Quark deconfinement in compact stars:

Quark deconfinement Quark deconfinement in compact stars:in compact stars:

Irene ParentiIrene Parenti

Univ. of FerraraUniv. of Ferrara ItalyItaly

connection with GRBsconnection with GRBs

International summer school: International summer school: ““Hot points in Astrophysics and Cosmology”Hot points in Astrophysics and Cosmology”

Dubna, RussiaDubna, Russia2 – 13 August 20042 – 13 August 2004

August 2004 Irene Parenti

INFN of FerraraINFN of FerraraItalyItaly

SummarySummary●Short overview on Gamma-Ray Bursts Short overview on Gamma-Ray Bursts (GRBs)(GRBs)

●Delayed nucleation of Quark MatterDelayed nucleation of Quark Matter

●How to generate Gamma-Ray Bursts How to generate Gamma-Ray Bursts from deconfinementfrom deconfinement

●ConclusionsConclusionsAugust 2004 Irene Parenti

●Implication for the mass and radius of Implication for the mass and radius of compact stars compact stars

Gamma-Ray Bursts (GRBs)Gamma-Ray Bursts (GRBs)

Spatial distribution:Spatial distribution: isotropicisotropic

Distance:Distance: cosmological (1-10)∙10cosmological (1-10)∙1099 ly ly

Energy range:Energy range: 100 KeV – a few MeV100 KeV – a few MeV

Emitted energy:Emitted energy: 10105151 erg (beamed/jets) erg (beamed/jets)

Duration:Duration: (0,01-300) s(0,01-300) s

short GRBsshort GRBsfew ms – 2 sfew ms – 2 s

long GRBslong GRBs2 s – few 100 s2 s – few 100 sJ.S. Bloom, D.A. Frail, S.R. Kulkarni, ApJ 594, 2003J.S. Bloom, D.A. Frail, S.R. Kulkarni, ApJ 594, 2003


GRB and supernovaeGRB and supernovae

Connection between GRB and SupernovaeConnection between GRB and Supernovae

Evidence for atomic lines in the spectra Evidence for atomic lines in the spectra of the X-ray afterglowof the X-ray afterglow

time delay time delay ΔΔt between the Supernova t between the Supernova explosion and the Gamma-Ray Burst.explosion and the Gamma-Ray Burst.


Time delay from SN to GRBTime delay from SN to GRB

GRBGRB 990705990705 ΔΔT ≈ 10 yr T ≈ 10 yr

Amati et al., Science 290, 2000, 953Amati et al., Science 290, 2000, 953

GRBGRB 011211011211 ΔΔT ≈ 4 daysT ≈ 4 days

Watson et al., ApJ 595, 2003, L29Watson et al., ApJ 595, 2003, L29

GRBGRB 030227030227 ΔΔT ≈ 3-80 daysT ≈ 3-80 days

Reeves etal. , Nature 2002Reeves etal. , Nature 2002August 2004 Irene Parenti

A two-stages scenarioA two-stages scenario11stst explosion: explosion:

SUPERNOVASUPERNOVA(birth of a NS)(birth of a NS)

22ndnd “explosion”: “explosion”:

CENTRAL ENGINECENTRAL ENGINEOF THE GRBOF THE GRB (ass. with the NS)(ass. with the NS)

●What is the origin of the 2What is the origin of the 2ndnd “explosion”? “explosion”?●How to explain the long time delay How to explain the long time delay

between the two events?between the two events?

open open questionsquestions


A. Drago, A. Lavagno and G. PagliaraA. Drago, A. Lavagno and G. PagliaraPhys. Rev. D69 (2004) 057505Phys. Rev. D69 (2004) 057505

when color superconductivity is taken in to account:when color superconductivity is taken in to account:●The conversion process can be delayed due to the effects The conversion process can be delayed due to the effects of the surface tension between the HM phase and the QM of the surface tension between the HM phase and the QM phase.phase.

●The nucleation time depends drammatically on the central The nucleation time depends drammatically on the central pressure of the HS.pressure of the HS.

●As a critical-size drop of QM is formed the HS is As a critical-size drop of QM is formed the HS is converted to a QS or a HyS.converted to a QS or a HyS.

●The conversion process releases: EThe conversion process releases: Econv. conv. ≈ 10≈ 1052 52 - 10- 105353 erg erg

Delayed collapse of a HS to a QSDelayed collapse of a HS to a QSZ. Berezhiani, I. Bombaci, A. Drago, F. Frontera and Z. Berezhiani, I. Bombaci, A. Drago, F. Frontera and A. Lavagno ApJ. 586 (2003) 1250A. Lavagno ApJ. 586 (2003) 1250

Pure HSPure HS Hybrid Star or Quark StarHybrid Star or Quark Star

Possible central Possible central engine for GRBengine for GRB


The Quark-Deconfinement Nova The Quark-Deconfinement Nova modelmodel


Finite-size effectsFinite-size effects●The formation of a critical-size drop of QM is The formation of a critical-size drop of QM is not immediate. not immediate. It’s necessary to have an It’s necessary to have an overpressure overpressure to form a to form a droplet having a size large enough to overcome thedroplet having a size large enough to overcome theeffect of the surface tension.effect of the surface tension.

