cooling of neutron stars with color superconducting quark cores

31 Pages·2012·0.87 MB·English

C N S
OOLING OF EUTRON TARS WITH
C S Q C
OLOR UPERCONDUCTING UARK ORES
David Blaschke
Universita¨t Bielefeld & JINR Dubna
Collaboration:
D. Aguilera, H. Grigorian, D. Voskresensky
(cid:15) EoS and QCD Phase Transition
(cid:15) Stability of Hybrid Stars
(cid:15) Cooling of Hadronic Stars
(cid:15) Hybrid Star Cooling:
2SC + X Quark Matter
(cid:15) Perspectives - a Conjecture
Picturetaken from
http://www.astroscu.unam.mx/neutrones/NS-Picture/
DAVID BLASCHKE
SEATTLE, JUNE 2004
1
I
NTRODUCTION
QCD Phase Diagram
early universe
ALICE
quark-gluon plasma
(cid:15) T = 0, (cid:22) = 0
RHIC
<yy> ~ 0
Tc ~ 170 MeV crossover (cid:22)
h i 6= 0 hadron phase
T
SPS quark matter chiral symmetry is broken.
(cid:15) T ! 1, (cid:22) ! 1
<yy> > 0
crossover
hadronic fluid
(cid:22)
superfluid/superconducting h i = 0 symmetry phase
phases ?
all symmetries are restored.
n = 0 n > 0 2SC <yy> > 0
B B CFL
vacuum nuclear matter neutron star cores
m ~ 922 MeV
o
m
Moderate T and (cid:22)? (cid:0)! heavy-ion collisions / compact stars interiors
*
S. Hands, The phase diagram of the QCD physics/0105022 (2001)
DAVID BLASCHKE
SEATTLE, JUNE 2004
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M
OTIVATION
Even at weak coupling, any attractive quark-quark interaction
#
condensate of Cooper pairs
#
Color superconductivity
(cid:15) with diquark condensates?
To explore dense matter EoS (T; (cid:22))
(cid:15) with strangeness?
l
(cid:15) with quark core - Quark matter EoS
To build a stable realistic neutron star
(cid:15) with hadron shell - Nuclear matter
EoS
DAVID BLASCHKE
SEATTLE, JUNE 2004
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Q M E S M
UARK ATTER O ODEL
Mass gap (cid:30) and diquark gap (cid:1) are order parameters for (cid:31)SB and CSC (cid:12)-equilibrium for
f f
the two flavor and three color case (N = 2 u;d, N = 3 r;b;g) requires different chemical
f c
potentials: (cid:22) = ((cid:22) + (cid:22) )=2 and (cid:22) = ((cid:22) (cid:0) (cid:22) )=2.
q u d I u d
(cid:30)2 (cid:1)2 2 1
2
(cid:10)((cid:30);(cid:1);(cid:22) ;(cid:22) ;T) = + (cid:0) dqq (N (cid:0) 2)f2E
q I c (cid:30)
4G 4G 2(cid:25)2
1 2 0
Z
E (cid:0) (cid:22) (cid:0) (cid:22) E (cid:0) (cid:22) + (cid:22)
(cid:30) q I (cid:30) q I
+T ln 1 + exp (cid:0) + T ln 1 + exp (cid:0)
T T
(cid:20) (cid:18) (cid:19)(cid:21) (cid:20) (cid:18) (cid:19)(cid:21)
E + (cid:22) (cid:0) (cid:22) E + (cid:22) + (cid:22)
(cid:30) q I (cid:30) q I
+T ln 1 + exp (cid:0) + T ln 1 + exp (cid:0) g
T T
(cid:20) (cid:18) (cid:19)(cid:21) (cid:20) (cid:18) (cid:19)(cid:21)
4 1
2
(cid:0) dqq fE + E
+ (cid:0)
2(cid:25)2
0
Z
E(cid:0) (cid:0) (cid:22) E(cid:0) + (cid:22)
(cid:30) I (cid:30) I
+T ln 1 + exp (cid:0) + T ln 1 + exp (cid:0)
T T
" !# " !#
E+ (cid:0) (cid:22) E+ + (cid:22)
(cid:30) I (cid:30) I
+T ln 1 + exp (cid:0) + T ln 1 + exp (cid:0) g (cid:0) (cid:10)
vac
T T
" !# " !#
The dispersion relations: E 2 = q2 + (m + g(q)(cid:30))2 for quarks of unpaired color
