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Merger of binary neutron stars in general relativity

Merger of binary neutron stars in general relativity. M. Shibata (U. Tokyo). Jan 19, 2007 at U. Tokyo. I Introduction: Binary neutron stars. Formed after 2 supernovae 4 BNS confirmed: Orbital Period < 0.5days, Orbital radius ~ Million km

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Merger of binary neutron stars in general relativity

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  1. Merger of binary neutron stars in general relativity M. Shibata(U. Tokyo) Jan 19, 2007 at U. Tokyo

  2. IIntroduction: Binary neutron stars • Formed after 2 supernovae • 4 BNS confirmed: • Orbital Period < 0.5days, • Orbital radius ~ Million km • Total Mass ~ 2.6—2.8 solar mass • PSRB1913+16, P=0.323 d, e=0.617, M=1.387, 1.441 • PSRB1534+12, P=0.421 d, e=0.274, M=1.333, 1.345 • PSRB2127+11, P=0.335 d, e=0.681, M=1.35, 1.36 • PSRJ0737-3039, P=0.102 d, e=0.088, M=1.25,1.34 I. H. Stairs, Science, 304, 547, 2004

  3. Evolve by gravitational radiation Gravitational waves TGW >> Period

  4. Merger time • PSRB1913+16, P=0.323 d, T=0.245 Billion yrs • PSRB1534+12, P=0.421 d, T=2.25 • PSRB2127+11, P=0.335 d, T=0.22 • PSRJ0737-3039, P=0.102 d, T=0.085 Merge within Hubble time ~ 13.7 B yrs  Merger could happen frequently.

  5. Merger rate • per ~10^4 yrs • in our Galaxy • ⇒1 per yrs in • ~ 50 Mpc • (<<4000Mpc) • Not rare event V. Kalogera et al. 04

  6. Frequency of GW in the last 15min r f = 10 Hz (r = 700 km) f = 1—1.2 kHz at onset of merger (r ~ 25 km) f ~ 3 kHz ? during merger f ~ 7 kHz ? black hole QNM ~ 8000 revolution from r=700 km Massive NS Black hole

  7. NS-NS merger = GW source 1st LIGO LIGO Advanced LIGO Frequency (Hz) TAMA VIRGO

  8. Status of first LIGO = Completed ! h(1/Hz^1/2/m) h～10^-21 f (Hz)

  9. Last 15 min of NS-NS 1st LIGO Current level ~100 events per yrs for A-LIGO Advanced LIGO Frequency (Hz)

  10. Before mergerAfter merger ? Need numerical relativity Inspiral signal = well-known Information on Neutron star & Strong gravity Information on mass and spin

  11. g-ray bursts (GRBs) • High-energy transient phenomena of very short duration 10 ms—1000 s • Emit mostly g-rays • Huge total energy E ~ 10^48－10^52 ergs  Central engine = BH + hot torus

  12. One of the Central issues in astrophysics

  13. ?

  14. To summarize Introduction NS-NS merger is • not rare, • promising source of GW, • candidate for short GRBs.  Deserves detailed study

  15. 2Simulation of binary neutron star merger Best approach • Solve Einstein equations & GR hydro equations with no approximation • With realistic initial condition • With realistic EOS GR Simulation is feasible now. Introduce our latest work.

  16. R-M relation of NSs Mass Quark star Lattimer & Prakash Science 304, 2004 Radius

  17. M-r relation for stiff EOS PSR J0751-1807 APR Sly FPS 2s level Choose stiff EOSs Clarify dependence of GW on EOS

  18. Qualitatively universal results Mass (a) 1.50 – 1.50 M_sun (b) 1.35 – 1.65 M_sun (c) 1.30 – 1.30 M_sun with APR EOS Grid #: 633 * 633 * 317 @ NAOJ Memory： 240 GBytes

  19. 1.5-1.5M_sun : Density in the z=0

  20. 1.35-1.65M_sun : Density in the z=0 1.65 1.35

  21. 1.5 – 1.5 M_sun case : final snapshot Apparent horizon X-Y X-Z Y Z ~ no disk mass X X

  22. 1.35 – 1.65 M_sun case : final snapshot Apparent horizon X-Y X-Z Y Z Small disk mass X X

  23. Gravitational waves; BH QNM ringing h ~ 5*10^{-23} at r = 100 Mpc f = 6.5 kHz for a=0.75 & M=2.9M_sun

  24. GW signal 1st LIGO 100kpc Too small Advanced LIGO Frequency (Hz)

  25. 1.3-1.3M_sun : Density in the z=0 Lapse

  26. Case 1.3 – 1.3 M_sun ：　　　　　　　　　　　　　　　　　　　　　　　Massive elliptical NS formation X-Y X-Z Y Z X X Dotted curve=2e14 g/cc center＝1.3e15 g/cc

  27. Gravitational waves from HMNS + mode Quasi-Periodic oscillation x mode Inspiral wave form

  28. For r ＜50Mpc Detectable ! GW signal 1st LIGO Detection = HMNS exists ⇒ Constrain EOS Advanced LIGO Frequency (Hz)

  29. Summary for merger: General feature • Large mass case (Mtot > Mcrit)Collapse to a BH in ~ 1ms. For unequal-mass merger ⇒ disk formation  May be Short GRB. • Small mass case (Mtot < Mcrit)Hypermassive NS (HMNS) is formed.Elliptical shape　⇒　Strong GW source Note: Mcrit depends on EOS. Mcrit ~ 2.8M_sun in APR EOS (M_max~2.20) ~ 2.7M_sun in SLY EOS ( ~2.04) ~ 2.4M_sun in FPS EOS ( ~1.80)

  30. Implication of the detection of quasiperiodic signal • Detection = Massive neutron star is formed. • Formation = EOS is sufficiently stiff: Because in soft EOSs, threshold mass is small. • Total mass of system will be determined by chirp signal emitted in the inspiral phase  the threshold mass is constrained constrain EOS • If GW from MHS of M=2.8Msun is detected, SLy & FPS EOSs are rejected: One detection is significant.

  31. 4 Summary • NS-NS merger: one per yrs in ~ 50 Mpc • GW from HMNS will be detected by advanced LIGO if it is formed  Constrain EOS • NS-NS merger may form a central engine of short GRBs. Candidates are • Unequal-mass NS-NS merger to BH. • NS-NS merger to HMNS.

  32. Fate: Summary Merger Elliptical HMNS with diff. rot. Black hole GW emission ~ Equal mass Unequal No disk Small Disk Spheroid T ~ 50 ms B-fields effects BH with Small disk Weak short GRB? BH with Heavy disk Short GRB?

  33. Massive NS • Discovery of PSR J0751-1807：　　　　　　　　　　　　　　　　　　　　Binary of heavy NS + WD • Mass of NS = 2.1 +- 0.2 M_sun (1 sigma)(Nice et al. astro-ph/0508050) Implying very stiff EOS is preferable • But, still large error bar.

  34. PSR J0751-1807 (astroph/0508050) Constrain by GW emission and Shapiro’s time delay Near edge-on

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