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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

Merger of binary neutron stars in general relativity

M. Shibata(U. Tokyo)

Jan 19, 2007 at U. Tokyo


I introduction binary neutron stars
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
Evolve by gravitational radiation

Gravitational waves

TGW >> Period


Merger time
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
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
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
NS-NS merger = GW source

1st LIGO

LIGO

Advanced LIGO

Frequency (Hz)

TAMA

VIRGO


Status of first ligo completed
Status of first LIGO = Completed !

h(1/Hz^1/2/m)

h~10^-21

f (Hz)


Last 15 min of ns ns
Last 15 min of NS-NS

1st LIGO

Current

level

~100 events

per yrs

for A-LIGO

Advanced LIGO

Frequency (Hz)


Before merger after merger
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
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


?


To summarize introduction
To summarize Introduction

NS-NS merger is

  • not rare,

  • promising source of GW,

  • candidate for short GRBs.

     Deserves detailed study


2 simulation of binary neutron star merger
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
R-M relation of NSs

Mass

Quark star

Lattimer & Prakash

Science 304, 2004

Radius


M r relation for stiff eos
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
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 5 m sun case final snapshot
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
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
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
GW signal

1st LIGO

100kpc

Too

small

Advanced LIGO

Frequency (Hz)



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
Gravitational waves from HMNS

+ mode

Quasi-Periodic oscillation

x mode

Inspiral wave form


Gw signal1

For r <50Mpc

Detectable !

GW signal

1st LIGO

Detection

= HMNS

exists

Constrain

EOS

Advanced LIGO

Frequency (Hz)


Summary for merger general feature
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
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
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
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
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
PSR J0751-1807 (astroph/0508050)

Constrain by GW emission and Shapiro’s time delay

Near edge-on