On the universal GeV emission in short GRBs

On the universal GeV emission in short GRBs

R. Ruffini11affiliation: ICRA and Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy 22affiliation: Université de Nice Sophia-Antipolis, Grand Château Parc Valrose, Nice, CEDEX 2, France 33affiliation: International Center for Relativistic Astrophysics Network, Piazza della Repubblica 10, I-65122 Pescara, Italy 44affiliation: ICRANet-Rio, Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290–180 Rio de Janeiro, Brazil , M. Muccino55affiliation: Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, I-00044 Frascati, Italy , Y. Aimuratov11affiliation: ICRA and Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy 22affiliation: Université de Nice Sophia-Antipolis, Grand Château Parc Valrose, Nice, CEDEX 2, France 66affiliation: Fesenkov Astrophysical Institute, Observatory 23, 050020 Almaty, Kazakhstan , M. Amiri33affiliation: International Center for Relativistic Astrophysics Network, Piazza della Repubblica 10, I-65122 Pescara, Italy 88affiliation: Department of Physics, Isfahan University of Technology, 84156-83111, Iran , C. L. Bianco11affiliation: ICRA and Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy 33affiliation: International Center for Relativistic Astrophysics Network, Piazza della Repubblica 10, I-65122 Pescara, Italy , Y.-C. Chen11affiliation: ICRA and Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy 33affiliation: International Center for Relativistic Astrophysics Network, Piazza della Repubblica 10, I-65122 Pescara, Italy , B. Eslam Panah33affiliation: International Center for Relativistic Astrophysics Network, Piazza della Repubblica 10, I-65122 Pescara, Italy 99affiliation: Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz 71454, Iran G. J. Mathews77affiliation: Center for Astrophysics, Department of Physics, University of Notre Dame, Notre Dame, IN, 46556, USA , R. Moradi11affiliation: ICRA and Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy 33affiliation: International Center for Relativistic Astrophysics Network, Piazza della Repubblica 10, I-65122 Pescara, Italy , G. B. Pisani11affiliation: ICRA and Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy 33affiliation: International Center for Relativistic Astrophysics Network, Piazza della Repubblica 10, I-65122 Pescara, Italy , D. Primorac11affiliation: ICRA and Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy 33affiliation: International Center for Relativistic Astrophysics Network, Piazza della Repubblica 10, I-65122 Pescara, Italy , J. A. Rueda11affiliation: ICRA and Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy 33affiliation: International Center for Relativistic Astrophysics Network, Piazza della Repubblica 10, I-65122 Pescara, Italy 44affiliation: ICRANet-Rio, Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290–180 Rio de Janeiro, Brazil , Y. Wang11affiliation: ICRA and Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy 33affiliation: International Center for Relativistic Astrophysics Network, Piazza della Repubblica 10, I-65122 Pescara, Italy
Abstract

Within the classification of gamma-ray bursts (GRBs) in different subclasses we give further evidence that short bursts, originating from binary neutron star (B-NS) progenitors, exist in two subclasses: the short gamma-ray flashes (S-GRFs) and the short gamma-ray bursts (S-GRBs). It has already been shown that S-GRFs occur when the B-NS mergers lead to a massive neutron star (M-NS), having the isotropic energy  erg and a soft spectrum with a peak at a value of  MeV. Similarly, S-GRBs occur when B-NS merging leads to the formation of a black hole (BH), with isotropic energy  erg and a hard spectrum with a peak at a value of  MeV. We here focus on 18 S-GRFs and 6 S-GRBs, all with known or derived cosmological redshifts following Fermi-LAT observations. We evidence that all S-GRFs have no GeV emission. The S-GRBs all have GeV emission and their  GeV luminosity light-curves as a function of time in the rest-frame follow a universal power-law,  erg s. From the mass formula of a Kerr BH we can correspondingly infer for S-GRBs a minimum BH mass in the range of and a corresponding maximum dimensionless spin in the range of .

Subject headings:
gamma-ray bursts: general — binaries: general — stars: neutron — supernovae: general — black hole physics — hydrodynamics

1. Introduction

Following the discovery of gamma-ray bursts (GRBs) by the Vela satellite (Klebesadel et al., 1973), the Compton Gamma-Ray Observatory (CGRO) provided the first spectral and temporal burst dataset which led, among others, to a classification into short and long bursts (Mazets et al. 1981; Klebesadel 1992; Dezalay et al. 1992; Kouveliotou et al. 1993; Tavani 1998, see also Mazets et al. 1981).

