Merger of binary neutron stars: Gravitational waves and electromagnetic counterparts Numerical-relativity study

Transcription

1 Merger of binary neutron stars: Gravitational waves and electromagnetic counterparts Numerical-relativity study Masaru Shibata Yukawa Institute for Theoretical Physics, Kyoto University In collaboration with Hotokezaka, Kiuchi, Kyutoku, Okawa Sekiguchi, M. Tanaka, & Wanajo

2 1. Brief introduction Contents 2. Current understanding of NS-NS mergers obtained by numerical relativity 3. Gravitational waves and equations of state 4. Mass ejection and electromagnetic signals: based on numerical-relativity results 5. Study of ejecta with finite-temperature EOS & neutrino effects

3 Why NS-NS mergers are important? 1. Most promising sources of gravitational waves for LIGO/VIRGO/KAGRA 2. Invaluable laboratory for studying high-density nuclear matter 3. Promising origins of short-hard GRBs 4. Sources of strong transient EM emission 5. Possible site for r-process heavy elements

4 2 Current understanding of NS-NS Mergers by numerical relativity Initial condition to be employed?

5 Parameters of compact NS-NS binaries PSR log B(G) P rot (ms) M(M sun ) T Mag T GW 1. B / B / B C / J / / / / J / J (12.2) (144) 1.29/1.32 (<0.1) 3.1 B-field and spin period of the first NS (perhaps second NS observed for J ) E.g., Lorimer Living Review M sun Spindown time *10 8 yrs Merger time T Mag T GW for many Small spin

6 Demorest Nature 2010 The most crucial uncertainty is EOS Suggestion by X-ray obs. 2.5 Mass (solar) J Many simula+ons with many EOSs 1.0 are needed for systema+c study Strong constraint: But not strong enough Radius (km) 10 km 12 km 14 km

7 NS-NS mergers: Initial conditions to be employed Parameters: Observations of NS-NS suggest u Mass: Likely to be in a narrow range m = M sun u Spin: Likely negligible or small : P rot > 20 ms & T Mag < T GW for many cases u B-field: 1 st NS ~ G, 2 nd NS ~ G u NS radius (EOS) is still uncertain à Well-defined problem except for EOS # For extra gal, metalicity may change this distribution

8 Expected fate Broadly speaking, there are two fates: 1. BH is formed promptly after the merger 2. Massive NS is formed at least transiently The fate could depend strongly on total mass & EOS employed However, latest observations constrain the EOS & mass of NS-NS certainly à Numerical-relativity shows Fate-2 is the case

9 Merger of M sun NS with four EOSs APR4: R=11.1km ALF2: R=12.4km H4: R=13.6km MS1: R=14.5km

10 Merger of M sun NS with four EOSs By hotokezaka Massive APR4: R=11.1km neutron stars are ALF2: remnants R=12.4km Log(ρ g/cc) Log(ρ g/cc) irrespective of EOS for canonical mass H4: R=13.6km MS1: R=14.5km

11 Evolution of remnant x EOS=SLy, Mass= M sun Meridian plane Long-lived HMNS forms Angular-momentum transport BH + torus: BH spin ~ torus-mass ~ M sun HMNS=Hyper Massive Neutron Star

12 Last 15 min of NS-NS (1.35M sun -1.35M sun ) Evolve by ~ 700 km GW emission Last 15 min; f GW ~ 10 Hz GW detectors will start detecting GWs Merger sets in at r ~ 30 km; f GW ~ 1 khz Case I Case II Black hole Soft EOS Stiff EOS (a ~ 0.6) Black hole is Hypermasive NS + torus are formed Angular momentum transport

13 3 Gravitational waves & EOS Early Inspiral ( r >> R ) orb NS Late inspiral ( ) r orb 5R NS Merger => Hypermassive NS Black hole & torus & GRB? Point mass phase Adiabatic phase Post-Newton Tidally dominated phase Post-Newton with tidal coupling or NR Dynamical & GR phase Numerical relativity h t/m

