BLACK HOLES, SUPERNOVAE AND GAMMA RAY BURSTS

Black Holes, Supernovae and Gamma Ray Bursts

REMO RUFFINI Dip. di Fisica, Sapienza University of Rome and ICRA
Piazzale Aldo Moro 5, I–00185, Rome, Italy
ICRANet, Piazzale della Repubblica 10, I–65122 Pescara, Italy
Université de Nice Sophie Antipolis, Nice, CEDEX 2
Grand Château Parc Valrose
E-mail: ruffini@icra.it
?? ?? 20138 August 2013
?? ?? 20138 August 2013
Abstract

We review recent progress in our understanding of the nature of gamma ray bursts (GRBs) and in particular, of the relationship between short GRBs and long GRBs. The first example of a short GRB is described. The coincidental occurrence of a GRB with a supernova (SN) is explained within the induced gravitational collapse (IGC) paradigm, following the sequence: 1) an initial binary system consists of a compact carbon-oxygen (CO) core star and a neutron star (NS); 2) the CO core explodes as a SN, and part of the SN ejecta accretes onto the NS which reaches its critical mass and collapses to a black hole (BH) giving rise to a GRB; 3) a new NS is generated by the SN as a remnant. The observational consequences of this scenario are outlined.

Black Hole; Supernova; Gamma Ray Burst.
\catchline{history}

1 Introduction

While supernovae (SNe) have been known and studied for a long time, from A.D. to the classic work of Baade and Zwicky in 1939, observations of GRBs only date from the detection by the Vela satellites in the early s, see e.g. Ref. \refcite1975ASSL…48…..G. It has only been after the observations by the Beppo-Sax satellite and the optical identification of GRBs that their enormous energetics, times larger than those of SNe, have been determined: energies of the order of erg, equivalent to the release of in few tens of seconds. This situation has become even more interesting after the observation of a temporal coincidence between the emission of a GRB and a SN, see e.g. GRB 980425[2] and SN 1998bw[3]. The explanation of this coincidence has led to a many-cosmic-body-interaction and therefore to the introduction of a cosmic matrix: a C-matrix. This totally unprecedented situation has lead to the opening of a new understanding of a vast number of unknown domains of physics and astrophysics.

1.1 CRAB — pulsars and NS rotational energy

Of all the objects in the sky none has been richer in results for physics, astronomy and astrophysics than the Crab Nebula. Although a result of the A.D. supernova observed by Chinese, Japanese and Korean astronomers, the nebula itself was not identified till 1731, and not associated with that supernova until the last century, but it has been of interest to astronomers, and later astrophysicists and theoretical physicists ever since, even very recently, see e.g. the discovery by Agile of the giant flare discovered in September [4]. It was only in 1968 that a pulsar was discovered at its center following the predicted existence of rapidly rotating NSs in that decade then soon after observed as pulsars.

However, there still remains to explain an outstanding physical process needed to model this object: the expulsion of the shell of the SN during the process of gravitational collapse to a NS. We are currently gaining some understanding of the physical processes governing NSs, motivated by the research on GRBs and BH formation which is being fully exploited to this end at the present time. Paradoxically the study of BHs was started by the discovery of the NS in the Crab Nebula. This study and the understanding of BH formation and consequently of the emission of GRBs is likely to lead, in this Faustian effort to learn the laws of nature, to the understanding of the process of NS formation and the expulsion of the remnant in the SN explosion.

Figure 1: Hubble Space Telescope photograph (2005) of the Crab Nebula.

That NSs exist in nature has been proven by the direct observation of pulsars. The year marked the discovery of the first pulsar, observed at radio wavelengths in November , by Jocelyn Bell Burnell and Antony Hewish [5]. Just a few months later, the pulsar NP was found in the center of the Crab Nebula (see Fig. 1) and observed first at radio wavelengths and soon after at optical wavelengths (see Fig. 2).

Figure 2: The sequence of black and white images on the right is separated by one millisecond intervals, from which it is clear that the left star is a pulsar with a period of milliseconds. This period changes with a rate of microseconds per year. The fact that the loss of rotational energy of a neutron star with moment of inertia is given by explains precisely the energetics of the pulsar and proves at once the existence of NSs [6].

The discovery of NSs led our small group working around John Wheeler in Princeton to direct our main attention to the study of continuous gravitational collapse introduced by Oppenheimer and his students (see Fig. 3). The work in Princeton addressed the topic of BHs, gravitational waves (GWs) and cosmology. A summary of that work can be found in Refs. \refciteLesHouches,1974bhgw.BOOK…..R, where a vast number of topics of relativistic astrophysics was reconsidered, including the cross-sections of GW detectors, the possible sources of GWs and especially, an entirely new family of phenomena occurring around BHs.

Figure 3: Standing to the left Tullio Regge, sitting on the desk Remo Ruffini and sitting on the chair John Wheeler.

1.2 The BH mass-energy formula

The most important result in understanding the physics and astrophysics of BHs has been the formulation of the BH mass-energy formula. From this formula, indeed, it became clear that up to of the mass-energy of a BH could be extracted by using reversible transformations [9]. It then followed that during the formation of a BH, some of the most energetic processes in the universe could exist, releasing an energy of the order of erg for a BH.

Figure 4: The Vela satellites, see e.g. the Ian Strong chapter in Ref. \refcite1975ASSL…48…..G.

1.3 VELA satellites and GRBs

In Ref. \refciteRRKerr I described how the observations of the Vela satellites were fundamental in discovering GRBs, see Fig. 4. Initially it was difficult to model GRBs to understand their nature since their distance from the Earth was unknown, and thousands of models were presented [11] attempting to explain the mystery they presented. Just a few months after the public announcement of their discovery [1], with T. Damour, a collaborator at Princeton, I formulated a theoretical model based on the extractable energy of a Kerr-Newmann BH through a vacuum polarization process as the origin of GRBs, see Fig. 5. In our paper [12], we pointed out that vacuum polarization occurring in the field of electromagnetic BHs could release a vast plasma which self-accelerates and gives origin to the GRB phenomenon. Energetics for GRBs all the way up to ergs was theoretically predicted for a BH. The dynamics of this plasma was first studied by J.R. Wilson and myself with the collaboration of S.-S Xue and J.D. Salmonson [13, 14].

Figure 5: The classic paper Ref. \refcite1975PhRvL..35..463D by Damour and Ruffini on the extractable energy of a Kerr-Newman BH through vacuum polarization.

1.4 The BATSE detectors and short and long GRBs

The launching of the Compton satellite with the BATSE detectors on-board (see Fig. 6) led to the following important discoveries:

  1. the homogeneus distribution of GRBs in the universe (see Fig. 6);

  2. the existence of short GRBs lasting less than 1 second (see Fig. 7); and

  3. the existence of long GRBs, lasting more than 1 second (see Fig. 7).

Figure 6: The BATSE detectors on-board the Compton satellite (taken from the NASA website http://science.nasa.gov/science-at-nasa/1997/ast15jan97).
Figure 7: Short and long GRB light curves and their temporal distribution from the 4 BATSE catalog, Ref. \refcite1999ApJS..122..465P

The crucial contribution to interpreting GRBs came from the Beppo-Sax satellite which led to a much more precise definition of their position in the sky obtained using a wide field X-ray camera and narrow field instrumentation. This enabled the optical identification of GRBs and the determination of their cosmological redshifts, and consequently of their energetics, which turned out to be up to erg, precisely the value predicted by Damour and myself in Ref. \refcite1975PhRvL..35..463D. Since that time no fewer than ten different X- and -ray observatory missions and numerous observations at optical and radio wavelengths have allowed us to reach a deeper understanding of the nature of GRBs.

After reviewing in the next paragraphs some recent theoretical progress motivated by the study of GRBs, I will turn to the first example of a genuine short GRB 090227B [16]. Then I will describe the analysis of the GRB 090618 in the fireshell scenario [17] and illustrate the first application of the IGC paradigm to it [18]. Finally I will indicate some recent results on a possible distance indicator inferred from a GRB-SN connection within the IGC paradigm [19], then giving some additional evidence coming from the identification of the NS created by the SN and its use as a cosmological candle.

1.5 Some recent theoretical progress

I would like just to present some key images and cite corresponding references to articles documenting some crucial progress we have made that is propedeutic for understanding the physics and astrophysics of GRBs.

1.5.1 Mass, charge and angular momentum in a Kerr-Newman BH: the dyadotorus

Fig. 8 summarizes the profound difference in analyzing the Kerr-Newman BH between the original paper of B. Carter [20] and our current approach to the physics of the dyadotorus. In Carter’s approach attention was focused on geodesics crossing through the horizon of an eternally existing BH and reaching either the BH singularity or analytic extensions to other asymptotically flat space-times. Instead our approach is directed to the fundamental physical processes occurring outside the horizon of a BH and to their possible detection in the dynamical phases of BH formation. Our major focus is to understand the quantum processes leading to vacuum polarization and pair creation and the resulting dynamical expansion to infinity. This mechanism is essential to extract energy from the BH, an amount which can be as high as of its total mass energy as already mentioned above. To reach a theoretical understanding of this problem, it was necessary to introduce the dyadotorus, see Fig. 8.

