The scenario of two families of compact stars 2. Transition from hadronic to quark matter and explosive phenomena
aa r X i v : . [ a s t r o - ph . S R ] D ec EPJ manuscript No. (will be inserted by the editor)
The scenario of two families of compact stars
2. Transition from hadronic to quark matter and explosive phenomena
Alessandro Drago and Giuseppe Pagliara
Dip. di Fisica e Scienze della Terra dell’Universit`a di Ferrara and INFN Sez. di Ferrara, Via Saragat 1, I-44100 Ferrara, ItalyReceived: date / Revised version: date
Abstract.
We will follow the two-families scenario described in the accompanying paper, in which compactstars having a very small radius and masses not exceeding about 1.5 M ⊙ are made of hadrons, while moremassive compact stars are quark stars. In the present paper we discuss the dynamics of the transition ofa hadronic star into a quark star. We will show that the transition takes place in two phases: a very rapidone, lasting a few milliseconds, during which the central region of the star converts into quark matterand the process of conversion is accelerated by the existence of strong hydrodynamical instabilities, anda second phase, lasting about ten seconds, during which the process of conversion proceeds as far as thesurface of the star via production and diffusion of strangeness. We will show that these two steps play acrucial role in the phenomenological implications of the model. We will discuss the possible implicationsof this scenario both for long and for short Gamma Ray Bursts, using the proto-magnetar model as thereference frame of our discussion. We will show that the process of quark deconfinement can be connectedto specific observed features of the GRBs. In the case of long GRBs we will discuss the possibility thatquark deconfinement is at the origin of the second peak present in quite a large fraction of bursts. Also wewill discuss the possibility that long GRBs can take place in binary systems without being associated witha SN explosion. Concerning short GRBs, quark deconfinement can play the crucial role in limiting theirduration. Finally we will shortly revisit the possible relevance of quark deconfinement in some specific typeof Supernova explosions, in particular in the case of very massive progenitors. PACS.
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In the accompanying paper (here and in the followingpaper 1) we have discussed the two-families scenario, inwhich compact stars having a mass not exceeding about1.5 M ⊙ are made of hadrons, while the most massivecompact stars are entirely made of quarks, i.e. they arequark stars [1]. We have also discussed the interestingmass range, located about (1 . − . M ⊙ , which can bepopulated both by hadronic and by quark stars. The lat-ters have a significantly larger radius and a larger momentof inertia. This scenario is somehow opposite respect to themore traditional one in which quark stars are extremelycompact with radii even smaller than about 10 km.In this second paper we discuss how the transition froma hadronic star into a quark star can take place and whichare the phenomenological implications of that transition.First, by looking at the plot of the two families alreadydiscussed in the accompanying review paper on the EoSone can recognize the possible situations in which quarkmatter and therefore quark stars can form. There are es-sentially three situations: Send offprint requests to : – via mass accretion or via slowing-down of a rapidly ro-tating pulsar, having a mass close to the critical one.This situation can for instance be realized in LMXBs,in which the neutron star accretes mass and angularmomentum from the companion. Under those condi-tions the critical deconfinement density can be reached(maybe more easily soon after the mass accretion stopsand the star starts slowing-down [2]). In these casesthe temperature immediately before deconfinement isquite low and plays no role. We will link this scenarioto the possibility of having long GRBs not connectedwith a SN explosion. See also the possible signature ofthe transition in the anomalous value of the eccentric-ity, as discussed in paper 1; – soon after the SN explosion of a massive progenitor.It is possible that a delay exists between the momentthe SN explodes and the moment quark deconfinementtakes place: it can be due again to the gradual slow-down of the neutron star or to mass accretion dueto the fall-back. This scenario can be linked to longGRBs displaying two active periods separated by aquiescent time. The possibility that the neutrino fluxgenerated by the phase transition can help revitalizing Alessandro Drago, Giuseppe Pagliara: The scenario of two families of compact stars a marginally failed SN explosion is not ruled out either.In this case the temperature before deconfinement canbe larger, order of 20-30 MeV. Although these tem-peratures can facilitate quark deconfinement they stillshould not play a crucial role; – after the merging of two neutron stars in a binary sys-tem. If a massive compact star forms immediately afterthe merging, in our scheme that star is unavoidably aquark star. This is maybe the most precise and strik-ing signature of the two-families scenario. Since thesemergers are supposed to be at the origin of short GRBswe expect to see rather clear signatures of the forma-tion of a quark star in the features of those GRBs.Also, the emission in gravitational waves associatedwith the process of merging should bear the imprintof the transition from the hadronic EoS to the quarkEoS (see the review paper by Bauswein et al. of thisvolume). In the process of merging very high temper-atures are reached (up to about 50 MeV [3] and evenlarger if the heat released by quark’s deconfinementis taken into account) and we will see that they playquite a significant role in the phenomenology.. The most important point about the microphysics ofthe transition from hadronic matter to quark matter con-cerns under which conditions the process of deconfinementcan start taking place. The very beginning of the processis the formation of a droplet of quark matter, stable atthe pressure at which it forms. In the two-families sce-nario that we are discussing the formation of quark starsdepends on the validity of the Bodmer-Witten hypothe-sis on the absolute stability of strange quark matter [4,5].If strange quarks play a role in the stability of the firstdroplet than it is clear that the process of deconfinementcannot start unless some strangeness content already ex-ists in the hadronic phase (we will come back to this pointwhen discussing the possible impact of quark deconfine-ment on SN explosions). Statistical fluctuations of the fla-vor composition of a small amount of matter can facil-itate the formation of an energetically favorable dropletof quark matter even if the average strangeness contentis not (yet) the optimal one (more strangeness can formlater if the droplet can live long enough that weak interac-tions can take place). On the other hand, if the hadronicphase does not contain any strangeness, either in the formof hyperons or in the form of condensed kaons, then adroplet of quark matter with a non-vanishing strangenesscontent cannot form on the time-scale of strong interac-tion, which is the one associated with the fluctuations ofhadrons into deconfined quarks [6]. We therefore assumethat the minimal value for the critical density correspondsto the one at which hyperons (or kaons) start forming.While this density is well defined at zero temperature, atfinite temperature hyperons form at any density, althoughtheir fractional density is very small at low temperaturesand low densities. The exact conditions at which the firstdroplet of stable strange quark matter can form at finitetemperature are complicated. A first attempt in exploringthat problem has been made in a few papers [7,8,9], but it will likely require more investigations to be completelyclarified. We will not discuss in details the process of for-mation of the first droplet of quark matter, because it isanalyzed in the papers of Lugones and Bombaci et al. ofthis volume.The whole process of quark deconfinement in a stellarobject can be divided in different steps: – via quantum fluctuations (if the temperature of thesystem is low) or thermal fluctuations (if the temper-ature is large) a first droplet of quark matter forms,large enough to keep expanding; – the droplet keeps expanding (or it merges with otherdroplets) till its size becomes macroscopic. This secondstep has, to our knowledge, never been analyzed; – the further expansion of the macroscopic bubble ofquark matter inside the hadronic star can be describedby using hydrodynamical equations and it divides intotwo sub-steps [10]: – a rapid burning, whose velocity is greatly augmentedby hydrodynamical instabilities. It lasts only a fewmilliseconds and it burns the central area of thestar; – a slow burning, due to production and diffusion ofstrangeness, lasting some ten seconds and trans-forming the star into a quark star.As we will see, the final process of burning can de-pend on the mass of the star to be transformed into aquark star and on its initial temperature. Two sub-cases,at least, need to be discussed: the case in which the massof the deconfining star is about (1.4-1.5) M ⊙ , the typicalsituation of deconfinement of a single star via mass accre-tion, and the case of deconfinement immediately after themerging of two compact stars in a binary system, forminga new compact object with a mass exceeding 2 M ⊙ . Inthis second case the temperature is quite larger and thiswill have important phenomenological implications. Since the formulation of the Bodmer-Witten hypothesis[4,5] and its implication on the existence of compact starsentirely composed by quark matter [11,12], the process ofconversion of hadronic stars into quark stars has been thesubject of many theoretical investigations. At the micro-scopic level this process is extremely complicated becauseit involves the deconfinement of quarks (driven by thestrong interaction) and flavor changing reactions amongquarks (driven by the weak interaction). In particular theprocess of deconfinement is clearly the most complicateddue to its non-perturbative nature. The simple kinetic the-ory approach proposed in Ref. [13] is still one of the mostwidely used: the conversion is described as a slow combus-tion by means of a one dimensional stationary reaction-diffusion-advection equation for the strange quarks con-centration. The two key quantities in this approach arethe quark diffusion coefficient D ( D ∼ − cm /sec for µ q ∼
300 MeV and T ∼
10 MeV [14]) and the time of con-version of down quarks into strange quarks τ ( τ ∼ − lessandro Drago, Giuseppe Pagliara: The scenario of two families of compact stars 3 sec for µ q ∼
300 MeV [15]). By simple dimensional anal-ysis (see [16]) one can obtain an estimate of the widthof the combustion zone δ ∼ √ Dτ ∼ − cm and of theburning velocity v ∼ p D/τ ∼ − cm/sec.Within the kinetic theory approach of [13] one doesnot take into account possible macroscopic collective flowsand hydrodynamical instabilities driven by pressure anddensity gradients between the fuel and the ashes fluids.On the other hand, in the context of type Ia Supernovae,in which the nuclear burning occurs, the Rayleigh-Taylorand the Landau-Darrieus instabilities have been provento turn the laminar combustion into a much faster tur-bulent combustion [17,18]. In principle one should couplethe equations of hydrodynamics (i.e. the equations of con-servation of baryon number, momentum and energy) andthe equation of conservation of chemical species (whichincludes the diffusion and the reaction rates within thecombustion zone) in multidimensional numerical simula-tions, see [19]. Due to the small width of the combustionzone in comparison with the radius of the star such a sim-ulation is clearly numerically unfeasible.In Ref. [10] it has been argued that such complicatedsimulations actually are not needed. Indeed one can dividethe process of conversion of a hadronic star into a quarkstar into two separated regimes: i) the turbulent regimewhich can be described by hydrodynamics under the as-sumption of an infinitely thin combustion zone; ii) the dif-fusive regime in which the two fluids, fuel and ashes are inmechanical equilibrium, but out of chemical equilibrium.This regime is described by an advection diffusion reactionequation. The separation between the two regimes can befound by imposing the so called Coll’s condition [20,21]on the thermodynamical variables of the two fluids as wewill explain in the following. The turbulent regime can be described within a purely hy-drodynamical approach in which the combustion zone isso thin to be considered as a surface of discontinuity, theso called flame front . We will follow the treatment of Refs.[20,21] where classical combustion theory has been gener-alized to the framework of relativistic hydrodynamics. Weindicate with p i , e i , n i , w i = e i + p i and X i = ( e i + p i ) /n i the pressure, energy density, baryon density, enthalpy den-sity and dynamical volume of fluid i . As in the case of thediscontinuity associated with a shock wave, also in the caseof the flame front one imposes the continuity equations forthe fluxes of baryon number, momentum and energy. Byindicating with j the number of baryons ignited per unittime and unit area of the flame front, the thermodynami-cal quantities of the hadronic fluid and of the quark fluidare related to each other by the following equations: n h u h = n q u q = j (1)( p q − p h ) / ( X h − X q ) = j (2) w h ( p h , X h ) X h − w q ( p q , X q ) X q = ( p h − p q )( X h + X q )(3) X p X Coll’s condition fulfilled A Coll’s condition not fulfilled
AO O’B’B B’ B
Fig. 1.
Illustrative plot of the detonation adiabat in the case inwhich the Coll’s condition is fulfilled (left panel) or not (rightpanel). A, B, B’ indicate respectively the initial hadronic stateand two possible final states for the quark phase. O and O’ arethe Chapman-Jouget points. Figure taken from [10]. the last equation is the so-called relativistic detonationadiabat. u h and u q are the four-velocities of hadronic andquark matter in the flame front rest frame. If one startsfrom hadronic matter in a initial state A: p h = p A and X h = X A and with a given value of j , Eqs. 1-3 allowto determine the final state B of quark matter, p q = p B and X q = X B which belongs to the detonation adiabat.The second equation represents a straight line in the (p,X)plane passing through A and with angular coefficient equalto − j . The intersections of this line with the detonationadiabat allow to find the state B of quark matter. Thevalue of j cannot be expressed in terms of the thermody-namical variables of the two fluids. It depends in generalon the transport properties of the two fluids (the thermalconductivity and the diffusion coefficient) and the rateof chemical reactions. Therefore it must be determinedwithin a kinetic theory approach such as the one of Ref.[13].The so-called “condition for exothermic combustion”(“Coll’s condition”) for the conversion of fluid 1 into fluid2 reads: e ( p, X ) > e ( p, X ), i.e. at fixed pressure and dy-namical volume, the energy density of fluid 1, the fuel,must be larger then the one of fluid 2, the ash. As shownin Ref. [22,10] if this condition is fulfilled the state A ofthe hadronic phase lies in the region of the (p,X) planebelow the detonation adiabat (see left panel of Fig. 1).As a consequence, there exist two values of j , j O and j O ′ , for which the lines passing through A are tangentto the detonation adiabat. The two points of tangencyare the Chapman-Jouget points. In particular, point Ocorresponds to the Chapman-Jouget detonation and it isthe only possible realization of detonation in a physicalsystem, such a compact star, in which no external forceis producing the shock wave, see [16]. If the Coll’s condi-tion is not fulfilled one cannot define the Chapman-Jougetpoints and the detonation combustion mode cannot takeplace. Alessandro Drago, Giuseppe Pagliara: The scenario of two families of compact stars
Coll’s condition is important also to establish whetherthe deflagration combustion mode can take place. Let usconsider the simplest case of a slow combustion for whichthe velocities v h and v q are much smaller than the soundvelocities c h and c q of the two fluids. By using Eqs.