Gamma-Ray-Bursts in Gamma-Ray-Bursts in Nuclear AstrophysicsNuclear Astrophysics

Giuseppe PagliaraGiuseppe Pagliara

Università di FerraraUniversità di Ferrara

Scuola di Fisica Nucleare “Raimondo Anni” Otranto 2006 Scuola di Fisica Nucleare “Raimondo Anni” Otranto 2006

OverviewOverview

• GRBs phenomenology GRBs phenomenology

• Theoretical models of the “inner engine” : Theoretical models of the “inner engine” : Collapsar Model vs Quark deconfinement Collapsar Model vs Quark deconfinement model model

Gamma-Ray Bursts (GRBs) Short (few seconds) bursts of Gamma-Ray Bursts (GRBs) Short (few seconds) bursts of 100keV- few MeV100keV- few MeV were discovered accidentally by were discovered accidentally by

Klebesadal Strong and Olson in 1967 Klebesadal Strong and Olson in 1967 using the Vela satellites using the Vela satellites

(defense satellites sent to monitor (defense satellites sent to monitor the outer space treaty). the outer space treaty).

The discovery was reported for the The discovery was reported for the first time only in 1973.first time only in 1973.

THE DISCOVERYTHE DISCOVERY

• There was an “invite prediction”. There was an “invite prediction”. S. Colgate was asked to predict S. Colgate was asked to predict GRBs as a scientific excuse for the GRBs as a scientific excuse for the launch of the Vela Satellites launch of the Vela Satellites

Duration 0.01-100sDuration 0.01-100s ~ 1 burst per day~ 1 burst per day Isotropic distribution Isotropic distribution - rate of ~2 rate of ~2

GpcGpc-3-3 yr yr-1 -1

~100keV photons~100keV photons Cosmological Origin (supposed)Cosmological Origin (supposed) The brightness of a GRB, The brightness of a GRB, E~10E~105252ergs,ergs,

is comparable to the brightness of the is comparable to the brightness of the

rest of the Universe combinedrest of the Universe combined..

BATSE EXPERIMENTBATSE EXPERIMENT

•Two classes:

1. Short: T90< 2 s,

harder

2. Long: T90> 2 s,

softer

DurationsDurations

Temporal structureTemporal structure

Three time scales:

Peaks intervals: secsec

Total durations: T = few tens of sT = few tens of s

Quiescent times: QT = tens of s QT = tens of s (see second part)

Single Single peak :FREDpeak :FRED

PrecursorsPrecursors•In 20% there is evidence In 20% there is evidence of emission above the of emission above the background coming from background coming from the same direction of the the same direction of the GRB. This emission is GRB. This emission is characterised by a softer characterised by a softer spectrum with respect to spectrum with respect to the main one and contains the main one and contains a small fraction (0.1 − 1%) a small fraction (0.1 − 1%) of the total event counts.of the total event counts.

•typical delays of several typical delays of several tens of seconds extending tens of seconds extending (in few cases) up to 200 (in few cases) up to 200 seconds. Their spectra are seconds. Their spectra are typically non-thermal typically non-thermal power-law. Such long power-law. Such long delays and the non-thermal delays and the non-thermal origin of their spectra are origin of their spectra are hard to reconcile with any hard to reconcile with any model for the progenitor.model for the progenitor. (Lazzati 2005)(Lazzati 2005)

SpectrumSpectrum

non-thermal spectrum !

Very high energy tail, up to GeV !

Band functionBand function

Compactness problemCompactness problem sec sec maximum maximum ssize of the sourceize of the source R R cc = 3 10 = 3 109 9

cm.cm.

EE 10 105151ergs.ergs.

Due to the large photon density and energyDue to the large photon density and energyee++ee--

= = nn R R 10101515 V Very large optical depth !ery large optical depth !

Expected thermal spectrum and no high energy Expected thermal spectrum and no high energy photonsphotons

? ?? ?

