach.

3 Three motivations 1. One of the most promising sources of gravitational waves 2. Huge laboratory of nuclear physics Information for high-density nuclear matter could be extracted 3. High-energy phenomena: Possible progenitor of short GRBs

4 BH/NS-NS merger = GW source LIGO LCGT: Funded! VIRGO GEO600

5 h=h(f) f Sensitivity (standard) 1st LIGO 2016 ~ AdvLIGO, VIRGO, LCGT Frequency (Hz)

6 Before merger (10 < f < ~khz) Chirp Post-Newtonian EOB T (sec) after merger (f > ~khz)? GR gravity Hydro-interaction Neutrino emission Magnetic field Numerical relativity

7 Three motivations 1. One of the most promising sources of gravitational waves 2. Huge laboratory of nuclear physics Information for high-density nuclear matter could be extracted 3. High-energy phenomena: Possible progenitor of short GRBs

8 Neutron-star composition is still unknown 10~15 km r 0 =2.8*10 14 g/cm 3 r ~ g/cm 3 : Too high Components: Neutron +????? Radius: km?

9 Mass (solar) Still many possibilities M km 12 km 14 km Radius (km)

10 Gravitational waves by numerical relativity GWs in the late inspiral and merger phases could constrain EOS of NS. Blue: R=15.2 km, Red : R=11.6 km Pink: Point particle Many templates are necessary

11 Three motivations 1. One of the most promising sources of gravitational waves 2. Huge laboratory of nuclear physics Information for high-density nuclear matter could be extracted 3. High-energy phenomena: Possible progenitor of short GRBs

12 -ray bursts (GRBs) High-energy transient phenomena of very short duration 10 ms 1000 s Emit mostly -rays with huge total energy E ~ ergs Central engine = BH + hot torus Should Verify!

13 Inspiral Evolution of NS-NS (on which I focus today) Formation (after two supernovae) Evolve as a result of GW emission Last 1 hour at r ~1000 km f GW ~ 7 Hz Merger starts when r ~ 30 km (f GW ~ 1 khz) If mass is high enough, a black hole is formed Case I Large EOS-dependence ~ 10 6 km ~ 10 8 yrs ~ 10 3 km ~1 h Case II Otherwise, hypermasive NS

14 Galactic compact NS-NS observed PSR P(day) e M(M sun ) M 1 M 2 T GW 1. B B B C J J J *10 8 yrs 5+1(GC) NS-NS, which will merge in Hubble time (13.7 Gyr), has been found. Merger time

15 Detection rate by population synthesis LIGO advligo V. Kalogera et al. 07 dot: NSNS solid: BHNS dashed: BHBH NSNS 10-2± 1 per year for LIGO ± 1 per year for advligo Latest study Kim san s talk

16 Numerical simulation for BH/NS-BH/NS G T [ ] F -4 j F r u 0 G c Radiation... T 0 We have to solve many equations including Einstein s equation Now, it is possible to numerically solve: Accurate simulations are feasible (except for radiation transfer)

17 Current status 1. Einstein s evolution equations solver 2. GR Hydrodynamic equations solver 3. Gauge conditions (coordinate conditions) 4. Realistic initial conditions 5. Gravitational wave extraction techniques 6. Apparent horizon (Event horizon) finder 7. Special techniques for handling BHs 8. Physics: EOS, neutrino processes, B-field, radiation transfer 9. Powerful supercomputers or AMR New frontier

18 Latest subjects in numerical relativity Derive gravitational waveforms in the late inspiral and merger phases, in particular, to clarify dependence on EOS of NS. (related to motivations I and II) Clarify the outcome formed the merger; to determine density, temperature, neutrino luminosity, magnetic field strength, etc. (related motivation III) In this lecture, I will focus on how to model NS matter current status of numerical simulations

