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

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.

[1]  M. Valle,et al.  Metallicity effects on cosmic Type Ib/c supernovae and gamma-ray burst rates , 2012 .

[2]  M. Valle,et al.  Metallicity effects on the cosmic SNIb/c and GRB rates , 2012, 1204.2417.

[3]  A. Melandri,et al.  The impact of selection biases on the correlation of gamma-ray bursts , 2012, 1203.0003.

[4]  A. J. van der Horst,et al.  THE FERMI GBM GAMMA-RAY BURST CATALOG: THE FIRST TWO YEARS , 2012, 1201.3099.

[5]  B. Schaefer,et al.  A SIGNIFICANT PROBLEM WITH USING THE AMATI RELATION FOR COSMOLOGICAL PURPOSES , 2011, 1112.4347.

[6]  S. Campana,et al.  A complete sample of bright Swift long gamma-ray bursts: testing the spectral-energy correlations , 2011, 1112.4470.

[7]  A. Melandri,et al.  A COMPLETE SAMPLE OF BRIGHT SWIFT LONG GAMMA-RAY BURSTS. I. SAMPLE PRESENTATION, LUMINOSITY FUNCTION AND EVOLUTION , 2011, 1112.1700.

[8]  D. Giannios.  The peak energy of dissipative GRB photospheres , 2011, 1111.4258.

[9]  Daniel Kocevski,et al.  ON THE ORIGIN OF HIGH-ENERGY CORRELATIONS IN GAMMA-RAY BURSTS , 2011, 1110.6173.

[10]  A. Melandri,et al.  Gamma-ray bursts in the comoving frame , 2011, 1107.4096.

[11]  D. Lazzati,et al.  HIGH-EFFICIENCY PHOTOSPHERIC EMISSION OF LONG-DURATION GAMMA-RAY BURST JETS: THE EFFECT OF THE VIEWING ANGLE , 2011, 1101.3788.

[12]  Giancarlo Ghirlanda,et al.  Fermi/GBM and BATSE gamma-ray bursts: comparison of the spectral properties , 2010, 1012.3968.

[13]  G. Ghisellini,et al.  Spectral properties of 438 GRBs detected by Fermi/GBM , 2010, 1012.2863.

[14]  A. MacFadyen,et al.  OFF-AXIS GAMMA-RAY BURST AFTERGLOW MODELING BASED ON A TWO-DIMENSIONAL AXISYMMETRIC HYDRODYNAMICS SIMULATION , 2010, 1006.5125.

[15]  R.A.M.J. Wijers,et al.  Jet simulations and gamma-ray burst afterglow jet breaks , 2010, 1005.3966.

[16]  S. Komissarov,et al.  Rarefaction acceleration of ultrarelativistic magnetized jets in gamma-ray burst sources , 2009, 0912.0845.

[17]  G. Ghisellini,et al.  GeV emission from gamma‐ray bursts: a radiative fireball? , 2009, 0910.2459.

[18]  C. Guidorzi,et al.  Extremely energetic Fermi Gamma-Ray Bursts obey spectral energy correlations , 2009, 0907.0384.

[19]  Robert J. Nemiroff,et al.  The Possible Impact of GRB Detector Thresholds on Cosmological Standard Candles , 2009, 0904.1464.

[20]  G. Ghirlanda,et al.  Short versus long gamma-ray bursts: spectra, energetics, and luminosities , 2009, 0902.0983.

[21]  Cosmology,et al.  EFFICIENCY OF MAGNETIC TO KINETIC ENERGY CONVERSION IN A MONOPOLE MAGNETOSPHERE , 2009, 0901.4776.

[22]  T. Sakamoto,et al.  JET BREAKS AND ENERGETICS OF Swift GAMMA-RAY BURST X-RAY AFTERGLOWS , 2008, 0812.4780.

[23]  A. Panaitescu.  An external-shock origin of the relation for gamma-ray bursts , 2008, 0811.2163.

[24]  C. Firmani,et al.  Time-resolved spectral correlations of long-duration γ-ray bursts , 2008, 0811.1578.

[25]  M. Nardini,et al.  A unifying view of gamma-ray burst afterglows , 2008, 0811.1038.

[26]  G. Ghisellini,et al.  Peak energy of the prompt emission of long gamma-ray bursts versus their fluence and peak flux , 2008, 0807.4931.

[27]  C. Firmani,et al.  The Epeak-Eiso plane of long Gamma Ray Bursts and selection effects , 2008, 0804.1675.

[28]  Li-Xin Li,et al.  Star formation history up to z = 7.4: implications for gamma-ray bursts and cosmic metallicity evolution , 2007, 0710.3587.

[29]  Nathaniel Butler,et al.  Gamma-Ray Burst Energetics in the Swift Era , 2007, 0707.4478.

[30]  D. N. Burrows,et al.  The First Survey of X-Ray Flares from Gamma-Ray Bursts Observed by Swift: Spectral Properties and Energetics , 2007, 0706.1564.

[31]  Olivier Godet,et al.  Swift and XMM-Newton Observations of the Extraordinary Gamma-Ray Burst 060729: More than 125 Days of X-Ray Afterglow , 2007 .

[32]  C. Firmani,et al.  Confirming the $\gamma$-ray burst spectral-energy correlations in the era of multiple time breaks , 2007, astro-ph/0702352.

[33]  S. Dado,et al.  On the Origin of the Correlations between Gamma-Ray Burst Observables , 2007, astro-ph/0701031.

