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Quark deconfinement in compact stars:. connection with GRBs. Irene Parenti. Univ. of Ferrara Italy. INFN of Ferrara Italy. International summer school: “Hot points in Astrophysics and Cosmology”. Dubna, Russia 2 – 13 August 2004. August 2004. Irene Parenti. Summary.

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Quark deconfinement in compact stars

Quark deconfinement in compact stars:

connection with GRBs

Irene Parenti

Univ. of Ferrara


INFN of Ferrara


International summer school:

“Hot points in Astrophysics and Cosmology”

Dubna, Russia

2 – 13 August 2004

August 2004

Irene Parenti



  • Short overview on Gamma-Ray Bursts


  • Delayed nucleation of Quark Matter

  • Implication for the mass and radius of

    compact stars

  • How to generate Gamma-Ray Bursts

    from deconfinement

  • Conclusions

August 2004

Irene Parenti

Gamma ray bursts grbs

short GRBs

few ms – 2 s

long GRBs

2 s – few 100 s

Gamma-Ray Bursts (GRBs)

Spatial distribution:isotropic

Distance:cosmological (1-10)∙109 ly

Energy range:100 KeV – a few MeV

Emitted energy:1051 erg (beamed/jets)

Duration:(0,01-300) s

J.S. Bloom, D.A. Frail, S.R. Kulkarni, ApJ 594, 2003

August 2004

Irene Parenti

Grb and supernovae

time delay Δt between the Supernova

explosion and the Gamma-Ray Burst.

GRB and supernovae

Connection between GRB and Supernovae

Evidence for atomic lines in the spectra

of the X-ray afterglow

August 2004

Irene Parenti

Time delay from sn to grb

GRB990705ΔT ≈ 10 yr

Amati et al., Science 290, 2000, 953

GRB011211ΔT ≈ 4 days

Watson et al., ApJ 595, 2003, L29

GRB030227ΔT ≈ 3-80 days

Reeves etal. , Nature 2002

Time delay from SN to GRB

August 2004

Irene Parenti

A two stages scenario

2nd “explosion”:



(ass. with the NS)

open questions

  • What is the origin of the 2nd “explosion”?

  • How to explain the long time delay

  • between the two events?

A two-stages scenario

1st explosion:


(birth of a NS)

August 2004

Irene Parenti

Delayed collapse of a hs to a qs

Pure HSHybrid Star or Quark Star

when color superconductivity is taken in to account:

A. Drago, A. Lavagno and G. Pagliara

Phys. Rev. D69 (2004) 057505

Delayed collapse of a HS to a QS

Z. Berezhiani, I. Bombaci, A. Drago, F. Frontera and

A. Lavagno ApJ. 586 (2003) 1250

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


  • 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. ≈ 1052 - 1053 erg

August 2004

Irene Parenti

The quark deconfinement nova model

The Quark-Deconfinement Nova model

August 2004

Irene Parenti

Finite size effects

quark-flavor must be conserved

during the deconfinement


Finite-size effects

  • 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

August 2004

Irene Parenti

Quark deconfinement

Quark deconfinement

virtual droplet of

deconfined quark


real droplet of

deconfined quark


real droplet of

strange matter

hadronic matter in a

metastable state

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


when p overcomes the

transition point

in a time τ

Soon afterwards the weak interactions change the

quark flavor fraction to lower the energy.

August 2004

Irene Parenti

Equation of state

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)]

August 2004

Irene Parenti

Hybrid star mass radius

Hybrid star: mass-radius

B=136,36 MeV/fm3

Hybrid star configuration

Hybrid Star: configuration

B=136,36 MeV/fm3

Strange star mass radius

Strange Star: mass-radius

B=74,16 MeV/fm3

Strange star configuration

Strange Star: configuration

B=74,16 MeV/fm3

Quantum nucleation theory

Droplet potential energy:

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

nQ* baryonic number density

in the Q*-phase at a

fixed pressure P.

μQ*,μHchemical potentials

at a fixed pressure P.

σ surface tension

(=10,30 MeV/fm2)

August 2004

Irene Parenti

Matter in the droplet

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 much

larger than that without

flavor conservation.

August 2004

Irene Parenti

Nucleation time

Nucleation time

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.

August 2004

Irene Parenti

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 < McrHS are metastable with a

long mean-life time.

MHS > McrThis HS are very unlikely

tobe observed.

The critical mass of metastable HS

August 2004

Irene Parenti

Two families of compact stars

Two families of compact stars

August 2004

Irene Parenti

Mass radius constraints

Mass-Radius constraints

  • X-ray burster EXO0748-676

    [Cottam et al., Nature 420, 2002]

  • z=0.35

  • X-ray pulsar 1E 1207.4-5209

  • [Sanwal et al.ApJ 574, 2002, L61]

  • z=0.12-0.23

  • X-ray binary 4U 1728-34

  • [Li et al. ApJ 527,1999,L51]

  • Very compact object

Mass radius constraints1

Mass-Radius constraints

Energy released

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)):

August 2004

Irene Parenti

How to generate grbs

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]

August 2004

Irene Parenti


  • Econv ≈ 1052 – 1053 erg GRBs


  • Neutron stars (HS) are metastable to

    HS ―> QS or to HS ―> HyS

  • 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

August 2004

Irene Parenti



  • Dr.Ignazio Bombaci

  • Dr.Isaac Vidaña

Univ. of Pisa

INFN of Pisa

Ref: I. Bombaci, I. P., I. Vidaña


Astroph. J., accepted

Other collaborators:

  • Dr. Alessandro Drago

  • Dr. Giuseppe Pagliara

Univ. of




August 2004

Irene Parenti

Quark deconfinement in compact stars


August 2004

Irene Parenti

Compact stars

Compact stars







    (SS or QS)


neutron stars

hyperon stars

August 2004

Irene Parenti

Probability of tunneling

Probability of tunneling

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