With the launch in 1996 of the Beppo-Sax mission, X-rays were added to the prompt emission gamma-ray observations, leading to three new fundamental discoveries that can be used as GRB diagnostics: 1) the X-ray afterglow (Costa et al., 1997), which allowed more precise GRB localizations in the optical bands (van Paradijs et al., 1997), 2) the determination of their cosmological redshifts (Metzger et al., 1997), which led to the proof of their cosmological nature and 3) the spatial and temporal coincidence of some long bursts with supernovae (SNe, see Galama et al., 1998).

These ground-breaking discoveries were soon enhanced by the observations of the Swift satellite (Gehrels et al., 2004) and further extended from MeV to GeV energy range by the Fermi satellite (Atwood et al., 2009).

In parallel to this sequence of fundamental observational discoveries, the theoretical comprehension of long GRBs has made significant progresses. In particular, from the earliest recognition of the expansion of the optically thick plasma as the acceleration process of GRBs, the requirement of a proper general relativistic treatment led to the introduction of four different time coordinates. Furthermore, the consideration of binary system was introduced to explain the GRB-SN coincidence (Ruffini et al., 2001a, b, c). Identification of the long GRB progenitors with initial state (in-states) tight binary system composed of a carbon-oxygen core (CO) led to the introduction of two long GRB subclasses. The core undergoes a SN explosion, forming a newborn neutron star (NS), and hypercritically accretes onto a companion NS. From the two subclasses the first is the X-ray flashes (XRFs), with a final-state (out-states) consisting of a NS-NS binary, and the second, the binary-driven hypernovae (BdHNe), with a out-state comprised of a NS-black hole (BH) binary. This progress has been summarized in three articles and references therein (Ruffini et al., 2016b; Becerra et al., 2016; Ruffini et al., 2018). The fundamental role of neutrinos has been recently discussed in Becerra et al. (2018).

The aim of this article is to use the information gained from Swift, Fermi and especially Fermi-LAT in order to probe the nature of two subclasses of short bursts: the short gamma-ray flashes (S-GRFs) and the genuine short gamma-ray bursts (S-GRBs).

The progenitor systems of short bursts have been identified in classic papers with binary NS mergers (see, e.g., Goodman, 1986; Paczynski, 1986; Eichler et al., 1989; Narayan et al., 1991, 1992; Mészáros & Rees, 1997; Berger, 2014), localized at large off-sets from their host galaxies and with no star formation evidence (see, e.g., Fox et al., 2005; Gehrels et al., 2005; Berger, 2014). This identification further evolved by the introduction of the two sub-classes of short bursts (Ruffini et al., 2015a, 2016a, 2016b; Aimuratov et al., 2017): A first sub-class corresponds to short bursts with isotropic energies  erg (in the rest-frame  keV energy band) and rest-frame spectral peak energies  MeV, expected to originate when the NS-NS merger leads to a single massive NS (M-NS) with the mass below the NS critical mass. We have defined these sources as short gamma-ray flashes (S-GRFs).

The second sub-class corresponds to the short bursts with  erg and  MeV. It is expected to originate from a NS-NS mergers in which the merged core overcomes the NS critical mass and gravitationally collapses to form a BH. We have defined them as genuine short GRBs (S-GRBs).

Indeed, the beginning of the prompt phase of S-GRBs exhibits GeV emission heralding the formation of the BH (see, e.g., Aimuratov et al., 2017; Ruffini et al., 2016a). This signature is missing in S-GRFs in which no BH is formed. For S-GRBs we derive the  GeV luminosity light-curves as a function of time in the rest-frame of the source, and show how such luminosity follows a universal power-law  erg s.

As summarized in section 2, seven different subclasses of GRBs have been identified. We update their number while recalling their in-states of the progenitors as well as their out-states in their cosmic matrix form (Ruffini et al., 2016c).