Figure 8: On the left: the dyadotorus as introduced in Ref. \refcite2009PhRvD..79l4002C; on the right: the space-time diagram representing the region inside the horizon of a Kerr-Newman BH Ref. \refcite1968PhRv..174.1559C.

1.5.2 Thermalization of an electron-positron plasma

A key result was obtained by analyzing the evolution of the plasma created in the dyadotorus by vacuum polarization. Cavallo and Rees [22] envisaged that the sudden annihilation of the pairs and the expansion of the thermal radiation in the circumburst medium (CBM) would lead to an explosion very similar to an H-bomb, a scenario identified as the fireball model.

By considering the essential role of three-body interactions, we have proven that the pairs do not annihilate all at once as claimed by Cavallo and Rees [22] but they thermalize with the photons [23] and keep expanding in a shell until transparency of the plasma is reached [24], a new paradigm for GRBs called the fireshell model.

Figure 9: The thermalization of a pure plasma, taken from Ref. \refcite2007PhRvL..99l5003A.

1.5.3 The new approach to analyzing NS equilibrium configurations in an unified approach encompassing all fundamental interactions

A completely new approach to NS equilibrium configurations was advanced in recent years and has evolved into a much more complicated model, fulfilling the criteria needed conceptually for the description of NSs [25, 26]. The first model for a NS was given by Gamow as a system entirely composed of neutrons governed by both Fermi statistics and Newtonian gravity. The extension of this model to general relativity was made by Oppenheimer and his students, leading to the classic Tolman-Oppenheimer-Volkoff (TOV) equilibrium equations [27, 28]. This was then extended to a system of three degenerate gases of neutrons, protons and electrons and solved by John Wheeler and his students and collaborators [29]. However, they assumed local charge neutrality for mathematical convenience. It was later realized that a more complete description was needed, since the previous analyses violated basic thermodynamic and general relativistic conditions required for conservation of the Klein potential [30]. A new much more complete treatment appeared to be needed involving in a self-consistent way all the fundamental forces. A new model has since emerged, extending the general relativistic Thomas-Fermi equations to the strong and weak interactions throughout the entire NS [26] (see Fig. 1012). This complete model satisfies instead global charge neutrality of the entire configuration and not strict local charge neutrality, an erroneous assumption usually made in the existing literature on NS models.

Figure 10: The Oppenheimer-Volkoff NS, see Ref. \refcite1939PhRv…55..374O.
Figure 11: From Ref. \refcite2011NuPhA.872..286R.
Figure 12: From Ref. \refcite2012NuPhA.883….1B.

With this short summary of the most relevant conceptual and theoretical issues, I now briefly summarize how some of them have allowed us to reach a new understanding of the short GRBs and the SN-GRB connection.

2 GRB 090227B: The Missing Link between the Genuine Short and Long GRBs

2.1 Introduction

Using the data obtained from the Fermi-GBM satellite [32], Ref. \refcite2013ApJ…763..125M has proven the existence of yet another class of GRBs theoretically predicted by the fireshell model [24, 33] which we define here as the “genuine short GRBs.” This canonical class of GRBs is characterized by extremely small values of the Baryon Load (see Fig. 13). The energy emitted in the proper GRB (P-GRB) described below is predominate with respect to the extended afterglow and its characteristic duration [16] is expected to be shorter than a fraction of a second (see Sec. 2.2.8).

Figure 13: The energy emitted in the extended afterglow (solid green curve) and in the P-GRB (solid red curve) in units of erg (dashed horizontal line), as functions of . The crossing point, corresponding to the condition , marks the division between the genuine short and the disguised short and long GRB regions.

A search has begun for these genuine short GRBs among the bursts detected by the Fermi-GBM instrument during the first three years of its mission. The initial list of short GRBs was reduced by requiring that no prominent X-ray or optical afterglow be observed. The GRB 090227B has been identified among the remaining bursts. A spectral analysis of its source has been performed from its observed light curves, and its cosmological redshift and all the basic parameters of the burst, as well as the isotropic energy, the Lorentz factor at transparency, and the intrinsic duration, have all been inferred from theory.

In Sec. 2.2 the relevant properties of the fireshell model are summarized. In Sec. 2.3 the observations of GRB 090227B by various satellites and their data analysis are reviewed. In Sec. 2.4 all the parameters characterizing this GRB within the fireshell scenario, including the redshift, are determined. In the conclusions we show that this GRB is the missing link between the genuine short and the long GRBs, with some common characteristics of both classes. Further analysis of genuine short GRBs with a smaller value of should lead to a P-GRB with an even more pronounced thermal component. The progenitor of GRB 090227B is identified as a symmetric binary system of two neutron stars, each of , see e.g. Ref. \refcite2012arXiv1205.6915R.

2.2 The fireshell versus the fireball model

2.2.1 The GRB prompt emission in the fireball scenario

A variety of models have been developed to theoretically explain the observational properties of GRBs, among which the fireball model [35] is one of those most often used. In Refs. \refcite1978MNRAS.183..359C,1986ApJ…308L..47G,1986ApJ…308L..43P it was proposed that the sudden release of a large quantity of energy in a compact region can lead to an optically thick photon-lepton plasma and to the production of pairs. The sudden initial total annihilation of the plasma was assumed by Cavallo and Rees [22], leading to an enormous release of energy pushing on the CBM: the “fireball.”

An alternative approach, originating in the gravitational collapse to a BH, is the fireshell model, see e.g. Refs. \refcitePhysRep,2011IJMPD..20.1797R. Here the GRB originates from an optically thick plasma in thermal equilibrium, with a total energy of . This plasma is initially confined between the radius of a BH and the dyadosphere radius

(1)

where is the usual fine structure constant, the Planck constant, the speed of light, and the mass of the electron. The lower limit of is assumed to coincide with the observed isotropic energy emitted in X-rays and gamma rays alone in the GRB. The condition of thermal equilibrium assumed in this model [23] distinguishes this approach from alternative ones, e.g. Ref. \refcite1978MNRAS.183..359C.

In the fireball model, the prompt emission, including the sharp luminosity variations [40], are caused by the prolonged and variable activity of the “inner engine” [41, 35]. The conversion of the fireball energy to radiation originates in shocks, either internal (when faster moving matter overtakes a slower moving shell, see Ref. \refcite1994ApJ…430L..93R) or external (when the moving matter is slowed down by the external medium surrounding the burst, see Ref. \refcite1992MNRAS.258P..41R). Much attention has been given to synchrotron emission from relativistic electrons in the CBM, possibly accompanied by Self-Synchrotron Compton (SSC) emission, to explain the observed GRB spectrum. These processes were found to be consistent with the observational data of many GRBs [43, 44]. However, several limitations have been reported in relation with the low-energy spectral slopes of time-integrated spectra [45, 46, 47, 48] and the time-resolved spectra [48]. Additional limitations on SSC emission have also been pointed out in Refs. \refcite2008MNRAS.384…33K,2009MNRAS.393.1107P.

The latest phases of the afterglow are described in the fireball model by assuming an equation of motion given by the Blandford-McKee self-similar power-law solution [51]. The maximum Lorentz factor of the fireball is estimated from the temporal occurrence of the peak of the optical emission, which is identified with the peak of the forward external shock emission [52, 53] in the thin shell approximation [54]. Several partly alternative and/or complementary scenarios have been developed distinct from the fireball model, e.g. based on quasi-thermal Comptonization [55], Compton drag emission [56, 57], synchrotron emission from a decaying magnetic field [58], jitter radiation [59], Compton scattering of synchrotron self-absorbed photons [60, 61], and photospheric emission [62, 63, 64, 65, 66, 67, 68]. In particular, it was pointed out in Ref. \refcite2009ApJ…702.1211R that photospheric emission overcomes some of the difficulties of purely non-thermal emission models.

2.2.2 The fireshell scenario

In the fireshell model, the rate equation for the pair plasma and its dynamics (the pair-electromagnetic pulse or PEM pulse for short) have been described in Ref. \refcite2000A&A…359..855R. This plasma engulfs the baryonic material left over from the process of gravitational collapse having a mass , still maintaining thermal equilibrium between electrons, positrons, and baryons. The baryon load is measured by the dimensionless parameter . Ref. \refcite1999A&AS..138..513R showed that no relativistic expansion of the plasma exists for . The fireshell is still optically thick and self-accelerates to ultrarelativistic velocities (the pair-electromagnetic-baryonic pulse or PEMB pulse for short [69]). Then the fireshell becomes transparent and the P-GRB is emitted [24]. The final Lorentz gamma factor at transparency can vary over a wide range between and as a function of and , see Fig. 14. For its final determination it is necessary to explicitly integrate the rate equation for the annihilation process and evaluate, for a given BH mass and a given plasma radius, at what point the transparency condition is reached [14] (see Fig. 15).

