Influence of Phase-Transition-Scenarios on the Neutron Star Characteristics Abrupt Changes Triggered by the Formation of Quark Phase

G. B. Alaverdyan

2nd Int. Conf. “The Modern Physics of Compact Stars and Relativistic Gravity” Sept. 18-21, 2013, Yerevan

Yerevan State University, Armenia

Nnnn

Introduction

Mixed phase is energetically favorable for small values of the surface tension

H. Heiselberg, M. Hjorth-Jensen, Phys. Rep. 328, 237, 2000

D. D. Ivanenko, D. F. Kurdgelaidze, Astrofizika 1, 479, 1965

Two scenarios for hadron-quark phase transition:

• Maxwell scenario ordinary first-order phase transition at constant pressure with a density jump

• Glendenning scenario formation of mixed hadron-quark matter with a continuous variation of pressure and density (N. K. Glendenning, Phys. Rev. D46, 1274, 1992)

Scalar Vector

Isoscalar

Isovector

2 2 2

2 2 2

1( ) ( ) ( ) ( )2

1 1 1( ) ( ) ( ) ( ( )) ( ) ( ) ( ) ( )2 2 41 1 1( ) ( ) ( ) ( ) ( ) ( ) ( ) ,2 2 4

N N N N Ni g x g x m g x g x

x x m x U x m x x x x

x x m x m x x R x R x

L

pN

n

( , , , ) x x t x y z ( ), ( ), ( ), ( ) x x x x

3 4( ) ( ) ( ) ,3 4Nb cU m g g

( ) ( ) ( ),

( ) ( ) ( ).

x x x

x x x

Model EOS for Compact Stars

RMF Lagrangian density of many-particle system of p, n, , , ,

Hadronic Matter EOS

2 * 2 (3)0 0

2 * 2 (3)0 0

1( ) ,21( ) .2

p p F p F p p

n n F n F n n

e k k m g g

e k k m g g

2 * 2 (3)0 0

2 * 2 (3)0 0

1( ) ,21( ) ,2

p p

n n

e k k m g g

e k k m g g

2 ( ) ,

s p sndUm g n nd

2 , p nm g n n

2 (3) , s p snm g n n

2 (3)0

1 ,2 p nm g n n

* (3)

* (3)

,

.

p N

n N

m m g g

m m g g

3 3

2 2, ,3 3

Fp Fn

p n

k kn n

*2

2 2 * 20

1 , F pk

ps p

p

mn k dk

k m

*2

2 2 * 20

1 . F nk

nsn

n

mn k dk

k m

0( ) ( ( ))x x

L L

Relativistic mean-field approach

(3) (3)0, , , ,g g g g

22 2 2

, , ,

gg g ga a a a

m m m m,n pn n

n

the asymmetry

parameter

13

13

( )(1 )2 2 2

20

( )(1 ) 2 2 2 22 2 2

20

1( , ) ( )

1 1( ) ( ) ,2

F

F

k n

N

k n

N

n k m k dk

k m k dk Ua a a a

13

13

( )(1 )22 2 2 2 23

20

( )(1 )22 2 2 2 23

20

2 2 2 2

1( , ) ( ) (1 ) ( ) ( )

1 ( ) (1 ) ( ) ( )

1( ) .2

F

F

k n

F N N

k n

F N N

P n k n m k m k dk

k n m k m k dk

Ua a a a

Parametric EOS for nuclear matter

Parameters of RMF theory

, , , , ,a a a a b c

* ,N Nm m 0 (1 ) Nm

0

00 0

00

( ,0)( , ) , ,Nn n

nd n Bm f fdn n A

2 20 0 0

0

1 ( ) ( ) N F Na m f k n mn

2 20 0 0 0 0( ) ( )N F Na n m f k n m

0( )2 2 30 0

0 02 2 20 0

( )2

( )

Fk nN

N

N

mk dk bm c

a k m

( 0 ) Symmetric nuclear matter

Saturation density 0( )n n

Binding energy per baryon

Parameters of RMF theory

2

20

1 ( , )( )2sym

d nE nn d

2( )sym

symE nn

Symmetry energy

0

22

0 2

0

( , )9 ( )n n

d nK ndn n

compressibility module

0( ) 22 2 2 3 4 20

0 0 0 0 0 0 020

2 1( ) ( )3 4 2

Fk n

N N Nb cn m f k m k dk m n a

a

Parameters

a , fm2 9.154 9.154

a , fm2 4.828 4.828

a , fm2 0 2.5

a, fm2 4.794 13.621

b , fm-1 1.654 10-2 1.654 10-2

c 1.319 10-2 1.319 10-2

Parameters of RMF theory

938,93Nm MeV

*

0,78N

N

mm

30 0,153n fm

0 16,3f MeV

300K MeV

(0) 32,5symE MeV

Characteristics of -equilibrium npe- plasma

( , , ) ( , ) ( ),NM e e en n

2 2 3/ 22

1( , , ) ( , ) ( ) ( )3NM e e e e e eP n P n m

G. B. Alaverdyan, Research in Astron. Astrophys,10, 1255, 2010

1 (1 )2

p e en n n

qn n

EOS of quark phase

Improved version of MIT bag model

Interactions between u, d, s quarks

in one-gluon exchange approximation E. Farhi, R. L. Jaffe, Phys. Rev. D30, 2379, 1984

5um MeV

7dm MeV150sm MeV

360 /B MeV fm

Maxwell Construction

GlendenningConstruction

30

3

3

2.11 /

114.5 /

271.4 /N

Q

P MeV fm

MeV fm

MeV fm

3

3

3

3

72.79 /

0.43 /

1280.9 /

327.75 /

N

N

Q

Q

MeV fm

P MeV fm

MeV fm

P MeV fm

Density discontinuity parameter 0/( ) 2.327Q N P

If 3/ 2 , neutron star with infinitesimal quark core is unstable Seidov criterion (H. Seidov, Astron. Zh. 48, 443, 1971 )

max 1.85M M

max 1.83M M

Glend.

Maxw.

Constituents population

Changes in the Stellar Parameters

Maxwell Construction Glendenning Construction

20( )bindE M M c

0M baryonic mass

2[ ( ) ( )]release N QE M C M C c

QS NSR R R

Catastrophic conversion due to deconfinement phase transition

Summary and conclusions

We calculate the neutron star matter EOS with quark-deconfinement phase transitions corresponding to the Maxwell and Glendenning scenarios.

We find the dependence of conversion energy on the baryonic mass of neutron stars and analyze the changes in stellar radiuses due to the deconfinement phase transition.

We show that for a fixed value of the baryonic mass of star the conversion energy in the case of Glendenning construction more than in the case of Maxwell construction.

It is found that in the case of the Maxwell construction, the minimum required baryonic mass for the catastrophic rearrangement of the neutron star and the formation of a quark core in the center of the star is greater than in the case of Glendenning one.

In the studied case, the quark deconfinement phase transition in the neutron star interior leads to the energy release of the order erg.

0M

50 5210 10

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