Properties of 18 S-GRFs are discussed in section 3. All of them were observed since the launch of Fermi up to the end of 2016 and have their cosmological redshifts provided. We confirm that their soft spectrum are in the range of MeV and that their isotropic energies are lower than  erg (Ruffini et al., 2016b). We also confirm that no GeV emission is observed in any of them, as expected.

In section 4 we first give the prompt and GeV emission properties for each of the 6 S-GRBs observed after the launch of Fermi, with known or derived cosmological redshifts. We confirm their harder spectra with a peak energy at MeV, and that their effective isotropic energy is larger than  erg, as expected (Ruffini et al., 2016b). For each source we give the reference in which their analysis has been done. We also present deducible from the -LAT light curve. Finally, we derive the universal power-law behavior of their GeV emission luminosity as a function of time in the rest-frame of the source, with an amplitude of and a power-law index of .

In section 5 we first recall the accretion of co-rotating or counter-rotating matter onto a Kerr BH as the possible source of the GeV emission (Ruffini et al., 2016a; Aimuratov et al., 2017). That approach, although energetically satisfactory, does not offer the possibility to infer either the mass or the spin of the BH. In this article, we indicate the basic equations relating the GeV emission to the spin and mass of the newly-formed BH for selected NS equations of state (EoS).

We summarize our main results in section 6, leading to the minimum mass and corresponding maximum dimensionless spin parameter for all 6 S-GRBs in the narrow range of and , respectively. We conclude that the observation of the GeV emission gives the necessary and sufficient condition to identify the existence of a BH in S-GRBs.

For the benefit of the reader, Table 1 summarizes the acronyms used in this work in alphabetical order.

Extended wording Acronym
Binary-driven hypernova BdHN
Binary neutron star B-NS
Black hole BH
Carbon-oxygen core CO
Gamma-ray burst GRB
Gamma-ray flash GRF
Massive neutron star M-NS
Neutron star NS
New neutron star NS
Short gamma-ray burst S-GRB
Short gamma-ray flash S-GRF
Supernova SN
Ultrashort gamma-ray burst U-GRB
White dwarf WD
X-ray flash XRF
Table 1List of acronyms used in this work.

2. Summary on seven subclasses of the fireshell model

In this paper we address the specific role of the GeV emission in order to further characterize the 7 subclasses of GRBs presented in Ruffini et al. (2016b). Toward this goal in the following we only consider sources observed after the launch of Fermi, when LAT data became available. Correspondingly, we have updated the number presented in Fig. 38 of Ruffini et al. (2018)a. In Table 2 we have, for each of the 7 subclasses of GRBs, indicated the name, the number of observed sources with definite cosmological redshift and the progenitors characterizing the initial state. In all cases the progenitors are binary systems composed of various combinations of a CO undergoing a SN explosion, a NS created in such an explosion and other compact objects, such as a white dwarf (WD), a NS or a BH. The outcome of the merging process is represented in Fig. 7 in (Ruffini et al., 2016b).

Sub-class Number In-state Out-state
(MeV) (erg) (erg)
I S-GRFs NS-NS MNS
II S-GRBs NS-NS BH
III XRFs CO-NS NS-NS
IV BdHNe CO-NS NS-BH
V BH-SN CO-BH NS-BH
VI U-GRBs NS-BH BH
VII GRFs NS-WD MNS
Table 2Summary of the GRB subclasses from (Ruffini et al., 2016b). In addition to the subclass name, we list the number of GRBs for each subclass updated by the end of 2016. We also summarize the “in-state” representing the progenitors and the “out-state”, as well as the and for each subclass. We indicate the GeV emission in the last column, which is uniquely for the BdHNe and BH-SN (in the case of long GRBs) and for the S-GRBs (in the case of short GRBs). In all of these events the GeV emission is greater than erg.

For the S-GRFs we have updated our classification and subdivided the 18 S-GRFs into three different groups: the ones without associated Fermi observations, the ones outside the boresight angle in the Fermi-LAT and the ones within the boresight angle of the Fermi-LAT; see Table 3. Their in-states are represented by a NS-NS binary and their out-state are represented by a M-NS. The absolute lower limit for the total energy of S-GRFs is  erg. Their spectral peak energy has the range of MeV  MeV and isotropic energy  erg. GeV emission is not observed in any of them.

