The faster the narrower: characteristic bulk velocities and jet opening angles of gamma-ray bursts

Abstract

The jet opening angle θ jet and the bulk Lorentz factor Γ 0 are crucial parameters for the computation of the energetics of Gamma Ray Bursts (GRBs). From the ∼30 GRBs with measured θ jet or Γ 0 it is known that: (i) the real energetic E γ , obtained by correcting the isotropic equivalent energy E iso for the collimation factor ∼ θ 2 jet , is clustered around 10 50 -10 51 erg and it is correlated with the peak energy E p of the prompt emission and (ii) the comoving frame E ′ p and E ′ γ are clustered around typical values. Current estimates of Γ 0 and θ jet are based on incomplete data samples and their observed distributions could be subject to biases. Through a population synthesis code we investigate whether different assumed intrinsic distributions of Γ 0 and θ jet can reproduce a set of observational constraints Assuming that all bursts have the same E ′ p and E ′ γ in the comoving frame, we find that Γ 0 and θ jet cannot be distributed as single power-laws. The best agreement between our simulation and the available data is obtained assuming (a) log-normal distributions for θ jet and Γ 0 and (b) an intrinsic relation between the peak values of their distributions, i.e θ jet 2.5 Γ 0 =const. On average, larger values of Γ 0 (i.e. the "faster" bursts) correspond to smaller values of θ jet (i.e. the "narrower"). We predict that ∼6% of the bursts that point to us should not show any jet break in their afterglow light curve since they have sin θ jet < 1/Γ 0 . Finally, we estimate that the local rate of GRBs is ∼0.3% of all local SNIb/c and ∼4.3% of local hypernovae, i.e. SNIb/c with broad-lines.

Unveiling the population of orphanγ-ray bursts

“…1 at three different frequencies. With p = 2.3, e = 0.02 and B = 0.008 (as already discussed in Ghirlanda et al 2013aGhirlanda et al , 2014, we obtain for the simulated population of GRBs cumulative flux distributions (dashed lines in Fig. 1), which nicely match the radio and optical flux distributions (solid lines in Fig.…”

“…Similarly, the high flux cut ensures that our sample is free from any threshold bias related to the GRB detector (BAT on board Swift in this case). Figure 1 shows the cumulative distribution of the optical flux (at 12 h after the burst) of the BAT6 sample (red solid line, adapted from Melandri et al 2014), the cumulative distribution of the X-ray flux (at 3 keV and at 11 h) of the BAT6 (blue solid line, adapted from D' Avanzo et al 2012), and the cumulative distribution of the radio flux (at 8.4 GHz between 1 and 6 days) of the BAT6 (green solid line, adapted from Ghirlanda et al 2013a). These are the observed distributions we aim to reproduce assigning to the simulated GRB population a set of values for the microphysical parameters (p, e , B ).…”

“…However, these works either extrapolated the properties of a few known GRB afterglows to the orphans (e.g., Totani & Panaitescu 2002) or assumed basic prescriptions for the known GRB population properties or for the afterglow emission model. We recently developed a population synthesis code (Ghirlanda et al 2013a) which, coupled with the most detailed model for the afterglow emission (van Eerten et al 2012), allows us to predict the properties of the population of OAs (Ghirlanda et al 2014), reproducing a large set of observed properties of the population of the "Earth-pointed" GRBs. So far, we considered the radio band predicting that the Square Kilometer Array (SKA), reaching the μJy flux limit, could see up to ∼0.2-1.5 OA deg −2 yr −1 (Ghirlanda et al 2014).…”

A Complete Sample of Long BrightSwiftGRBs

“…This sample has been used to study the properties of the long GRB population and their evolution with redshift. Apart from the results highlighted here, the BAT6 sample has also been used to study the distributions of the GRB jet opening angle θ jet and the bulk Lorentz factor Γ 0 [13], the properties of precursors [14], and the distribution of GRB afterglow radio fluxes [15].…”

GRB Orphan Afterglows in Present and Future Radio Transient Surveys

“…In this paper we use a population synthesis code PSYCHE (Ghirlanda et al 2013a;2013b) summarised in Section 2 which has already been used to predict the detectability of on-axis GRB afterglows in the radio band (Ghirlanda et al 2013b). Here we explore for the first time with such a code the radio emission properties of Orphan Afterglows (Section 3) and compare with the current limits on the detection rates at radio frequencies (Section 4).…”