RR

cmcm22

Need of relativistic motionNeed of relativistic motion

ΔR ΔR ΔR 2c 2c 22

blue shift: blue shift: EEphph (obs) = (obs) = E Ephph (emitted) (emitted)

NN(E)dE=E(E)dE=E--dE correction dE correction -2-2+2+2

TTo haveo have <<11

GRBs are the most relativistic objects known todayGRBs are the most relativistic objects known today

= = nn RR

T=T=R/v - R/v - R/cR/c

The Internal-External Fireball ModelThe Internal-External Fireball Model

Internal shocks can convert only a Internal shocks can convert only a fractionfraction of the kinetic energy to of the kinetic energy to radiationradiation

It should be followed by additional It should be followed by additional emissionemission..

Internal shocks between

shell with different

Emission mechanismEmission mechanismPrompt emission: Synctrotron – Inverse Compton … ?Prompt emission: Synctrotron – Inverse Compton … ?

synctrotronsynctrotron High energy photonsHigh energy photons

Some interesting correlationsSome interesting correlations

isotropic-equivalent peak luminosities isotropic-equivalent peak luminosities L of these bursts positively correlate L of these bursts positively correlate with a rigorously-constructed measure with a rigorously-constructed measure of the variability of their light curvesof the variability of their light curves

(Reichart et al 2001)(Reichart et al 2001)

The spectral evolution timescale The spectral evolution timescale of pulse structures is of pulse structures is anticorrelated with peak anticorrelated with peak luminosityluminosity

(Norris et al 2000)(Norris et al 2000)

Still unexplained Still unexplained !!

SAX EXPERIMENTSAX EXPERIMENT The Italian/Dutch The Italian/Dutch satellitesatellite BeppoSAXBeppoSAX discovered x-ray afterglowdiscovered x-ray afterglow on 28 February 1997on 28 February 1997 (Costa et. al. 97)(Costa et. al. 97). .

Immediate discovery of Immediate discovery of OpticalOptical afterglow afterglow (van Paradijs et. al 97).(van Paradijs et. al 97).

Afterglow: Afterglow: slowing down of relativistic flow and slowing down of relativistic flow and synchrotron emission fit the data to a large extentsynchrotron emission fit the data to a large extent

Panaitescu et al APJ 2001Panaitescu et al APJ 2001

Beaming of GRB Beaming of GRB

1/

If the GRB is collimated If the GRB is collimated

Relativistic beaming effectRelativistic beaming effect

Corrected Energy =(1-cosCorrected Energy =(1-cos)E)Eisoiso~10~105151ergsergs

decreases with timedecreases with time

GRB990510GRB990510

Redshift from the afterglowRedshift from the afterglow

Optical counternpart- absorption linesOptical counternpart- absorption lines

1+z= 1+z= obsobs/ / emitemit

z=0.83z=0.83

Confirm the cosmological Confirm the cosmological origin and the large amount origin and the large amount of energy, galaxies star of energy, galaxies star forming regions forming regions ddz z 10 109 9 light yearslight years

GRB970508GRB970508

Metzger et al Nature 1997Metzger et al Nature 1997

SN-GRB connectionSN-GRB connectionSN 1998bw/GRB 980425

““spatial (within a few spatial (within a few arcminutes) and temporal arcminutes) and temporal (within one day) consistency (within one day) consistency with the optically and with the optically and exceedingly radio bright exceedingly radio bright supernova 1998bw”supernova 1998bw”

(Pian et al ApJ 2000)(Pian et al ApJ 2000)

a group of small faint sourcesa group of small faint sources

““Absorption Absorption x–ray emission of x–ray emission of GRB 990705. This feature GRB 990705. This feature can be modeled by a can be modeled by a medium located at a medium located at a redshift of 0.86 and with redshift of 0.86 and with an iron abundance of 75 an iron abundance of 75 times the solar one. The times the solar one. The high iron abundance found high iron abundance found points to the existence of a points to the existence of a burst environment burst environment enriched by a supernova enriched by a supernova along the line of sight”…along the line of sight”…

““The supernova explosion The supernova explosion is estimated to have is estimated to have occurred about 10 years occurred about 10 years before the burst “before the burst “

(Amati et al, Science (Amati et al, Science 2000)2000)

Spectroscopic “evidences”Spectroscopic “evidences”

