Gravitational waves and dynamical mass ejection from binary neutron-star mergers

Transcription

1 Gravitational waves and dynamical mass ejection from binary neutron-star mergers Masaru Shibata Yukawa Institute for Theoretical Physics, Kyoto University In collaboration with Hotokezaka, Kiuchi, Kyutoku, Okawa Sekiguchi, M. Tanaka, & Wanajo

2 Contents 1. One page introduction 2. Our latest numerical-relativity activity for NS-NS Ø Gravitational waves from late inspiral Ø Dynamical mass ejection

3 Why NS-NS mergers are important? Most promising sources of gravitational waves for LIGO/VIRGO/KAGRA Invaluable laboratory for studying high-density nuclear matter Promising origins of short-hard GRBs Sources of strong transient EM emission Possible site for r-process heavy elements Numerical relativity is the powerful tool for exploring these issues quantitatively?

4 2A Gravitational waves (see John s talk ) Early Inspiral ( r >> R ) orb NS Late inspiral ( ) r orb 5R NS Merger => Hypermassive NS Black hole & torus & GRB? M~ M sun Point mass phase Adiabatic phase Post-Newton Tidally deformed phase Late inspiral Dynamical & GR phase Post merger f ~ 6.5 khz h f <~1000 Hz f ~ 2 4 khz t/m

5 Analytic Computation (Effective One-Body) M sun, EOS: MS1 (R=14.5km) without tidal effects with tidal effects Appreciable phase difference Calculation by Hotokezaka EOB version (a bit old): Damour et al., (2012) Predicting more accurate GWs is urgent

6 Three key elements for deriving accurate gravitational waves in numerical rela ² Longterm simulation ² Eccentricity reduction for initial condition ² Extrapolation using high-quality data # Eccentricity reduction by Kyutoku (e <~0.001) # Constraint propagation by BSSN+Z4c prescription (we locally used Z4c) (Hilditch & Bernuzzi) à less numerical error & good convergence u See also the talk by Roland Haas

7 Our 15-orbits simulation with eccentricity reduction y (km) It looks nice, however. Hotokezaka, Kyutoku, Okawa, Shibata, PRD 91, 2015 H4-EOS: R=13.6km Mass: M sun x (km)

8 However, at best, 3 rd 4 th -order convergence We can never obtain exact numerical waveform in hydrodynamics simulation!! à Extrapolation is needed for an almost solution t η t, Φ= Gravitational wave phase 2π f d ( η t) : η = const Extrapolated phase Φ Φ N=72 N=60 N=48 N=40 (N=60)-(N=72) (N=48)-(N=72) (N=40)-(N=72) Best resolu8on 2 nd 3 rd 4 th ~3.5±0.5 th - order convergence Error > 3 radian t ret (ms) Φ Φ N=72 N=60 N=48 N=40 (N=60)-(N=72) (N=48)-(N=72) (N=40)-(N=72) Error < ~ 0.2 radian t ret (ms)

9 Extrapolated waveform for R=13.6 km h D / m 0 h D / m N=60 N=72 EOB H4 An error-less waveform (phase error < ~0.5 rad) Numerical + extrapolated Numerical + extrapolated EOB 30 cycles t ret (ms)

10 Comparison with effective-one-body approach Extrapolated EOB EOB latest (Bernuzzi et al. 2015) Φ 100 Φ EOB result has error with ~3 radian in the last orbit. This suggests that some effects are missing in the current EOB t ret (ms)

11 Comparison with EOB: frequency f (Hz) Extrapolated EOB EOB gives slower evolution 1 f/f Good match but for the final ~2 cycles t ret (ms)

12 Extrapolated waveform for R=11.1 km h D / m 0 h D / m N=60 N=72 EOB APR4 Good match for compact NS! t ret (ms)

13 For soft EOS, current EOB is good Φ Φ Extrapolated EOB EOB is promising but need improvement for last orbits for less-compact NS Phase error is less than 1 radian t ret (ms)

14 Good match f (Hz) Extrapolated EOB 1 f/f EOB is promising but need improvement for last orbits t ret (ms)

15 h D / m 0 These data will be used for data analysis simulation (Talk by John) ALF2 APR4 H4 Mass: solar mass t ret (ms) Many simulations with a variety of tabulated EOS are ongoing.

