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

I Introduction: Binary neutron stars PSRB , P=0.323 d, e=0.617, M=1.387, PSRB , P=0.421 d, e=0.274, M=1.333, PSRB , P=0.335 d, e=0.681, M=1.35, 1.36 PSRJ , P=0.102 d, e=0.088, M=1.25, 1.34 Formed after 2 supernovae 4 BNS confirmed: Orbital Period < 0.5days, Orbital radius ~ Million km Total Mass ~ 2.6—2.8 solar mass I. H. Stairs, Science, 304, 547, 2004

Evolve by gravitational radiation Gravitational waves T GW >> Period

Merger time PSRB , P=0.323 d, T=0.245 Billion yrs PSRB , P=0.421 d, T=2.25 PSRB , P=0.335 d, T=0.22 PSRJ , P=0.102 d, T=0.085 Merge within Hubble time ~ 13.7 B yrs  Merger could happen frequently.

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

Frequency of GW in the last 15min 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 r ~ 8000 revolution from r=700 km Massive NS Black hole

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

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

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

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

 -ray bursts (GRBs) High-energy transient phenomena of very short duration 10 ms—1000 s Emit mostly  -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 not rare, promising source of GW, candidate for short GRBs.  Deserves detailed study NS-NS merger is

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

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

M -  relation for stiff EOS PSR J  level APR Sly FPS 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 * NAOJ Memory ： 240 GBytes

M_sun : Density in the z=0

M_sun : Density in the z=

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

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

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

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

M_sun : Density in the z=0 Lapse

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

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

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

Summary for merger: General feature 1. Large mass case (M tot > M crit ) Collapse to a BH in ~ 1ms. For unequal-mass merger ⇒ disk formation  May be Short GRB. 2. Small mass case ( M tot < M crit ) Hypermassive NS (HMNS) is formed. Elliptical shape ⇒ Strong GW source Note: M crit depends on EOS. M crit ~ 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 1.Unequal-mass NS-NS merger to BH. 2.NS-NS merger to HMNS.

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

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

PSR J ( astroph/ ) Near edge-on Constrain by GW emission and Shapiro’s time delay