Group S-GRF Fermi GCN GeV observed Comments
keV ( erg) (deg)
090426 no
090515 no
100724A no
No Fermi 101219A no
Observation 120804A no x-ray (GCN 13841)
130603B no kilonova (GCN 14893, 14895, 14913)
140622A no
140903A no
090927 408.64 GCN 9974 no
Outside 100117A 625.73 GCN 10345 no
Boresight 100625A 701.81 GCN 10912 no
Angle 131004A 202.45 GCN 15315 no
141004A 268.99 GCN 16900 no
080905A 443.12 GCN 8204 no
Inside 100206A 748.34 GCN 10381 no
Boresight 111117A 857.40 GCN 12573 no
Angle 150101B 141.88 GCN 17276 no Fong et al. (2015), x-ray (GCN 17431)
160821B 97.44 GCN 19843 no kilonova
Table 3List of short gamma-ray flashes (S-GRFs) divided in three different groups: 1) without Fermi-LAT observation (upper group); 2) with the Fermi-LAT observation but the boresight , and 3) those within the Fermi-LAT boresight angle (lower group, ). None of the S-GRFs have associated GeV emission detected. In the first column we indicate the name of the source, in the second their redshift, in the third column the deducible from the data, in the fourth column we estimate the which is systematically lower than the erg. For the convenience we also add both the specific GCN of the source as well as the boresight angle of the LAT observation. We also note the non-observation of the Gev emission. The last column contains comments about Kilonova emission. The symbol “” indicates no information on the LAT boresight angle due to the lack of GBM observation.

For the S-GRBs we focus our analysis on sources detected after the launch of Fermi (namely 6 sources): all of them were observed by LAT and show GeV emission implying a very broad emission angle, i.e. almost isotropic, and all of them have energies larger than  erg. The in-states corresponded to a NS-NS binary and their out-state consist of a single BH. The spectral peak energy is in the range of  MeV, with their isotropic energy in the range of  erg, with  erg. More details can be seen in section 4.

After the launch of Fermi, sources have been indicated as XRFs, with their ”in-states” represented by a CO-NS binary and their out-state represented by a NS, originated in the SN explosion of a CO and a companion NS. Their spectral peak energy is in the range of  keV and their isotropic energy in  erg range. No GeV emission has been observed in these sources. The complete list of XRFs which updates the one in Ruffini et al. (2016b) is given in the accompanying paper “On the universal GeV emission in BdHNe and their inferred morphological structure” (Ruffini et al., 2018c).

The first list of BdHNe was introduced in Pisani et al. (2016); Ruffini et al. (2016b), it was further extended in Ruffini et al. (2018)a, still further extended in the accompanying paper Ruffini et al. (2018c). 327 BDHNe sources have been identified after the launch of Fermi, all with redshift provided. Their in-states are represented by a CO-NS binary and their out-states represented by a NS, originating in the SN explosion of a CO, and a companion BH. Their spectral peak energy has the range of  MeV. Their isotropic energy is in the range of  erg and their isotropic GeV emission is  erg. Two subclasses of BdHNe have been found corresponding to the presence or absence of the GeV emission.

Concerning the BH-SN systems, they are a subset of BdHNe group, corresponding to particularly energetic sources and a BH with a larger mass, all the way to 29 M. Their progenitor is a CO-BH binary and their out-state consisting of a NS, originating in the SN explosion of a CO and a companion BH. Their spectral peak energy is larger than 2 MeV. Their isotropic energies are  erg and their isotropic GeV emission is  erg. Details will be given in a forthcoming paper (Ruffini et al., 2018c).

U-GRBs are expected to originate from the remnant of a BdHN when the NS merges inside the newly born BH. We have not yet observed the U-GRBs (Ruffini et al., 2016b; Fryer et al., 2015). From a theoretical standpoint they must exist, still we have not yet been able to identify these sources, their spectral distribution nor their timescale, while, in principle, they should be as common as BdHNe (Ruffini et al., 2016b). Indeed, the U-GRBs are of great interest for their conceptual novelty, and since their T still has to be identified, their identification represents an additional challenge.