16 Overall spectrum f h f (r=100 Mpc) APR4 ALF2 H4 aligo BH-BH Much better overall spectra than previous ones BH-BH by SpEC 1 f (khz)

17 2A Dynamical mass ejection WHY important? Ø That could shine and be an EM counterpart of GW source (radioactively-powered nova, radio flare, ) Ø That could be main source of r-process elements Probably there will be many talks! New topics in numerical relativity! Tanvir nd peak 1 st peak Pagel (1997) 3 rd peak N=50 N=82 N=126

18 Dynamical mass ejection mechanism 2 major effects drive ejection 1) Strong shock at the merger à enhanced thermal pressure ejects material (like supernova) 2) Tidal torque by non-axisymmetric merger remnant à Give angular momentum to the material in the envelope, subsequently ejected. v Note that other effects like magnetic or viscous or neutrino wind could play a role (e.g., talks by Kiuchi, Just, )

19 Mass ejection at merger Model : 1.2M sun 1.5M sun, EOS=APR4, R ~11 km Equatorial plane 300 km x 300 km 2400 km x 2400 km Log(ρ g/cc) Hotokezaka + PRD 2013

20 Mass ejection at merger Model : 1.2M sun 1.5M sun, EOS=APR4, R ~11 km Equatorial plane 300 * 300 km Head 2400 speed * 2400 v ~ km 0.8c 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

21 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)

22 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) 300 * 150 km 2400 * 1200 km Ejecta is quasi-spherical: Shock heating plays a key role.

23 Dynamical ejection mechanism Two components } Tidal component } Low-temperature } Shock-heated component } High-temerature x-z For strong shock, GR gravity is crucial

24 Amount of ejecta depends strongly on EOS Soft EOS à strong gravity à high-mass ejection APR4 SLy Steiner Tidal effect is dominant Mass ra8o Shock heating is important! ALF2 H4 MS1 Total mass = 2.7 solar mass Error bar for 1 < Q < 1.25 Small radius Hotokezaka + PRD 2013 (See also Bauswein+ 2013)

25 Proton number Stable nuclei τ n capture < τ β decay Neutron number

26 Galactic r-process elements Numerical-relativity simulations show ejected mass per event of NS-NS could be ~ M sun Total amount of observed r-process elements in our galaxy is ~ 10 4 solar mass Predicted merger rate ~ one every 10 4 yrs or less à total merger events ~ 10 6 or less in our Galaxy We want mass ejection per event ~ 0.01 M sun à If other contributions were absent, relatively soft EOS would be necessary IF EOS is stiff (NS has a large radius), we would need other sources or other mechanisms

27 r-process nucleosynthesis study of ejecta (By Sekiguchi & Wanajo +) Universality of three peaks for heavy elements found in solar system & metal-poor stars Universality indicates the presence of single main origin Question: Could NS-binary merger reproduce abundance pattern (all three peaks)? Z=N=28 1 st peak N=50 2 nd peak N=82 Pagel (1997) 3 rd peak N=126 27

28 Key quantity for producing heavy elements: electron fraction per baryon: Y e =[p]/([n]+[p]) u If high Y e > 0.45 = neutron less-rich à 3 rd peak is not well reproduced 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). (e.g., CCSN, Roberts, Janka+, Wanajo+ 1..) st 2 nd 3 rd u If too neutron rich, Y e ~ 0.1 e.g., BH-NS or NS-NS in Newtonian simulation à 3 rd peak dominant; no/weak 1 st & 2 nd peaks e.g., Goriely et al Mass fraction Solar E.g., Korobkin+ (2012) 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). Appropriate blending of Y e is needed: HOW? à Perform numerical relativity simulation! tions otherwise, as prescribed in the BRUSLIB nuclear astrophysics library (Xu et al. 2013) Figure 8 shows the final nuclear abundance patterns for the M mergers described by the NL3 (blue), DD2 (red) and SFHO (green) EoSs. For every model A