19 Thermal condition of NS 1 Late inspiral phase = NS is cold ; NS of age > 10 7 yrs long-term + cooling T < 10 5 K ~ 10 ev E F ~ 100 MeV NS should be modeled by cold EOS (EOS is still unknown; need systematic survey) Merger phase: Shock heating rapidly increases temperature to kt ~ E F ~ 10 MeV Finite temperature effects, lepton fraction Y e, neutrino thermal pressure, neutrino cooling, etc could play an important role (need many runs for many EOS, too, but there are only a few EOSs; need more)

20 Cooling curve models of NS surface Surface temperature No S.F. With accretion via emission of neutrinos For M=1.35M sun With superfluid Photon cooling No S.F. Lai & Harding 06 Age

21 Two approaches will be suitable 1. Inspiral + Early merger with cold EOS Detailed calculation of gravitational waveforms for late inspiral + early merger phases to clarify their dependence on NS s cold EOSs relatively easy, low costs 2. Merger Hypermassive NS/ BH + disk with Finite temperature EOS + neutrino cooling (and B-fields): This is required in particular for the study for GRBs expensive, need details of microphysics; Frontier

22 Log P I Cold EOSs by piecewise polytrope Too many EOSs by nuclear theory: For systematic studies, analytic EOS with few parameters is preferable Piecewise polytrope: P = K i r Gi for r i < r < r i+1 Piecewise polytrope with 3 or 4 parameters is good for most of EOSs; DP/P < ~1% (Read et al. (UWM) PRD79, 2009) EOS zoo Log r

23 Piecewise polytrpoe by UWM Log P (cgs) Necessary only for massive NS 4 parameters G 3 P 1 G 1 G 2 EOS of NS is stiff: G 1 = G 0 ~4/3 Fixed for crust We approximately know Log r (g/cm 3 )

24 Nuclear-theory based cold EOS

25 Piecewise polytrope with 2 pieces for low mass Read+ (2009) P 1 2 G r 1 G r 2 r r 1 r r 1 Match well crust

26 Some of latest numerical results I here focus on Gravitational waveforms & their dependence of EOS Status for simulations with microphysics Latest progress in MHD simulations will be presented by Luca Baiotti

27 Typical NR formulation Einstein s eqs solver: BSSN formalism with 4 th -order finite difference in time & space Hydro: Shock capturing scheme; 3 rd -order in space (no shock); 1 st -order (around shock) Gauge: Dynamical gauge (puncture gauge) Quasiequilibrium initial condition (LORENE library) with a large orbital separation (MW ~ 0.02) Gravitational waves are extracted by NP formalism Black hole is determined by finding apparent horizon Adaptive mesh refinement (ours=sacra)

28 9.5 orbits A result of long-term evolution

29 Gravitational waveform M sun R=11.6 km Blue: Enhanced post-newtonian (TT4) Red: Numerical-relativity

30 For all, M sun NS BH R=11.6 km One-moment NS BH R=11.0 km BH 26.6 ms R=10.7 km

31 For all, M sun NS BH R=11.6 km Short inspiral phase HMNS R=15.2 km 26.6 ms

32 Fourier spectrum For all, M sun 11.6km R=15.2 km QNM of BH Appreciable dependence on EOS in high frequency 3 4 k Blue=11.0km Pink=10.7 km Cyan=10.3 km

33 @100 Mpc h Spectrum Cut-off depeds on EOS Initial LIGO ~ 2-4kHz HMNS form f -1/6 advligo Frequency f (Hz) ~ 6 khz BH form Assume BH: 10M sun NS: 1.4M sun

34 Developing a template for extracting EOS is urgent 2 Baiotti et al. (2011)

35 NS-NS II: With non-cold EOS Study with finite-temperature-eos + neutrino physics The purpose is to clarify the detail in the merger: evolution of hypermassive neutron stars & BH-torus, and possible relation with short GRBs Our current implementation (by Sekiguchi): Shen s (tabulated) EOS + electron, positron, neutrinos; Neutrino cooling by a GR leakage scheme Magnetic field Luca s talk

