The canonical Gamma‐Ray Bursts and their “precursors”

Abstract

The fireshell model for Gamma‐Ray Bursts (GRBs) naturally leads to a canonical GRB composed of a proper‐GRB (P‐GRB) and an afterglow. P‐GRBs, introduced by us in 2001, are sometimes considered “precursors” of the main GRB event in the current literature. We show in this paper how the fireshell model leads to the understanding of the structure of GRBs, with precise estimates of the time sequence and intensities of the P‐GRB and the of the afterglow. It leads as well to a natural classification of the canonical GRBs which overcomes the traditional one in short and long GRBs.

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arXiv:0901.1545v1 [astro-ph.HE] 12 Jan 2009
The canonical Gamma-Ray Bursts and their “precursors”
Remo Ruffini∗,†, Alexey G. Aksenov∗∗, Maria Grazia Bernardini∗,†, Carlo Luciano
Bianco∗,†, Letizia Caito∗,†, Maria Giovanna Dainotti∗,†, Gustavo De Barros∗,†,
Roberto Guida∗,†, Gregory V. Vereshchagin∗and She-Sheng Xue∗
∗ICRANet, Piazzale della Repubblica 10, 65122 Pescara, Italy.
†Dipartimento di Fisica, Università di Roma “La Sapienza”, P.le Aldo Moro 5, 00185 Roma, Italy.
∗∗Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya, 25, 117218 Moscow, Russia
Abstract. Thefireshell model for Gamma-Ray Bursts(GRBs)naturally leads toa canonical GRB composed of aproper-GRB
(P-GRB) and an afterglow. P-GRBs, introduced by us in 2001, are sometimes considered “precursors” of the main GRB event
in the current literature. We show in this paper how the fireshell model leads to the understanding of the structure of GRBs,
with precise estimates of the time sequence and intensities of the P-GRB and the of the afterglow. It leads as well to a natural
classification of the canonical GRBs which overcomes the traditional one in short and long GRBs.
Keywords: Gamma-Ray: Bursts
PACS: 98.70.Rz
The so-called “prompt emission” light curves of many Gamma-Ray Bursts (GRBs) present a small pulse preceding
the main GRB event, with a lower peak flux and separated by this last one by a quiescent time. The nature of such
GRB “precursors” is one of the most debated issues in the current literature [see Ref. 1, as well as G. Ghisellini’s talk
at this Meeting]. Already in 2001 [2], within the “fireshell” model, we proposed that GRB “precursors” are the Proper
GRBs (P-GRBs) emitted when the fireshell becomes transparent, and we gave precise estimates of the time sequence
and intensities of the P-GRB and the of the afterglow.
Within our approach, in fact, we assume that all GRBs originate from the gravitational collapse to a black hole
[2, 3]. The e±plasma created in the process of the black hole formationreaches thermal equilibriumon a time scale on
the order of ∼ 10−13s [4]. Then it expands as an optically thick and spherically symmetric “fireshell” with a constant
width in the laboratory frame, i.e. the frame in which the black hole is at rest [5]. During its expansion, the fireshell
engulfs the surrounding baryonic remnants [6]. This optically thick self-acceleration phase of the fireshell lasts until
the transparency condition is reached and the Proper-GRB (P-GRB) is emitted [2, 3]. This phase is fully determined
by the only two free parameters characterizing the source [2, 3], namely the total initial energy Etot
and the fireshell engulfed baryon loading B ≡ MBc2/Etot
dynamics to reach ultrarelativistic velocities after the baryonic matter engulfment it must be B < 10−2[6]. After the
transparency condition is reached and the P-GRB has been emitted, it remains an accelerated optically thin fireshell
formed only of baryons, which is ballistically expandinginto the CircumBurst Medium (CBM). Such a baryonic shell
progressively loses its kinetic energy interacting with the CBM, and this gives rise to the “afterglow” emission, which
comprises a rising part, a peak and a decaying tail [2, 3, see also Bianco et al. contribution in this volume].
We define a “canonical GRB” light curve with two sharply different components: the P-GRB and the afterglow.
Their relative energetics and time separation are functions of Etot
in this volume]. In this respect, in the current literature [see e.g. Refs. 9, 10, and references therein] there is somewhat
a state of confusion: what is usually called the “prompt emission” comprises the P-GRB, the rising part and the peak
of the afterglow. Similarly, what is usually called the “afterglow” is just its decaying tail.
We have recently shown [11] that a thermal spectrum still occurs in presence of e±pairs and baryons. By solving
the rate equation we have evaluated the evolution of the temperature during the fireshell expansion, all the way
up to when the transparency condition is reached [5, 6]. In the upper panel of Fig. 1 we plot, as a function of
B, the fireshell temperature T◦at the transparency point, i.e. the temperature of the P-GRB radiation. The plot is
drawn for four different values of Etot
energies. We plot both the value in the co-moving frame Tcom
Tobs
◦
= (1+β◦)γ◦Tcom
◦
, where β◦is the fireshell speed at the transparency point in units of c [6].
In the middle panel of Fig. 1 we plot, as a function of B, the fireshell Lorentz gamma factor at the transparency
e± of the e±plasma
e±, where MBis the total baryons’ mass [6]. For the fireshell
e±and B [2, 7, 3, 8, see also Bianco et al. contribution
e±in the interval [1049,1055] ergs, well encompassing GRBs’ observed isotropic
and the one Doppler blue-shifted toward the observed
◦