●A virtual droplet moves back and forth in the A virtual droplet moves back and forth in the potential energy well on a time scale:potential energy well on a time scale:

νν00-1-1~10~10-23-23 s « s « ττweakweak

quark-flavor must be conservedquark-flavor must be conservedduring the deconfinement during the deconfinement transition.transition.


virtual droplet ofvirtual droplet ofdeconfined quark deconfined quark

mattermatterstable phasestable phasewhen p overcomes the when p overcomes the

transition pointtransition point

Quark deconfinementQuark deconfinement

hadronic matter in ahadronic matter in ametastable statemetastable state

in a time in a time ττ

real droplet of real droplet of deconfined quark deconfined quark

mattermatterThis form of deconfined This form of deconfined matter has the same matter has the same flavor content of the flavor content of the ββ-stable hadronic system -stable hadronic system at the same pressure.at the same pressure.We call it: We call it: Q*-phaseQ*-phase..

Soon afterwards the weak interactions change the Soon afterwards the weak interactions change the quark flavor fraction to lower the energy.quark flavor fraction to lower the energy.

The drop grows with no The drop grows with no limitation.limitation.

real droplet of real droplet of strange matterstrange matter


Equation of StateEquation of State

Hadronic phaseHadronic phase:: Relativistic Mean Field Theory Relativistic Mean Field Theory of hadrons interacting via meson exch.of hadrons interacting via meson exch. [e.g. Glendenning, Moszkowsky, PRL 67(1991)][e.g. Glendenning, Moszkowsky, PRL 67(1991)]

Quark phaseQuark phase:: EOS based on the MIT bag model EOS based on the MIT bag model for hadronsfor hadrons.. [[Farhi, Jaffe, Phys. Rev. D46(1992)]Farhi, Jaffe, Phys. Rev. D46(1992)]

Mixed phaseMixed phase:: Gibbs construction for a multicom-Gibbs construction for a multicom-ponent system with two conserved “charges”.ponent system with two conserved “charges”.[Glendenning, Phys. Rev. D46 (1992)][Glendenning, Phys. Rev. D46 (1992)]


Hybrid star: mass-radiusHybrid star: mass-radiusB=136,36 MeV/fmB=136,36 MeV/fm33

Hybrid Star: configurationHybrid Star: configurationB=136,36 MeV/fmB=136,36 MeV/fm33

Strange Star: mass-radiusStrange Star: mass-radiusB=74,16 MeV/fmB=74,16 MeV/fm33

Strange Star: configurationStrange Star: configurationB=74,16 MeV/fmB=74,16 MeV/fm33

Quantum nucleation theoryQuantum nucleation theoryI.M. Lifshitz and Y. Kagan, Sov. Phys. JETP 35 (1972) 206I.M. Lifshitz and Y. Kagan, Sov. Phys. JETP 35 (1972) 206K. Iida and K. Sato, Phys. Rev. C58 (1998) 2538K. Iida and K. Sato, Phys. Rev. C58 (1998) 2538

Droplet potential energy:Droplet potential energy:

2323** 4

34)( RaRaRRnRU sVHQQ

nnQ*Q* baryonic number density baryonic number density in the Q*-phase at a in the Q*-phase at a fixed pressure P.fixed pressure P.μμQ*Q*,,μμHH chemical potentialschemical potentials at a fixed pressure P.at a fixed pressure P.σσ surface tension surface tension (=10,30 MeV/fm(=10,30 MeV/fm22))


Matter in the dropletMatter in the dropletFlavor fractions are theFlavor fractions are thesame of same of the the ββ-stable-stablehadronic system at thehadronic system at thesame pressure:same pressure:

The pressure needed forThe pressure needed forphase transition is much phase transition is much larger than that withoutlarger than that withoutflavor conservation.flavor conservation.


Nucleation timeNucleation timeThe The nucleation timenucleation time is the time needed to form is the time needed to form a critical droplet of deconfined quark matter.a critical droplet of deconfined quark matter.It can be calculated for different values of the It can be calculated for different values of the stellar central pressure (and then of the stellar stellar central pressure (and then of the stellar mass, as implied by TOV).mass, as implied by TOV).


The nucleation time dramatically depends The nucleation time dramatically depends on the value of the stellar central pressure on the value of the stellar central pressure and then on the value of the stellar mass.and then on the value of the stellar mass.