36 T hydro " rad" Neutrino leakage in GR Qu hydro hydro " rad" ; Q cooling function T r P / r u u + Pg T -Qu Assume ( T + T ) 0 T En n + F n + F n + P " rad" We have to evolve electron fraction: u t dy dt e n -QY : Y or ru Y -rq e e e e Y nbaryon Need extension for radiation transfer: but a mile-stone development e

37 Neutrino emission & absorption Emission Absorption - electron capture: e + p n + e + positron capture: e + n p + e - + pair annihilation: e + e + Plasmon decay: + - n+ n+ n + e e + p Scattering p + v p + + p + e e + n N + N +

38 NS-NS merger with finite-temp EOS + neutrino r g/cm 3 L(erg/cm 3 /s) y y Long x lived hypermassive neutron star is formed: HMNS is supported by thermal pressure. y T(MeV) L x Shen s EOS M sun x Sekiguchi et al. PRL in press

39 NS-NS merger with finite-temp EOS + neutrino x-z plane; only after the merger r g/cm 3 L(erg/cm 3 /s) z z x x High neutrino luminosity in the polar surface May be favorable for pair annihilation near the polar region

40 Related quantities Red: M= Green: M= Blue: M= HMNS :T~20-30 MeV BHdisk: T~10 MeV HMNS : L~3-5x10 53 erg/s BHdisk: L~1x10 53 erg/s Merger

41 Gravitational waveforms Spheroidal HMNS is formed BH is formed

42 NS-NS merger with hyperon (x-y plane) r g/cm 3 L(erg/cm 3 /s) y y Collapse is triggered by hyperon production: By softening x of equation of state x T(MeV) y Shen s + hyperon EOS M sun x Sekiguchi et al. in submission

43 NS-NS merger with hyperon (x-z plane) r g/cm 3 L(erg/cm 3 /s) z z x only after the BH formation is shown Disk mass ~ 0.1 M sun High mass & high luminosity disk L x

44 Gravitational waveforms Appearance of hyperon is reflected

45 Summary of NSNS Inspiral and merger of NS-NS is being explored by several groups in detail in numerical relativity NS-NS merger is an excellent field for exploring the nature of nuclear EOS Appropriate modeling of gravitational waveform is the next step NS-NS merger often produce HMNS which may be progenitor of short GRB More detailed physical modeling, e.g., neutrino radiation transfer is needed

46 Merger simulations of BH-NS M. Shibata Yukawa Institute for Theoretical Physics, Kyoto University

47 Coalescence of BH-NS binaries 1. Promising source of gravitational waves 2. Experimental field for high-density matter 3. Possible source of central engine of gamma-ray bursts as in NS-NS binaries

48 Inspiral Evolution of BH-NS (mass = 4.2:1.4) At formation Evolve as a result of GW emission Last 1 hour at r ~3500 km (f GW ~ 1 Hz) Merger starts at r ~ 5GMc -2 (f GW ~ 1 khz) r ~ 10 6 km ~ 10 8 yrs ~ 10 3 km ~1 h Case I Case II NS is swallowed by BH for small R NS or M BH >> M NS NS is disrupted Large EOS-dependence

49 Two kinds of the final fate 1. No tidal disruption 2. NS is tidally disrupted before merger The fate is determined by 4 parameters NS mass ~ M sun NS radius ~ km? BH mass : no information BH spin : no information A wide range has to be surveyed

50 Condition for tidal disruption BH tidal force > NS self-gravity R BH MNS 3 BH MNS BH R NS M M M r r r R M MBH 2 M NS M BH r R M NS / 2 M BH 3/ 2 R 2.0 M 1.5 5M NS NS Low-mass BH or Large NS radius is necessary 3/ 2 M BH r 1 c=g=1 R* M NS 2 R

51 Condition for tidal disruption Hereafter Mass ratio Q M M BH 3/ 2-3/ 2 3/ 2 C Q 2.0 NS, Compactness C C No spin BH( =1) Q ~ C Max spin BH( =6) Q ~ / 2-3/ 2 M R NS Approximate guideline

52 Gravitational-wave frequency at the onset of merger f 3 3/ 2 1 GM c 6GM 3 3/ 2 2 r 6 GM rc -1 3/ 2 M 6GM 440 Hz M + M 10M rc -1 3/2 M 6GM 880 Hz 1.4M 3.6M 2 + 5M rc GM The frequency may be cf s 3 c lower than for NS-NS: Good.