GRB991216, Piro et al Nature 2001GRB991216, Piro et al Nature 2001

““We report on the discovery of We report on the discovery of two emission features observed in two emission features observed in the X-ray spectrum of the the X-ray spectrum of the afterglow of the gamma-ray burst afterglow of the gamma-ray burst (GRB) of 16 Dec. 1999 by the (GRB) of 16 Dec. 1999 by the Chandra X-Ray Observatory… Chandra X-Ray Observatory… ions of iron at a redshift z = ions of iron at a redshift z = 1.00±0.02, providing an 1.00±0.02, providing an unambiguous measurement of unambiguous measurement of the distance of a GRB. Line width the distance of a GRB. Line width and intensity imply that the and intensity imply that the progenitor of the GRB was a progenitor of the GRB was a massive star system that ejected, massive star system that ejected, before the GRB event, 0.01Mbefore the GRB event, 0.01Msun sun of of iron at 0.1c”iron at 0.1c”……the simplest explanation of our the simplest explanation of our results is a mass ejection by the results is a mass ejection by the progenitor with the same velocity progenitor with the same velocity implied by the observed line implied by the observed line width. The ejection should have width. The ejection should have then occurred R/v = then occurred R/v = (i.e., a few (i.e., a few months) before the GRB.months) before the GRB.

““The X-ray spectrum reveals evidence for The X-ray spectrum reveals evidence for emission lines of Magnesium, Silicon, emission lines of Magnesium, Silicon, Sulphur, Argon, Calcium, and possibly Sulphur, Argon, Calcium, and possibly Nickel, arising in enriched material with an Nickel, arising in enriched material with an outflow velocity of order 0.1c. …outflow velocity of order 0.1c. …

The observations strongly favour models The observations strongly favour models where a supernova explosion from a where a supernova explosion from a massive stellar progenitor precedes the massive stellar progenitor precedes the burst event and is responsible for the burst event and is responsible for the outflowing matter…. delay between an outflowing matter…. delay between an initial supernova and the onset of the initial supernova and the onset of the gamma ray burst is required, of the gamma ray burst is required, of the order several months”. order several months”.

(Reeves et al., Nature 2001)(Reeves et al., Nature 2001)

Still debated !

Still debated !

Hjorth et al Nature 2003Hjorth et al Nature 2003

Typical afterglow Typical afterglow power-low spectrumpower-low spectrum

SN spectrumSN spectrum

““Here we report evidence that a Here we report evidence that a very energetic supernova (a very energetic supernova (a hypernova) was temporally and hypernova) was temporally and spatially coincident with a GRB at spatially coincident with a GRB at redshift redshift z z = = 0.1685. The timing of 0.1685. The timing of the supernova indicates that it the supernova indicates that it exploded within a few days of the exploded within a few days of the GRB”GRB”

HETE IIHETE II

Simultaneous Simultaneous measurements in measurements in X UV X UV

Afterglows of SGRBAfterglows of SGRB

SWIFT EXPERIMENTSWIFT EXPERIMENT

No association No association with SN with SN probably NS-probably NS-NS, NS-BHNS, NS-BH

12.8 Gyr12.8 Gyr

GRBs as standard candles to study CosmologyGRBs as standard candles to study Cosmology

correlation between the peak of the –correlation between the peak of the –ray spectrum Epeak and the collimation ray spectrum Epeak and the collimation corrected energy emitted in –rays. The corrected energy emitted in –rays. The latter is related to the isotropically latter is related to the isotropically equivalent energy E,iso by the value of equivalent energy E,iso by the value of the jet aperture angle. The correlation the jet aperture angle. The correlation itself can be used for a reliable itself can be used for a reliable estimate of E,iso, making GRBs estimate of E,iso, making GRBs distance indicatorsdistance indicators

Ghirlanda et al APJ 2004Ghirlanda et al APJ 2004

supernovaesupernovae

GRBGRB

ConclusionsConclusions•Afterglow:good understanding Afterglow:good understanding (external shocks), collimation. Orphan (external shocks), collimation. Orphan afterglow?afterglow?

•Prompt emission: good “description” Prompt emission: good “description” of temporal structure (internal of temporal structure (internal shocks), still not completely shocks), still not completely understood the mechanism. High understood the mechanism. High energy photons, neutrinos?energy photons, neutrinos?