14 Two interesting phases for EOS study A. Late Inspiral (Lai+, Hinderer+, Damour+, Baiotti+, Bernuzzi+, Hotokezaka+) : Effects of tidal deformation enhanced f ~ 0.5 1kHz B. Merger à MNS (Basuwein+, Hotokezaka+) GW from MNS/HMNS f ~ 2k 4kHz Chirp GWs from MNS MNS Both waveforms could be used for constraining EOS of neutron stars

15 A Tidal effects in a binary inspiral (originally pointed out by Lai+ 1992) Close Binary System Tidal deformation; Quadrupole is induced r ~ GM φ r C 6 r 5PN correction but large coefficient C ~ MR 5, R ~ 5 8 M For r ~ 2R, it could play a role. h = h(, t M, M, C, C )

16 Analytic Computation (Effective One-Body) M sun, EOS: MS1 (R=14.5km) without tidal effects with tidal effects Significant phase difference Calculation by Hotokezaka For EOB, see, e.g., Pan et al., (2011) Damour et al., (2012)

17 Late-phase chirp signal by TT4 Larger radius TT4 TT4 + tidal (Hinderer-Flanagan) Phase difference

18 Status of this reserach Analysis in terms of EOB by Damour, Nagar (2012) suggests that for M sun (or less massive) NS- NS, EOS could be constrained for S/N > 16 events Wade+, PRD show that systematic error in the template will give serious damage Can EOB provide accurate templates? à Bernuzzi+, Hotokezaka+ showed it acceptable for most of inspiral phase except last a few orbits But, their simulations are not very long, and initial condition has non-negligible eccentricity More sophisticated study is necessary

19 Efforts in numerical relativity Effort of eccentricity reduction by Kyutoku (UWM) h + at 100Mpc 2.5e-22 2e e-22 1e-22 5e e-23-1e e-22-2e-22 H4-135-QC H4-135-Iter1 H4-135-Iter2 H4-135-Iter t ret (ms) arxiv (PRD2014) Initial eccentricity ~ 10-3 Caltech team (R. Haas et al.) is also working in very long-term accurate simulations These further studies are necessary and ongoing

20 Amplitude: Modulation is suppressed 4,22 D m H4-135-QC H4-135-Iter1 H4-135-Iter2 H4-135-Iter3 iteration t ret (ms)

21 Our 15 orbits simulation: Preliminary dx=220m EOB y (km) Re( 4 ) D m x (km) Eccentricity <~ Hotoke, Kyutoku, Okawa, Shibata t ret (ms) Z4c formulation (Hilditch & Bernuzzi) H4-EOS: R=13.6km M sun

22 Early phase: I plotted two curves Re( 4 ) D m e e Red: Numerical Black: EOB t ret (ms)

23 Convergence ~ 4 th order Final phase: need more consideration Preliminary m dx=330m dx=275m dx=220m extrap EOB t ret (ms)

24 Convergence ~ 4 th order Preliminary Final phase: need more consideration D m dx=330m dx=275m dx=220m extrap EOB t ret (ms)

25 B GW from MNS: M 1 =1.3, M 2 =1.4M sun Inspiral R=11.1km R = 12.4 km BH MNS Inspiral HMNS khz khz R =13.6 km R = 14.5 km Inspiral MNS Inspiral MNS khz ~2 khz

26 f h f (r=50 Mpc) 2.5e-21 2e e-21 1e-21 5e-22 Fourier spectrum APR ALF H MS aligo,nsns aligo,design f ± Δf Δf ~ 0.2 khz LIGO, design EOS is reflected in the typical frequency f (Hz)

27 Clear correlation between peak and radius Peak frequency Radius could be constrained with ~ 1km error Bauswein & Janka Ours Radius of 1.6 solar-mass NS

