The Luminosity and Angular Distributions of Long-Duration Gamma-Ray Bursts

By D. Guetta, T. Piran, E. Waxman. 2003

162 citations recorded by the source corpus.

The realization that the total energy of gamma-ray bursts (GRBs) is correlated with their jet break angles motivates the search for a similar relation between the peak luminosity L and the jet break angles, L ∝ θ-2. Such a relation implies that the GRB luminosity function determines the angular distribution. We rederive the GRB luminosity function using the BATSE peak flux distribution and compare the predicted distribution with the observed redshift distribution. The luminosity function can be approximated by a broken power law with a break peak luminosity of 4.4 × 1051 ergs s-1, a typical jet angle of 0.12 rad, and a local GRB rate of 0.44 h Gpc-3 yr-1. The angular distribution implied by L ∝ θ-2 agrees well with the observed one and implies a correction factor to the local rate due to beaming of 75 ± 25 (instead of 500, as commonly used). The inferred overall local GRB rate is 33 ± 11 h Gpc-3 yr-1. The luminosity function and angle distribution obtained within the universal structured jet model, where the angular distribution is essentially ∝θ and hence the luminosity function must be ∝L-2, deviate from the observations at low peak fluxes and, correspondingly, at large angles. The corresponding correction factor for the universal structure jet is ~20 ± 10.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4b02227333397dd0afbb01c203eb391ffcd7e7bd

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In Astronomy and Astrophysics

1. Bing Zhang
2. E. Liang
3. Pawan Kumar
4. Binbin Zhang
5. D. Burrows
6. Xuefeng Wu
7. E. Berger
8. T. Piran

In Instrumentation

1. Bing Zhang
2. E. Liang
3. Binbin Zhang
4. K. Ioka
5. M. Della Valle
6. T. Piran
7. D. Wanderman
8. D. Burrows

In Statistical and Nonlinear Physics

1. Bing Zhang
2. K. Ioka
3. M. Della Valle
4. A. Tchekhovskoy
5. O. Bromberg
6. Kohta Murase
7. S. Nagataki
8. D. Guetta

Citations in the corpus

• A COMPLETE SAMPLE OF BRIGHT SWIFT LONG GAMMA-RAY BURSTS. I. SAMPLE PRESENTATION, LUMINOSITY FUNCTION AND EVOLUTION (2011, background): “In the last few years, this problem has been faced by many different authors ((e.g. Porciani & Madau 2001, Firmani et al. 2004, Guetta et al. 2005, Natarajan et al. 2005, Daigne et al. 2006, Salvaterra & Chincarini 2007, Salvaterra et al. 2009b, Butler et al. 2010, Wanderman & Piran 2010, Campisi…”
• The luminosity function and the rate of Swift's Gamma Ray Bursts (2009, background): “…this proportionality, numerous studies examined the typical luminosity assuming at first standard candles (e.g. Wijers et al. 1998a; Totani 1999) and later more elaborate shapes of the luminosity function (e.g. Schmidt 1999, 2001b,a; Guetta et al. 2005; Firmani et al. 2004; Guetta and Piran 2005).”
• Gamma-Ray Bursts in the Swift Era (2007, background): “This factor is currently not included in most GRB population studies (e.g., Perna et al. 2003; Lloyd-Ronning et al. 2004; Zhang et al. 2004a; Lambet al. 2005a; Dai & Zhang 2005; Guetta et al. 2005; Lin et al. 2005; Xu et al. 2005b; Liang et al. 2006c, etc.).”
• On the Rates of Gamma-Ray Bursts and Type Ib/c Supernovae (2006, methodology): “Following Guetta et al. (2004, 2005), we assume that GRBs trace the star formation history and adopt the Rowan-Robinson star formation rate (SFR),R (z) pGRB (Rowan-Robinson 1999).”
• THE COSMIC RATE, LUMINOSITY FUNCTION, AND INTRINSIC CORRELATIONS OF LONG GAMMA-RAY BURSTS (2009, background): “Finally, it will be important to better constrain the role of GRB beaming and the way this shapes the distributions in numbers, Eiso, Epk, etc. (e.g., Guetta et al. 2005; Lamb et al. 2005).”
• Relativistic MHD simulations of core-collapse GRB jets: 3D instabilities and magnetic dissipation (2015, methodology): “In the GRB case, we take a jet with a typical power of 3 × 1049 erg/s (e.g. Guetta et al. 2005), that propagates in a fiducial Wolf-Rayet star of mass M∗ = 10M , radius r∗ = 10 11 cm, and density profile ρa ∝ r−α, with α = 2.5.”
• High-Energy Neutrinos and Cosmic Rays from Low-Luminosity Gamma-Ray Bursts? (2006, methodology): “Guetta et al. (2005) argued that no bright burst z < 0.17 should be observed by a HETE-like instruments within the next 20 years, assuming that GRB 060218-like bursts follow the logN-logP relationship of HL-GRBs.”
• DISCERNING THE PHYSICAL ORIGINS OF COSMOLOGICAL GAMMA-RAY BURSTS BASED ON MULTIPLE OBSERVATIONAL CRITERIA: THE CASES OF z = 6.7 GRB 080913, z = 8.2 GRB 090423, AND SOME SHORT/HARD GRBs (2009, background): “Luminosity Function The luminosity function of long duration GRBs is categorized by a broken power law with a break ∼ 1052 erg s−1 (Guetta et al. 2005; Liang et al. 2007; Virgili et al. 2009a).”
• Low-Luminosity Gamma-Ray Bursts as a Unique Population: Luminosity Function, Local Rate, and Beaming Factor (2006, methodology): “69, 2259 Marzke, R. O., da Costa, L. N., Pellegrini, P. S., Willmer, C. N. A., & Geller, M. J. 1998, ApJ, 503, 617 Mazzali, P. A., Deng, J. S., Nomoto, K., Sauer, D. N., et al. 2006, Nature, 442, 1018 Malesani, D., Tagliaferri, G., Chincarini, G. Covino, S. et al. 2004, ApJ, 609, L5 Mirabal, N., Hal”