The critical mass of metastable HSThe critical mass of metastable HS●We fixed the time of nucleation at 1 yr.We fixed the time of nucleation at 1 yr.●The gravitational mass corresponding toThe gravitational mass corresponding to this nucleation time is called this nucleation time is called critical masscritical mass: :

)1( yrMM HScr

MMHS HS < M< Mcrcr HS are metastable with a HS are metastable with a long mean-life time.long mean-life time.

MMHSHS > M > Mcrcr This HS are very unlikely This HS are very unlikely toto be observed.be observed.

We assume that during the stellar conversion process We assume that during the stellar conversion process the total numbers of baryons in the star (and then the the total numbers of baryons in the star (and then the baryonic mass) is conserved.baryonic mass) is conserved. [I. Bombaci and B. Datta, ApJ. 530 (2000) L69][I. Bombaci and B. Datta, ApJ. 530 (2000) L69]

The gravitational mass of the final star The gravitational mass of the final star is taken to be the mass in the stable configu-is taken to be the mass in the stable configu-ration corresponding to that baryonic mass.ration corresponding to that baryonic mass.


Two families of compact starsTwo families of compact stars


Mass-Radius constraintsMass-Radius constraints●X-ray burster X-ray burster EXOEXO 0748-6760748-676[Cottam et al., Nature 420, 2002][Cottam et al., Nature 420, 2002]

z=0.35z=0.35

●X-ray pulsar X-ray pulsar 1E 1207.4-52091E 1207.4-5209[Sanwal et al.[Sanwal et al. ApJ 574, 2002, L61ApJ 574, 2002, L61]]

z=0.12-0.23z=0.12-0.23

●X-ray binary X-ray binary 4U 1728-344U 1728-34[Li et al. ApJ 527,1999,L51][Li et al. ApJ 527,1999,L51]

Very compact objectVery compact object

Mass-Radius constraintsMass-Radius constraints

Energy releasedEnergy releasedThe total energy released in the stellar conversionThe total energy released in the stellar conversionis given by the difference between the gravitational is given by the difference between the gravitational mass of the initial hadronic star (Mmass of the initial hadronic star (Minin=M=Mcrcr) and the ) and the mass of the final hybrid or strange stellar mass of the final hybrid or strange stellar configuration (Mconfiguration (Mfinfin=M=MQSQS(M(Mbb

crcr)):)):2)( cMME fininconv


The reaction that generate gamma-ray is:The reaction that generate gamma-ray is:

The efficence of this reaction in a strong The efficence of this reaction in a strong gravitational field is:gravitational field is:

[J. D. Salmonson and J. R. Wilson, ApJ 545 (1999) 859][J. D. Salmonson and J. R. Wilson, ApJ 545 (1999) 859]

How to generate GRBsHow to generate GRBs

2 ee

%10

The energy released is carried out by pairs The energy released is carried out by pairs of neutrinos – antineutrinos.of neutrinos – antineutrinos.

ergEE conv5251 1010


ConclusionsConclusions●Neutron stars (HS) are Neutron stars (HS) are metastablemetastable to to HS ―> QS or to HS ―> HySHS ―> QS or to HS ―> HyS

●EEconvconv ≈ 10 ≈ 105252 – 10 – 105353 erg erg GRBsGRBs

●Our model explains the connection and the Our model explains the connection and the time delay between SN and GRBs.time delay between SN and GRBs.

● possible existence of two different possible existence of two different families of compact stars:families of compact stars:

pure Hadronic Starspure Hadronic Stars Hybrid stars Hybrid stars oror Strange Stars Strange Stars


CollaboratorsCollaborators

●Dr.Dr. Ignazio BombaciIgnazio Bombaci●Dr.Dr. Isaac VidañaIsaac Vidaña Univ. of PisaUniv. of Pisa INFN of PisaINFN of Pisa


Ref: I. Bombaci, I. P., I. VidaRef: I. Bombaci, I. P., I. Vidaña ña arXiv:astro-ph/0402404arXiv:astro-ph/0402404 Astroph. J., acceptedAstroph. J., accepted

●Dr. Alessandro DragoDr. Alessandro Drago●Dr. Giuseppe PagliaraDr. Giuseppe Pagliara

Other collaborators:Other collaborators:

Univ. ofUniv. ofFerraraFerrara

INFN ofINFN ofFerraraFerrara

AppendixAppendix


●HADRONIC HADRONIC STARSSTARS (HS)(HS)

●HYBRID STARSHYBRID STARS (HyS)(HyS)

●STRANGE STARSSTRANGE STARS(SS or QS)(SS or QS)

Compact starsCompact stars

conventionalconventional neutron starsneutron stars

hyperon starshyperon stars


Probability of tunnelingProbability of tunneling

Quark deconfinement in compact stars:

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