28 GWs from NS-NS & EOS: Summary If D < ~100 Mpc, late inspiral waveforms could be used to constrain EOS (aligo/virgo/kagra): à But, need a more precise template for late inspiral (Wade+, PRD ) à NR If D < ~ 30 Mpc, merger waveforms could be used to constrain EOS (aligo/virgo/kagra) à Need a data-analysis study; how accurate? ² Note that if GR is violated, the situation could be different (MS+, PRD 2014 for a scalar-tensor theory)

29 4 Mass ejection and EM counterparts In NS-NS merger at least 2 effects drive ejection 1) At the merger, strong shock is generated, thermal pressure is enhanced, and material is ejected from the system (like supernova). 2) During the merger, non-axisymmetric merger remnant is formed. Also, after the merger, a massive ellipsoidal NS is formed. à These non-axisymmetric objects exert torque to the material in the envelope, which is subsequently ejected. ü Other effects like neutrino or magnetic wind may play a role

30 Mass ejection at merger Model : 1.2M sun 1.5M sun, EOS=APR4, R ~11 km 300 km x 300 km 2400 km x 2400 km Log(ρ g/cc)

31 Mass ejection at merger Model : 1.2M sun 1.5M sun, EOS=APR4, R ~11 km 300 km x 300 km 2400 km x 2400 km Log(ρ g/cc) Tidal torque plays an important role Ejecta mass ~ 0.01M sun, v ~ 0.2c in average

32 Mass ejection on the meridian plane (x-z plane) Model : 1.2M sun 1.5M sun, EOS=APR4, R ~11 km 300 km x 150 km 2400 km x 1200 km Log(ρ g/cc)

33 Mass ejection on the meridian plane (x-z plane) Model : 1.2M sun 1.5M sun, EOS=APR4, R ~11 km 300 km x 150 km 2400 km x 1200 km Log(ρ g/cc) Ejecta is quasi-spherical: Shock heating plays a key role.

34 Amount of ejection depends strongly on EOS (Relatively) Soft EOS is favored APR4 SLy Steiner Tidal effect is dominant Mass rado Shock heating is important ALF2 H4 MS1 Total mass = 2.7 solar mass Error bar: 1 < Q < 1.25 Small radius Hotokezaka + PRD 2013 (See also Bauswein+ 2013)

35 Mass ejection and EM signals Material ejected could generate astronomically observable EM signals via Ø Kilonova/Macronova = radioactively powered: Decay of r-process-heavy nuclei (Li & Paczynski 1998, Kulkarni 05, Metzger+ 10, Barnes, Kasen+ 13, Tanaka-Hotokezaka 13) à Signal appears for 1 10 days after merger Ø Afterglow-type radio flare: shock powered (Nakar-Piran 2011) à Signal appears for ~ 1 10 years after merger

36 τ n capture < τ β decay

37 Kilonova/macronova Scenario (Li-Paczyski 1998) Neutron-rich ejecta à r-process nucleosynthesis (Lattimer-Schramm 74, Symbalisty-Schramm 82) à Production of unstable nuclei à β-decay/fission à heating material à After adiabatic expansion à τ diffusion τ expansion à UV ~ IR (Li-Paczynski 98) τ n capture < τ β decay

38 Estimate by Li-Paczynski (ApJ 1998) Maximum R / v = R 2 ρκ / c : " L max ~ M % ergs/s $ # 0.01M ' & " M % at t ~ 5 days $ # 0.01M ' & 1/2 " κ % $ ' # 10 cm 2 / g & 1/2 " $ # v 0.2c % ' & " $ # v 0.2c 1/2 1/2 % ' & 1/2 " f % r-proc $ # ' & " κ % $ ' # 10 cm 2 / g & ~ 10 3 times higher than Eddington luminosity ergs/s M = 15.0 mag m= Mpc These depend strongly on mass, velocity, & opacity; Opacity ~ 10 cm 2 /g (Kasen+, Tanaka-Hotokezaka 2013) 1/2