29 GR neutrino-radiation hydrodynamics (Sekiguchi s GR radiation hydro code) Einstein s eq : BSSN + puncture (+ local Z4c) Radiation : Leakage + fully covariant truncated moment scheme with M1 closure (gray) for heating # pure M1 scheme (gray) works but expensive EOS : SFHo, IUFSU, DD2, TMA, TM1 Grid size : 580*580*290*9 level (fixed mesh refinement) with Δx= m for the finest domain CPU time : k node-hours by K-computer with ~7000 cores (864 nodes) Binary mass : , , , , (ongoing)

30 Variety of EOS table (we appreciate Hempel) 14.5km TM1 (Shen EOS) TMA 13.2km DD2 IUFSU 11.8km SFHo (Steiner) Smaller radius LaRmer s recommended region 30

31 SFHo (R~11.9 km): M sun ρ Rest-mass density (x-y) Neutrino luminosity ν e ν e ν others Rest-mass density (x-z) Ejecta mass ~ 0.01M sun Sekiguchi et al. (2015) 31

32 SFHo (R~11.9 km): M sun Specific entropy S Both high & low entropy ν regions are e present ν e ν others Entropy [k] Sekiguchi et al. (2015) 32

33 SFHo (R~11.9 km): M sun High temperature γγ e + e +, n + e + p +ν e Y e Electron fraction (x-y) ν e ν e ν others Electron fraction (x-z) Sekiguchi et al. (2015) 33

34 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 } GR plays a key role Produce very heavy elements Produce mildly heavy elements

35 Fraction of mass as a function of Y e Large NS radius TM1 Moderate NS radius DD2 Small NS radius SFHo Broad distribution is naturally obtained Sekiguchi et al. (2015) 35

36 DD2 (R~13.2 km): M sun Y e Neutrino heating from remnant MNS is important! n +ν p + e 36

37 However, for stiff EOS, ejecta mass is small Convergent results for SFHo to DD2 in dx = 150m and 250m runs Mej is larger for soyer EOS Consistent with piecewise- polytrope studies Only SFHo will give Mej ~ 0.01 Msun Signature of ν- driven components ~ several ms ayer merger

38 Effects of neutrino heating Ejecta mass SFHo Average Y e SFHo DD2 DD2 } Amount of ejecta mass can be increased by ~ 10-3 M sun } Average Y e can change by 0.02~0.03 } For DD2 & TM1, ejecta mass is O(0.001 solar) } Viscous heating?? 38

39 Our first result (Wanajo et al. ApJ 2014) mass fraction x-y x-z y-z Y e Broad distribution for Y e could be suitable for reproducing wide abundance pattern Project is ongoing by Wanajo, Nishimura, Sekiguchi+

40 Summary Gravitational waves from late inspiraling phase of NS-NS is a valuable site for exploring NS EOS à high-resolution numerical-relativity simulations are ongoing for constructing templates (also by Bernuzzi-Nagar +, Haas +,.) Mass ejected in NS-NS merger is ~ solar mass à EM counterparts (tomorrow s talks) NS-NS could be r-process nucleosynthesis site: Three peaks could be well reproduced by shock + neutrino heating (Sekiguchi ; works ongoing) Next issue: Adding viscous effects to remnant NS and/or BH+torus

41 Announcement from Yukawa Institute, Kyoto University Longterm workshop on Nuclear Physics and Compact Stars 2016 (NPACS 2016) Oct.17 (Mon.), Nov.18 (Fri.), In the third week, conference on Birth, Life, and Death of Neutron Stars and Nuclei (YKIS 2016) will be held Oct.31 (Mon.), Nov.4 (Fri.), 2016

42 Ejecta temperature: Depends on EOS SFHo EOS: NS=Small radius High temperature SFHo } TM1 EOS: NS=Large radius } Low temperature à n rich TM1 x-z x-y High temperature γγ e + e +, n + e + p +ν e 42

43 Unequal mass NS- NS system: SFHo

44 Unequal mass NS- NS system: SFHo

45 Unequal mass NS- NS system: SFHo Orbital plane : Tidal effects play an important role, ejecta is neutron rich Meridian plane : shock + neutrinos play roles, ejecta less neutron rich