•High redshift and SN-GRB connectionHigh redshift and SN-GRB connection

•What about the inner engine? See What about the inner engine? See next lecture next lecture

INNER ENGINE OF INNER ENGINE OF GRBsGRBs

• Huge energy:Huge energy: E~10E~105252ergs (10ergs (1051 51 bbeamingeaming))

• Provide adequate energy at high Lorentz Provide adequate energy at high Lorentz factorfactor

• TTime scales: total duration few tens of ime scales: total duration few tens of second, variability <0.1s, quiescent timessecond, variability <0.1s, quiescent times

• SN(core collapse)-GRB connection SN(core collapse)-GRB connection

REQUIREMENTS:REQUIREMENTS:

The Collapsar modelThe Collapsar model

Collapsars (WoosleyCollapsars (Woosley 1993 1993))

• Collapse of a massive (WR) Collapse of a massive (WR) rotating star that does not rotating star that does not form a successful SN to a BH form a successful SN to a BH ((MMBH BH ~~ 3 3MMsolsol ) surrounded by ) surrounded by a thick accretion disk. The a thick accretion disk. The hydrogen envelope is lost by hydrogen envelope is lost by stellar winds, interaction stellar winds, interaction with a companion, etc.with a companion, etc.

• The viscous accretion onto The viscous accretion onto the BH strong heating the BH strong heating thermal thermal ̃̃ annihilating annihilating preferentially around the preferentially around the axis .axis .

Outflows are collimated by Outflows are collimated by passing through the stellar passing through the stellar mantle. mantle.

+ Detailed numerical + Detailed numerical analysis of jet analysis of jet formation.formation.

Fits naturally in a Fits naturally in a general scheme general scheme describing collapse of describing collapse of massive stars.massive stars.

--

SN – GRB time delay: less SN – GRB time delay: less then 100 s.then 100 s.

jj1616 = j/(10 = j/(101616 cm cm22 s s−1−1), j), j1616 <3, <3, material falls into the black material falls into the black hole almost uninhibited. No hole almost uninhibited. No outflows are expected. For joutflows are expected. For j1616 > 20, the infalling matter is > 20, the infalling matter is halted by centrifugal force halted by centrifugal force outside 1000 km where outside 1000 km where neutrino losses are negligible. neutrino losses are negligible. For 3 < jFor 3 < j1616 < 20, however, a < 20, however, a reasonable value for such reasonable value for such stars, a compact disk forms at stars, a compact disk forms at a radius where the a radius where the gravitational binding energy gravitational binding energy can be efficiently radiated as can be efficiently radiated as neutrinos.neutrinos.

The Quark-Deconfinement Nova modelThe Quark-Deconfinement Nova model

I.M. Lifshitz and Y. Kagan, Sov. Phys. JETP 35 (1972) 206I.M. Lifshitz and Y. Kagan, Sov. Phys. JETP 35 (1972) 206

K. Iida and K. Sato, Phys. Rev. C58 (1998) 2538K. Iida and K. Sato, Phys. Rev. C58 (1998) 2538

I.M. Lifshitz and Y. Kagan, Sov. Phys. JETP 35 (1972) 206I.M. Lifshitz and Y. Kagan, Sov. Phys. JETP 35 (1972) 206

K. Iida and K. Sato, Phys. Rev. C58 (1998) 2538K. Iida and K. Sato, Phys. Rev. C58 (1998) 2538

Droplet potential energy:Droplet potential energy:Droplet potential energy:Droplet potential energy:

2323** 4

3

4)( 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))

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))

Quantum nucleation theoryQuantum nucleation theory

Delayed formation of quark Delayed formation of quark matter in Compact Starsmatter in Compact Stars

Quark matter cannot appear before the Quark matter cannot appear before the PNS has deleptonized (Pons et al 2001)PNS has deleptonized (Pons et al 2001)

Quark droplet nucleation timeQuark droplet nucleation time“mass filtering”“mass filtering”

Critical mass for = 0 B1/4 = 170 MeV

Mass accretion

Critical mass for= 30 MeV/fm2

B1/4 = 170 MeV

Age of the Universe!