39 2.7 M sun NS-NS Merger and remnant Radioactively powered EM signals γ ray? GRB Observer No GRB Observer Original figure by Hotokezaka R-process β decay A relativistic jet with narrow opening angle? A black hole and accretion torus: BH spin ~ Expanding spheroidal ejecta confine jet

40 Model luminosity curve of 200Mpc (Numerical-relativity + radiation transfer simulation by M. Tanaka & Hotokezaka, ApJ 775, 2013) OpDcal OpDcal Infrared For sufficient mass ejection, EM signal could 0.01M sun be observed by 4m-8m-class-telescopes (small- radius NS) /space-telescopes for duration 1 10 days 0.004M sun Signal is strong in near-infrared bands M sun (Large- radius (reconfirmed NS) the results by D. Kasen+) Infrared Infrared Infrared

41 Straight lines are models of GRB afterglow Kilonova Tanvir et al. Nature 2013 r- band Near infrared Approximate kilo/macronova models X- ray This bump is an evidence of excess: Cannot be explained by GRB afterglow

42 Progenitor models of GRB130603B: NS-NS case GR+radiation transfer work by Hotokezaka +, ApJL778, 2013 Ejecta mass 0.02 M sun M sun Infrared excess observation Ø Small-radius EOS & high-heating rate can reproduce this event Heating rate has uncertainty of factor of ~2

43 5 r-process nucleosynthesis study of ejecta (By Sekiguchi & Wanajo +: Note: I am a beginner) Question: Could NS-NS merger reproduce solar abundance? à Simulation for various EOS 1 st peak 2 nd peak Pagel (1997) 3 rd peak Z=N=28 N=50 N=82 N=126 43

44 Key quantity: electron fraction per baryon Y e u High Y e > 0.4 à neutron less-rich à Third peak is not reproduced (e.g., CCSN) u neutron rich, <Y e > ~ 0.1 e.g., BH-NS or tidal-effect dominant NS-NS à 2 nd & 3 rd peak dominant (e.g., Janka, Goriely, Rosswog) Appropriate value of <Y e >, i.e., appropriate blending is needed: HOW?

45 Earlier result Fig. 8. Nuclear abundance pattern for the M mergers with the NL3 (blue), DD2 (red) and SFHO (green) EoSs compared to the solar r-process abundance distribution (black). Our latest result (Wanajo et al. ApJ) Mass fraction Solar DD2 NL3 SFHO Fig. 9. Nuclear abundance pattern for the M mergers with the NL3 (blue), DD2 (red) and SFHO (green) EoSs compared to the solar r-process abundance distribution (black). Bauswain, Goriely, & Janka (2013) See also Korobkin et al. (2012) tions otherwise, as prescribed in the BRUSLIB nuclear astrophysics library (Xu et al. 2013) Figure Non-GR 8 shows the final nuclear abundance patterns for the M simulation mergers described by the NL3 (blue), DD2 (red) and SFHO (green) EoSs. For every model Tidal-effect dominant about 200 trajectories were processed, which roughly correspond to about one tenth of the total ejecta. Comparing the à final abundance Neutron-rich distributions of the DD2 EoS for about 200 and the full set of 1000 fluid-element histories A GR simulation Particular EOS (SFHo) Particular mass solar Tidal-effect + shock play roles But no neutrino heating in GR simulation

46 Thermodynamical properties of ejecta Mass ejection from BNS merger : two components } Tidal component } Low-temp, low Ye x-z } Shock-heated component } High-temp, high Ye

47 Variety of EOS table (we appreciate Hempel) 14.5km TM1 (Shen EOS) TMA 13.2km DD2 IUFSU 11.8km SFHo (Steiner) Smaller radius 47

48 Our latest study (Sekiguchi s code) GR: BSSN/Z4c + moving puncture gauge Radiation Hydro: Leakage+ (see below) Evolution of electron fraction per baryon Variety of EOS based on relativistic mean field theory by Hempel Ø Leakage for optically thick region Ø Radiation-moment formulation for freestreaming region with neutrino heating

