Probing Neutron Star EOS Probing Neutron Star EOS in Gravitational Waves & Gamma-in Gravitational Waves & Gamma-

ray Burstsray Bursts

Kim Young-Min, Cho Hee-Suk

Lee Chang.-Hwan, Park Hong-Jo

(Pusan National University)

Dense Matter in Dense Matter in AstrophysicsAstrophysics

ContentsContentsIntroduction to Gravitational Wave

RadiationNeutron Star Binary System - (astrophysical part) In-Spiral & Mass

Transfer(RLOF) - (dense matter part) Neutron Star StructuresNumerical Result - Mass transfer time scales - Polarization amplitude of GWR in case by case - Comparison between normal NS and Quark starConclusion & Outlook

What is the GWR?What is the GWR?

Ripples in the Fabric of the Space-Time

Gravitational radiationGravitational radiation

''

)',/'(4 34

xdxx

xcxxtT

ch

fg

Thff )2

1(

T

c

GRgRG

4

8

2

1

Wave Equation

0 h

Einstein Field Equation

Linearized field equation

Gravitational radiationGravitational radiation

0000

00

00

0000

)(2

''

)',/'(44

'34 hh

hh

c

rtQ

rc

Gxd

xx

xcxxtT

ch ij

xrxx

)(2cos)1(

4)(

24

22

rtq

q

ac

MG

rth

Polarization amplitude

for compact binary system

4

2

5

5

5

4

5

15

32

5

1

q

q

a

M

c

G

QQc

GL ijijGW

4

2

2/75

2/92/7

)1(5

32

q

q

ac

MGJGW

Angle dependenceAngle dependence

0000

00

00

0000

)(hh

hhth TTij

0000

0)cos1(2

1cos0

0cos)cos1(2

10

0000

)(2

2

hh

hhth TTij

z'z

Rotate axis

Gravitational wave from NS Gravitational wave from NS binarybinary

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 GWRSources of the GWR

GRB~1051ergSN~1040ergSun~1033ergH Bomb~1020ergNuclear Power Plant~1015ergLight Bulb~108erg

Neutron Star-Neutron StarNeutron Star-Black HoleBlack Hole-Black Hole

Compact Star binary

Source of GRB ,too

Callapsar: Woosley et al.

In-spiral In-spiral ＆＆ Mass transferMass 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 OverFlowRoche Lobe OverFlow

Lagrange point

Roche lobe

Roche radius

CM

Orbit

M m

Roche radius =stellar radiusStable Mass transfer

“Roche lobe overflow”

Neutron Star structureNeutron Star structure

Calculated By C.Y. Ryu @ Sungkyunkwan Univ.

TOV equation

Nuclear matter1) The properties of nuclear matter2) N-N interaction3) RMF models - Baryon octet - Kaon condensation

Quark matter - MIT bag model

Neutron Star structureNeutron Star structure

0 2 4 6 8 10 12 14 160.0

0.5

1.0

1.5

2.0

Mas

s(M

⊙)

Radius(km)

Hyperon Kaon np quark

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2-2.0

-1.5

-1.0

-0.5

0.0

0.5

q=0

q=1/4

q=1/5

q=1/3

q=1/2

q=2/3

q=1

α(d

lnR

/dln

M)

Mass(M⊙

)

hyperon kaon n+p quark

Calculated By C.Y. Ryu @ Sungkyunkwan Univ.

Mass-Radius relation of Neutron Star

Initial mass transfer rate Initial mass transfer rate

14

MBH=3MSUN

1311 10~10

810~

110~

X-ray binary

BH-WD

Mass transfer time scaleMass transfer time scale

15

SHB duration ~2 s

s

Merging time ~2

MBH=3MSUN

Mass transfer time scaleMass transfer time scale

16

Proto-neutron

Kaon

Quark

BH spin upBH spin up

17

5351 10~10

5310~

BH spin energy

SHB energy

ergs

ergs

MBH=3MSUN

2008 Nuclear Physics School

Kaon model NP model

Hyperon model Quark model

Normal NS vs. Quark StarNormal NS vs. Quark Star(kaon vs. quark)(kaon vs. quark)

~ 2 times higher

Polarization amplitude(M⊙)

~ 100 times quickly

(After mass transfer occur)

Kaon model Quark model

Normal NS vs. Quark StarNormal NS vs. Quark Star(kaon vs. quark)(kaon vs. quark)

Frequency

Quark Star

Higher than Normal NS

Nearly constant after mass transfer

Conclusions Conclusions ＆＆ OutlookOutlook

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??