53 Groups working Albert-Einstein Institute Cornell-Caltech-CITA-Washington Illinois Kyoto Louisiana-New-york-Perimeter. Similar results have been published in the past 3 years.

54 Moving puncture framework Brandt-Bruegmann 97, AEI, UIUC, Kyoto employ Einstein-Rosen bridge + NS mbh dl ~ dx + dy + dz ; r - r No singularity BSSN formalism + dynamical gauge BH Horizon NS Coordinate singularities

55 Excision framework CCCW, Lousiana- Horizon NS Generalized Harmonic gauge approach Excision at apparent horizon Two approaches have given similar results (e.g., Shibata-Taniguchi, Living Review 2011)

56 A Black-hole Spin=0 I focus on the dependence of EOS and BH spin Piecewise polytrope is employed for EOS Based on Kyutoku, Shibata, Taniguchi, PRD 82, (2010)

57 Piecewise polytrope EOS P = K i r Gi for r i < r < r i+1 (Cold EOS) + approximate thermal correction: P corr G-1r th Piecewise polytrope with 3 or 4 parameters is a good approximation for most of cold EOSs; DP/P < ~1% (Read et al. (UWM) PRD79, 2009) 2-parameter PWP is OK for low-mass NS: We here present results by 2-parameter case

58 BH-NS: tidal disruption case Example: Black-hole neutron-star binary (Animation by K. Kyutoku) M BH =2M NS =2.4M sun, R=15.2 km (EOS 2H) Neutron star with large radius is tidally disrupted before swallowed by black hole BH + disk is the results

59 M BH =2M NS =2.4M sun, R=15.2 km (EOS 2H) Log(r g/cm 3 )

60 BH-NS: no tidal disruption case Example: Black-hole neutron-star binary (Animation by K. Kyutoku) M BH =3M NS =4.05M sun, R=11.0 km (EOS B) Neutron star with small radius is not tidally disrupted before swallowed by black hole

61 M BH =3M NS =4.05M sun, R=11.0 km (EOS B) Log(r g/cm 3 )

62 M BH =2.7M sun, M NS =1.35M sun sudden shutdown R=15.2 km BH ringdown R=11.6 km Green= Tayloy T4

63 Imprint of EOS in tidal disruption Large NS Radius tidal disruption at a distant orbit & a low frequency Assume the same mass Small NS Radius tidal disruption at a high frequency

64 BH-NS with piecewise polytrope For all, M sun Clear dependence on NS radius Larger radius of NS

65 Baker et al. PRD, 2007 BH-BH

66 3 Types of spectrum BHQNM No TD Amp f cut Weak TD TD during inspiral f -1/6 3 types D=100Mpc frequency f (Hz)

67 f cut vs compactness fcut C ~ GM/c 2 R

68 Disk mass: Q=2, various EOSs Smaller radius

69 B with black-hole Spin Spin-Orbit interaction turns on Assume that BH spin and orbital angular momentum are parallel Angular velocity, W, is smaller than that for S=0 for a given orbital separation Tidal force depends weakly on separation Tidal disruption occurs for lower W de GW / dt is smaller for smaller W, and lifetime of binary is longer Effective GW amplitude is higher

70 Effect of the BH spin II The BH spin changes the ISCO radius --- For Schwarzschild BH, risco 6M BH --- For extreme Kerr, risco M BH for prograde orbits: BH due to spin-orbit coupling (prograde = parallel, aligned) For prograde orbits, tidal disruption is enhanced even for a heavy BH or large mass ratio Q For a retrograde (anti-parallel) case, tidal disruption is suppressed.