Concerning GRFs, 13 have been identified with only after the launch of Fermi (see Table 4 which gives their cosmological redshift , peak energy and isotropic energy ). Here we have updated their number since the previous publication (Table 11 in Ruffini et al., 2016b). Their in-state is a binary merger of a NS with a massive WD (della Valle et al., 1992, 1994) and their out-state is a M-NS. Spectral peak energy is in  MeV MeV range, and their isotropic energy in the range of  erg. The range of the cosmological redshift is (see Table 4). Note, many such WD-NS systems are expected to be in larger number than the NS-NS events (Ruffini et al., 2016c; Rueda et al., 2018). Possibly their emission is below the threshold of Swift and Fermi and a new class of soft X-ray missions should be envisaged. For this subclass of GRBs no SN association is expected, nor observed also in the case of nearby sources (Della Valle et al., 2006). GRB 060614 has shown to be the more clear case (Caito et al., 2009), therefore becoming of great relevance for the possible role of such binary systems as progenitors of kilonova events (Yang et al., 2015; Rueda et al., 2018).

Group GRF GCN and reference
keV ( erg)
050724 N12
050911 N12
051227 GCN 4400
060505 GCN 5142
060614 N12
061006 N12
pre-Fermi era 061021 GCN 5744-48
061210 N12
070506 GCN 6376
070714B N12
071227 N12
080123 GCN 7205
no Fermi-GBM 150424A GCN 17752-61
Table 4Updated list of gamma-ray flashes (GRFs) with known redshift from Ruffini et al. (2016b). There is no Fermi observation for this subclass. N12 = Norris, J.P., et al., 2010, ApJ, 717, 411.

In the following, the main objective is to see how the GeV radiation can be used to discriminate between S-GRFs and S-GRBs. This is going to be accomplished by having developed a basic procedure for the determination of the BH mass and spin, see section 5.

3. Short gamma-ray flashes (S-GRF)

In Table 3 we report on short gamma-ray flashes (S-GRFs) with known redshifts (extending the previous catalog taken from Ruffini et al., 2016b). These include sources observed after 2008, when Fermi started to operate, till the end of 2016.

Of these 18 S-GRFs, 8 were not triggered by Fermi. All of them were observed by Swift, and in some cases by Konus-Wind (upper group). The most interesting case is the Kilonova 130603B which historically is the first Kilonova ever observed (Tanvir et al., 2013) which has essential complementary data in the Optical and infrared to analyze the B-NS merging. The remaining 10 sources have been observed both by Fermi and by Swift. However, only 5 sources are outside the Fermi-LAT boresight angle (middle group, ), and 5 are within the Fermi-LAT boresight angle (lower group, ). None of the last 5 exhibit associated GeV emission. In all of them the is systematically lower than ergs. In the first column of Table 3 we indicate the name of the source, in the second their redshift and in third column the , deduced from the Fermi data. In the fourth column we estimate , which is systematically lower than  erg. For convenience, we also add both the specific GCN of the Fermi source as well as the boresight angle of the LAT observation in the column of the non-observation of the GeV emission. Where existing, we have indicated the evidence for associated kilonovae emission, particularly for the case of 160821B which presents some specific kilonova features.

4. Short gamma-ray bursts (S-GRBs)

Here we give short summary for each of 6 S-GRBs: 081024B, 090227B, 090510A, 140402A, 140619B and 160829A. We then extend our previous considerations of the specific luminosity of the GeV emission dependence as a function of time evaluated in the rest-frame of these sources. A technique which was already followed in our previous papers (Ruffini et al., 2016a; Aimuratov et al., 2017).

Finding the P-GRB and the prompt emission of the GRBs using Fermi-GBM is crucial to infer the source cosmological redshift and, consequently, all the physical properties of the plasma at the transparency radius (Muccino et al., 2013; Ruffini et al., 2015b; Abdo et al., 2010). Two observational values are needed for deriving the source redshift: the observed P-GRB temperature and the ratio between the P-GRB fluence and the total one. For more details on the method see Muccino et al. (2013).

  1. GRB 081024B: This source had the first clear detection of GeV emission from a short duration gamma-ray bursts (Abdo et al., 2010). Applying the fireshell model to this S-GRB the redshift is derived to be and, therefore,  erg,  MeV, and  erg. This GRB has  erg and the baryon load of . The average circumburst medium (CBM) number density inferred from the prompt emissions of GRB 081024B is  cm, typical of the S-GRB galactic halo environments. For more details see Table. 2 in Aimuratov et al. (2017).