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0
10-11
0.2
0.4
0.6
0.8
1
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Energy/Etot
e
±
B
P-GRB Afterglow
Etot
e
Etot
e
Etot
e
Etot
e
± ≅ 1.44x1049 erg
± ≅ 1.68x1051 erg
± ≅ 1.77x1053 erg
± ≅ 1.22x1055 erg
102
103
104
Lorentz gamma factor at transparency
Etot
e
Etot
e
Etot
e
Etot
e
Asymptotic value 1/B
± ≅ 1.44x1049 erg
± ≅ 1.68x1051 erg
± ≅ 1.77x1053 erg
± ≅ 1.22x1055 erg
10-2
10-1
100
101
102
103
104
Fireshell temperature at transparency (keV)
In the co-moving frame
Doppler blue-shifted toward the observer
Etot
e
Etot
e
Etot
e
Etot
e
± ≅ 1.44x1049 erg
± ≅ 1.68x1051 erg
± ≅ 1.77x1053 erg
± ≅ 1.22x1055 erg
FIGURE 1.
temperature in the co-moving frame Tcom
in the source cosmological rest frame Tobs
asymptotic value γ◦= 1/B; (Below) The energy radiated in the P-GRB (thinner lines, rising when B decreases) and the one
converted into baryonic kinetic energy and later emitted in the afterglow (thicker lines, rising when B increases), in units of Etot
At the fireshell transparency point, for 4 different values of Etot
(ticker lines) and the one Doppler blue-shifted along the line of sight toward the observer
(thinner lines); (Middle) The fireshell Lorentz gamma factor γ◦together with the
e±, we plot as a function of B: (Above) The fireshell
◦
◦
e±.