71 M BH =4.05M sun, M NS =1.35M sun, R=11.6 km a=0 QNM a=0.75 TD Dash= Tayloy T4 Longter lifetime UIUC originally pointed out

72 GW spectrum for Q=2, M NS =1.35M sun Spin increases

73 GW spectrum for Q=3, a=0.75 ALIGO Broadband ALIGO ET

74 GW spectrum for Q=4, a=0.75, M NS =1.35M sun ALIGO LCGT ET f cut may be detectable in near future

75 Enhanced disk mass Example: Black-hole neutron-star binary HB_q5_M135.a75.gif Animation by K. Kyutoku M BH =5M NS =6.75M sun, R=11.6 km (EOS HB), a=0.75 Wide disk with mass ~ 0.1 M sun

76 M BH =5M NS =6.75M sun, R=12.3 km (EOS H), a=0.75 Log(r g/cm 3 )

77 Disk mass: Q=3, M NS =1.35M sun, R=11.6km Significant increase UIUC, CCCW group originally pointed out

78 Disk mass with high spin

79 Disk mass vs spin

80 Disk mass vs compactness

81 Summary Gravitational waves in the merger phase reflect the radius (EOS) of neutron star Appreciable dependence on EOS is found for frequency 1 3 khz (high frequency) Advanced LIGO (+ special design for high-frequency GWs) could constrain EOS for data with high spin and Q ~ 4, 5 Mass of disk is > 0.1 M sun for spin a=0.75 even for Q ~ 5 with realistic compactness of NS, C ~

82 Summary for 2 days Many simulations are ongoing for NS-NS and BH-NS: Current primary interest is to clarify gravitational waveforms. In ~3 years, a variety of theoretical waveforms will be derived. First implementation of finite-temperature EOS + neutrino physics + cooling is done by Sekiguchi for astrophys. simulation Simulation with (approximate) neutrino transfer will be one of challenges for PFlopes machine in the next ~ 3-5 years.

83

84 Merger to NS 1.4M sun 1.4M sun

85 How mass and spin of BH and NS are determined These could be determined by GWs in the inspiral phase -5/ / 2 t 5 GM M GMc M 2 P 512 c r r 4 t P Adiabatic

86 LCGT was funded last year! 3 km-3 km In operation from ~2017 Super Kamioka around here

87 Inside of Kamioka place Japan sea/east sea

88 Merger to BH+disk 1.35M sun 1.65M sun file

89 Gravitational waveform for black hole formation case Qualitatively universal Kiuchi et al. Ring down Inspiral Merger

90 Universal spectrum for BH formation No disk Inspiral h eff ~ f n n~-1/6 Damp Merger Qualitatively depends on disk mass & mass ratio BH QNM Kiuchi et al. 6000

91 GR leakage works well Neutrino luminosities consistent with result by 1D-GR radiation hydro (Liebendoefer et al. 04) Collapse of 15 M sun model by WHW02 Besides convection induced modulation in luminosities Neutrino luminosities in BNS merger will be estimated Results by Sekiguchi (2009) Liebendoerfer et al. (2004) Full-Boltzman Electron neutrino

92 Numerical relativity Relativity, Mathemetical relativity Numerical computation Physics Astrophysics

93 Adaptive Mesh Refinement GW L >> GM/c 2 l ~ 4GM/c 2 For each box ~ grids (+12 for margin) NS diameter is covered by ~100 grids. Number of levels ~ 7 (3 coarse*1 + 4 fine*2) Number of variables ~ 150 in our SACRA code Memory ~ 15 GBytes Computation is feasible by PC of ~\200,000JP!

94 Binary home (@office) Core i7x, 3.33 GHz, 4 cores, 12 or 24 GB memory Better than supercomputer of 10 yrs ago 121*121*61 *10 AMR domains 15 GB memory About 40 days for ~7 orbits by SACRA code Parameter parallel by ~30 machines now