(cid:30)
E(cid:6)2 = (E (cid:6) (cid:22))2 + g(q(cid:22))(cid:1)2 for quarks of paired colors
(cid:30) (cid:30)
DAVID BLASCHKE
SEATTLE, JUNE 2004
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F F
ORM ACTORS
The following cases are considered: Gaussian (g ),Lorentzian (g ) and NJL cutoff (g ).
G L NJL
2 2 2 (cid:3)[GeV] G (cid:3)2 m[MeV]
Gaussian g (q) = exp((cid:0)q =(cid:3) ) 1
G G
1 g 1:025 3:761 2:41
2 G
Lorentzian g (q) =
L (cid:3)2 + (q=(cid:3) )4 g 0:894 2:436 2:34
L
L
2
NJL g (q) = (cid:2)(1 (cid:0) q=(cid:3) )
NJL NJL g 0:900 1:944 5:10
NJL
The parameters (cid:3), G , G and m are fixed at T = (cid:22) = 0 by m = 140 MeV, f = 93 MeV,
1 2 (cid:25) (cid:25)
m (0) = 330 MeV and by choosing G =G = 4=3.
q 1 2
S. Schmidt, D. Blaschke, Y. Kalinovsky, Phys. Rev. C 50 (1994) 435.
Q M C S C
UARK ATTER IN OMPACT TAR ORES
The quark matter core of compact stars consists of u, d, e, (cid:23) ;(cid:23)(cid:22) under the conditions:
e e
(cid:15) (cid:12)-equilibrium d ! u + e(cid:0) + (cid:23)(cid:22) (cid:22) = (cid:22) + (cid:22) + (cid:22)
e d u e (cid:23)(cid:22)e
(cid:22) + (cid:22) = (cid:0)2(cid:22)
e (cid:23)(cid:22)e I
(cid:15) Charge neutrality 2n (cid:0) 1n (cid:0) n = 0
u d e
3 3
n + 3n (cid:0) 6n = 0
q I e
DAVID BLASCHKE
SEATTLE, JUNE 2004
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T P , G E
HERMODYNAMICAL OTENTIAL AP QUATIONS
The extrema of (cid:10) correspond to Gap equations for the order parameters (cid:30) , (cid:1) :
0 0
@(cid:10) @(cid:10)
= = 0
@(cid:30) (cid:30)=(cid:30)0;(cid:1)=(cid:1)0 @(cid:1) (cid:30)=(cid:30)0;(cid:1)=(cid:1)0
(cid:12) (cid:12)
(cid:12) (cid:12)
f [GeV]
= 0 D
As T or (cid:22) changes, (cid:10) can have several local = 0
minima in the (cid:30);(cid:1) plane. The lowest mini- m =0
m =0.292
mum describes the lowest free energy state 0.0004
m =0.35
and is preferred. As an example, (cid:10)(T;(cid:22)) at
0.0002
T = 0, (cid:22) = 0:292 GeV is plotted. Two de-
generate minima can coexist at the values: W 0
(cid:30) = 0:4 GeV, (cid:1) = 0 and (cid:30) = 0, (cid:1) = 0:072
-0.0002
GeV. This corresponds to a first order transi-
tion at which two phases with equal pressure -0.0004
can coexist. 0 0.05 0.1 0 0.2 0.4
D f
@(cid:10)
(cid:10)((cid:30) ;(cid:1) ;(cid:22) ;(cid:22) ;T) = (cid:15) (cid:0) Ts (cid:0) (cid:22) n (cid:0) (cid:22) n = (cid:0)P ; n =
0 0 q I q q I I i
@(cid:22) T;(cid:30)=(cid:30)0;(cid:1)=(cid:1)0
i
(cid:12)
DAV(cid:12)ID BLASCHKE
SEATTLE, JUNE 2004
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E F T
FFECT OF INITE EMPERATURE
GAP EQUATION SOLUTIONS AND (cid:22)I IN (cid:12)-EQUILIBRIUM
(cid:15) The diquark condensate does not
feel the difference in partial or
f , T = 0
D , T = 0 complete restoration of the chiral
m , T = 0
I
0.3 f , T = 20 MeV symmetry.
D , T = 20 MeV
m , T= 20 MeV
I (cid:15) At low temperatures color su-
f , T = 40 MeV
]
V 0.2 D , T = 40 MeV perconductivity at (cid:22) immediately
Ge m , T= 40 MeV
I
[ above the first order phase transi-