The fireshell scenario does not require any prolonged activity of the inner engine. After transparency, the remaining accelerated baryonic matter still expands ballistically and starts to slow down from collisions with the CBM of average density . In the standard fireball scenario [70], the spiky light curve is assumed to be caused by internal shocks. In the fireshell model the entire extended-afterglow emission is assumed to originate from an expanding thin shell, which maintains energy and momentum conservation during its collision with the CBM. The condition of a fully radiative regime is assumed [24]. This in turn allows one to estimate the characteristic inhomogeneities of the CBM, as well as its average value.

It is appropriate to point out another difference between our treatment and others in the current literature. The complete analytic solution of the equations of motion of the baryonic shell were developed in Refs. \refcite2004ApJ…605L…1B,2005ApJ…620L..23B, while elsewhere the Blandford-McKee self-similar approximate solution is almost always adopted without justification [73, 74, 75, 76, 77, 78, 79, 80, 81, 64]. The analogies and differences between the two approaches have been explicitly explained in Ref. \refcite2005ApJ…633L..13B.

In our general approach, a canonical GRB bolometric light curve is composed of two different parts: the P-GRB and the extended afterglow. The relative energetics of these two components and the observed temporal separation between the corresponding peaks is a function of the above three parameters , , and the average value of the . The first two parameters are inherent to the accelerator characterizing the GRB, i.e., the optically thick phase, while the third one is inherent to the environment surrounding the GRB which gives rise to the extended-afterglow. For the observational properties of a relativistically expanding fireshell model, a crucial concept has been the introduction of the EQui-Temporal Surfaces (EQTS). Here too our model differs from those in the literature by having deriving an analytic expression of the EQTS obtained from the solutions to the equations of motion [82].

2.2.3 The emission of the P-GRB

The lower limit for is given by the observed isotropic energy emitted in the GRB. The identification of the energy of the afterglow and of the P-GRB determines the baryon load and from these it is possible to determine the value of the Lorentz factor at transparency, the observed temperature as well as the temperature in the comoving frame and the laboratory radius at transparency, see Fig. 15. We can indeed determine from the spectral analysis of the P-GRB candidate the temperature and the energy emitted at the point of transparency. The relation between these parameters cannot be expressed analytically, only through numerical integration of the entire set of fireshell equations of motion. In practice we need to perform a trial-and-error procedure to find a set of values that fits the observations.

Figure 14: Evolution of the Lorentz factor until the transparency emission for a GRB of a fixed = 1.22 10 (upper panel),and = 1.44 10, for different values of the baryon load . This computation refers to a BH mass of 10 M and the transparency condition , where is the Thomson cross-section and the integration is over the thickness of the fireshell [69].
(a) (b)
(c) (d)
Figure 15: fireshell temperature in the comoving and observer frame and the laboratory radius at the transparency emission (panels (a) and (b)), the Lorentz factor at the transparency (panel (c)) and the energy radiated in the P-GRB and in the afterglow in units of (panel (d)) as a function of the baryon load for four different values of .

The direct measure of the temperature of the thermal component at transparency offers very important new information on the determination of the GRB parameters. Two different phases are present in the emission of the P-GRB: one corresponding to the emission of the photons when transparency is reached and another corresponding to the early interaction of the ultra-relativistic protons and electrons with the CBM. A spectral energy distribution with both a thermal and a non-thermal component should be expected to result from these two phases.

2.2.4 The extended afterglow

The majority of articles in the current literature have analyzed the afterglow emission as the result of various combinations of synchrotron and inverse Compton processes [35]. It appears, however, that this description is not completely satisfactory [48, 49, 50].

We adopted a pragmatic approach in our fireshell model by making full use of the knowledge of the equations of motion, of the EQTS formulations [72], and of the correct relativistic transformations between the comoving frame of the fireshell and the observer frame. These equations, which relate four distinct time variables, are necessary for interpreting the GRB data. They are: a) the comoving time, b) the laboratory time, c) the arrival time, and d) the arrival time at the detector corrected for cosmological effects. This is the content of the relative space-time transformation paradigm, essential for the interpretation of GRB data [83]. This paradigm requires a global rather than a piecewise description in time of the GRB phenomenon [83] and has led to a new interpretation of the burst structure paradigm [24]. As mentioned in the introduction, a new conclusion arising from the burst structure paradigm has been that emission by the accelerated baryons interacting with the CBM is indeed occurring already in the prompt emission phase, just after the P-GRB emission. This is the extended-afterglow emission, which exhibits in its “light curve” a rising part, a peak, and a decaying tail. Following this paradigm, the prompt emission phase consists therefore of the P-GRB emission and the peak of the extended afterglow. Their relative energetics and observed time separation are functions of the energy , of the baryon load , and of the CBM density distribution (see Fig. 16). In particular, fordecreasing , the extended afterglow light curve “squeezes” itself on the P-GRB and the P-GRB peak luminosity increases (see Fig. 17).

Figure 16: Plots of the arrival time separation between the P-GRB and the peak of the extended afterglow as a function of for four different values of , measured in the source cosmological rest frame. This computation has been performed assuming four values of the constant CBM density particles/cm.
Figure 17: The dependence of the shape of the light curve on . The computations have been performed assuming ergs, particles/cm, for three different values of the baryon load and the P-GRB duration fixed, i.e., s. For decreasing , the extended afterglow light curve squeezes itself onto the P-GRB and the peak becomes sharper and higher.

To evaluate the extended-afterglow spectral properties, we adopted an ansatz for the spectral properties of the emission in the collisions between the baryons and the CBM in the comoving frame. We then evaluated all observational properties in the observer frame by integrating over the EQTS. The initial ansatz of a thermal spectrum [24] has recently been modified to

(2)

where is a phenomenological parameter defined in the comoving frame of the fireshell [84], determined by the optimization of the simulation of the observed data. It is well known that in the ultrarelativistic collision of protons and electrons with the CBM, collective processes of ultrarelativistic plasma physics are expected, which are not yet fully explored and understood (e.g. the Weibel instability, see Ref. \refcite1999ApJ…526..697M). Promising results along this line have already been obtained in Refs. \refcite2008ApJ…673L..39S,2009ApJ…700..956M and may lead to the understanding of the physical origin of the parameter in Eq. 2.

To take into due account the filamentary, clumpy and porous structure of the CBM, we introduced the additional parameter , which describes the fireshell surface-filling factor. It is defined as the ratio between the effective emitting area of the fireshell and its total visible area , see e.g. Refs. \refcite2002ApJ…581L..19R,2005AIPC..782…42R.

One of the main features of the GRB afterglow has been the observation of hard-to-soft spectral variation, which is generally absent in the first spike-like emission, and which we have identified as the P-GRB [89, 90, 91, 92]. An explanation of the hard-to-soft spectral variation has been advanced on the grounds of two different contributions: the curvature effect and the intrinsic spectral evolution. In particular, Ref. \refcite2011AN….332…92P used the model developed in Ref. \refcite2002A&A…396..705Q for the spectral lag analysis, taking into account an intrinsic band model for the GRBs and using a Gaussian profile for the GRB pulses to take into account angular effects, and they found that both provide a very good explanation for the observed time lags. Within the fireshell model we can indeed explain a hard-to-soft spectral variation in the extended-afterglow emission very naturally. Since the Lorentz factor decreases with time, the observed effective temperature of the fireshell will drop as the emission goes on, and consequently the peak of the emission will occur at lower energies. This effect is amplified by the curvature effect, which originates from the EQTS analysis. Both these observed features are considered to be responsible for the time lag observed in GRBs.

2.2.5 The simulation of a GRB light curve and spectra of the extended afterglow

The simulation of a GRB light curve and the respective spectrum also requires the determination of the filling factor and of the CBM density . These extra parameters are extrinsic and they are just functions of the radial coordinate from the source. The parameter , in particular, determines the effective temperature in the comoving frame and the corresponding peak energy of the spectrum, while determines the temporal behavior of the light curve. Particularly important is the determination of the average value of . Values on the order of - particles/cm have been found for GRBs exploding inside star-forming region galaxies, while values on the order of particles/cm have been found for GRBs exploding in galactic halos [89, 90, 92]. It is found that the CBM is typically formed of “clumps”. This clumpy medium, already predicted in pioneering work by Fermi on the theoretical study of interstellar matter in our galaxy [95, 96], is by now well-established both from the GRB observations and by additional astrophysical observations, see e.g. the CBM observed in SNe [97], or by theoretical considerations involving a super-giant massive star clumpy wind [98].

