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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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