Transcript The QCD phase diagram in Neutron Stars

Stability of CFL phase in hybrid
stars
Giuseppe Pagliara
in collaboration with Jürgen Schaffner-Bielich
Institut für Theoretische Physik
Frankfurt am Main
Germany
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
QCD phase diagram in NJL
FrankfurtDarmstadt EoS
Blaschke et al Phys.Rev.D 2005
Rüster et al Phys.Rev.D 2005
Two first order phase transitions:
Hadronic matter
2SC
CFL
CS in cold compact stars (NJL model)
M. Buballa Phys. Rep. 2005
Klähn et al Phys.Lett.B 2007
CFL cores are unstable !! No CS in Compact stars
or (small) 2SC cores in some cases
...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
No 2SC in compact stars
Alford, Rajagopal JHEP 2002
Stable CFL hybrid stars
Alford, Reddy Phys.Rev.D 2003
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
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
“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)
two phase transitions: chiral
and superconducting
Is the diquark condensate a good order
parameter for deconfinement at finite
density ??
(see also Bentz et al Nucl.Phys.A 2002)
Mass-Radius for NJL without CS
B*/B0  few %
Phase transition to CS
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
The mass of the strange quark
Within the NJL model ms=550 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
Astrophysical implications
• Double emission episodes in GRB
• Quark formation during core collapse SN
The Quark-Deconfinement Nova model
Two families of CSs
Conversion from HS
to HyS (QS) with the
same MB
How to generate GRBs
The energy released is carried out by neutrinos and antineutrinos.
The reaction that generates gamma-ray is:
   e  e  2


The efficency of this reaction in a strong gravitational field is:
  10%
[J. D. Salmonson and J. R. Wilson, ApJ 545 (1999) 859]
E   Econv  10 10 erg
51
52
Temporal structure of GRBs
ANALYSIS of the distribution of peaks intervals
Lognormal
distribution
“… the quiescent
times are made by
A different mechanism
then the rest of the
intervals”
Nakar and Piran 2002
Dormant inner engine during QTs
Double GRBs generated by double phase transitions
Drago, Pagliara ApJ 2007
Two steps (same barionic mass):
1)
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
2SC formation during SN ?
2SC pairing is favored
for symmetric matter
Critical densities from NM to 2SC
matter (NM within the Shen EoS)
MIT bag results
Densities reachable during the
collapse of a SN ??
Could the new energy released
help SN to explode ??
Di Toro et al. Nucl.Phys.A 2006
Pagliara, Sagert, Schaffner-Bielich
work in progress
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
Appendix
The vacuum in the NJL model
Mean field approach
Bogoliubov-Valatin variational
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
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, E~1051ergs
(beaming effect), is
comparable to the
brightness of the rest of
the Universe combined.
Very complex time-structure
of prompt emission,
Quiescent times
SN-GRB connection
Time delays from second
to years
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 ?
Delayed formation of quark matter
in Compact Stars
Quark matter cannot appear before the
PNS has deleptonized (Pons et al 2001)
Quantum nucleation theory
Droplet potential energy:
4
U(R )   n Q* Q*   H  R 3  4 R 2  a V R 3  a s R 2
3
nQ* baryonic number density
in the Q*-phase at a
fixed pressure P.
μQ*,μH chemical potentials
at a fixed pressure P.
σ 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
Quark droplet nucleation time
“mass filtering”
Critical mass for
=0
B1/4 = 170 MeV
Critical mass for
 = 30 MeV/fm2
B1/4 = 170 MeV
Age of the
Universe!
Mass accretion triggers the transition, possible long SN-GRB time delay
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
Analysis of PreQE and PostQE
Same “variability”: the same emission mechanism, internal
shocks
Same dispersions but
different average duration
PreQE: 20s
PostQE:~40s
QTs:~ 80s
Three characterisitc
time scales
No evidence of a continuous
time dilation
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
Blaschke et al. Phys.Rev.D 2005