(1-3) one finds in this regime that p h = p A = p q = p B ′ and ( e A + p A ) /n A = ( e B ′ + p A ) /n B ′ , i.e. the enthalpy perbaryon is conserved during the combustion (see [16] for thecase of non-relativistic hydrodynamics). Coll’s conditionimplies that X ′ B > X A i.e. ( e B ′ + p A ) /n B ′ > ( e A + p A ) /n A which together with the conservation of the enthalpy perbaryon leads to n B ′ < n A . Moreover, from n A ( e B ′ + p A ) = n B ′ ( e A + p A ) < n A ( e A + p A ) one obtains e B ′ < e A . Thusthe quark phase is produced with baryon density and en-ergy density smaller than the one of the hadronic phase:these conditions are necessary for the Rayleigh-Taylor in-stabilities to take place. As shown in Refs. [23,24], theRayleigh-Taylor instabilities do indeed occur during theconversion of a hadronic star and they substantially in-crease the efficiency of burning leading to time scales ofthe order of ms for the conversion of a big portion of thestar . In Fig.2, we display one example of the dynamicsof the combustion of a hadronic star during the turbulentregime. The simulation consists in solving the Euler equa-tions in 3+1D by using a well-tested grid code that em-ploys a finite volume discretization, the so-called piecewiseparabolic method, see [24] and references therein. More-over a level-set method has been used to follow the evolu-tion of the flame front. The Rayleigh-Taylor instabilitiesare clearly visible (the typical mushroom structures) andrender the conversion turbulent. After about 4 ms, almostthe whole star is converted and, at the same time, the tur-bulent eddies stop. The star has reached a configurationof mechanical equilibrium. In particular, the pressure, theenergy density and the baryon density of the two phasesare continuous at the interface. This is equivalent to theColl’s equality: e h ( p, X ) = e q ( p, X ). The turbulent regimethus stops at the critical density of the hadronic phase, n h , for which the Coll’s equality is satisfied. For n h < n h ,the Coll’s condition is violated. This implies that the newphase is produced with e B ′ > e A and thus the hydrody-namical instabilities causing turbulence cannot anymoretake place. Notice however that at the interface the tem-perature and the chemical of the two fluids are discontinu-ous. Therefore the burning can proceed but with velocitieswhich are dominated by the diffusion and the rate of the Notice that our framework is similar to what in the liter-ature is known as pre-mixed combustion. The distinction be-tween a premixed and non-premixed scheme is related to thevalue of the diffusive burning velocity. If that velocity is verylarge, as suggested in Ref.[14] then the increase of the velocitydue to turbulence is marginal (if any at all). This is close to theresult of Ref.[24] (see Fig.7) because in that paper the laminarvelocity estimated in [14] has been adopted for the numericalsimulations. In our scheme, we are instead using the velocitiesestimated in [13,15] which are significantly smaller and the in-crease of the velocity due to turbulence is much larger. Thisis due to the dependence of the Gibson scale on the laminarvelocity. chemical reactions and which are much smaller than thevelocities obtained during the turbulent regime. A naturalquestion arises: is the process still exothermic during thediffusive regime? As discussed before (see also Ref.[16]),a slow combustion is characterized by the continuity ofthe pressure and the enthalpy per baryon across the com-bustion front. Those two continuity conditions allow tocompute the state of the newly produced quark matter.We have numerically solved these equations in [10] andwe have verified that the new phase is produced at a tem-perature higher than the temperature of the fuel. This isactually the condition of exothermicity because it impliesthat some heat will be released from the star because ofthe conversion. It is interesting to notice that an analyticargument can be provided to show that the conversionremains exothermic till the surface of the star, see [10].
Let us now discuss how do we model the subsequent evo-lution of the conversion during the diffusive regime. First,we need an initial density profile of the star after the tur-bulent regime: this configuration is composed by hot quarkmatter for densities larger than n h and by cold hadronicmatter for densities smaller than n h (we are discussinghere the case of the conversion of cold hadronic stars). TheEoS of hot quark matter is computed by requiring thatat fixed pressure, the enthalpy per baryon of the quarkphase is equal to the one of the hadronic phase as in thecase of a slow combustion. The underlying hypothesis hereis that the kinetic energy of the turbulent eddies takingplace during the first stage of conversion dissipates intoheat. Notice that since the turbulent regime lasts few ms,neutrino cooling (occurring on time scales of seconds) isnot active during the first stage of the conversion. In Fig.3, we show one example for the configuration of a 1 . M ⊙ hadronic star which contains hyperons (black lines) whichhas undergone the turbulent conversion into a star almostentirely composed by quark matter (red lines). The upperpanel displays the mass enclosed and the lower panel theradius as functions of the baryon density. Notice that af-ter the turbulent regime (the density at which this regimestops is indicated by the red dashed line) a mass of about0 . M ⊙ remains unburnt within a layer with a thickness ofabout 3km.The dynamics of the diffusive regime is regulated bytwo differential equations, one describing the propagationof the flame front and the other describing the thermalevolution of the star in presence of the neutrino coolingprocess and taking into account the heat gradually re-leased by the conversion of the layers left unburnt duringthe turbulent regime. Concerning the position of the flamefront, by labeling with r f ( t ) its radial coordinate, one canwrite: d r f d t = v lf ( µ q , T ) (4)where v lf is the laminar velocity of the front with respectto the quark matter fluid (see [10]). The initial condition lessandro Drago, Giuseppe Pagliara: The scenario of two families of compact stars 5(a) t = 0 (b) t = 0 . t = 1 . t = 4 . Fig. 2. (color online) Conversion front (red) and surface of the neutron star (yellow) at different times t . Spatial units 10 cmtaken from [25]. reads r f (0) = r where r is obtained from the baryon den-sity profile by using the equation n h ( r ) = n h . The ther-mal evolution is in principle very complex since one shouldconsider how the heat progressively generated in the con-version of the external layers is distributed within the starand one should implement a diffusion transport code forhandling the propagation of neutrinos. This last task hasbeen treated in Ref.[25] for the configuration obtained justafter the turbulent regime but without considering the fur-ther conversion of the star in the diffusive regime. A sensi-ble approximation is to consider the thermal evolution ofthe star as being dominated, during the first few seconds,by the diffusion of the heat deposited during the rapidburning of its central region (the burning and the cool-ing of the external layer is sub-leading). After this periodof time the external layers of the star are almost isother-mal [25] therefore we can make the simplifying assump-tion that in the subsequent evolution within the diffusiveregime the star is basically isothermal. The simple pictureis then the following: the flame propagates towards the surface and releases the heat of the conversion; the neu-trino cooling operates via a black body surface emissionwith a corresponding luminosity L = 21 / σ ( T /K ) πr s erg/s [26] with r s the radius of the neutrinosphere (we willassume that it is located at the interface between the innercrust and the outer crust) The thermal evolution equationthen reads: C ( T ) d T d t = − L ( T ) + 4 πr f j ( r f , T ) q ( r f , T ) (5)where C is the heat capacity of the star, L the neutrinoluminosity, j is the number of baryons ignited per unittime and unit area and q is the heat per baryon releasedby the conversion. Concerning the heat capacity, we use C = 2 × M/M ⊙ ( T / ) erg/K obtained in Ref. [26]for a uniform density quark star or a hadronic star.By solving simultaneously Eqs. 4 and 5 with initialconditions: r (0) = r , T (0) = T MeV (which is the tem-perature of the star for r > r after the turbulent regime
Alessandro Drago, Giuseppe Pagliara: The scenario of two families of compact stars and it is of the order of 5 MeV as found in [25]) we cancalculate the time needed to complete the conversion ofthe star and the neutrino luminosity due to the conver-sion of the material left unburnt after the turbulent stage.In Fig.4, we show three cases corresponding to differentvalues of the parameter a maxQ ∗ which is related to the min-imum amount of strangeness needed to render the conver-sion process exothermic and enters in the expression of v lf ,see [10]. We also show a curve of luminosity correspond-ing to a simple exponential parametrization of the neutri-nos released from the heat generated during the turbulentregime: L ( t ) = Q/τ e − t/τ with τ ∼ Q ∼ . × erg (see Fig.5 for the luminosities computed in [25].)A remarkable feature is that during the diffusive regimethe neutrino luminosity displays a quasi-plateau (particu-larly evident for the smallest value of a maxQ ∗ ). This featureis related to the scaling of the burning velocity with thetemperature: v lf ∝ T − / . As the conversion proceeds,the temperature increases due to the release of energyand therefore the velocity decreases. It is a self-regulatingmechanism which rapidly leads to an almost constant ve-locity of burning and an almost constant luminosity