Transcript Merger of binary neutron stars in GR

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
Total Mass ~ 2.6—2.8 solar mass
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•
•
•
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,
PSRB1534+12, P=0.421 d,
PSRB2127+11, P=0.335 d,
PSRJ0737-3039, P=0.102 d,
T=0.245 Billion yrs
T=2.25
T=0.22
T=0.085
Merge within Hubble time ~ 13.7 B yrs
 Merger could happen frequently.
Merger rate
1 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
f = 10 Hz
(r = 700 km)
r
~ 8000 revolution
from r=700 km
f = 1—1.2 kHz
at onset of merger
(r ~ 25 km)
f ~ 3 kHz ?
during merger
f ~ 7 kHz ?
Massive
black hole QNM
NS
Black hole
NS-NS merger = GW source
1st LIGO
LIGO
Advanced LIGO
Frequency (Hz)
TAMA
VIRGO
h(1/Hz^1/2/m)
Status of first LIGO = Completed !
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 merger
After merger
?
Need
numerical
relativity
Inspiral signal
= well-known
Information on
mass and spin
Information on
Neutron star &
Strong gravity
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
NS-NS merger is
• not rare,
• promising source of GW,
• candidate for short GRBs.

Deserves detailed study
2 Simulation 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
2s 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 * 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-Y
Y
Apparent
horizon
X-Z
Z
X
~ no disk mass
X
1.35 – 1.65 M_sun case : final snapshot
X-Y
Y
Apparent
horizon
X-Z
Z
X
Small disk
mass
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
Advanced LIGO
Frequency (Hz)
100kpc
Too
small
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
center＝1.3e15 g/cc
X
Dotted curve=2e14 g/cc
+ mode
Gravitational waves from HMNS
x mode
Quasi-Periodic oscillation
Inspiral wave form
h  10
22
 R ,   100Mpc 

 0.31km  
r



GW signal
For r ＜50Mpc
Detectable !
1st LIGO
Advanced LIGO
Frequency (Hz)
Detection
= HMNS
exists
⇒
Constrain
EOS
Summary for merger: General feature
1. Large mass case (Mtot > Mcrit)
Collapse to a BH in ~ 1ms.
For unequal-mass merger
⇒
disk formation  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
M  M thr
Merger
Black hole
~ Equal
mass
No disk
Unequal
Small Disk
Weak short
GRB?
GW
emission
M  M thr
Elliptical HMNS
with diff. rot.
T ~ 50 ms
Spheroid
BH with
Small disk
B-fields
effects
Short GRB?
BH with
Heavy disk
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