The determination of the parameter and depends essentially on the reproduction of the shape of the extended-afterglow and of the respective spectral emission in a fixed energy range. Clearly, the simulation of a source within the fireshell model is much more complicated than simply fitting the photon spectrum of the burst (number of photons at a given energy) with analytic phenomenological formulas for a finite temporal range of the data. It is a consistent picture, which has to find the best value for the parameters of the source, the P-GRB [24], its spectrum, its temporal structure, as well as its energetics. For each spike in the light curve the parameters of the corresponding CBM clumps are computed, taking into account all the thousands of convolutions of comoving spectra over each EQTS that leads to the observed spectrum [72, 82]. It is clear that, since the EQTSs encompass emission processes occurring at different comoving times weighted by their Lorentz and Doppler factors, the “fitting” of a single spike is not only a function of the properties of the specific CBM clump but of the entire previous history of the source. Any mistake at any step of the simulation process affects the entire evolution that follows and conversely, at any step a fit must be made consistently with the entire previous history: because of the nonlinearity of the system and the EQTSs, any change in the simulation produces observable effects up to a much later time. This leads to an extremely complicated trial and error procedure in the data simulation, in which the variation of the parameters defining the source are increasingly narrowed down, reaching uniqueness very quickly. Of course, we cannot expect the last parts of the simulation to be very accurate, since some of the basic hypotheses about the equations of motion and possible fragmentation of the shell can affect the procedure.

In particular, the theoretical photon number spectrum to be compared with the observational data is obtained by an averaging procedure over instantaneous spectra. In turn, each instantaneous spectrum is linked to the simulation of the observed multiband light curves in the chosen time interval. Therefore, the simulation of the spectrum and of the observed multiband light curves have to be performed together and have optimized simultaneously.

2.2.6 The canonical long GRBs

According to the fireshell model theory, the canonical long GRBs are characterized by a baryon load varying in the range and they occur in a typical galactic CBM with an average density particle/cm. As a result the extended afterglow is predominant with respect to the P-GRB (see Fig. 13).

2.2.7 The disguised short GRBs

After the observations by Swift of GRB 050509B [99], which was declared in the literature as the first short GRB with an extended emission ever observed, it has become clear that all such sources are actually disguised short GRBs [92]. It is conceivable and probable that also a large fraction of the declared short duration GRBs in the BATSE catalog, observed before the discovery of the afterglow, are members of this class. In the case of the disguised short GRBs the baryon load varies in the same range of the long bursts, while the CBM density is of the order of particles/cm. As a consequence, the extended afterglow results in a “deflated” emission that can be exceeded in peak luminosity by the P-GRB [89, 100, 90, 91, 92]. Indeed the integrated emission in the extended afterglow is much larger than the one of the P-GRB (see Fig. 13), as expected for long GRBs. With these understandings long and disguised short GRBs are interpreted in terms of long GRBs exploding, respectively, in a typical galactic density or in a galactic halo density. This interpretation has been supported by direct optical observations of GRBs located in the outskirts of the host galaxies [101, 102, 103, 104, 105, 106, 107].

2.2.8 The class of genuine short GRBs

The canonical genuine short GRBs occur in the limit of very low baryon load, e.g. with the P-GRB predominant with respect to the extended afterglow. For such small values of the afterglow peak emission shrinks over the P-GRB and its flux is lower than that of the P-GRB (see Fig. 17).

Since the baryon load is small but not zero, in addition to the predominant role of the P-GRB, which has a thermal spectrum, a nonthermal component originating from the extended afterglow is expected.

The best example of a genuine short GRB is GRB 090227B (see details in Ref. \refcite2013ApJ…763..125M).

2.3 Observations and data analysis of GRB 090227B

At 18:31:01.41 UT on February 27, 2009, the Fermi-GBM detector [108] triggered and located the short and bright burst GRB 090227B (trigger 257452263/090227772). The on-ground calculated location, using the GBM trigger data, was (RA, Dec)(J2000)=(114836, 32), with an uncertainty of 1.77 (statistical only). The angle from the Fermi LAT boresight was 72. The burst was also located by IPN [109] and detected by Konus-Wind [110], showing a single pulse with duration s ( keV – MeV). No X-rays or optical observations were reported on the GCN Circular Archive, so the redshift of the source is unknown.

To obtain the Fermi-GBM light-curves and the spectrum in the energy range keV – MeV, we made use of the RMFIT program. For the spectral analysis, we have downloaded from the gsfc website 111ftp://legacy.gsfc.nasa.gov/fermi/data/gbm/bursts the TTE (Time-Tagged Events) files, suitable for short or highly structured events. We used the light curves corresponding to the NaI-n2 ( keV) and the BGO-b0 ( keV – MeV) detectors. The ms binned GBM light curves show one very bright spike with a short duration of s, in the energy range keV – MeV, and a faint tail lasting up to s after the trigtime in the energy range keV – MeV. After the subtraction of the background, we have proceeded with the time-integrated and time-resolved spectral analyses.

2.3.1 Time-integrated spectral analysis

We have performed a time-integrated spectral analysis in the time interval from s to s, which corresponds to the duration of the burst. We have fit the spectrum in this time interval considering the following models: comptonization (Compt) plus power-law (PL) and band [111] plus PL, as outlined, e.g. in Ref. \refcite2010ApJ…725..225G, as well as a combination of black body (BB) and band (see Fig. 18). Within the time interval, the BB+Band model improves the fit with respect to the Compt+PL model at a confidence level of . The comparison between Band+PL and Compt+PL models is outside such a confidence level (about ). The direct comparison between BB+Band and Band+PL models, which have the same number of degrees of freedom, provides almost the same C-STAT values for the BB+Band and Band+PL models (). This means that all three models are viable. For the BB+Band model, the ratio between the fluxes of the thermal component and the non-thermal (NT) component is . The BB component is important for the determination of the peak of the spectrum and has an observed temperature keV.

Figure 18: The 64 ms time-binned NaI-n2 light curve (top left panel) and the NaI-n2+BGO-b0 spectra (top right BB+Band, bottom left Band+PL, bottom right Compt+PL) of GRB 090227B in the time interval.

We have then focused our attention on the spike component, namely the time interval from s to , which we indicate in the following as the . We have repeated the time-integrated analysis considering the same spectral models of the previous interval (see Fig. 19). Within the time interval, both the BB+Band and Band+PL models marginally improve the fit of the data with respect to the Compt+PL model within a confidence level of . Again, the C-STAT values of the BB+Band and Band+PL models are almost the same () and they are statically equivalent in the . For the BB+Band model, the observed temperature of the thermal component is keV and the flux ratio between the BB and NT components increases up to .

Figure 19: The same considerations as in Fig. 18, in the time interval.

We have performed a further analysis in the time interval from s to s, which we indicate as , by considering the BB+PL, Compt and PL models (see Fig. 20). The statistical comparison shows that the best fit is the Compt model and a thermal component is ruled out. For details, see Ref. \refcite2013ApJ…763..125M.

In view of the above, we have focused our attention on the fit of the data of the BB+Band model within the fireshell scenario, being equally probable from a mere statistical point of view with the other two choices, namely the Band+PL and Compt+PL. According to the fireshell scenario (see Sec. 2.2.3), the emission within the time interval is related to the P-GRB and is expected to be thermal. In addition the transition between the transparency emission of the P-GRB and the extended afterglow is not sharp. The time separation between the P-GRB and the peak of the extended afterglow depends on the energy of the plasma , the baryon load and the CBM density (see Fig. 17). As shown in Figs. 16 and 17, for decreasing values of an early onset of the extended afterglow in the P-GRB spectrum occurs and thus an NT component in the is expected. As a further check, the theory of the fireshell model indeed predicts in the early part of the prompt emission of GRBs a thermal component due to the transparency of the plasma (see Sec. 2.2), while in the extended afterglow no thermal component is expected (see Sec. 2.2.4), as observed in the time interval.

Our theoretical interpretation has shown to be consistent with the observational data and the statistical analysis. From an astrophysical point of view the BB+Band model is preferred over the other two models, statistically equivalent in view of the above theoretical considerations.

Figure 20: The 64 ms time-binned NaI-n2 light curve (top left panel) and the NaI-n2+BGO-b0 spectra (top right BB+PL, bottom left Compt, bottom right PL) of GRB 090227B in the time interval.

2.3.2 Time-resolved spectral analysis

We have performed a time-resolved spectral analysis on selected shorter time intervals of ms (see Fig. 21) in order to correctly identify the P-GRB, namely finding out in which time interval the thermal component exceeds or at least has a comparable flux with respect to the NT one due to the onset of the extended afterglow. In this way we can single out the contribution of the NT component in the spectrum of the P-GRB.

Figure 21: The ms time-binned NaI-n2 light curve of GRB 090227B in the time interval from s to s; each time bin corresponds to the time-resolved interval considered in the Sec. 2.3.2.

Within the first time-resolved interval the BB+PL model has a thermal flux times bigger than the PL flux; the fit with the BB+Band provides , where the NT component is in this case the band model. In the second and fourth intervals, the BB+Band model provides an improvement at a significance level of in the fitting procedure with respect to the simple band model. In the third time interval as well as in the remaining time intervals up to s the band spectral models provide better fits with respect to the BB+NT ones.

This is exactly what we expect from our theoretical understanding: from s to s we have found the edge of the P-GRB emission, in which the thermal components have fluxes higher or comparable to the NT ones. The third interval corresponds to the peak emission of the extended afterglow (see Fig. 24). The contribution of the extended afterglow in the remaining time intervals increases, while the thermal flux noticeably decreases.

