Transcript Effects of color superconductivity on the nucleation of

Metastability of Hadronic
Compact Stars
I. Vidaña
&
I. Bombaci, P. K. Panda, C. Providência
“The Complex Physics of Compact Stars”
Ladek Zdroj, Poland, 24-29 February 2008
arXiv:0802.1794; PRD in press
In this work:
 We perform a systematic study of the metastability of pure hadronic
compact stars with respect to the conversion to quark stars using different
relativistic models for the hadronic EoS: Non Linear Walecka Model
(NLWM) & Quark Meson Coupling (QMC).
 We explore the effect of different hyperon couplings on the critical mass
and on the stellar conversion energy, finding that the increase of the hyperon
coupling shift the bulk transition point for quark deconfinement to higher
densities and makes the conversion to quark stars less likely.
 For the QMC model, the formation of a quark star is only possible with a
soft quark matter EoS.
 Both QMC and GM1 with the largest hyperon-meson couplings predict
critical masses which may be as high as 1.9-2.1 M, compatible with highly
massive compact stars, suchs as the of the millisecond pulsar PSR
B1516+02B and nearly the one PSR J1748-2021B.
Astrophysical Scenario
Nucleation of quark matter in neutron stars has been studied by many
authors, due to its potential connection with explosive events such as
supernovae and gamma-ray bursts.
 Thermal nucleation: (Horvath et al.,1994; Olesen & Madsen 2004; Benvenuto & Lugones 1999)
The prompt formation of a critical-size drop of QM via thermal activation
is possible for T > 2-3 MeV
Pure hadronic stars are converted to quark
stars within the first seconds after their birth.
However, neutrino trapping in the protoneutron star phase strongly
precludes the formation of a quark matter phase
 Quantum nucleation:(Grassi 1998; Iida & Sato 1998, Berezhiani et al., 2003, Bombaci et al.,
2004, Drago et al., 2004)
It is possible that the star survives the early stages of its evolution as
a pure hadronic star. In this case, nucleation of QM would be triggered
by quantum fluctuations in degenerate (T=0) neutrino-free hadronic
matter.
Formation of a quark matter bubble at the centre of a
Neutron Star (I)
Hadron matter
Direct nucleation of the -stable quark
matter: high order weak process 
suppressed by a factor ~ GF2N/3, with
N=100-1000.
-stable
quark-matter bubble
Ruled out: even when the final
state has a lower energy
Berezhiani et al. 2003 (unpaired)
Drago, Lavagno & Pagliara 2004 (CFL)
Formation of a quark matter bubble at the centre of a
Neutron Star (II)
W ~ 10-8 s
S ~ 10-23 s
Hadron matter
Non--stable
quark-matter bubble
-stable
quark-matter bubble
Q* (Non- stable)
Q* (Non- stable)
Has the intermediate phase lower energy than hadron matter ?
The intermediate non -stable quark phase
 Each flavor is color neutral
 Flavor is conserved
Iida & Sato 1998 ; Bombaci, Parenti & Vidaña 2004
Lifshitz-Kagan quantum nucleation theory
Quantum fluctuation of a virtual drop of QM in HM
L =  M R 
2
 dR 
1 
 + M R   U R 
dt


 nQ*  3
M R = 4  H 1
 R
 n H 
2
4
UR = nQ* Q*  H R3 +4R2  8R  E c
3
 =10 50MeV / fm2




Nucleation Time
Oscillation frequency of the virtual drop
inside the potential well and Penetrability
of the potential barrier (WKB)
 dI 1
 0 =   ; E = E o
dE 
 AE0  
p0 = exp 

 


R1
IE  = 2  dR
2MR+ E  URE  UR
Action over and
under the barrier
0
AE  = 2
R2
 dR 2MR+ E  U RU R  E 
R1

Nucleation time
 =  0 p0Nc  ;Nc 1048
1
Critical mass of metastable hadronic stars
Definition: Mcr = MHS(= 1 yr)
Hadronic stars with MHS< Mcr are metastable with  = 1 yr to infinity
Hadronic stars with MHS> Mcr are very unlikely observed
“The critical mass Mcr plays the role of an
effective maximum mass for the hadronic
branch of compact stars”
Berezhiani et al. 2003 ; Bombaci et al.
2004
Few words on the EoS considered …
 Non Linear Walecka Model
We use the Glendenning-Moszkowski (GM) parametrizations GM1 & GM3 of the
NLWM (PRL 67, 2414 (1991)), where the hyperon-nucleon couplings,
x gY/gN x gY/gN and x gY/gN , are constrained by the binding
of the  hyperon in nuclear matter
B 
  28MeV  x g 0  x g 
 A 
Neutron star masses, in addition, restrict x to the range 0.6 - 0.8. Here, we will take
x x and will consider x =0.6, 0.7, 0.8.

 Quark Meson Coupling Model
Baryons described as a system of non-overlaping spherical bags containing three
valence quarks interacting by the exchange of ,  and  mesons coupled directly
to the confined quarks. (PLB 200, 235 (1988)). Here we will take x 0.7, x=0.78
and x is an output of the model ~ 0.7.
 Quark phase: MIT bag model (Farhi & Jaffe, PRD 30, 2379 (1984))
Hadronic Equation of State
 Higher value of the hyperon couplings
stiffer EoS.
 Onset of hyperons at higher densities for larger values of the couplings.
 QMC EoS softer/stiffer than NLWM.
Gibbs free energy & bulk transition point for quark deconfinement
The lower the values of hyperon couplings, the softer the EoS and
the lower the pressure P0 at the crossing between the hadronic and
the Q* phase
lower critical masses for smaller hyperon
coupling values.
Stable, mestastable and unstable hadron star configurations (I)
NLWM (GM1)
QMC
=30 MeV/fm2
Very narrow metastability region for QMC. The formation of a quark star is only
possible in this model for a soft quark matter EoS (i.e., for small values of B).
Stable, mestastable and unstable hadron star configurations (II)
NLWM (GM1)
QMC
 When Mcr star is almost on the top of P0, these stars lie on or close to the plateau
that contains the maximum mass configuration.
 A large separation between these two configurations corresponds to a phase
transition which occurs during the rise of the MP curve before the plateau.
QMC
Large critical masses
due to the softness of
the QMC EoS
Critical Mass
Hyperon coupling
Critical Mass
Bag cosnatnt
NLWM (GM1)
M=2.081 M, R=12.6 km, fY,cr ~ 30%, RY ~ 8.7 km.
Compatible with highly-massive compact stars, such as the one associated to the
millisecond pulsar PSR B1516+02B (1.94(+0.17-0.19) M (1)) , and nearly the
one PSR J1748-2021B (2.74 (+0.41-0.51) M (2))
Summary & Conclusions 4564)
We have performed a systematic study of the metastability of pure
hadronic compact stars with respect to the conversion to quark stars using
different relativistic models for the EoS: Non Linear Walecka Model
(NLWM) & Quark Meson Coupling (QMC).
We have explored the effect of different hyperon couplings on the critical
mass and on the stellar conversion energy, finding that the increase of the
hyperon coupling shift the bulk transition point for quark deconfinement to
higher densities and makes the conversion to quark stars less likely.
For the QMC model, the metastability region is very narrow. The EoS is
very sofy and therefore the onset of hyperons occurs at quite high densities,
which gives rise to large critical masses. The converstion to a quark star
will occur only for a small value of the bag constant.
Both QMC and GM1 with the largest hyperon-meson couplings predict
critical masses which may be as high as 1.9-2.1 M, compatible with the
masses of the millisecond pulsar PSR B1516+02B and nearly the one PSR
J1748-2021B
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