tion. Color superconductivity per-
, d 0.1
D
,
I sists up to T(cid:1) = 45 MeV.
m c

0 (cid:15) The onset of the diquark conden-
sation is found at higher (cid:22) if the
q
temperature is increased.
-0.1
0 0.2 0.4 0.6 0 0.2 0.4 0.6 (cid:15) BCS theory predicts that T(cid:1) =
m [GeV] c
q 0:57F((cid:22))2(cid:1) (T = 0)
0
m = 0 (left) and m = 2:41 MeV, (right)
q q
DAVID BLASCHKE
SEATTLE, JUNE 2004
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E F F
FFECT OF ORM ACTORS
GAP EQUATION SOLUTIONS AND (cid:22)I IN (cid:12)-EQUILIBRIUM
(cid:15) The maximum of the diquark con-
densate ((cid:25) 150 MeV) roughly 0.4
f
F
form factor independent. G
F a=2
L
0.3 F a=10
(cid:15) The critical values of the phase L
F a=50
transition temperature and L
0.2 F
NJL
chemical potential depend on
D
]
smoothness of form factors. V
e 0.1
G
[
(cid:15) At T = 0 the critical chemical po- 0
tentials are: (cid:22)G = 320 MeV, (cid:22)L =
qc qc
m
345 MeV and (cid:22)NJL = 360 MeV. -0.1
qc I
¨
D.B., Fredriksson, Grigorian, Oztas,
-0.2
0.2 0.3 0.4 0.5 0.6 0.7
NPA 736 (2004) 203 m
[GeV]
q
DAVID BLASCHKE
SEATTLE, JUNE 2004
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E S Q S M
O FOR UARK TAR ATTER
TEMPERATURE AND ANTINEUTRINO EFFECTS
P + (cid:15) = sT + (cid:22) n + (cid:22) n , n = n + n ,
q q I I q u d
n = n (cid:0) n
I u d
Temperature effect
Antineutrino effect
T = 0
1000
T = 40 MeV
T = 50 MeV
T = 20 MeV
]
] e 3
3 m
-m 100
100 f
f 100 1000 /
V V
e 1000 e
M M
[ [
P
100 P m = 0
P 10 n e
m
= 100 MeV
n
10
e
m
= 200 MeV
n
e
1
1000 100 1000 10000
e [MeV fm-3] e [MeV/fm3]
DAVID BLASCHKE
SEATTLE, JUNE 2004
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C Q S S
ONFIGURATION OF UARK TARS WITHOUT HELL
CONDENSATE AND TEMPERATURE EFFECT
2
Gaussian
Tolman-Oppenheimer-Volkoff equations
1.5
dP [(cid:15)(r) + P(r)][m(r) + 4(cid:25)r3P(r)]
= (cid:0)
]
n dr r[r (cid:0) 2m(r)]
u
Ms T = 0, D = 0
[ 1 T = 0 r

M
T = 40 MeV 2
m = 4(cid:25) r (cid:15)(r)dr
T = 60 MeV
0
Z
The integral parameters M and R feel the ex-
0.5
istence of the diquark condensation: the EoS
becomes softer. At higher temperature both
M and R decrease approximately 10%
0 max max
3 6 9 6 8 10
compared to T = 0 and (cid:1) = 0 cases.
n [n ] R [km]
B 0
DAVID BLASCHKE
SEATTLE, JUNE 2004
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