We have then explored the possibility of a further rebinning of the time interval , taking advantage of the large statistical content of each time bin. We have plotted the NaI-n2 light curve of GRB 090227B using time bins of 16 ms (see Fig. 22, left panels). The re-binned light curves show two spike-like substructures. The duration of the first spike is ms and it is clearly distinct from the second spike. In this time range the observed BB temperature is keV and the ratio between the fluxes of the thermal and non-thermal components is . Consequently, we have interpreted the first spike as the P-GRB and the second spike as part of the extended afterglow. Their spectra are shown in Fig. 22, right panels.

Figure 22: The 16 ms time-binned NaI-n2 light curves of the P-GRB (left upper panel) and the extended afterglow (left lower panel) and their NaI-n2+BGO-b0 spectra (on the right, the upper panel for the P-GRB and the lower one for the extended afterglow). The fit of the P-GRB is composed of a BB superimposed by a band spectrum; the extended afterglow is well fit by a simple band function.

2.4 Analysis of GRB 090227B in the fireshell model

The identification of the P-GRB is fundamental in order to determine the baryon load and the other physical quantities characterizing the plasma at the transparency point (see Fig. 15). It is crucial to determine the cosmological redshift, which can be derived by combining the observed fluxes and the spectral properties of the P-GRB and of the extended afterglow with the equation of motion of our theory. From the cosmological redshift we derive and the relative energetics of the P-GRB and of the extended afterglow components (see Fig. 15). Having so derived the baryon load and the energy , we can constrain the total energy and simulate the canonical light curve of the GRBs with their characteristic pulses, modeled by a variable number density distribution of the CBM around the burst site.

2.4.1 Estimation of the redshift of GRB 090227B

Having determined the redshift of the source, the analysis consists of equating (namely is a lower limit on ) and inserting a value of the baryon load to complete the simulation. The right set of and is determined when the theoretical energy and temperature of the P-GRB match the observed ones of the thermal emission [namely and ].

In the case of GRB 090227B we have estimated (see Ref. \refcite2013ApJ…763..125M) the ratio from the observed fluences

(3)

where is the luminosity distance of the source and are the fluences. The fluence of the BB component of the P-GRB is erg/cm. The total fluence of the burst is erg/cm and has been evaluated in the time interval from s to s. This interval differs slightly from because of the new time boundaries defined after the rebinning of the light curve at a resolution of ms. Therefore the observed energy ratio is . As is clear from the bottom right diagram in Fig. 15, for each value of this ratio we have a range of possible parameters and . In turn, for each of their values we can determine the theoretical blue-shifted toward the observer temperature (see the top right diagram in Fig. 15). Correspondingly, for each pair of values of and we estimate the value of by the ratio between and the observed temperature of the P-GRB ,

(4)

In order to remove the degeneracy , we have made use of the isotropic energy formula

(5)

in which is the photon spectrum of the burst and the integrals are due to the bolometric correction on . By imposing the condition , we have found the values for and ergs. The complete quantities determined in this way are summarized in Table 2.4.1.

\tbl

The results of the simulation of GRB 090227B in the fireshell model. fireshell Parameter Value  [erg]  [cm]  [keV] [particles/cm]

2.4.2 The analysis of the extended afterglow and the observed spectrum of the P-GRB

As mentioned in Sec. 2.2, the arrival time separation between the P-GRB and the peak of the extended afterglow is a function of and and depends on the detailed profile of the CBM density. For (see Fig. 16) the time separation is s in the source cosmological rest frame. In this light, there is an interface between reaching transparency in the P-GRB and the early part of the extended afterglow. This connection has already been introduced in the literature, see e.g. Refs. \refcite2012MNRAS.420..468P,2012A&A…543A..10I,2012A&A…538A..58P.

\tbl

The density mask of GRB 090227B: in the first column we list the number of CBM clouds, in the second one their distance away from the BH, and in the third one the number density with the associated error box. Cloud Distance [cm] [/cm]

Figure 23: The radial CBM density distribution of GRB 090227B (black line) and its range of validity (red shaded region).
Figure 24: The NaI-n2 simulated light curve of the extended-afterglow of GRB 090227B; each spike corresponds to the CBM density profile described in Table 2.4.2 and Fig. 23. The zero of the lower -axis corresponds to the trigtime ; the zero of the upper -axis is the time from which we have started the simulation of the extended afterglow, , namely s after .
Figure 25: Left panel: the simulated photon number spectrum of the extended-afterglow of GRB 090227B (from s to s) in the energy band keV, compared to the NaI-n2 data in the same time interval. Right panel: the same simulated spectrum, with the same parameters, extended up to MeV and compared to the NaI-n2 and the BGO-b0 data in the same time interval.

From the determination of the initial values of the energy ergs, the baryon load , and the Lorentz factor , we have simulated the light curve of the extended afterglow by deriving the radial distribution of the CBM clouds around the burst site (see Table 2.4.2 and Fig. 23). In particular, each spike in Fig. 23 corresponds to a CBM cloud. The error boxes on the number density on each cloud is defined as the maximum possible tolerance to ensure agreement between the simulated light curve and the observed data. The average value of the CBM density is particles/cm with an average density contrast (see also Table 2.4.1). These values are typical of the galactic halo environment. The filling factor varies in the range , up to cm away from the burst site, and then drops to the value . The value of the parameter has been found to be along the entire duration of the GRB. In Fig. 24 we show the NaI-n2 simulated light curve ( keV) of GRB 090227B and in Fig. 25 (left panel) the corresponding spectrum in the early s of the emission, using the spectral model described by Eq. 2. The simulation of the extended afterglow starts s after the trigtime . At the 13 Marcel Grossmann Meeting in 2012, G. Vianello suggested extending our simulations from MeV all the way to MeV, since significant data are available from the BGO detector. Without changing the parameters used in the theoretical simulation of the NaI-n2 data, we have extended the simulation up to MeV and have compared the results with the BGO-b0 data (see Fig. 25, right panel). The theoretical simulation we performed, optimized on the NaI-n2 data alone, is perfectly consistent with the observed data all over the entire range of energies covered by the Fermi-GBM detector, both NaI and BGO.

We turn now to the emission of the early ms. We have studied the interface between the P-GRB emission and the on-set of the extended afterglow emission. In Fig. 26 we have plotted the thermal spectrum of the P-GRB and the fireshell simulation (from s to s) of the early interaction of the extended afterglow. The sum of these two components is compared with the observed spectrum from the NaI-n2 detector in the energy range keV (see Fig. 26, left panel). Then again, from the theoretical simulation in the energy range of the NaI-n2 data, we have verified the consistency of the simulation extended up to MeV with the observed data all over the range of energies covered by the Fermi-GBM detector, both NaI and BGO. The result is shown in Fig. 26 (right panel).

Figure 26: Left panel: the time-integrated (from s to s) fireshell simulation in the energy band keV, dashed blue line, and the BB emission, dashed-dotted green line; the sum of the two components, the solid red line, is compared to the observed P-GRB emission. Right panel: the same considerations including the BGO data up to MeV.

2.5 Conclusions

The comprehension of this short GRB has been improved by analyzing the different spectra in the , and time intervals. We have shown that within the and the all the considered models (BB+Band, Band+PL, Compt+PL) are viable, while in the time interval, the presence of a thermal component is ruled out. The result of the analysis in the time interval gives an additional correspondence between the fireshell model (see Sec. 2.2.4) and the observational data. According to this picture, the emission within the time interval is related to the P-GRB and it is expected to have a thermal spectrum with in addition an extra NT component due to an early onset of the extended afterglow. In this time interval a BB with an additional band component has been observed and we have shown that it is statistically equivalent to the Compt+PL and the Band+PL models. Our theoretical interpretation is consistent with the observational data and statistical analysis. From an astrophysical point of view the BB+Band model is preferred over the Compt+PL and the Band+PL models, being described by a consistent theoretical model.

GRB 090227B is the missing link between the genuine short GRBs, with the baryon load and theoretically predicted by the fireshell model [115, 24, 83], and the long bursts.

From the observations, GRB 090227B has an overall emission lasting s with a fluence of erg/cm in the energy range keV – MeV. In absence of an optical identification, no determination of its cosmological redshift and of its energetics was possible.

Thanks to the excellent data available from Fermi-GBM [32], it has been possible to probe the comparison between the observations and the theoretical model. In this sense, we have then performed a more detailed spectral analysis on the time scale as short as ms of the time interval . As a result we have found in the early ms a thermal emission which we have identified with the theoretically expected P-GRB component. The subsequent emission of the time interval has been interpreted as part the extended afterglow. Consequently, we have determined the cosmological redshift , as well as the baryon load , its energetics, ergs, and the extremely high Lorentz factor at the transparency .

