Download Gravitational Waves in Binary Neutron Star systems

Dense Matter in Astrophysics
Probing Neutron Star EOS
in Gravitational Waves & Gamma-ray Bursts
Kim Young-Min, Cho Hee-Suk
Lee Chang.-Hwan, Park Hong-Jo
(Pusan National University)
Contents
Introduction to Gravitational Wave Radiation
 Neutron Star Binary System

- (astrophysical part) In-Spiral & Mass Transfer(RLOF)
- (dense matter part) Neutron Star Structures

Numerical Result
- Mass transfer time scales
- Polarization amplitude of GWR in case by case
- Comparison between normal NS and Quark star

Conclusion & Outlook
What is the GWR?
Ripples in the Fabric of the Space-Time
Gravitational radiation
Einstein Field Equation
G

R

1  
8G 
 g R   4 T
2
c
Linearized field equation

  ( f
h 

g      f
  h   0
1  
  f )      h   T 
2
 

4 T (t  x  x ' / c, x ' ) 3 
 4 
d x'
 
c
x  x'

Wave Equation

Gravitational radiation
h 
0 0

 





4 T (t  x  x ' / c, x ' ) 3  x  x '  r  x 2G 
r
 0 h
 4 
d
x
'





Q
(
t

)


 
ij
0 h
c
x  x'
rc 4
c


0 0

1G
5 c5
32 G 4


5 c5
LGW 
0
h
 h
0
 Q

Q
ij ij
M 5 q2
a 5 1  q 4
32 G 7 / 2 M 9 / 2
q2

J GW 
5 c 5 a 7 / 2 (1  q) 4
Polarization amplitude for
compact binary system
4 G2M 2
q
h (t ) 
cos 2 (t  r )
4
2
r ac (1  q)
0

0
0

0 
Angle dependence
0 0

 0 h
TT
hij (t )  
0 h

0 0

0
h
 h
0
0

0
0

0 
0
0

1
(1  cos 2  )h
0
Rotate axis
2
hij TT (t )  
0
cos h

0
0

ẑ

ẑ '
0
cos h
1
 (1  cos 2  )h
2
0
0

0

0

0 
Gravitational wave from NS binary
B1913+16
Hulse & Taylor (1975)
 1993 Nobel Prize
Cumulative shift of periastron
time decay due to the effect of
Gravitational Wave Radiation
Sources of the GWR
Compact Star binary
Neutron Star-Neutron Star
Neutron Star-Black Hole
Black Hole-Black Hole
Source of GRB ,too
GRB~1051erg
SN~1040erg
Sun~1033erg
H Bomb~1020erg
Nuclear Power Plant~1015erg
Light Bulb~108erg
Callapsar: Woosley et al.
In-spiral ＆Mass transfer
Orbit shrinks due to the
gravitational radiation
Orbit increases due to
the conservation of AM
and mass transfer by
Roche lobe over flow
Roche Lobe OverFlow
Lagrange point
m
M
CM
Roche radius
Stable Mass transfer
Roche lobe
Roche radius =stellar radius
Orbit
“Roche lobe overflow”
Neutron Star structure
TOV equation
Nuclear matter
1) The properties of
nuclear matter
2) N-N interaction
3) RMF models
- Baryon octet
- Kaon condensation
Quark matter
- MIT bag model
Calculated By C.Y. Ryu
@ Sungkyunkwan Univ.
Neutron Star structure
Mass-Radius relation of Neutron Star
0.5
2.0
0.0
q=2/3
⊙
α (dlnR/dlnM)
1.5
Mass(M )
q=1
Hyperon
Kaon
np
quark
1.0
-0.5
q=1/2
q=1/3
-1.0
hyperon
kaon
n+p
quark
0.5
-1.5
q=1/4
q=1/5
q=0
0.0
0
2
4
6
8
10
Radius(km)
12
14
16
-2.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Mass(M )
⊙
Calculated By C.Y. Ryu
@ Sungkyunkwan Univ.
1.4
1.6
1.8
2.0
2.2
Initial mass transfer rate
11
MBH=3MSUN
13
10 ~ 10
X-ray binary
~ 10
8
BH-WD
~ 10
1
14
Mass transfer time scale
MBH=3MSUN
Merging time
~2 s
SHB duration
~2 s
15
Mass transfer time scale
Proto-neutron
Kaon
Quark
16
BH spin up
MBH=3MSUN
BH spin energy
~ 1053 ergs
SHB energy
10 51 ~ 10 53ergs
17
Kaon model
Hyperon model
NP model
Quark model
2008 Nuclear Physics School
Normal NS vs. Quark Star
(kaon vs. quark)
Polarization amplitude(M⊙)
(After mass transfer occur)
Kaon model
~ 2 times higher
Quark model
~ 100 times quickly
Normal NS vs. Quark Star
(kaon vs. quark)
Frequency
Quark Star
Higher than Normal NS
Nearly constant
after mass transfer
Conclusions ＆Outlook
Possibility of probing NS EOS in GW & GRBs.
(At least, may be able to exclude some EOS)
 Need to consider the spin & eccentricities of
NS-BH binaries
 And something more??
