Merger of binary neutron stars in general relativity M. Shibata(U. Tokyo) Jan 19, 2007 at U. Tokyo
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
Evolve by gravitational radiation Gravitational waves TGW >> Period
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.
Merger rate • per ~10^4 yrs • in our Galaxy • ⇒1 per yrs in • ~ 50 Mpc • (<<4000Mpc) • Not rare event V. Kalogera et al. 04
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
NS-NS merger = GW source 1st LIGO LIGO Advanced LIGO Frequency (Hz) TAMA VIRGO
Status of first LIGO = Completed ! h(1/Hz^1/2/m) h～10^-21 f (Hz)
Last 15 min of NS-NS 1st LIGO Current level ~100 events per yrs for A-LIGO Advanced LIGO Frequency (Hz)
Before mergerAfter merger ? Need numerical relativity Inspiral signal = well-known Information on Neutron star & Strong gravity Information on mass and spin
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
One of the Central issues in astrophysics
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To summarize Introduction NS-NS merger is • not rare, • promising source of GW, • candidate for short GRBs. Deserves detailed study
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.
R-M relation of NSs Mass Quark star Lattimer & Prakash Science 304, 2004 Radius
M-r relation for stiff EOS PSR J0751-1807 APR Sly FPS 2s level Choose stiff EOSs Clarify dependence of GW on EOS
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
1.5-1.5M_sun : Density in the z=0
1.35-1.65M_sun : Density in the z=0 1.65 1.35
1.5 – 1.5 M_sun case : final snapshot Apparent horizon X-Y X-Z Y Z ~ no disk mass X X
1.35 – 1.65 M_sun case : final snapshot Apparent horizon X-Y X-Z Y Z Small disk mass X X
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
GW signal 1st LIGO 100kpc Too small Advanced LIGO Frequency (Hz)
1.3-1.3M_sun : Density in the z=0 Lapse
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
Gravitational waves from HMNS + mode Quasi-Periodic oscillation x mode Inspiral wave form
For r ＜50Mpc Detectable ! GW signal 1st LIGO Detection = HMNS exists ⇒ Constrain EOS Advanced LIGO Frequency (Hz)
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)
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.
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.
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?
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.
PSR J0751-1807 (astroph/0508050) Constrain by GW emission and Shapiro’s time delay Near edge-on
