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