[34]  H. Spruit,et al.  Spectral and timing properties of a dissipative γ-ray burst photosphere , 2006, astro-ph/0611385.

[35]  Italy Universita dell'Insubria,et al.  The Remarkable Afterglow of GRB 061007: Implications for Optical Flashes and GRB Fireballs , 2006, astro-ph/0610660.

[36]  Felix Ryde,et al.  Gamma-Ray Burst Spectral Correlations: Photospheric and Injection Effects , 2006, astro-ph/0608363.

[37]  M. Rees,et al.  Thermalization in Relativistic Outflows and the Correlation between Spectral Hardness and Apparent Luminosity in Gamma-Ray Bursts , 2006, astro-ph/0608282.

[38]  G. Ghisellini,et al.  Are GRB 980425 and GRB 031203 real outliers or twins of GRB 060218 , 2006, astro-ph/0605431.

[39]  P. B. Cameron,et al.  Relativistic ejecta from X-ray flash XRF 060218 and the rate of cosmic explosions , 2006, Nature.

[40]  L. A. Antonelli,et al.  The variable X-ray light curve of GRB 050713A: the case of refreshed shocks , 2006, astro-ph/0602387.

[41]  A. Hopkins,et al.  On the Normalization of the Cosmic Star Formation History , 2006, astro-ph/0601463.

[42]  Yuki Kaneko,et al.  The Complete Spectral Catalog of Bright BATSE Gamma-Ray Bursts , 2006, astro-ph/0601188.

[43]  C. Thompson.  Deceleration of a Relativistic, Photon-rich Shell: End of Preacceleration, Damping of Magnetohydrodynamic Turbulence, and the Emission Mechanism of Gamma-Ray Bursts , 2005, astro-ph/0507387.

[44]  N. Gehrels,et al.  Bright X-ray Flares in Gamma-Ray Burst Afterglows , 2005, Science.

[45]  Tsvi Piran,et al.  Outliers to the peak energy–isotropic energy relation in gamma-ray bursts , 2005 .

[46]  D. Eichler,et al.  The Difference between the Amati and Ghirlanda Relations , 2005, astro-ph/0504125.

[47]  D. Jontof-Hutter,et al.  The Blast Energy Efficiency of Gamma-Ray Bursts , 2005, astro-ph/0503537.

[48]  C. Firmani,et al.  Probing the existence of the Epeak–Eiso correlation in long gamma ray bursts , 2005, astro-ph/0502186.

[49]  Robert D. Preece,et al.  Testing the Gamma-Ray Burst Energy Relationships , 2005, astro-ph/0501559.

[50]  Italy.,et al.  A new method optimized to use gamma-ray bursts as cosmic rulers , 2005, astro-ph/0501395.

[51]  M. Rees,et al.  Dissipative Photosphere Models of Gamma-Ray Bursts and X-Ray Flashes , 2004, astro-ph/0412702.

[52]  G. Ghirlanda,et al.  The Collimation-corrected Gamma-Ray Burst Energies Correlate with the Peak Energy of Their νFν Spectrum , 2004, astro-ph/0405602.

[53]  K. Ioka,et al.  Peak Energy-Isotropic Energy Relation in the Off-Axis Gamma-Ray Burst Model , 2004, astro-ph/0401044.

[54]  T. Q. Donaghy,et al.  A Unified Jet Model of X-Ray Flashes, X-Ray-rich Gamma-Ray Bursts, and Gamma-Ray Bursts. I. Power-Law-shaped Universal and Top-Hat-shaped Variable Opening Angle Jet Models , 2003, astro-ph/0312634.

[55]  T. Piran,et al.  The Luminosity and Angular Distributions of Long-Duration Gamma-Ray Bursts , 2003, astro-ph/0311488.

[56]  D. Yonetoku,et al.  Gamma-Ray Burst Formation Rate Inferred from the Spectral Peak Energy-Peak Luminosity Relation , 2003, astro-ph/0309217.

[57]  N. Masetti,et al.  Intrinsic spectra and energetics of BeppoSAX Gamma-Ray Bursts with known redshifts , 2002, astro-ph/0205230.

[58]  S. Djorgovski,et al.  Beaming in Gamma-Ray Bursts: Evidence for a Standard Energy Reservoir , 2001, astro-ph/0102282.

[59]  T. Piran.  Gamma-ray bursts and the fireball model , 1998, astro-ph/9810256.

[60]  C. Kouveliotou,et al.  The 4B BATSE gamma-ray burst catalog , 1998 .

[61]  D. Palmer,et al.  BATSE observations of gamma-ray burst spectra. I: Spectral diversity , 1993 .

[62]  submitted to THE ASTROPHYSICAL JOURNAL LETTERS, 07/13/01 FUNDAMENTAL PHYSICAL PARAMETERS OF COLLIMATED GAMMA-RAY BURST AFTERGLOWS , 2001 .

[63]  J. Bloom,et al.  ApJ Accepted Preprint typeset using L ATEX style emulateapj v. 10/09/06 GENERALIZED TESTS FOR SELECTION EFFECTS IN GRB HIGH-ENERGY CORRELATIONS , 2022 .

[64]  Submitted to ApJ Preprint typeset using L ATEX style emulateapj v. 10/09/06 A COMPLETE CATALOG OF SWIFT GRB SPECTRA AND DURATIONS: DEMISE OF A PHYSICAL ORIGIN FOR PRE-SWIFT HIGH-ENERGY CORRELATIONS , 2022 .