We are led to the conclusion [34] that the progenitor of this GRB is a binary neutron star, which for simplicity we assume to have the same mass, by the following considerations:

  1. the very low average number density of the CBM, particles/cm; this fact points to two compact objects in a binary system that have spiraled out in the halo of their host galaxy [89, 100, 116, 90, 91, 92];

  2. the large total energy, ergs, which we can indeed infer in view of the absence of beaming, and the very short time scale of the emission also point to two neutron stars. We are led to a binary neutron star with total mass larger than the neutron star critical mass, . In light of the recent neutron star theory in which all the fundamental interactions are taken into account, see Ref. \refcite2012NuPhA.883….1B, we obtain for simplicity in the case of equal neutron star masses, , radii km, where we have used the NL3 nuclear model parameters for which ;

  3. the very small value of the baryon load is consistent with the above two neutron stars which have crusts km thick. The new theory of the neutron stars developed in Ref. \refcite2012NuPhA.883….1B leads to the prediction of GRBs with still smaller baryon load and consequently shorter periods. We indeed infer an absolute upper limit on the energy emitted via gravitational waves of ergs [34].

Figure 27: The energy emitted in the extended afterglow (green curve) and in the P-GRB (red curve) in units of the total energy erg are plotted as functions of the parameter . In the figure are also shown some values of the baryon load: in black GRB 090227B and in red and blue some values corresponding to, respectively, some long and some disguised short GRBs that we analyzed.
\tbl

List of the long and disguised short GRBs labeled in Fig. 27 with in addition GRB 090227B. For each burst the total energy of the plasma, the baryon load, and the average CBM density are indicated. label GRB [erg] [#/cm] (a) 090618 (b) 080319B (c) 991216 (d) 030329 (e) 031203 (f) 050509B (g) 060614 (h) 970228 090227B

We can then generally conclude the existence of three different possible structures for the canonical GRBs (see Fig. 27 and Table 2.5):

  1. long GRBs with baryon load , exploding in a CBM with average density of particle/cm, typical of the inner galactic regions;

  2. disguised short GRBs with the same baryon load as the previous class, but occurring in a CBM with particle/cm, typical of galactic halos [89, 100, 116, 90, 91, 92];

  3. genuine short GRBs which occur for with the P-GRB predominant with respect to the extended afterglow and exploding in a CBM with particle/cm, typical again of galactic halos, GRB 090227B being the first example.

Finally, if we turn to the theoretical model within a general relativistic description of the gravitational collapse to a BH, see e.g. Refs. \refcite2003PhLB..573…33R,2005IJMPD..14..131R and Fig. 2 in Ref. \refcite2006NCimB.121.1477F, we find it necessary to use time resolutions on the order of a fraction of a ms, possibly down to s, in order to follow such a process. One would need new space missions with larger collecting area to prove with great accuracy the identification of a thermal component. It is likely that an improved data acquisition with high signal to noise ratio on a shorter time scale would show more clearly the thermal component as well as distinguish more effectively different fitting procedures.

3 Unveiling the GRB-SN Connection

3.1 Introduction

Until recently, all the X- and -ray activities of a signal sufficiently short in time, less than s, and of extragalactic origin have been called a GRB. A new situation has occurred with the case of GRB 090618 [120] in which the multi-component nature of GRBs has been illustrated. This GRB is a member of a special class of bursts associated with a SN. It is now clear from the detailed analysis that there are at least three different components in the nature of this GRB: episode 1 which corresponds to the early emission of the SN event with Lorentz factor ; episode 2 which corresponds to the GRB with Lorentz factor ; and episode 3 which appears to be related to the activities of the newly born NS. I will describe a few key moments in the recent evolution of our understanding of this system which is very unique within physics and astrophysics.

3.2 The case of GRB 090618

GRB 090618 represents the prototype of a class of energetic ( erg) GRBs, characterized by the presence of a supernova observed 10 (1+z) days after the trigger time, and the observation of two distinct emission episodes in their hard X-ray light curve (see details in Ref. \refcite2012A&A…543A..10I).

It was discovered by the Swift satellite [121]. The BAT light curve shows a multi-peak structure, whose total estimated duration is 320 s and whose T duration in the (15–350) keV range was 113 s [122]. The first 50 s of the light curve shows a smooth decay trend followed by a spiky emission, with three prominent peaks at 62, 80, and 112 s after the trigger time, respectively, and each have the typical appearance of a FRED pulse [123], see Fig. 29. The time-integrated spectrum, (t - 4.4, t + 213.6) s in the (15–150)keV range, was found to agree with a power-law spectral model with an exponential cut-off, whose photon index is = 1.42 0.08 and a cut-off energy = 134 19 keV [124]. The XRT observations started 125 s after the BAT trigger time and lasted 25.6 ks [125] and reported an initially bright uncatalogued source, identified as the afterglow of GRB 090618. Its early decay is very steep, ending at 310 s after the trigger time, when it starts a shallower phase, the plateau. Then the light curve breaks into a steeper late phase.

GRB 090618 was observed also by the Gamma-ray Burst Monitor (GBM) on board the Fermi satellite [32]. From a first analysis, the time-integrated spectrum, (, + 140) s in the (8–1000)keV range, was fit by a band [111] spectral model, with a peak energy = 155.5 keV, = and = [126], but with strong spectral variations within the considered time interval.

The redshift of the source is and it was determined thanks to the identification of the MgII, Mg I, and FeII absorption lines using the KAST spectrograph mounted at the 3 m Shane telescope at the Lick observatory [127]. Given the redshift and the distance of the source, we computed the emitted isotropic energy in the 8 – 10000 keV energy range, with the Schaefer formula [128]: using the fluence in the (8–1000 keV) as observed by Fermi-GBM, S = 2.7 10 [126], and the Cold Dark Matter (CDM) cosmological standard model = 70 km/s/Mpc, = 0.27, = 0.73, we obtain for the emitted isotropic energy the value of E = 2.90 10 erg.

This GRB was observed also by Konus-WIND [129], Suzaku-WAM [108], and by the AGILE satellite [130], which detected emission in the (18–60) keV and in the MCAL instrument, operating at energies greater than 350 keV, but it did not observe high-energy photons above 30 MeV. GRB 090618 was the first GRB observed by the Indian payloads RT-2 on board the Russian satellite CORONAS-PHOTON [131, 132, 133].

Thanks to the complete data coverage of the optical afterglow of GRB 090618, the presence of a supernova underlying the emission of its optical afterglow was reported [134]. The evidence of a supernova emission came from the presence of several bumps in the light curve and by the change in - color index over time: in the early phases, the blue color is dominant, typical of the GRB afterglow, but then the color index increases, suggesting a core-collapse SN. At late times, the contribution from the host galaxy was dominant.

Figure 28: RT2 light curves of GRB 090618.

3.2.1 Data analysis

We have analyzed GRB 090618, considering the BAT and XRT data of the Swift satellite together with the Fermi-GBM and RT2 data of the Coronas-PHOTON satellite (see Fig. 28). The data reduction was made with the Heasoft v6.10 packages222http://heasarc.gsfc.nasa.gov/lheasoft/ for BAT and XRT, and the Fermi-Science tools for GBM. The details of the data reduction and analysis are given in Ref. \refcite2012A&A…543A..10I.

In Table 3.2.1 we give the results of our spectral analysis. The time reported in the first column corresponds to the time after the GBM trigger time t = 267006508 s, where the parameter was not constrained, we used its averaged value, = -2.3 0.10, as delineated in Ref. \refcite2011A&A…525A..53G. We considered the chi-square statistic for testing our data fitting procedure. The reduced chi-square , where is the number of degrees of freedom (dof), which is for the NaI dataset and for that of the BGO.

For the last pulse of the second episode, the band model is not very precise ( = 2.24), but a slightly better approximation is given by a power-law with an exponential cut-off, whose fit results are shown for the same intervals in the last two columns. From these values, we built the flux light curves for both detectors, which are shown in Fig. 29.

Figure 29: Fermi-GBM flux light curve of GRB 090618 referring to the NaI (8–440 keV, left panel) and BGO (260 keV – 40 MeV, right panel) detectors.
\tbl

Time-resolved spectral analysis of GRB 090618. We considered six time intervals, each one corresponding to a particular emission feature in the light curve. We fit the GBM (8 keV – 10 MeV) observed emission with a band model [111] and a power-law function with an exponential cut-off. In columns 2–4 we list the band model low-energy index , the high-energy and the break energy , with the reduced chi-square value in the 6 column. The last three columns list the power-law index , the cut-off energy and the reduced chi-square value respectively, as obtained from the spectral fit with the cut-off power-law spectral function. Time Interval (keV) (keV) 0 - 50 -0.77 -2.33 128.12 1.11 0.91 180.9 1.13 50 - 57 -0.93 -2.30 0.10 104.98 1.22 1.11 168.3 1.22 57 - 68 -0.93 -2.43 264.0 1.85 1.01 340.5 1.93 68 - 76 -1.05 -2.49 243.9 1.88 1.12 311.0 1.90 76 - 103 -1.06 -2.65 125.7 1.23 1.15 157.7 1.39 103 - 150 -1.50 -2.30 0.10 101.1 1.07 1.50 102.8 1.06

3.2.2 Spectral analysis of GRB 090618

We proceed now to the detailed spectral analysis of GRB 090618. We divide the emission into six time intervals, shown in Table 3.2.1, each one identifying a significant feature in the emission process. We then fit for each time interval the spectra by a band model and a blackbody with an extra power-law component, following Ref. \refcite2004ApJ…614..827R. In particular, we are interested in estimating the temperature and the observed energy flux of the blackbody component. The specific intensity of emission of a thermal spectrum at energy in energy range into solid angle is

(6)

The source of radius is seen within a solid angle , and its full luminosity is . What we are fitting, however, is the background-subtracted photon spectra , which is obtained by dividing the specific intensity by the energy :

(7)

where , and are the Planck, Boltzmann, and Stefan-Boltzmann constants respectively, is the speed of light and is the observed energy flux of the blackbody emitter. The great advantage of Eq. (7) is that it is written in terms of the observables and , so from a spectral fitting procedure we can obtain the values of these quantities for each time interval considered. To determine these parameters, we must perform an integration of the actual photon spectrum over the instrumental response of the detector that observes the source, where denotes the different instrument energy channels. The result is a predicted count spectrum

(8)

where and are the boundaries of the -th energy channel of the instrument. Eq. (8) must be compared with the observed data by a fit statistic.

