Stability of CFL phase in hybrid stars

1
Stability of CFL phase in hybrid stars

• Giuseppe Pagliara
• in collaboration with Jürgen Schaffner-Bielich
• Institut für Theoretische Physik
• Frankfurt am Main
• Germany

2
Punchline

• Within the NJL model of quark matter hybrid stars
  with CFL cores could be stable
• Possible configurations with two phase
  transitions NM - 2SC - CFL

3
QCD phase diagram in NJL
Frankfurt-Darmstadt EoS
Blaschke et al Phys.Rev.D 2005
Rüster et al Phys.Rev.D 2005
Two first order phase
transitions Hadronic matter 2SC
CFL
4
CS in cold compact stars (NJL model)
Klähn et al Phys.Lett.B 2007
M. Buballa Phys. Rep. 2005
CFL cores are unstable !! No CS in Compact stars
or (small) 2SC cores in some cases
5
...on the other hand CFL in MIT bag model
For small value of ms it is still convenient to
have equal Fermi momenta for all quarks
(Rajagopal Wilczek PRL 2001)
Binding energy density of quarks near Fermi
surface ? ?VN ??2 ?2
Stable CFL hybrid stars Alford, Reddy Phys.Rev.D
2003
No 2SC in compact stars Alford, Rajagopal JHEP
2002
6
A toy model for the HM-QM transition
Hadronic EOS relativistic mean field
model Quark EoS p a e free parameters p0, ?e,
a
The pressure onset of phase transition is the
most important parameter for the stability of a
new phase
7
Bag pressure in the NJL model
p(?) -?(?)const. the const. is fixed by
requiring p(0)0 (Asakawa-Yazaki Nucl. Phs.A504
668) i.e. it is fixed in a regime where NJL EoS
can not be applied due to its lack of
confinement. It turns out that bag ? (200 MeV)4,
larger than the MIT bag. Pressure onset ? 200
MeV/fm3 the chemical potential of the phase
transition is ? 1400 Mev by far larger than the
chiral symmetry restoration chemical potential
which is ? 1100 MeV
Quarks in stars are present only in the mixed
phase !
Schertler et al Phys.Rev.C 99
8
Deconfinement and chiral symmetry restoration
The NJL model at finite density can be applied
starting from the chiral symmetry restoration
(before the density is vanishing!!) The bag can
be fixed by requiring that the pressures of QM
and NM are the same at the chiral phase
transition assumption that deconfinement and
chiral symmetry restoration coincide (see also
Bender et al. Phys.Lett.B 1998)
Is the diquark condensate a good order parameter
for deconfinement at finite density ?? (see also
Bentz et al Nucl.Phys.A 2002)
two phase transitions chiral and superconducting
9
Mass-Radius for NJL without CS
B/B0 ? few
10
Phase transition to CS
11
Mass-radius relations
for smaller values of the bag p0 decreases
for larger values of the gap (? 150 MeV as in
Klähn et al Phys.Lett.B 2007 ) p0 decreases but
?e increases (even softer EoS!!) the effect of p0
dominates and the stars are stable
Vector interactions larger maximum of the mass
(see Klähn et al Phys.Lett.B 2007)
Hybrid stars with a crust of nucleonic matter a
layer of 2SC and a core of CFL phase are stable
( if the bag is small and the gap ? 150 MeV )
G.P. and J. Schaffner-Bielich 2007
12
The mass of the strange quark
Within the NJL model ms550 MeV at ?300
MeV Within the Schwinger-Dyson approach a smaller
dynamical quark mass is obtained, CFL favored
also at low density Nickel, Alkofer Wambach,
Phys.Rev.D 2006
Favors the stability of CFL phase in compact stars
13
Astrophysical implications

• Double emission episodes in GRB
• Quark formation during core collapse SN

14
The Quark-Deconfinement Nova model
15
Two families of CSs
Conversion from HS to HyS (QS) with the same MB
16
How to generate GRBs
The energy released is carried out by neutrinos
and antineutrinos.
The reaction that generates gamma-ray is The
efficency of this reaction in a strong
gravitational field is J. D. Salmonson and
J. R. Wilson, ApJ 545 (1999) 859
17
Temporal structure of GRBs
ANALYSIS of the distribution of peaks intervals
the quiescent times are made by A different
mechanism then the rest of the intervals Nakar
and Piran 2002
Lognormal distribution
Dormant inner engine during QTs
18
Double GRBs generated by double phase transitions
Drago, Pagliara ApJ 2007