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10-3
10-2
10-1
100
101
102
103
10-8
10-7
10-6
10-5
B
10-4
10-3
10-2
Time delay between P-GRB and afterglow peak (s)
Etot
e
Etot
e
Etot
e
Etot
e
± ≅ 1.44x1049 erg
± ≅ 1.68x1051 erg
± ≅ 1.77x1053 erg
± ≅ 1.22x1055 erg
FIGURE 2.
the peak of the afterglow (i.e. the “quiescent time between the “precursor” and the main GRB event), measured in the source
cosmological rest frame. This computation has been performed assuming a constant CBM density ncbm= 1.0 particles/cm3. The
points represents the actually numerically computed values, connected by straight line segments.
For 4 different values of Etot
e±, we plot as a function of B the arrival time separation ∆tabetween the P-GRB and
point γ◦. The plot is drawn for the same four different values of Etot
value γ◦= 1/B, which corresponds to the condition when the entire initial internal energy of the plasma Etot
converted into kinetic energy of the baryons [6]. We see that such an asymptotic value is approached for B → 10−2.
We see also that, if Etot
In the lower panel of Fig. 1 we plot, as a function of B, the total energy radiated at the transparency point in the
P-GRB and the one converted into baryonic kinetic energy and later emitted in the afterglow. The plot is drawn for
the same four different values of Etot
P-GRB is always larger than the one emitted in the afterglow: we have what we call a “genuine” short GRB [2, 12, 8,
see also Bianco et al. contribution in this volume]. On the other hand, for 3.0×10−4? B < 10−2the total energy
emitted in the P-GRB is always smaller than the one emitted in the afterglow. If it is not below the instrumental
threshold, the P-GRB can be observed in this case as a small pulse preceding the main GRB event (which coincides
with the peak of the afterglow), i.e. as a GRB “precursor” [2, 13, 8]. The only exception to this rule is when we are
in presence of a peculiarly small CBM density which “deflates” the afterglow peak luminosity with respect to the P-
GRB one and gives rise to a “disguised” short GRB [12, 8, see also Bianco et al. contribution in this volume]. Finally,
for 10−5? B ? 3.0×10−4we are in an intermediate case, and the energetic predominance of the P-GRB over the
afterglow depends on the value of Etot
Particularly relevant for the new era of the Agile and GLAST satellites is that for B < 10−3the P-GRB emission
has an observed temperature up to 103keV or higher. This high-energy emission has been unobservable by the Swift
satellite.
In Fig. 2 we plot, as a functionof B, the arrivaltime separation∆tabetweenthe P-GRB andthe peakof the afterglow
measured in the cosmological rest frame of the source. Such a time separation ∆tais the “quiescent time” between the
precursor (i.e. the P-GRB) and the main GRB event (i.e. the peak of the afterglow). The plot is drawn for the same
four different values of Etot
profile of the CBM density. In this plot it has been assumed a constant CBM density ncbm= 1.0 particles/cm3. We can
see that, for 3.0×10−4? B < 10−2, which is the condition for P-GRBs to be “precursors” (see above), ∆taincreases
both with B and with Etot
instead, ∆tapresents a behavior which qualitatively follows the opposite of γ◦(see middle panel of Fig. 1).
Finally, in Fig. 3 we present three theoretical afterglow bolometric light curves together with the corresponding
P-GRB peak luminosities for three different values of B. The durationof the P-GRBs has been assumed to be the same
in the three cases (i.e. 5 s). The computations have been performed assuming the same Etot
CBM density profile of GRB991216 [13]. In this picture we clearly see how, for B decreasing, the afterglow light
curve “squeezes” itself on the P-GRB and the P-GRB peak luminosity increases.
e±of the upper panel. Also plotted is the asymptotic
e±has been
e±increases, the maximum values of γ◦are higher and they are reached for lower values of B.
e± of the upper panel. We see that for B ? 10−5the total energy emitted in the
e±.
e±of Fig. 1. The arrival time of the peak of the afterglow emission depends on the detailed
e±. We can have ∆ta> 102s and, in some extreme cases even ∆ta∼ 103s. For B ? 3.0×10−4,
e± and the same detailed

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1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
100
101
102
103
104
Detector arrival time (s)
105
106
107
108
109
1010
Source luminosity (erg/(s*strad))
B=10-2
B=10-3
B=10-4
FIGURE 3.
(the horizontal segments). The computations have been performed assuming the same Etot
three different values of B. The P-GRBs have been assumed to have the same duration in the three cases, i.e. 5 s. For B decreasing,
the afterglow light curve squeezes itself on the P-GRB.
We plot three theoretical afterglow bolometric light curves together with the corresponding P-GRB peak luminosities
e± and CBM structure of GRB991216 and
Before closing, we like to mention that, using the diagrams represented in Figs. 1-2, in principle one can compute
the two free parameters of the fireshell model, namely Etot
GRB and of the afterglow and from the temporal separation between the peaks of the corresponding bolometric light
curves. None of these quantities depends on the cosmological model. Therefore, one can in principle use this method
to compute the GRBs’ intrinsic luminosity and make GRBs the best cosmological distance indicators available today.
Theincrease ofthe numberof observedsources,as well as the moreaccurateknowledgeof theirCBM densityprofiles,
will possibly make viable this procedure to test cosmological parameters, in addition to the Amati relation [14, 15].
e±and B, from the ratio between the total energies of the P-
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