The main parameters obtained from the fitting procedure are shown in Table 3.2.2. We divide the entire GRB into two main episodes, as proposed in Ref. \refciteTEXAS: one lasting the first 50 s and the other from 50 to 151 s after the GRB trigger time, see Fig. 30. Clearly, the first 50 s of emission, corresponding to the first episode, are well-fit by a band model as well as a blackbody with an extra power-law model, Fig. 31. The same happens for the first 9 s of the second episode (from 50 to 59 s after the trigger time), Fig. 32. For the subsequent three intervals corresponding to the main peaks in the light curve, the blackbody plus a power-law model does not provide a satisfactory fit. Only the band model fits the spectrum with good accuracy, with the exception of the first main spike (compare the values of in the table). We find also that the last peak can be fit by a simple power-law model with a photon index = 2.20 0.03, better than by a band model.

The result of this analysis points to a different emission mechanism in the first 50 s of GRB 090618 and in the next 9 s. A sequence of very strong pulses follows, whose spectral energy distribution is not attributable either to a blackbody or a blackbody and an extra power-law component. Good evidence for the transition is shown by the test of the data fitting, whose indicator is given by the changing of () for the blackbody plus a power-law model for the different time intervals, see Table 3.2.2. Although the band spectral model is an empirical model without a clear physical origin, we checked its validity in all time-detailed spectra with the sole exception of the first main pulse of the second episode. The corresponding to the band model for this main pulse, although better than that corresponding to the blackbody and power-law case, is unsatisfactory. We now directly apply the fireshell model to make the above conclusions more stringent and reach a better understanding of the source.

\tbl

Time-resolved spectral analysis (8 keV – 10 MeV) of the second episode in GRB 090618. Time Interval (s) A 0 - 50 -0.74 0.10 -2.32 0.16 118.99 21.71 1.12 32.07 1.85 1.75 0.04 1.21 B 50 - 59 -1.07 0.06 -3.18 0.97 195.01 30.94 1.23 31.22 1.49 1.78 0.03 1.52 C 59 - 69 -0.99 0.02 -2.60 0.09 321.74 14.60 2.09 47.29 0.68 1.67 0.08 7.05 D 69 - 78 -1.04 0.03 -2.42 0.06 161.53 11.64 1.55 29.29 0.57 1.78 0.01 3.05 E 78 - 105 -1.06 0.03 -2.62 0.09 124.51 7.93 1.20 24.42 0.43 1.86 0.01 2.28 F 105 - 151 -2.63 -1 -2.06 0.02 unconstrained 1.74 16.24 0.84 2.23 0.05 1.15

Figure 30: Two episode nature of GRB 090618.
Figure 31: Time-integrated spectra for the first episode (from 0 to 50 s) of GRB 090618 fit with the band, = 1.12 (left) and blackbody + power-law (right) models, = 1.28. In the following we will consider the case of a blackbody + power-law model and infer some physical consequences. The corresponding considerations for the band model are in progress and will be published elsewhere.
Figure 32: Time-integrated spectra for the first 9 s of the second episode (from 50 to 59 s after the trigger time) of GRB 090618 fit with the band, = 1.23 (left) and blackbody + power-law (right) models, = 1.52.

3.3 Analysis of GRB 090618 in the fireshell scenario: from a single GRB to a multi-component GRB

3.3.1 Attempt for a single GRB scenario: the role of the first episode

We first approach the analysis of GRB 090618 by assuming that we observe a single GRB and attempt identification of the P-GRB emission of a canonical GRB within the fireshell scenario (see panel A in Fig. 32 and Table 3.2.2). This has been shown to be inconsistent (see details in Ref. \refcite2012A&A…543A..10I). We then turn to a multicomponent emission.

3.3.2 The multi-component scenario: the second episode as an independent GRB

The identification of the P-GRB of the second episode.

We now proceed to the analysis of the data between 50 and 150 s after the trigger time as a canonical GRB in the fireshell scenario, namely the second episode [120], see Fig. 30. We proceed to identify the P-GRB within the emission between 50 and 59 s, since we find a blackbody signature in this early second-episode emission. Considerations based on the time variability of the thermal component bring us to conclude that the first 4 s of this time interval to due to the P-GRB emission. The corresponding spectrum (8–440 keV) is well fit () with a blackbody of a temperature keV (norm = 3.51 0.49), and an extra power-law component with photon index = 1.85 0.06, (norm = 46.25 10.21), see Fig. 33. The fit with the band model is also acceptable (), which gives a low-energy power-law index , a high-energy index and a break energy , see Fig. 33. In view of the theoretical understanding of the thermal component in the P-GRB (see Section 3.2), we focus below on the blackbody + power-law spectral model.

The isotropic energy of the second episode is = (2.49 0.02) 10 ergs. The simulation within the fireshell scenario is made assuming . From the observed temperature, we can then derive the corresponding value of the baryon load. The observed temperature of the blackbody component is , so that we can determine a value of the baryon load of 10, and deduce the energy of the P-GRB as a fraction of the total . We therefore obtain a value of the P-GRB energy of 4.33 10 erg.

Now we can derive the radius of the transparency condition, to occur at = 1.46 10 cm. From the third panel we derive the bulk Lorentz factor of = 495. We compare this value with the energy measured only in the blackbody component of = 9.24 10 erg, and with the energy in the blackbody plus the power-law component of = 5.43 10 erg, and verify that the theoretical value is in between these observed energies. We have found this result to be quite satisfactory: it represents the first attempt to relate the GRB properties to the details of the BH responsible for the overall GRB energetics. The above theoretical estimates were based on a nonrotating BH of 10 M, a total energy of = 2.49 10 erg and a mean temperature of the initial plasma of 2.4 MeV, derived from the expression for the dyadosphere radius, Eq. 1. Any refinement of the direct comparison between theory and observations will have to address a variety of fundamental problems such as 1) the possible effect of rotation of the BH, leading to a more complex dyadotorus structure, 2) a more detailed analysis of the transparency condition of the plasma, simply derived from the condition = [69], and 3) an analysis of the general relativistic, electrodynamical, strong interaction descriptions of the gravitational core collapse leading to BH formation [21, 137, 69].

Figure 33: Left panel, the time-integrated spectrum (8–440 keV) for the P-GRB emission episode (from 50 to 54 s after the trigger time) of GRB 090618 fit with the blackbody + power-law models, = 1.15, while the right panel shows the fit with a band model, = 1.25.
Figure 34: Fireshell simulation, green line, and the sole blackbody emission, red line, of the time-integrated (t0+50, t0+54 s) spectrum of the P-GRB emission. The sum of the two components, the blue line, is the total simulated emission in the first 4 s of the second episode.
The analysis of the extended afterglow of the second episode.

The extended afterglow starts at the above given radius of the transparency, with an initial value of the Lorentz factor of = 495. To simulate the extended-afterglow emission, we need to determine the radial distribution of the CBM around the burst site, which we assume for simplicity to be spherically symmetric, from which we infer a characteristic size of cm. We already described above how the simulation of the spectra and of the observed multi-band light curves have to be performed together and need to be jointly optimized, leading to the determination of the fundamental parameters characterizing the CBM medium [138]. This radial distribution is shown in Fig. 35 and is characterized by a mean value of = 0.6 part/cm and an average density contrast with a 2, see Fig. 35 and Table 3.3.2. The data up to 8.5 10 cm are simulated with a value for the filling factor , while the data from this value on with . From the radial distribution of the CBM density, and considering the effect on the fireshell visible area, we found that the CBM clumps causing the spikes in the extended-afterglow emission have masses on the order of g. The value of the parameter was found to be along the total duration of the GRB.

In Fig. 36 we show the simulated light curve (8–1000 keV) of the GRB and the corresponding spectrum, using the spectral model described in Refs. \refcite2004ApJ…605L…1B,2011IJMPD..20.1983P.

We focus our attention on the structure of the first spikes. The comparison between the spectra of the first main spike (t+59, t+66 s) of the extended afterglow of GRB 090618 obtained with three different assumptions is shown in Fig. 37: in the upper panel we show the fireshell simulation of the integrated spectrum (t0+59, t0+66 s) of the first main spike, in the middle panel we show the best fit with a blackbody and a power-law component model and in the lower panel the best fit using a simple power-law spectral model.