• Two steps (same barionic mass)
• transition from hadronic matter to unpaired or
  2SC quark matter. Mass filtering
• 2) the second phase transition triggered by
  cooling and deleptonization (see Sandin talk!!
  Sandin-Blaschke Phys.Rev.D2007)

Burning of Hadronic stars into quark or hybrid
stars Drago, Lavagno, Parenti ApJ 2007
Always a deflagration with an unstable front.
Hydrodynamical instabilities can increase the
velocity by up to 2 orders of magnitude, but in
general do not transform the deflagration into a
detonation
Nucleation time of CFL phase
19
2SC formation during SN ?
Critical densities from NM to 2SC matter (NM
within the Shen EoS)
2SC pairing is favored for symmetric matter
MIT bag results
Densities reachable during the collapse of a SN
?? Could the new energy released help SN to
explode ??
Pagliara, Sagert, Schaffner-Bielich work in
progress
Di Toro et al. Nucl.Phys.A 2006
20
Conclusions
Rich structure of the QCD phase diagram chiral
broken phase, 2SC, CFL... Two possible phase
transitions in stable hybrid stars Possible
signature double emission in GRBs could be a
signal of the two phase transitions as the
central density of the star increases and the
temperature decreases
21
Appendix
22
The vacuum in the NJL model
Bogoliubov-Valatin variational approach
Mean field approach
two flavor NJL-like Hamiltonian
Buballa, Phys.Rep. 2005
the pressure of the vacuum phase is positive
(metastable phase which converts into a stable
phase at a density of 0.3 fm-3)
Alford, Rajagopal and Wilczek, Phys.Lett.B 1998
23
General features of GRBs

• Duration 0.01-1000s
• 1 burst per day (BATSE)
• Isotropic distribution - rate of 2 Gpc-3 yr-1
• 100keV photons
• Cosmological Origin
• The brightness of a GRB, E1051ergs (beaming
  effect), is comparable to the brightness of the
  rest of the Universe combined.

Very complex time-structure of prompt emission,
Quiescent times
24
SN-GRB connection
Time delays from second to years
25
The Collapsar model

• Rotating massive stars, whose central region
  collapses to a black hole surrounded by an
  accretion disk.
• Outflows are collimated by passing through
  the stellar mantle.
• Detailed numerical analysis of jet
  formation.
• Fits naturally in a general scheme
  describing collapse of massive stars.
• - Large angular momentum needed, difficult to
  achieve.
• SN GRB time delay less then
  100 s.
• Can it explain long time delay precursors ?

26
Delayed formation of quark matter in Compact Stars
Quark matter cannot appear before the PNS has
deleptonized (Pons et al 2001)
Quantum nucleation theory
nQ baryonic number density in the Q-phase
at a fixed pressure P. µQ,µH chemical
potentials at a fixed pressure P. s
surface tension (10,30 MeV/fm2)
I.M. Lifshitz and Y. Kagan, Sov. Phys. JETP 35
(1972) 206 K. Iida and K. Sato, Phys. Rev. C58
(1998) 2538
27
Quark droplet nucleation timemass filtering
Critical mass for s 0 B1/4 170 MeV
Critical mass for s 30 MeV/fm2 B1/4 170 MeV
Age of the Universe!
Mass accretion triggers the transition, possible
long SN-GRB time delay
28
Excluding QTs
Deviation from lognorm power law tail (slope
-1.2)
Probability to find more than 2 QT in the same
burst
Drago Pagliara 2005
Analysis on 36 bursts having long QT (red dots)
the subsample is not anomalous
29
Analysis of PreQE and PostQE
Same variability the same emission mechanism,
internal shocks
30
Same dispersions but different average
duration PreQE ?20s PostQE40s QTs 80s Three
characterisitc time scales
No evidence of a continuous time dilation
31

• Interpretation
• 1)Wind modulation model during QTs no collisions
  between the emitted shells
• 2) Dormant inner engine during the long QTs

Huge energy requirements No explanation for the
different time scales It is likely for short QT
Reduced energy emission Possible explanation of
the different time scales in the Quark
deconfinement model It is likely for long QT
32
Blaschke et al. Phys.Rev.D 2005