Two families of CSsTwo families of CSs

Conversion from HS Conversion from HS to HyS (QS) with the to HyS (QS) with the same Msame MBB

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

The efficency of this reaction in a strong gravitational field is:The efficency of this reaction in a strong 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]

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

The efficency of this reaction in a strong gravitational field is:The efficency of this reaction in a strong 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 (in the The energy released (in the strong deflagrationstrong deflagration) is carried out by ) is carried out by neutrinos and antineutrinos.neutrinos and antineutrinos.The energy released (in the The energy released (in the strong deflagrationstrong deflagration) is carried out by ) is carried out by neutrinos and antineutrinos.neutrinos and antineutrinos.

ergEE conv5251 1010

Hadronic Stars Hadronic Stars Hybrid or Quark Stars Hybrid or Quark StarsZ.Berezhiani, I.Bombaci, A.D., F.Frontera, A.Lavagno, ApJ586(2003)1250Z.Berezhiani, I.Bombaci, A.D., F.Frontera, A.Lavagno, ApJ586(2003)1250

Drago, Lavagno Pagliara 2004, Bombaci Parenti Vidana 2004…Drago, Lavagno Pagliara 2004, Bombaci Parenti Vidana 2004…

Metastability due to delayed production of Quark Matter .Metastability due to delayed production of Quark Matter .

1) conversion to Quark Matter (it is NOT a detonation (see Parenti ))1) conversion to Quark Matter (it is NOT a detonation (see Parenti ))

2) cooling (neutrino emission) 2) cooling (neutrino emission)

3) neutrino – antineutrino annihilation 3) neutrino – antineutrino annihilation

4)(possible) beaming due to strong magnetic field and star rotation4)(possible) beaming due to strong magnetic field and star rotation

++ Fits naturally into a scheme describing QM production. Fits naturally into a scheme describing QM production.

Energy and duration of the GRB are OK.Energy and duration of the GRB are OK.

- - No calculation of beam formation, yet.No calculation of beam formation, yet.

SN – GRB time delay: minutes SN – GRB time delay: minutes years years

depending on mass accretion ratedepending on mass accretion rate

Temporal structure of Temporal structure of GRBsGRBs

… … back to the databack to the data

ANALYSIS of the distribution of peaks intervalsANALYSIS of the distribution of peaks intervals

Lognormal distribution

“… the quiescentthe quiescenttimes are made by a different times are made by a different

mechanism mechanism then the rest of the intervals”then the rest of the intervals”

Nakar and Piran 2002Nakar and Piran 2002

Lognormal distributionLognormal distribution

Central limit theoremCentral limit theorem

Drago & Pagliara Drago & Pagliara 20052005

Excluding QTs

Deviation from lognorm & power law tail (slope = -1.2)

Probability to find more than 2 QT in the same burst

Analysis on 36 bursts having long QT (red dots): the subsample is not Analysis on 36 bursts having long QT (red dots): the subsample is not anomalousanomalous

Analysis of PreQE and PostQEAnalysis of PreQE and PostQE

Same “variability”: the same emission mechanism, Same “variability”: the same emission mechanism, internal shocks internal shocks

Same dispersions but Same dispersions but different average durationdifferent average duration

PreQE: PreQE: 10s10s

PostQE:PostQE:~20s~20s

QTs:~ 50s QTs:~ 50s

Three characterisitc Three characterisitc time scalestime scales

No evidence of a continuous No evidence of a continuous time dilationtime dilation

Interpretation:Interpretation:

1)Wind modulation 1)Wind modulation model: during QTs no model: during QTs no collisions between the collisions between the emitted shellsemitted shells

2) Dormant inner engine 2) Dormant inner engine during the long QTs during the long QTs

Huge energy Huge energy requirementsrequirements

No explanation for No explanation for the different time the different time scalesscales

It is likely for short It is likely for short QTQT

Reduced energy Reduced energy emissionemission

Possible explanation Possible explanation of the different time of the different time scales in the Quark scales in the Quark deconfinement model deconfinement model

It is likely for long QTIt is likely for long QT

… … back to the theoryback to the theoryIn the first version of the Quark In the first version of the Quark

deconfinement model only the MIT bag EOS deconfinement model only the MIT bag EOS was consideredwas considered

……butbut

in the last 8 years, the study of the QCD phase diagram in the last 8 years, the study of the QCD phase diagram revealed the possible existence of Color revealed the possible existence of Color

Superconductivity at “small” temperature and large Superconductivity at “small” temperature and large densitydensity

High density: Color flavor High density: Color flavor lockinglocking

Gap equation solutionsGap equation solutions

~

From perturbative QCD at high density: attractive interaction among From perturbative QCD at high density: attractive interaction among u,d,s Cooper pairs having binding energies u,d,s Cooper pairs having binding energies 100 MeV 100 MeV

At low densitity,NJL-type Quark At low densitity,NJL-type Quark modelmodel

BCS theory of SuperconductivityBCS theory of Superconductivity

CFL pairing CFL pairing patternpattern

Vanishing mass for s !Vanishing mass for s !