ofneutrinos. The process goes on until the whole star is con-verted. The kink appearing in the luminosity curves sig-nals the end of the conversion: the following evolution isgoverned only by the cooling and the standard power lawluminosity is obtained. Typical time scales to completethe conversion, in this specific case, are of the order of fewtens of seconds. Actually these times scales can be reducedby considering that, due to gravity, the external layer willtend to fall onto the conversion front as the flame propa-gates. This would lead to an acceleration of the front whichreduces the time of the conversion by roughly a factor ofthree/four . GRBs are divided into two subclasses, long GRBs, havinga duration of more than 2s, and short GRBs, lasting lessthan 2s [27,28]. This division is clearly schematic and onecannot rule out the possibility that elements of one classintrude the other. The characteristics of the GRBs in thetwo classes should derive from the different astrophysicalscenario at their origin. Short GRBs are generally assumedto be generated by the merging of two compact stars in abinary system. We will discuss them in the next Section.The origin of long GRBs instead is typically associatedwith the collapse of one massive star, either forming ablack-hole (collapsar model [29,30]) or forming a millisec-ond proto-magnetar, a model also known as evolutionarywind model [31]. At the moment it is not obvious if alllong GRBs should be produced by only one of the twoproposed models, or if both possibilities are realized inNature, under different initial conditions of the collaps-ing star. In particular, the proto-magnetar model requiresvery strong magnetic fields, of the order of 10 G and arotation period of the newly formed magnetar of the order Drago and Pagliara, work in progress. M / M s un HSHS+quark core n[fm -3 ] R [ k m ] M=1.5 M/M sun
Hyperonsthreshold
Turbulent regimeDiffusive regime
Fig. 3.
Enclosed gravitational mass and radius as a function ofthe baryon density for a 1 . M ⊙ hadronic star before the turbu-lent conversion (black lines) and after the turbulent conversion(red lines). The black dashed line marks the appearance ofhyperons: the seed of strange quark matter is formed at densi-ties larger than this threshold. The red dashed line marks thedensity below which Coll’s condition is no more fulfilled andthe turbulent combustion does not occur anymore. Below thisdensity, the combustion proceeds via the slow diffusive regime.Figure taken from [10]. t[s] L [ e r g / s ] a Q*max = 0.3a
Q*max = 0.5a
Q*max = 0.7Core combustion
Fig. 4.
Neutrino luminosity associated with the burning dur-ing the diffusive regime of the combustion for three choices ofthe parameter a maxQ ∗ . The black line represents the luminosityobtained from the rapid combustion of the core. Figure takenfrom [10]. of a millisecond. It is not obvious how easy these two con-ditions can be reached and the possibility that, at least ina few cases, some GRB is generated by the collapsar modelis still open, even though long GRBs associated with a SNare probably compatible with the proto-magnetar modeland not with the collapsar’s one [32].In this review we will shortly discuss both possibilitiesand we will see under which conditions quark deconfine- lessandro Drago, Giuseppe Pagliara: The scenario of two families of compact stars 7 t[s] L [ e r g / s ] Sun
Sun
Fig. 5.
Total neutrino luminosity as a function of time. Thetwo curves refer to the turbulent (and thus not complete) con-version of a 1 . M ⊙ and a 1 . M ⊙ stars. Figure taken from [25]. ment can play a role and produce some observable signa-ture. Any realistic model for the inner engine of long GRBsshould take into account a few basic findings: – the total energy emitted in x-rays and in γ -rays islarge, of the order of 10 − erg; – the typical duration of the initial very luminous phase,called prompt emission, is of the order of a few tensof seconds, although much longer durations have beenobserved in a few cases; – in a significant fraction of long GRBs a prolongatedemission has been observed, lasting up to 10 − s.While its luminosity is much lower than that of theprompt emission the total energy emitted during this”quasi-plateau” phase is not much smaller than theenergy emitted during the prompt phase; – the photons observed during the prompt phase canbe well described if one assumes that they are pro-duced by internal shocks of a ultrarelativistic plasma,expanding with a Lorentz factor Γ of the order of10 − ; – the rapid variations in the luminosity of the promptphase, taking place on a submillisecond scale, implythat the source has to be compact; – the position of the source has been located in a fewcases and it corresponds to a star formation area ofthe host-galaxy [33].All these data suggest that the inner engine of longGRBs is a collapsing massive star and that in many casessome activity still exists 10 − s after the collapse.The main difference between the two models lies in theultimate source of the energy used to produce the burst:in the collapsar model one uses the energy in the accretion disk around the black-hole (in principle one can also usethe energy of the rotating black-hole), extracted by theneutrinos. Instead, in the evolutionary wind model thesource of the energy is the rotational energy of the proto-magnetar. As we will see, in both cases one can imaginethat quark deconfinement can be used to modify the modeland the energy associated with the phase transition canbe used to power a burst. The central idea behind the collapsar model is rooted intothe ultimate fate of very massive stars [34], in particularstars having a mass larger than about 25 − M ⊙ andwhose external hydrogen and helium layers have been lostdue to strong winds (Wolf-Rayet stars), see Fig. 6. Themain points of the model are the following: – the progenitor starts collapsing. A failed supernova fol-lows and a black-hole forms either directly or due tothe large fallback ; – an accretion disk forms. If the angular momentum inthe disk is appropriate most of the energy in the diskcan be extracted by neutrino-antineutrino emission [29]; – due to the toroidal geometry neutrino-antineutrino an-nihilation is a rather efficient mechanism and a plasmaof electrons and positrons forms in the area around theblack-hole; – the rotation of the progenitor allows the formation ofa empty channel along the rotation axis (funnel) on atime scale of the order of ten seconds; – the electron-positron plasma can escape the cocoon ofthe progenitor along the funnel. In that way a colli-mated jet can also form; – a fraction of the energy of the jet can also be used to re-power the supernova producing a successful explosionof the Ic type.The model is very predictive and this lead initially to spec-tacular confirmations and more recently, with more precisedata, to some possible problems. In particular the asso-ciation between GRBs and Ic SNae has been confirmedin a few cases [35,36,37]. On the other hand one prob-lem appeared: the energy of the associated SN has anenergy of about 10 erg, much larger than the energyof the jet, what makes the idea of a SN revitalized bythe GRB difficult to justify. The energy of the SN on theother hand is similar to the rotational energy of a mil-lisecond pulsar, what can be a strong argument in favorof the proto-magnetar model [36]. There is also anotherpossible problem: at least in one case no associated SNhas been observed [38]. Finally, in a significant number ofcases the prompt emission is made of two well separatedactive periods (3 active periods have been observed onlyin one case), with a long quiescent time in between. It isstill not clear if there is a statistical evidence of an ex-cess of bursts having long quiescent times respect to thedistribution of all intervals (long or short) separating theactive phases. In a few papers in the past, that evidencewas apparently found [39,40], but a recent re-analysis [41] Alessandro Drago, Giuseppe Pagliara: The scenario of two families of compact stars 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Type I collapsar: GRB / JetSN 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Je t S N T y p e I c o ll a p sa r : 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T y p e II c o ll a p sa r : Je t S N BH b y f a ll b ack ( w eak S N ) BH b y f a ll b ack ( w eak S N ) i r on c o r e c o ll a p se O / N e / M g c o r e c o ll a p se l o w m ass s t a r s −− w h i t e d w a r f s d i r ec t b l ack ho l e direct black hole d i r ec t b l ack ho l e no H e n ve l op e
25 60 100 14040initial mass (solar masses)9 10 a bou t s o l a r m e t a l − f r ee
34 260 m e t a lli c i t y ( r ough l y l og a r i t h m i c sca l e ) Fig. 6.
