1. Quark deconfinement in compact stars: University of Ferrara, Italy
connection with GRB
Irene Parenti
University of Ferrara, Italy
INFN of Ferrara, Italy
International symposium:
“The QCD-phase diagram”
Skopelos, Hellas
29 May – 2 June 2004
1 June 2004
Irene Parenti

2. Summary Short overview on Gamma-Ray Bursts (GRBs)
Delayed nucleation of Quark Matter
How to generate Gamma-Ray Bursts
from deconfinement
Conclusions
1 June 2004
Irene Parenti

3. Gamma-Ray Bursts (GRBs)
Spatial distribution: isotropic
Distance: cosmological (1-10)∙109 ly
Energy range: 100 KeV – a few MeV
short GRBs
few ms – 2 s
long GRBs
2 s – few 100 s
Emitted energy: 1051 erg (beamed/jets)
Duration: (0,01-300) s
J.S. Bloom, D.A. Frail, S.R. Kulkarni, ApJ 594, 2003
1 June 2004
Irene Parenti

4. GRB and supernovae Connection between GRB and Supernovae
Evidence for atomic lines in the spectra
of the X-ray afterglow
time delay Δt between the Supernova
explosion and the Gamma-Ray Burst.
1 June 2004
Irene Parenti

5. Time delay from SN to GRB
GRB ΔT ≈ 10 yr
Amati et al., Science 290, 2000, 953
GRB ΔT ≈ 4 days
Watson et al., ApJ 595, 2003, L29
GRB ΔT ≈ 3-80 days
Reeves etal. , Nature 2002
1 June 2004
Irene Parenti

6. A two-stages scenario open questions 1st explosion: SUPERNOVA
(birth of a NS)
2nd “explosion”:
CENTRAL ENGINE
OF THE GRB
(ass. with the NS)
What is the origin of the 2nd “explosion”?
How to explain the long time delay
between the two events?
open questions
1 June 2004
Irene Parenti

7. Delayed collapse of a HS to a QS
Z. Berezhiani, I. Bombaci, A. Drago, F. Frontera and
A. Lavagno ApJ. 586 (2003) 1250
Pure HS Hybrid Star or Quark Star
Possible central
engine for GRB
The conversion process can be delayed due to the effects
of the surface tension between the HM phase and the QM
phase.
The nucleation time depends drammatically on the central
pressure of the HS.
As a critical-size drop of QM is formed the HS is
converted to a QS or a HyS.
The conversion process releases: Econv. ≈ erg
A. Drago, A. Lavagno and G. Pagliara
Phys. Rev. D69 (2004)
when color superconductivity is taken in to account:
1 June 2004
Irene Parenti

8. The Quark-Deconfinement Nova model
1 June 2004
Irene Parenti

9. Finite-size effects quark-flavor must be conserved
The formation of a critical-size drop of QM is
not immediate.
It’s necessary to have an overpressure to form a
droplet having a size large enough to overcome the
effect of the surface tension.
A virtual droplet moves back and forth in the
potential energy well on a time scale:
ν0-1~10-23 s « τweak
quark-flavor must be conserved
during the deconfinement
transition.
1 June 2004
Irene Parenti

10. Quark deconfinement stable phase
virtual droplet of
deconfined quark
matter
real droplet of
strange matter
hadronic matter in a
metastable state
real droplet of
deconfined quark
matter
stable phase
This form of deconfined
matter has the same
flavor content of the
β-stable hadronic system
at the same pressure.
We call it: Q*-phase.
The drop grows with no
limitation.
in a time τ
when p overcomes the
transition point
Soon afterwards the weak interactions change the
quark flavor fraction to lower the energy.
1 June 2004
Irene Parenti

11. Equation of State Hadronic phase: Relativistic Mean Field Theory
of hadrons interacting via meson exch.
[e.g. Glendenning, Moszkowsky, PRL 67(1991)]
Quark phase: EOS based on the MIT bag model
for hadrons.
[Farhi, Jaffe, Phys. Rev. D46(1992)]
Mixed phase: Gibbs construction for a multicom-
ponent system with two conserved “charges”.
[Glendenning, Phys. Rev. D46 (1992)]
1 June 2004
Irene Parenti

12. Quantum nucleation theory
I.M. Lifshitz and Y. Kagan, Sov. Phys. JETP 35 (1972) 206
K. Iida and K. Sato, Phys. Rev. C58 (1998) 2538
Droplet potential energy:
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)
1 June 2004
Irene Parenti

13. Nucleation time The nucleation time dramatically depends
The nucleation time is the time needed to form
a critical droplet of deconfined quark matter.
It can be calculated for different values of the
stellar central pressure (and then of the stellar
mass, as implied by TOV).
The nucleation time dramatically depends
on the value of the stellar central pressure
and then on the value of the stellar mass.
1 June 2004
Irene Parenti

14. The critical mass of metastable HS
We fixed the time of nucleation at 1 yr.
The gravitational mass corresponding to
this nucleation time is called critical mass:
We assume that during the stellar conversion
process the total numbers of baryons in the
star (and then the baryonic mass) is
conserved. [I. Bombaci and B. Datta, ApJ. 530 (2000) L69]
The gravitational mass of the final star
is taken to be the mass in the stable configu-
ration corresponding to that baryonic mass.
MHS < Mcr HS are metastable with a
long mean-life time.
MHS > Mcr This HS are very unlikely
to be observed.
1 June 2004
Irene Parenti

15. Two families of compact stars
1 June 2004
Irene Parenti

16. Energy released The total energy released in the stellar conversion
is given by the difference between the gravitational
mass of the initial hadronic star (Min=Mcr) and the
mass of the final hybrid or strange stellar
configuration (Mfin=MQS(Mbcr)):
1 June 2004
Irene Parenti

17. How to generate GRBs The energy released is carried out by pairs
of neutrinos – antineutrinos.
The reaction that generate gamma-ray is:
The efficence of this reaction in a strong
gravitational field is:
[J. D. Salmonson and J. R. Wilson, ApJ 545 (1999) 859]
1 June 2004
Irene Parenti

18. Conclusions Neutron stars (HS) are metastable to
HS ―> QS or to HS ―> HyS
Econv ≈ 1052 – 1053 erg GRBs
Our model explains the connection and the
time delay between SN and GRBs.
possible existence of two different
families of compact stars:
pure Hadronic Stars
Hybrid stars or Strange Stars
1 June 2004
Irene Parenti

19. Collaborators Dr. Ignazio Bombaci Dr. Isaac Vidaña
INFN of Pisa
University of Pisa
Ref: I. Bombaci, I. P., I. Vidaña
arXiv:astro-ph/
1 June 2004
Irene Parenti

20. Appendix
1 June 2004
Irene Parenti

21. Compact stars (HS) (HyS) HADRONIC STARS HYBRID STARS STRANGE STARS
(SS or QS)
conventional
neutron stars
hyperon stars
1 June 2004
Irene Parenti

22. Probability of tunneling
Oscillation frequency of the virtual drop inside the
potential well:
Penetrability of the potential barrier:
Nucleation time:
Nc=number of nucleation centers in the star core
1 June 2004
Irene Parenti

23. Matter in the droplet Flavor fractions are the same of the β-stable
hadronic system at the
same pressure:
The pressure needed for
phase transition is more
larger than that without
flavor conservation.
1 June 2004
Irene Parenti