We can see that the fit with the last two models is not satisfactory: the corresponding is 7 for the blackbody + power-law and 15 for the simple power-law. We cannot give the of the fireshell simulation, since it is not represented by an explicit analytic fitting function, but it originates in a sequence of complicated highly nonlinear procedures. It is clear from a direct scrutiny that it correctly reproduces the low-energy emission, thanks in particular to the role of the parameter, which was described previously. At higher energies, the theoretically predicted spectrum is affected by the cut-off induced by the thermal spectrum. The temporal variability of the first two spikes is well simulated.

We are not able to accurately reproduce the last spikes of the light curve, since the equations of motion of the accelerated baryons become very complicated after the first interactions of the fireshell with the CBM [138]. This happens for various reasons. First, a possible fragmentation of the fireshell can occur [138]. Moreover, at larger distances from the progenitor, the fireshell visible area becomes larger than the transverse dimension of a typical blob of matter, consequently a modification of the code for a three-dimensional description of the interstellar medium will be needed. This is unlike the early phases in the prompt emission, which is the main topic we address at the moment, where a spherically symmetric approximation applies. The fireshell visible area is smaller than the typical size of the CBM clouds in the early phases of the prompt radiation [139].

The second episode, lasting from 50 to 151 s, agrees with a canonical GRB in the fireshell scenario. Particularly relevant is the problematic presented by the P-GRB. It interfaces with the fundamental physics problems, related to the physics of the gravitational collapse and the BH formation. There is an interface between reaching transparency of the P-GRB and the early part of the extended afterglow. This connection has already been introduced in the literature, see e.g. Ref. \refcite2012MNRAS.420..468P. We studied this interface in the fireshell by analyzing the thermal emission at the transparency with the early interaction of the baryons with the CBM matter, see Fig. 34.

We now aim to reach a better understanding of the meaning of the first episode, between 0 and 50 s of the GRB emission. To this end we examine the two episodes with respect to 1) the Amati relation, 2) the hardness variation, and 3) the observed time lag.

Figure 35: Radial CBM density distribution for GRB 090618. The characteristic masses of each cloud are on the order of 10 g and 10 cm in radii.
\tbl

Final results of the simulation of GRB 090618 in the fireshell scenario. Parameter Value 2.49 0.02 10 ergs 1.98 0.15 10 495 40 29.22 2.21 keV 4.33 0.28 10 ergs

\tbl

Physical properties of the three clouds surrounding the burst site: the distance from the burst site (column 2), the radius of the cloud (column 3), the particle density (column 4), and the mass (the last column). Cloud Distance (cm) r (cm) (#/cm) M (g) First 4.0 10 1 10 1 2.5 10 Second 7.4 10 5 10 1 3.1 10 Third 1.1 10 2 10 4 2.0 10

Figure 36: Simulated light curve and time integrated (t0+58, t0+150 s) spectrum (8–440 keV) of the extended-afterglow of GRB 090618.
Figure 37: Simulated time-integrated (t0+58, t0+66 s) count spectrum (8-440 keV) of the extended afterglow of GRB 090618 (upper panel), count spectrum (8 keV – 10 MeV) of the main pulse emission (t0+58, t0+66), and best fit with a blackbody + power-law model (middle panel) and a simple power-law model (lower panel).

3.3.3 A different emission process in the first episode

The time-resolved spectra and temperature variation.

One of the most significant outcomes of the multi-year work of Felix Ryde and his collaborators Ref. \refcite2010ApJ…709L.172R has been the identification and the detailed analysis of the thermal plus power-law features observed in time-limited intervals in selected BATSE GRBs. Similar features have also been observed in the data acquired by the Fermi satellite [140, 141]. We propose to divide these observations into two broad families. The first family presents a thermal plus power-law(s) feature, with a temperature changing in time following a precise power-law behavior. The second family is also characterized by a thermal plus power-law component, but with the blackbody emission generally varying without a specific power-law behavior and on shorter time scales. It is our goal to study these features within the fireshell scenario to possibly identify the underlying physical processes. We have already shown in Sec. 2.2.3 that the emission of the thermal plus power-law component characterizes the P-GRB emission. We have also emphasized that the P-GRB emission is the most relativistic regime occurring in GRBs, uniquely linked to the process of BH formation, see Sec. 2.2.3. This process appears to belong to the second family considered above. Our aim here is to see if the first episode of GRB 090618 can lead to the identification of the first family of events: those whose temperature changes with time following a power-law behavior on time scales from 1 to 50 s. We have already pointed out in the previous section that the hardness-ratio evolution and the long time lag observed for the first episode [133] points to a distinct origin for the first 50 s of emission, corresponding to the first episode.

We made a detailed time-resolved analysis of the first episode, considering different time bin durations to obtain good statistics in the spectra and to take into account the sub-structures in the light curve. We then used two different spectral models to fit the observed data, a classical band spectrum [111], and a blackbody with a power-law component.

To obtain more accurate constraints on the spectral parameters, we made a joint fit considering the observations from both the n4 NaI and the b0 BGO detectors, covering a wider energy range in this way, from 8 keV to 40 MeV. To avoid some bias from low-photon statistics, we considered an energy upper limit of the value of 10 MeV. In the last three columns of Table 3.3.3 we report the spectral analysis performed in the energy range of the BATSE LAD instrument ( keV), as analyzed in Ref. \refcite2009ApJ…702.1211R as a comparison tool with the results described in that paper. Our analysis is summarized in Figs. 38 and 39, and in Table 3.3.3, where we report the residual ratio diagram and the reduced- values for the spectral models.

Figure 38: Evolution of the BB+powerlaw spectral model in the spectrum of the first emission of GRB 090618. It shows the cooling with time of the blackbody and associated nonthermal components. We only plot the fitting functions for clarity.
\tbl

Time-resolved spectral analysis of the first episode in GRB 090618. We considered seven time intervals and used two spectral models, whose best-fit parameters are shown here. Time (keV) (keV) A:0 - 5 -0.45 0.11 -2.89 0.78 208.9 36.13 0.93 59.86 2.72 1.62 0.07 1.07 B:5 - 10 -0.16 0.17 -2.34 0.18 89.84 17.69 1.14 37.57 1.76 1.56 0.05 1.36 C:10 - 17 -0.74 0.08 -3.36 1.34 149.7 21.1 0.98 34.90 1.63 1.72 0.05 1.20 D:17 - 23 -0.51 0.17 -2.56 0.26 75.57 16.35 1.11 25.47 1.38 1.75 0.06 1.19 E:23 - 31 -0.93 0.13 unconstr. 104.7 21.29 1.08 23.75 1.68 1.93 0.10 1.13 F:31 - 39 -1.27 0.28 -3.20 1.00 113.28 64.7 1.17 18.44 1.46 2.77 0.83 1.10 G:39 - 49 -3.62 1.00 -2.19 0.17 57.48 50.0 1.15 14.03 2.35 3.20 1.38 1.10

We conclude that both the band and the proposed BB+PL spectral models fit the observed data very well. Particularly interesting is the clear evolution in the time-resolved spectra, which corresponds to the blackbody and power-law component, see Fig. 38. In particular the parameter of the blackbody shows a strong decay, with a temporal behavior well-described by a double broken power-law function, see the upper panel in Fig. 39. From a fitting procedure we find that the best fit (R-statistic = 0.992) for the two decay indexes for the temperature variation are = -0.33 0.07 and = -0.57 0.11. In Ref. \refcite2009ApJ…702.1211R an average value for these parameters on a set of 49 GRBs is given: = -0.07 0.19 and = -0.68 0.24.

The results presented in Figs. 38 and 39, and Table 3.3.3 point to a rapid cooling of the thermal emission with time of the first episode. The evolution of the corresponding power-law spectral component also appears to be strictly related to the change of the temperature . The power-law index falls, or softens, with temperature, see Fig. 38. An interesting feature appears to occur at the transition of the two power-laws describing the observed decrease of the temperature. The long time lag observed in the first episode has a clear explanation in the power-law behavior of the temperature and corresponding evolution of the photon index (see Figs. 38 and 39).

The radius of the emitting region.

We turn now to estimate an additional crucial parameter for identifying the nature of the blackbody component: the radius of the emitter . We proved that the first episode is not an independent GRB and not part of a GRB. We can therefore provide the estimate of the emitter radius from nonrelativistic considerations, just corrected for the cosmological redshift . In fact we find that the temperature of the emitter , and that the luminosity of the emitter, due to the blackbody emission, is

(9)

where is the emitter radius and is the Stefan-Boltzmann constant. From the luminosity distance definition, we also have that the observed flux is given by

(10)

We then obtain

(11)

The above radius differs from the radius given in Eq. (1) of Ref. \refcite2009ApJ…702.1211R, which was also clearly obtained by interpreting the early evolution of GRB 970828 as belonging to the photospheric emission of a GRB and assuming a relativistic expansion with a Lorentz gamma factor

(12)

where