Collapsar types resulting from single massive stars asa function of initial metallicity and initial mass. The main dis-tinction is between collapsars that form from fallback (TypeII; red) and directly (Type I; pink). One can subdivide theseinto those that have a hydrogen envelope (cross hatching), onlyable to form jet-powered supernovae (JetSNe) and hydrogen-free collapsars (diagonal cross hatching), possibly making ei-ther JetSNe or GRBs. The first subclass is located below thethick green line of loss of the hydrogen envelope and the sec-ond is above it. The light brown diagonal hatching at high massand low metallicity indicates the regime of very massive blackholes formed directly (Type III collapsars) that collapse on thepair-instability and photo-disintegration. Since the collapsarsscenario require the formation of a BH, at low mass (left in thefigure) or high metallicity (top of the figure) and in the stripof pair-instability supernovae (lower right) no collapsars occur(white). Figure taken from [34]. indicates that maybe all inter-peaks durations can be de-scribed by using a same statistical distribution. On theother hand it is not trivial to explain quiescent times ofthe order of minutes just assuming that they are due tosome statistical fluctuation: a more detailed description ofhow they do take place seems mandatory.The collapsar model has also some difficulties in ex-plaining the long emissions taking place, in many cases,after the prompt emission. While the idea of debris stillcollapsing onto the black-hole on that long time-scale can-not be completely ruled-out it seems difficult to justifyconsidering the regularity of the emission.
The central idea behind the evolutionary wind model isthat at the origin of a long GRB there is a successful SNproducing a rapidly rotating magnetar [31]. The sequenceof the events in the model is the following, see Fig.7: – after the SN explosion a magnetar forms, with a mag-netic field of the order of 10 G and a period of aboutone millisecond; – the magnetar starts cooling down by emitting neutri-nos and antineutrinos; – whatever charged material is ejected from the star itis strongly accelerated by the large Poynting flux ˙ E due to the enormous magnetic field and the very rapidrotation; – the strong neutrino emission ablates material from thesurface of the star. For some ten seconds the baryonflux is so large that the forming jet has a low Lorentzfactor due to the baryonic contamination; – the neutrino luminosity reduces and similarly the bary-onic flux. The Poynting flux remains almost constantand a jet with a Γ ∼ − can form. These arethe right conditions to generate strong internal shocksin the expanding plasma: they are at the origin of theobserved emission; – the baryonic flux further reduces and the jet becomesalmost baryon free. Under these conditions the motionof the particles in the plasma is almost collinear andinternal shocks are suppressed. The prompt emissionterminates; – the magnetar is still rapidly rotating (although lessrapidly) and a pulsar-type emission can take place, ex-plaining the long quasi-plateau phases [42,43].This model has many interesting features: the mostimportant one is that it allows to explain the order ofmagnitude of the energy of the associated SN explosion:it is the rotational energy of the magnetar. Another ex-tremely nice feature is that it explains in a very naturalway the quasi-plateau emissions, as due to a pulsar-likeactivity. It is indeed possible to model in a very preciseway all the quasi-plateau just by fitting two numbers: themagnetic field and the rotation’s period [42,43]. It has onepossible weak point: the maximum Lorentz factor σ firstincreases due to the reduction of the baryonic flux andthen slowly decreases, due to the gradual slow-down ofthe rotation of the star. It is therefore impossible to ex-plain within the model the temporal structure of GRBshaving two active periods separated by minutes of qui-escence. We will see how quark deconfinement can solvethat problem. Also, the model predicts that all GRBs areassociated with a successful SN, while at least in one caseno SN has been observed. Again quark deconfinement canprovide a possible explanation. As discussed in the previous subsections, there are twoproblems which are quite difficult to solve either in thecollapsar or in the proto-magnetar model. The first is asso-ciated with GRBs displaying a second peak in the promptemission, separated from the first peak by a long quies-cent time. The second problem is the possible existence ofGRBs not associated with a SN explosion. In the followingwe discuss these two problems and we show how they canbe solved in the two-families scenario. lessandro Drago, Giuseppe Pagliara: The scenario of two families of compact stars 9
Fig. 7.
Wind power ˙ E (right axis) and magnetization σ (left axis) of the proto-magnetar wind as a function of time sincecore bounce, calculated for a neutron star with mass M = 1 . M ⊙ , initial spin period P = 1 . B dip = 2 × G, and magnetic obliquity χ = π/