  2. GRB 090227B: This is the prototype of genuine short gamma-ray bursts showing the presence of GeV emission. The theoretically deduced redshift using the fireshell model of . From that, we inferred  erg,  MeV, and  erg. This GRB has  erg and the baryon load of . The CBM number density inferred from the prompt emission is  cm see Table. 5 and Table. 6 in Muccino et al. (2013)

  3. GRB 090510A: This is the brightest short gamma-ray burst with emission in the whole electromagnetic range and with spectroscopic redshift of and a theoretically deduced redshift using the fireshell model of , giving  erg,  MeV and  erg. This GRB has  erg and the baryon load of . The CBM number density inferred from the prompt emission is  cm, see Table. 3 in Ruffini et al. (2016a) for more details. The overlap between the late X-ray emission of 090510A and that of 130603B, Fig. 1, was the object of interest in the GCN 14913 (R. Ruffini et al., GCN 14913). Recently, the work of Tanvir et al. (2013) reported on a possible kilonova of GRB 130603B. This together with the overlapping between the optical emission of these two sources at time 800 s (Rueda et al., 2018), gives support to the possibility that kilonova process may occur in the final evolution of a B-NS leading to a BH in addition to the more common one of a B-NS leading to a M-NS (Tanvir et al., 2013).

  4. GRB 140402A: The theoretically derived redshift from the fireshell model for this S-GRB is . This implies the  erg,  MeV, and  erg. GRB 140402A has  erg and the baryon load is . The average CBM number density in the case of GRB 140402A is  cm. For more details see Table. 4 in (Aimuratov et al., 2017). A long-lived GeV emission within  s has been reported (Bissaldi et al., 2014).

  5. GRB 140619B: The theoretically derived redshift from the fireshell model is . This implies:  erg,  MeV and  erg. GRB 140402A has  erg and the baryon load is . The average CBM number density in the case of GRB 140619B is  cm. For more details see Table. 3 in Aimuratov et al. (2017); Ruffini et al. (2015b).

  6. GRB 160829A: The theoretically inferred redshift from the fireshell model is . This implies that  erg,  MeV and  erg. This GRB has  erg and the baryon load is . More details on this source will be published elsewhere.

The values of are calculated by multiplying the average luminosity in each time bin by the corresponding rest-frame time duration and then, by summing all bins. We must point out that since at late time the GeV emission observation could be prevented due to the instrument threshold of the LAT, these values are the lower limits to the GeV isotropic energies.

Figure 1.— The rest-frame  KeV luminosity light-curves of S-GRBs 130603B and 090510. The overlap between the X-ray emissions of the two GRBs can be seen at late times.

In Table 5 we summarize the prompt and the GeV emission properties for six S-GRBs, i.e., the redshift , , , , the position of the source from the LAT boresight and the likelihood test statistic (TS, to ascertain that the GeV photons belong to the burst and not to the -ray background sources).

Source Fermi GCN TS
(MeV) ( erg) ( erg) (deg)
081024B ,
090227B
090510A , possible kilonova
140402A ,
140619B ,
160829A
Table 5List of 6 S-GRBs within the Fermi-LAT boresight angle. All of these events have associated GeV photons: prompt and GeV emission properties of S-GRBs. In the first column we indicate the name of these sources. The second column gives their redshift. The third column gives the deduced from the best fit model of the -GBM and remarkably different from those observed in S-GRFs. The fourth column gives the associated Fermi GCN number. In 5 column we estimate the characteristic , which is systematically larger than the lower limit of  erg. Column 6 shows the value of deduced from the -LAT. Column 7 shows the position of the source from the LAT boresight . Column 8 is the likelihood test statistic (TS).

In previous papers (Ruffini et al., 2016a; Aimuratov et al., 2017) we introduced a specific luminosity dependence as a function of the rest-frame time of the GeV emission. This approach followed the corresponding one for the long GRBs originally introduced in Pisani et al. (2016). The rest-frame  GeV isotropic luminosity light-curves follow a power-law behavior

(1)

where is the rest-frame time and is the luminosity at 1 second. This has been well established in all S-GRBs, see, e.g. (Nava et al., 2014; Ruffini et al., 2015a, b) and here is represented in Fig. 2.

