merger of binary neutron stars in general relativity m. shibata (u. tokyo) jan 19, 2007 at u. tokyo

Merger of binary neutron stars in general relativity

M. Shibata 　 (U. Tokyo)

Jan 19, 2007 at U. Tokyo

I 　 Introduction: Binary neutron stars

• 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

•　 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

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

V. Kalogera et al. 04

1 per ~10^4 yrsin 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 mergerf ~ 7 kHz ? black hole QNM

r

~ 8000 revolution from r=700 km

MassiveNS Black hole

NS-NS merger = GW source

LIGO

VIRGO

TAMA

Advanced LIGO

1st LIGO

Frequency (Hz)

Status of first LIGO = Completed !h(

1/H

z^1/

2/m

)

f (Hz)h ～ 10^-21

Last 15 min of NS-NS

Advanced LIGO

1st LIGO

~100 eventsper yrs for A-LIGO

Frequency (Hz)

Currentlevel

Before merger 　　 After merger

Inspiral signal = well-known

Neednumerical relativity

Information on mass and spin

Information onNeutron 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 issuesin astrophysics

?

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 & PrakashScience 304, 2004

Quark star

M- relation for stiff EOS

PSR J0751-1807

2 levelAPRSlyFPS

Choose stiff EOSs

Clarify dependenceof 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

X X

ZY

X-Y X-ZApparent horizon

~ no disk mass

1.35 – 1.65 M_sun case : final snapshot

X X

ZY

X-Y X-ZApparent horizon

Small disk mass

Gravitational waves; BH QNM ringing

f = 6.5 kHzfor 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)

1.3-1.3M_sun : Density in the z=0

Lapse

　　　 Case 1.3 – 1.3 M_sun ：　　　　　　　　　　　　　　　　　　　　　　　 Massive elliptical NS formationY

X

Dotted curve=2e14 g/cccenter ＝ 1.3e15 g/cc

Z

X-Y X-Z

X

Gravitational waves from HMNS+

mod

ex

mod

e

Quasi-Periodic oscillation

,22 100Mpc10

0.31km

Rh

r

Inspiral wave form

GW signal

Detection= HMNS exists⇒Constrain EOS

For r ＜ 50MpcDetectable !

Frequency (Hz)

Advanced LIGO

1st LIGO

　 Summary for merger: General feature

1. Large mass case (Mtot > Mcrit) 　　　　　　　　　　　　　　　　　　　　　Collapse to a BH in ~ 1ms. 　　　　　　　　　　　　　　　　　　　 For unequal-mass merger disk for⇒mation May be Short GRB.

2. 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

1. Unequal-mass NS-NS merger to BH.

2. NS-NS merger to HMNS.

Fate: Summary

thrM MthrM M

Merger

Black hole

Small Disk

Elliptical HMNS with diff. rot.

BH with Small disk

SpheroidT ~ 50 ms

~ Equal mass

Unequal

No disk

Weak short GRB?

GWemission

B-fieldseffects

BH with Heavy diskShort 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)

Near edge-on

Constrain by GW emission and Shapiro’s time delay