2. Figure taken from [31].
In a few cases GRBs display a prompt emission composedof two events separated by a period of quiescence whichcan be very long. The most spectacular case is the one ofGRB 110709B [44] (see Fig.8) in which the two events areseparated by more than ten minutes. The two emissionspresent similar luminosities and light curve characteristics(although with a different time evolution of the spectralproperties). Interestingly, GRBs presenting more than twowell separated events are very rare and probably the onlyrelevant example is that of GRB 091024 [45] presentingthree episodes of comparable emission. The question istherefore how to justify what seems a case of reactivationof the inner engine.The statistical analysis of Refs. [39,40] indicated anexcess of long quiescence times respect to a log-normaldistribution fitted to reproduce inter-pulse durations ofwhatever length. Those analysis were therefore suggestinga possible different physical origin for the long quiescencetimes. A very recent reanalysis on the other hand seems toindicate that when the peak detection efficiency is takeninto account the log-normal distribution has to be sub-stituted with a power-law which is able to describe thewaiting-time distribution of all the pulses. The authors of[41] are therefore suggesting that the pulses are due tothe fragmentation of the accretion disk, within the collap-sar model. While that model seems good at interpretingthe distribution of the waiting-times, at least two possiblyconnected questions remain open: – the analysis performed in [39] indicates that on the av-erage the second episode lasts twice as long as the first one: GRB 110709B is just one representative exampleof that situation; – explicit simulations are not suggesting that, if the diskfragments, the inner part (the one powering the firstepisode) is smaller than the second one.Within the two-families scenario it is rather naturalto interpret the second episode as due to quark decon-finement within the proto-magnetar model. The possiblescheme is the following: – the first episode of the long GRB is generated ex-actly as described with the proto-magnetar model: thebaryons are ablated from the surface of the compactstar by the neutrinos associated with the cooling of thenewly formed compact star whose temperature was ofabout 20-30 MeV immediately after the collapse; – the star starts slowing down (the initial rotation periodis of the order of the millisecond) and therefore itscentral density increases; – if the central density of the star during the first episodewas slightly below the critical density needed to decon-fine the quarks than during the process of slow-downthe critical density can be reached; – the process of quark deconfinement is strongly exother-mic and the inner temperature of the star increasesagain up to a temperature comparable to the one reachedbefore; – baryons are again ablated from the surface of the form-ing quark star, as long as the surface is not completelyconverted into quark matter: a new episode of the GRBcan therefore take place.. This scheme presents at least a couple of delicate pointsthat will need to be examined in details in the future.The first point is the neutrino emission during deconfine-ment. As we have seen in Section II the neutrino lumi-nosity due to deconfinement has two components: one isassociated with the cooling of the central area of the starwhich has deconfined very rapidly, the other is associatedwith the heat deposited in the outer part of the star whilethe process of deconfinement keeps going till it reachesthe surface. The first component can be approximated as L cν ∼ Q/τ diff exp( − t/τ diff ). In the case of long GRBs theheat Q deposited during the rapid deconfinement corre-sponds roughly to half of the total deconfinement energy ∆E of a compact star having a initial mass of about (1.4-1.5 M ⊙ ). ∆E ∼ . M ⊙ ∼ . × erg (see paper 1)and therefore Q ∼ × erg, while τ diff ∼ (2-3) s. Thetypical neutrino energy is about 10 MeV. After some tenseconds, the luminosity of the neutrinos associated withthe cooling of the central area becomes comparable withthat associated with the deconfinement of the outer regionand, more importantly, it becomes sufficiently low to al-low the possibility of having Γ ∼ − if the Poyntingflux ˙ E remains similar to the one of the first event.The second delicate point concerns the evolution of thePoynting flux. One peculiarity of the two-families modelis that the quark star formed after the transition has alarger radius and therefore a larger moment of inertia thanthe hadronic star before the transition. Therefore there isa rather strong reduction of the angular velocity duringthe transition and this implies a strong reduction of thePoynting vector unless the magnetic field increases at thesame time. The behavior of the magnetic field during aquark deconfinement phase transition can be quite com-plicated. Buoyancy forces can move an internal toroidalmagnetic field towards the surface and quark deconfine-ment can help by reducing the anti-buoyancy forces [46,47,48]. Since the internal magnetic field is typically largerthan the external one it is possible that during the pro-cess of quark deconfinement the external magnetic field in-creases. In that way the Poynting flux could remain moreor less constant. Clearly at the moment these are littlemore than speculations and will need to be addressed infuture calculations. Both the collapsar’s and the proto-magnetar model arebased on a strict association between a long GRB and aSN explosion. Indeed in a few cases a type Ic SN has beenfound associated with the GRB. One can also imagine thatthe more the GRB is far away the more it is difficult todetect the associated SN. On the other hand at least onecase exists, GRB 060614 [38,49,50], of a close-by GRB forwhich no associated SN has been observed. This suggeststhe possibility of GRBs generated through a mechanismnot involving a SN explosion . The merger of two NSs is It is also possible that the associated SN is sub-luminousbecause of the fallback of Ni onto the BH see Ref.[51]. C oun t s / s Time (s) 1st trigger2nd trigger
Fig. 8.
BAT count rates of GRB 110709B. such a possibility, but it is associated with short GRBs, aswe will discuss in the next session. Here we instead con-sider the possibility of a phase transition triggered by massaccretion onto the neutron star in a LMXB system. In thetwo families scenario it is rather easy to have quark decon-finement at the end of mass accretion [2] and that transi-tion deposits about 4 . × erg of heat in the compactstar. Still, to generate a strong GRB one needs to trans-form that heat into a plasma made mainly of electron-positron pairs and of photons and to collimate the jet.One possibility is to consider neutrino-antineutrino anni-hilation, a not very efficient process in the case of sphericalsymmetry (it is difficult to have head-on collisions betweenthe neutrinos) so to produce a plasma of about 10 − erg. The magnetic field (which in accreting LMXBs can-not be larger than about 10 G) and the rapid rotationwould then beam the plasma, generating a burst that ispresumably less energetic and less collimated than a typi-cal GRB. The ultimate source of the energy of this burst isthe one deposited in the plasma by neutrino-antineutrinoannihilation.Another possibility is to assume that the neutron starmerges with the white dwarf. It has been shown that thisprocess produces a spinning Thorne-Zytkow-like objectwith a low temperature, T ∼ K [52]. If large magneticfields are generated, for instance via magneto-rotationalinstabilities, the conditions for producing a powerful GRBare fulfilled. Such a burst would be similar to a short GRBbecause it is associated with the merger of two compactstars, but its duration would be comparable with the oneof long GRBs. These features are in agreement with theproperties of GRB 060614. lessandro Drago, Giuseppe Pagliara: The scenario of two families of compact stars 11
Short Gamma-Ray Bursts are characterized by durationstypically not longer than about 2 s, and they are assumedto be associated with the merger of compact stars (NS-NSor NS-BH) in binary systems [28].While short GRBs were discovered through their lumi-nous prompt emission (similarly to what happened in thecase of long GRBs) an extended emission was later foundto exist in a significant fraction of short GRBs [53]. Itwas generally assumed that the prompt emission of shortGRBs is spectrally harder than the one of long GRBs,but the differences are less evident when the sample is re-stricted to short GRBs with the highest peak fluxes [54]or when considering only the first ∼ E peak − L iso correlation. In otherwords, if the central engine of a long GRB would stop af-ter ∼ . × (1 + z ) seconds the resulting event would beindistinguishable from a short GRB [56].The similarities between long and short GRBs are notlimited to the prompt emission: actually by comparing thequasi-plateau of long GRBs and the extended emission ofshort GRBs one discovers that they can both be describedby assuming that a proto-magnetar formed, rotating witha period of the order of a few milliseconds and by associat-ing the prolongated emissions to the pulsar-like emissionof that object [57]. The rotation period requested is inboth cases of a few milliseconds, the magnetic field is ofthe order of a few 10 G for the long and roughly oneorder of magnitude larger for the shorts, see Fig.9.A recent analysis [58] suggests that short GRBs canbe classified in three categories: a) those without any ex-tended emission; b) those with an extended emission fol-lowed by a rapid decay of the luminosity; c) those withan extended emission slowly decaying. They propose toassociate the three cases to: a) formation of a BH soonafter the merging; b) formation of a supramassive starcollapsing into a BH after having lost part of its angu-lar momentum; c) formation of a very massive and stablecompact star after the merging. In this way they also es-timate the mass distribution of the post-merger remnantas 2 . . − . M ⊙ . Although this distribution includes alsosupramassive stars, it indicates that very massive compactstars do exist.A question naturally arises: if both the long and theshort GRBs can be explained, at least in a fraction ofcases, by assuming that a proto-magnetar forms, with sim-ilar values for the rotation period and for the magneticfield, why then the prompt emission of long GRBs laststens of seconds and those of shorts tenths of seconds? Inboth cases the ablation of material from the surface ofthe proto-magnetar, due to neutrino cooling, will providethe crucial ingredient to generate a jet with the properLorentz factor. The cleaner environment and the highertemperatures [3] reached after the merger respect to thepost-supernova case would suggest that the duration of Fig. 9.