GRB 090510 is the S-GRB showing the longest GeV light-curve, lasting for  s in its cosmological rest-frame. The other sources have some data points overlapping with GRB 090510.

By fitting all data points together using a common power-law, we confirm the power-law index and the luminosity at  second  ergs  (see Fig. 2) , as previously obtained for first 5 sources in Aimuratov et al. (2017). We can see that, apart from the S-GRB 090227B, which was outside the nominal LAT field of view (FoV, i.e., ), all S-GRBs exhibit GeV emission. This fact points to the almost spherical symmetry or to a large angle emission for the GeV radiation from all these sources.

Figure 2.— The rest-frame  GeV isotropic luminosity light-curves of all S-GRBs with LAT emission. The black line indicate the common power-law behavior of the GeV emission with the slope of .

In support of the classification of short bursts in two subclasses we confirm that the GeV emission is uniquely observed in S-GRBs and is related to the presence of the BH.

5. The GeV emission and the extractable energy from a Kerr BH

The first proposal for identifying the rotational energy of the newly formed BH as originating the GeV emission was indicated in the case of S-GRB 090510 (Ruffini et al., 2016a). For this case, as well as for the S-GRBs 081024B and 140402A (Aimuratov et al., 2017), we proposed that the GeV energy budget, , can be explained by the mass-accretion process onto the newly born Kerr BH. From this assumption we estimated lower limits on the amount of mass needed to explain as due to the gravitational energy gained by accretion. Therefore, we adopted , where is the amount of accreted mass corresponding to the choice of the parameter , that is the efficiency of the conversion of gravitational energy into GeV radiation. The value of depends on whether the infalling material is in co- (+ sign) or counter-rotating (– sign) orbit with respect to the BH and attains a maximum value of and . This method successfully indicated the accretion energy onto a Kerr BH is a sufficient condition to explain the entire observed GeV emission. It was not, however, sufficient to infer either the BH mass or spin.

We now introduce an alternative procedure which again is a sufficient condition to explain the GeV energetics, but also constrains both the mass and spin of the BH. Namely, we verify the condition that the GeV emission observed in the S-GRBs can originate from the BH extractable energy. We will address the same procedure for the BdHNe in accompanying paper Ruffini et al. (2018c). In geometric units () and introducing the dimensionless intrinsic angular momentum (the spin), the irreducible mass of a Kerr BH with mass and angular momentum can be obtained from the BH mass-formula (see Eq. 2 in Christodoulou & Ruffini, 1971):

(2)

Solving Eq. (2) to find , the extractable energy , which is a function of and given by

(3)

For an extreme Kerr BH () we recover the well-known results that . For the maximum spin parameter attainable by a rotating NS, ,111This value is independent on the NS EOS; see e.g. Cipolletta et al. (2015). the maximum extractable energy is smaller: .

Assuming , we can obtain as a function of , . Since in S-GRBs the BH is formed out of a NS-NS merger, we request the condition , where is the NS critical mass against gravitational collapse to a BH. It is easy to verify that this equality sets the minimum mass and, correspondingly, the maximum for the newly-formed BH.

The NS critical mass is given by the secular axisymmetric instability limit, when the star becomes unstable with respect to axially-symmetric perturbations. Following the turning-point method by Friedman et al. (1988), it is given by the critical point of a constant angular-momentum sequence of increasing central density, , i.e. when . For instance, for the NL3, GM1 and TM1 EOS, Cipolletta et al. (2015) obtained a formula that fits the numerical calculation results with a maximum error of 0.45%, the numerical calculation results:

(4)

where and are parameters that depend upon the nuclear EOS, is the critical mass in the non-rotating (spinless) case and is the dimensionless angular momentum parameter . For illustration we limit our investigation here, for the sake of example, to two nuclear EOSs: the TM1 EOS that leads to , and  M, and to the very stiff NL3 EOS, that leads to , and  M (Cipolletta et al., 2015). The maximum value of is given by the secularly unstable configuration that is also maximally rotating, i.e. with . The Eq. (4) is a non-linear algebraic equation which cannot be solved analytically to obtain the relation. Fig. 3 shows the numerical solution of Eq. (4) for the NL3 and TM1 EOS.