(Alford Rajagopal Wilczek (Alford Rajagopal Wilczek 1998)1998)

Modified MIT Modified MIT bag model for bag model for

quarksquarks

Hadron-Quark first order phase transition and Mixed PhaseHadron-Quark first order phase transition and Mixed Phase

For small value of mFor small value of mssit is it is still convenient to have still convenient to have equal Fermi momenta for equal Fermi momenta for all quarks (Rajagopal all quarks (Rajagopal Wilczek 2001)Wilczek 2001)

Binding energy density of quarks near Binding energy density of quarks near Fermi surface Fermi surface VN VN 2 2 22

Intermediate densityIntermediate density

Chiral symmetry Chiral symmetry breaking at low densitybreaking at low density

MMss increases too much increases too much andand

is not respectedis not respected

No more CFL pairing ! No more CFL pairing ! KKFuFu KKFsFs

More refined calculationsMore refined calculations

Two first order phase transitions:

Hadronic matter Unpaired Quark Matter(2SC) CFL

CFL cannot appear until CFL cannot appear until the star has deleptonizedthe star has deleptonized

Ruster et al hep-ph/0509073Ruster et al hep-ph/0509073

Double GRBs generated by double phase Double GRBs generated by double phase transitionstransitions

Two steps (same barionic mass):Two steps (same barionic mass):

1)1) transition from hadronic matter to transition from hadronic matter to unpaired or 2SC quark matter. unpaired or 2SC quark matter. “Mass filtering”“Mass filtering”

2) The mass of the star is now fixed. 2) The mass of the star is now fixed. After strangeness production, After strangeness production, transition from 2SC to CFL quark transition from 2SC to CFL quark matter. Decay time scale matter. Decay time scale ττ few tens few tens of second of second

Nucleation time of CFL phaseNucleation time of CFL phase

Energy releasedEnergy released

Energy of the second transition larger than the first Energy of the second transition larger than the first transition due to the large CFL gap (100 MeV)transition due to the large CFL gap (100 MeV)

Bombaci, Lugones, Vidana Bombaci, Lugones, Vidana 20062006

Drago, Lavagno, Pagliara Drago, Lavagno, Pagliara 20042004

… … a very recent M-R a very recent M-R analysisanalysis

Color superconductivity (and other Color superconductivity (and other effects ) must be included in the quark effects ) must be included in the quark

EOSs !!EOSs !!

Other possible signaturesOther possible signatures

For a single Poisson processFor a single Poisson process

Variable ratesVariable rates

SOLAR FLARESSOLAR FLARES

Power law distribution for Solar flares Power law distribution for Solar flares waiting times (waiting times (Wheatland APJ 2000Wheatland APJ 2000))

The initial masses of The initial masses of the compact stars are the compact stars are distributed near Mdistributed near Mcrit, crit,

different central desity different central desity and nucleation times and nucleation times

of the CFL phase f(of the CFL phase f((M))(M))

Could explain Could explain the power law the power law

tail of long tail of long QTs ?QTs ?

Origin of power law:Origin of power law:

Are LGRBs Are LGRBs signals of the signals of the

successive successive reassesments of reassesments of Compact stars?Compact stars?

Low density: Hyperons - Kaon condensates…Low density: Hyperons - Kaon condensates…

ConclusionsConclusions

• A “standard model” the A “standard model” the Collapsar modelCollapsar model

• One of the alternative model: One of the alternative model: the quark deconfinement the quark deconfinement modelmodel

• Possibility to connect GRBs and Possibility to connect GRBs and the properties of strongly the properties of strongly interacting matter! interacting matter!

Appendici

Probability of tunneling