Magnetic field and spin period of the magnetar fitsto the extended emission of both long (black “+”) and shortGRBs. The latter are further separated in stable magnetars(blue stars) and unstable magnetars collapsing to form a BH(green circles). Figure taken from [57]. the short should be at least comparable to the one of thelong. Which is then the mechanism stopping the promptemission in the case of short GRBs? In the next subsec-tion we will show how quark deconfinement can play thecrucial role in this situation.
One of the best known properties of quark stars is thatonce formed it is impossible to ablate hadrons from its sur-face (unless by neutrinos having energies exceeding about1 GeV). This is due to the confinement of quarks whichdoes not let them to be ejected if not inside a colorlessobject as a hadron. A cumulative transfer of energy andmomentum to a single quark by multiple neutrino scatter-ing would also not allow to produce a hadron, because thatfour-momentum is rapidly shared with the other quarksby strong interactions (a similar idea has been discussedin Ref.[59]). This property of quark stars opens the pos-sibility of explaining the rapid truncation of the promptemission of short GRBs. Notice that in the two-familiesscenario, if a compact star (and not a BH) forms after themerging, it is unavoidably a quark star.In Ref.[60] the following scheme has been developed: – a few milliseconds after the merging, the conditionsare favourable for the formation of deconfined quarkmatter in the hot and rapidly rotating compact object; – following the scheme described in Sec.2 in a few mil-liseconds the central region of the star converts into quark matter. The new object, made of an inner partof stiff quark matter and of an external part made ofhadrons is mechanically stable (although not chemi-cally stable, since it keeps converting into quarks); – in some ten seconds the star entirely converts into aquark star: until that moment it still has a surfacemade of nucleons which can be ablated. Since the staris still very hot the baryon flux during that first stageis too large to allow the formation of a jet with a largeenough Lorentz factor; – once the surface of the star has completely convertedinto quarks, baryons can no more be ablated and thepossibility of generating a GRB no more exists; – the GRB can be produced only during the short timeassociated with the the switch-off of the baryon flux.The time needed to convert the entire surface of therapidly rotating (and therefore strongly deformed star)plays a fundamental role in regulating the duration ofthe GRB. The possible influence of quark deconfinement on SN ex-plosions has been explored in a few papers, starting fromRefs.[61,62]. In those papers it was assumed that quarkdeconfinement takes place before deleptonization (QDBDfollowing the notation of Ref.[63]), either at the momentof the collapse or a fraction of a second after, when ma-terial falls back due to the failure of the SN explosion.Since in the mixed phase the adiabatic index is very low,the collapse continues rapidly through the mixed phasetill the central density reaches the second critical densityseparating mixed phase and pure quark matter. At thispoint, the adiabatic index becomes large again and thecollapse halts. A shock wave is then produced. One fea-ture of this mechanism is that it requires a particularlysoft EoS, since the formation of a mixed phase of quarksand hadrons has to take place at the relatively low densi-ties reached at the moment of core bounce, or immediatelyafter, during the fallback but anyway before deleptoniza-tion [64]. Since the densities reached at the moment of thebounce are only moderately dependent on the mass of theprogenitor, this mechanism is rather ”universal”, affectingmost of the SNe, although its effect on the explosion canstill depend on the mass of the progenitor. This first pos-sibility, QDBD, is not compatible with the two-familiesscenario, because it would imply that almost all compactstars are quark stars, since quark deconfinement wouldtake place at very low densities.The second possibility, QDAD, is that quark decon-finement takes places only after an at least partial delep-tonization [65,66]. It is well known, in fact, that whenthe pressure due to leptons decreases, the central baryonicdensity increases and therefore the deconfinement processbecomes easier.The process of deconfinement can then take place intwo possible ways: either as a smooth transition or as afirst order one, associated with the formation of some in-termediate meta-stable phase. In order for the transition to be completely smooth two conditions need to be sat-isfied: finite-volume effects are irrelevant (so that even asingle nucleon can melt into quarks above a given criticaldensity) and no critical value for the strangeness fractionof the quark phase should exist. The latter point is par-ticularly important, because the existence of a minimumcritical value for the strangeness fraction implies the exis-tence of a second minimum (either local or global) in theenergy per baryon vs density function, separated from theminimum at strangeness equal zero by a barrier. In thecase of hybrid stars it is possible to satisfy in particularthe second condition, as analyzed e.g. in Ref.[65]. Instead,since the two-families scenario is based on the existence ofquark stars, a critical value for the strangeness must ex-ist (instead ordinary matter would just decay into strangequark matter). Therefore the process of deconfinement inthe two-families scenario always goes through the forma-tion of a metastable phase.If a critical strangeness fraction needs to be reachedin order to deconfine, the question concerns the way onereaches that critical value soon after the pre-supernovacollapse. The most simple way is to imagine that due tomass fallback and/or to the slow-down in case of a rapidlyrotating star the central density increases. At a certaindensity hyperons will start being produced. While it isdifficult to estimate which can be the critical density ofhyperons (and therefore of strangeness) necessary to trig-ger quark deconfinement, it is clear that it must be atleast of the order of a few percent of the total baryons,instead the strange quarks in the hyperons will be too faraway one from the other in order to interact and to drivethe process of deconfinement. As mentioned in the intro-duction, it is well possible that statistical fluctuations willplay the crucial role, so that at a certain moment a largeenough number of hyperons will be contained in a smallvolume and the process of deconfinement will start.A important point can be noticed from Fig. 4 of paper1: at the temperature reached in the compact star imme-diately after the collapse, the densities of hyperons arestill not very different from the ones at zero temperature.Therefore one can conclude that only the stars having amass close to about 1.5 M ⊙ will undergo a phase tran-sition soon after the SN explosion. Stars having a massof about 1.3-1.4 M ⊙ will not be affected and the mecha-nism by which they explode will not be linked to quarkdeconfinement.It is well known that at the moment the standardmechanism has difficulties in explaining SNae associatedwith the collapse of massive progenitors, the ones which inprinciple will generate the most massive neutron stars. Apossible way-out is the following: if the proto-neutron staris rapidly rotating (a condition similar to the one neededto produce GRBs in the proto-magnetar model) the rateof fallback can be reduced, allowing the system the timeto deconfine and to generate a powerful burst of neutrinosassociated with the cooling from the heat released by de-confinement. Notice that the neutrinos are generated at adepth of few km inside the star and therefore they needa few tenths of a second to start flowing out of the star. lessandro Drago, Giuseppe Pagliara: The scenario of two families of compact stars 13 If the star is rapidly rotating, so that it does not collapseto a black hole during that time, the neutrino flux can besufficient to revitalize the supernova explosion. In Fig.5we show the neutrino luminosities computed in Ref.