Figure 3.— NS critical mass as a function of the spin parameter for the NL3 and TM1 EOS. We recall that the maximum spin parameter of a uniformly rotating NS is , independently of the NS EOS; see e.g. Cipolletta et al. (2015).

For the TM1 model, Eq. (4) leads to a maximum critical-mass value  M (see Fig. 3). For this, Eq. (3) gives a corresponding extractable energy  erg. For the NL3 model, we obtain  M (see Fig. 3) and  erg.

We can now apply the above procedure on the values of in Table 5 to constrain the mass and spin of the newborn BH in S-GRBs.

Table 6 lists the inferred values of the minimum mass and corresponding maximum spin of the BH, as inferred from this procedure, for both the TM1 and the NL3 nuclear EOS. The large uncertainty on the LAT energy mainly affects the estimate of the dimensionless angular momentum and also, but not so sensitively, on the estimate of the mass. This can be easily noted from Fig. 3: a small ranges of mass translate in large intervals of the axis, at least for which is the case for all S-GRBs.

TM1 NL3
Source
(M) (M)
S-GRB 081024B
S-GRB 090227B
S-GRB 090510A
S-GRB 140402A
S-GRB 140619B
S-GRB 160829A
Table 6Minimum mass and corresponding maximum spin parameters of the newly-formed BH, as inferred from the values of for all S-GRBs in Fig. 2, and for the TM1 and the NL3 nuclear equations of state.

We can then conclude that the formation of a Kerr BH is sufficient to explain the observed GeV emission, either by accretion process or by using the BH extractable energy. This has been shown only to occur in S-GRBs.

6. conclusion

In this article we have discussed if the existence of the GeV radiation can be used as a further confirmation and an additional means to discriminate between the S-GRF and S-GRB subclasses, along with their different energetics and spectra (S-GRF with  erg and  MeV; S-GRBs with  erg,  MeV). The GeV emission gives the necessary condition for the formation of the BH in the merging of the two NSs. In turn, the presence of the BH is sufficient to explain the entire energetics of the GeV emission by the BH mass and spin. The new feature identified in this article is the existence of the universal power-law behavior of S-GRBs GeV emission luminosity as a function of time in the rest-frame of the source, with amplitude and a power-law index . Such a relation makes possible, in principle, to follow quantitatively the energy producing process in S-GRBs and their temporal evolution, as well as identifying the essential parameters of the BH, namely its mass and intrinsic spin.

The great interest for short bursts has been spurred by the refine observation of kilonova. This points to the possible occurrence of a kilonova within such profoundly different binary systems as S-GRBs, S-GRFs and GRFs. This promises to be a fertile topic for further investigation (Rueda et al., 2018).

In an accompanying paper (Ruffini et al., 2018c, to be submitted) we further examine the role of GeV emission for long-duration GRBs. By examining XRFs and BdHNe, we show how the GeV emission provides an additional criteria for differentiating between these two subclasses. The universal power-law behavior of  GeV luminosity light-curves as a function of time is confirmed for a subset of BdHNe. In particular, by using the mass formula of the Kerr BH, for BdHNe we can infer a minimum BH mass in the range and a corresponding maximum dimensionless spin in the range of . Most importantly, using the GeV data from Fermi-LAT we can infer a new morphology of the SN ejecta accreting onto the newly-formed BH within the binary system.

Finally, it is also appropriate to mention that the results obtained here have many implications regarding the possible detection of gravitational waves coming from S-GRBs and S-GRF, especially concerning the potential connection with Kilonovae emission, as recalled in section 4. These are the subject of two forthcoming papers (Rueda et al. (2018) and accompanying paper Ruffini et al. (2018c)).

This work made use of data supplied by the UK Swift Science Data Center at the University of Leicester. Y. A. is supported by the Erasmus Mundus Joint Doctorate Program Grant N. 2014-0707 from EACEA of the European Commission. Y. A. acknowledges partial support by the Targeted Financing Program BR05336383 of Aerospace Committee of the Ministry of Defense and Aerospace Industry of the Republic of Kazakhstan. G. J. M is supported by the U.S. Department of Energy under Nuclear Theory Grant DE-FG02-95-ER40934.

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