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The faster the narrower: characteristic bulk velocities and jet opening angles of Gamma Ray Bursts
High Energy Astrophysical Phenomena · Submitted 3 Oct 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim On average, larger values of Gamma_0 (i.e. the "faster" bursts) correspond to smaller values of theta_jet (i.e. the "narrower").
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The abstract, sentence by sentence
The jet opening angle theta_jet and the bulk Lorentz factor Gamma_0 are crucial parameters for the computation of the energetics of Gamma Ray Bursts (GRBs). From the ~30 GRBs with measured theta_jet or Gamma_0 it is known that: (i) the real energetic E_gamma, obtained by correcting the isotropic equivalent energy E_iso for the collimation factor ~theta_jet^2, 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'_gamma are clustered around typical values. Current estimates of Gamma_0 and theta_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 Gamma_0 and theta_jet can reproduce a set of observational constraints. Assuming that all bursts have the same E'_p and E'_gamma in the comoving frame, we find that Gamma_0 and theta_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 theta_jet and Gamma_0 and (b) an intrinsic relation between the peak values of their distributions, i.e theta_jet^2.5*Gamma_0=const. On average, larger values of Gamma_0 (i.e. the "faster" bursts) correspond to smaller values of theta_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(theta_jet)<1/Gamma_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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The jet opening angle theta_jet and the bulk Lorentz factor Gamma_0 are crucial parameters for the computation of the energetics of Gamma Ray Bursts (GRBs). | background 1.00 | 0.05 | 0.03 | asserted 1.00 |
| s1 | From the ~30 GRBs with measured theta_jet or Gamma_0 it is known that: (i) the real energetic E_gamma, obtained by correcting the isotropic equivalent energy E_iso for the collimation factor ~theta_jet^2, 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'_gamma are clustered around typical values. | background 0.98 | 0.08 | 0.06 | asserted 1.00 |
| s2 | Current estimates of Gamma_0 and theta_jet are based on incomplete data samples and their observed distributions could be subject to biases. | gap 0.76 | 0.08 | 0.02 | hedged possibility 0.85 |
| s3 | Through a population synthesis code we investigate whether different assumed intrinsic distributions of Gamma_0 and theta_jet can reproduce a set of observational constraints. | method 0.65 | 0.80 | 0.03 | asserted 0.65 |
| s4 | Assuming that all bursts have the same E'_p and E'_gamma in the comoving frame, we find that Gamma_0 and theta_jet cannot be distributed as single power-laws. | result 1.00 | 0.95 | 0.10 | asserted 1.00 |
| s5 | The best agreement between our simulation and the available data is obtained assuming (a) log-normal distributions for theta_jet and Gamma_0 and (b) an intrinsic relation between the peak values of their distributions, i.e theta_jet^2.5*Gamma_0=const. | result 1.00 | 0.95 | 0.52 | asserted 1.00 |
| s6 | On average, larger values of Gamma_0 (i.e. the "faster" bursts) correspond to smaller values of theta_jet (i.e. the "narrower"). | result 0.88 | 0.89 | 0.77 | asserted 0.99 |
| s7 | 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(theta_jet)<1/Gamma_0. | result 0.95 | 0.89 | 0.07 | asserted 0.80 |
| s8 | 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. | result 1.00 | 0.89 | 0.05 | asserted 0.94 |
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Original abstract
The jet opening angle theta_jet and the bulk Lorentz factor Gamma_0 are crucial parameters for the computation of the energetics of Gamma Ray Bursts (GRBs). From the ~30 GRBs with measured theta_jet or Gamma_0 it is known that: (i) the real energetic E_gamma, obtained by correcting the isotropic equivalent energy E_iso for the collimation factor ~theta_jet^2, 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'_gamma are clustered around typical values. Current estimates of Gamma_0 and theta_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 Gamma_0 and theta_jet can reproduce a set of observational constraints. Assuming that all bursts have the same E'_p and E'_gamma in the comoving frame, we find that Gamma_0 and theta_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 theta_jet and Gamma_0 and (b) an intrinsic relation between the peak values of their distributions, i.e theta_jet^2.5*Gamma_0=const. On average, larger values of Gamma_0 (i.e. the "faster" bursts) correspond to smaller values of theta_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(theta_jet)<1/Gamma_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.
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Similarly, large values have been derived in other bursts in which a thermal component dominates [ref] .
Wind-confined jet collimation revealed by the acceleration-phase photosphere of GRB 220426A · A collimating dense circumburst shell · 0.84
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