49 TM1 (R~14.5 km): M sun Rest-mass density Preliminary 49

50 TM1 (R~14.5 km): M sun Electron fraction Preliminary 50

51 TM1 (R~14.5 km): M sun Specific entropy Preliminary Entropy [k] 51

52 SFHo (R~11.8 km): M sun Rest-mass density Preliminary 52

53 SFHo (R~11.8 km): M sun Electron fraction Preliminary 53

54 SFHo (R~11.8 km): M sun Specific entropy Preliminary Entropy [k] 54

55 Ejecta rest mass Reconfirm larger mass for smaller NS radius Evidence for neutrino-driven wind Preliminary BH forms Ejecta mass gradually increase in the late phase 11.8km Dependence of ejecta mass on EOS is consistent with Piecewise- polytrope study 55

56 SFHo EOS: shock heating High temperature SFHo Ejecta temperature Preliminary } TM1 EOS: tidal orogin } Low temperature TM1 x-z x-y 56

57 γγ à e + + e -, SFHo EOS Preliminary n + e + à p + ν: Y e increases SFHo TM1 x-z x-y Higher T : more e + Wider high- Ye region : less neutron rich Lower T : less e + smaller Ye < 0.25 : very neutron rich 57

58 Fraction of mass as a function of Ye Smaller radius results in high- Ye frac+on Shock hea+ng à Ye increases For DD2 & TM1, neutrino hea+ng seems to play a role in increasing high- Ye frac+on Preliminary Which is good for solar abundance? à Work ongoing by Wanajo, Nishimura, & Sekiguchi. 58

59 Summary Gravitational waves from NS-NS merger is a valuable site for exploring EOS of NS: Efforts in numerical relativity are ongoing Mass ejection in NS-NS merger is likely to emit strong EM signal, in particular for EOS with relatively small-ns radius Total mass of ejecta depends strongly on the EOS of NS à EM counterpart observation together with GW observation may be used to constrain EOS Study for r-process is ongoing

60 Step 1. Neutrinos are divided into trapped and streaming parts T = T + T a ( ν, trap) (weak) (leak) Trapped : interact sufficiently atb = Qb Qb frequently with maber a ( ν, stream) (leak) atb = Qb Streaming : phenomenological flow of freely streaming neutrinos (characterized by leakage +mescale) Step2. Trapped- ν is combined with fluid part: Solve advecdon term using truncated moment formalism with a closure Source term. ( ν ) ( ν,trap) ( ν,stream) ab ab ab Leakage scheme with heating a a T T a (fluid) b a ( ν, trap) b = Q = Q (weak) b (weak) b Q (leak) b a ( ν, trap) b a ( ν, stream) b T = T + T ( fluid ) ( ν,trap) ab ab Q cool includes e± captures, pair annihiladon,plasmon decay, Bremsstrahlung Q diff is calculated based on Rosswog & Liebendoerfer (2004) Electron, neutrino, and total lepton fracdons are also evolved a ( T a T a b + T = Q Q a (leak) = (1 e τ )Qa (diff ) + e τ Qa (weak) ab (leak) b Q (weak) a ) = Q = Q = Q (weak) b (cool) (cool) u u a a + Q (heat) a κ ν J ν u a

61 Limiter prescription ConservaDon equadons for electron and trapped neutrino fracdons Weak Dmescale appears We introduce a limiter to solve them explicitly Use µν (trapped) esdmated from Yν for the cooling source terms Use µν (free) esdmated from radiadon field (Jν) for headng β-eq EOS non-β-eq EOS dyl dt = γ (leak) Yl dy dt dy dt e ν = γ = γ (weak) Ye (weak) Yν γ (leak) Yν

62 DD2 (R~13.2 km): M sun Specific entropy Preliminary Entropy [k] 62

63 DD2 (R~13.2 km): M sun Electon fraction Preliminary 63