[25]by using a slightly different set of EoS respect to the onesdiscussed here: the luminosities peak at about 3 × erg, a value comparable to the one obtained at the mo-ment of the collapse. The luminosities computed with theEoSs described in paper 1 would have even higher peakssince the total energy released by deconfinement is larger. The only SN neutrinos detected till now are those fromSN1987A. Indeed, on February 23, 1987, at 2 h 53 m (UT)LSD detector observed 5 events [67]; at 7 h 36 m (UT)IMB, Kamiokande-II and Baksan [68,69,70] detectors ob-served 8, 11 and 5 events respectively. The progenitor wasa blue supergiant with estimated mass of ∼ M ⊙ .The observations of Kamiokande-II, IMB and Baksancan be explained very well within the standard scenariofor core collapse SNe, assuming that the events are dueto ¯ ν e p → ne + . The observations are consistent with thepresence of an initial, high luminosity phase of neutrinoemission, followed by a thermal phase due to the cool-ing of the newborn neutron star [71,72]. Such an initialand luminous phase is expected; indeed, it should triggerthe subsequent explosion of the star. The standard sce-nario for core collapse SNe does not predict the existenceof multiple pulses of neutrino emission and thus cannotaccommodate LSD data.An interesting possibility is that the first burst is dueto a very intense neutronization phase by e − p → nν e ; itwas noted in [73] that electron neutrinos with an energy of30 −
40 MeV can be more easily seen in the LSD detectorthan in the other detectors. In the astrophysical scenarioof [73], the rapid rotation of the collapsing core leads toa delay between the first and the second burst. However,the nature of the second burst is not discussed in [73].In Ref.[63] it was discussed the possibility that Kamiokan-deII, Baksan and IMB observations are due to the burningof hadrons into quarks. The sequence of events, in thatcase, could be the following: – the rapid rotation of the collapsing core halts the col-lapse at subnuclear densities, forming a so-called ”fiz-zler” [74]; – an initial intense phase of neutronization accounts forthe LSD observations as in [73]; – the rapid rotation of the core leads to the formationof a metastable neutron star, that looses its angularmomentum in a time scale of several hours; – the central density of the metastable star becomes largeenough that deconfinement can take place. Again, therapid release of energy at the beginning of the laststage could be sufficient to lead to the explosion of thestar.This scheme, although interesting, is strictly based on thepossibility of having very large values of angular momen-tum in the central region of the star, what seems at odd with the results of Ref.[75]. On the other hand a simi-lar criticism can be applied to the model for GRBs basedon the formation of a millisecond proto-magnetar, a modelthat is having a great phenomenological success. We thinktherefore that the analysis of the distribution of the angu-lar momentum in the collapsing core cannot yet be con-sidered concluded. The possible connection between quark deconfinement andexplosive astrophysical phenomena has a relatively longstory. The papers discussing this relation have concen-trated on some specific associations. The oldest proposedconnections have to do with suggestions on how deconfine-ment can help SNae to explode by providing a soft EoSin the mixed phase, followed by a stiff EoS in the purequark matter phase [61,62], on how GRBs can be associ-ated with the energy released by the deconfinement [46,76] and on how quark stars can help to generate the GRBby providing a cleaner environment [77,78].The discovery of very massive compact stars has changedthe scenario concerning the possible impact of quark de-confinement on SNae and on GRBs, since one needs toclarify the composition of the most massive stars beforediscussing the transition from hadronic to hybrid or quarkstars. As we have tried to clarify in this review, once a spe-cific proposal for the EoS of matter at high densities hasbeen formulated, the possible transitions from hadronicto quark (or, in other schemes, hybrid) stars appear in anatural way and the phenomenological implications canbe outlined rather precisely.An attempt at systematizing a variety of phenomenainto a unique scheme has been made during many yearsby Ouyed and collaborators. The scheme they have de-veloped, named Quark-Nova, is based on the idea thatthe process of deconfinement takes place as a detonationand that therefore quite a significant amount of matter isejected by a mechanical shock at the end of the process.The mass ejection can interact with the material alreadypresent in the surroundings of the compact star and itcan originate a variety of phenomena: nucleosynthesis inneutron-rich ejecta [79]; GRBs, both by releasing a hugeamount of energy from the surface of the quark star viaphoton emission [80] and also by using the interaction ofthe ejecta from the Quark-Nova with the ejecta of the pre-ceding SN in order to generate a late-time x-ray emission[81]. Also it has been proposed to explain the long-timeduration and the spectral features of SN 2006gy as due tothe interaction of the Quark-Nova ejecta with the ejectaof the preceding SN [82].While the suggested associations between explosive phe-nomena and quark deconfinement are very interesting, twointer-correlated questions arise. First, explicit analysis ofthe process of quark deconfinement are not indicating adetonation, but a deflagration, as discussed at the begin-ning of this review. Second, it would be interesting to seeif the detonation plays really the crucial role or if the mass ejected e.g. by neutrino ablation in the case of a deflagra-tion can be sufficient to interpret some of the phenomenaas due to quark’s deconfinement but not to the specificQuark-Nova model. A work in that direction is e.g. [83],indicating a significant amount of mass ejection during theformation of a quark star due to the neutrino emission.This result is compatible with the more recent analysiswe made [10] and it opens the possibility of re-discussingsome of the phenomena by using a deflagration instead ofa detonation.
In this and in the accompanying paper 1 we have presentedthe two-families scenario and we have discussed the manyimplications it has on astrophysics. We have seen in pa-per 1 that the measure of the radius of a few compactstars would likely confirm or rule-out the model. Possibleconfirmations could also come from the study of LMXBswhich are displaying in a few cases large eccentricity whoseorigin is still unknown, and it could be originated by thephase transition to quark star of the neutron star in thebinary system.The most spectacular implications of the two-familiesscenario are though probably connected with explosivephenomena and in particular with short GRBs. First, adirect outcome of the two-families scenario is that if acompact star and not a BH forms after the merging thanthat object is a quark star. This very strong implicationcan be tested e.g. by studying gravitational waves emit-ted immediately before and immediately after the merger(see e.g. the review paper by Bauswein, Stergioulas andJanka). Another striking implication of the formation ofa quark star immediately after the merger is the possibil-ity of explaining both long and short GRBs by using theproto-magnetar model as described in Sec.4.1. Notice thatin these two examples one would not generically test theformation of quark matter inside the compact star, but theformation of a quark star, and therefore the two-familiesscenario.While many aspects of the scenario still need to beworked out, as for instance the behaviour of the magneticfield during the formation of the quark star, we are con-fident that in the near future the scenario will be testedand therefore confirmed or ruled out by a multitude ofexperiments and observations, ranging from the analysisof GW emission, to the measure of the radii of compactstars, to the analysis of the emission of GRBs. The pos-sibility of being tested is ultimately the divide between atheory and a speculation.A.D. would like to thank V. Hislop for the moral sup-port during the preparation of the paper. G.P. acknowl-edges financial support from the Italian Ministry of Re-search through the program Rita Levi Montalcini.
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