Lower Limits on Lorentz Factors in Gamma-Ray Bursts

By Y. Lithwick, R. Sari. 2000

371 citations recorded by the source corpus.

As is well known, the requirement that gamma-ray bursts be optically thin to high-energy photons yields a lower limit on the Lorentz factor (γ) of the expansion. In this paper, we provide a simple derivation of the lower limit on γ due to the annihilation of photon pairs and correct the errors in some of the previous calculations of this limit. We also derive a second limit on γ due to scattering of photons by pair-created electrons and positrons. For some bursts, this limit is the more stringent. In addition, we show that a third limit on γ, obtained by considering the scattering of photons by electrons that accompany baryons, is nearly always less important than the second limit. Finally, we evaluate these limits for a number of bursts.

Subfields: Astronomy and Astrophysics, Pulmonary and Respiratory Medicine

View Paper: https://www.semanticscholar.org/paper/10f4d10b8781acf698c4c6362384b9ce8d639d97

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In Astronomy and Astrophysics

1. Bing Zhang
2. B. Metzger
3. E. Berger
4. Pawan Kumar
5. E. Nakar
6. E. Quataert
7. J. McKinney
8. A. Tchekhovskoy

In Pulmonary and Respiratory Medicine

1. Bing Zhang
2. E. Nakar
3. P. Mészáros
4. A. Pe’er
5. Xuefeng Wu
6. J. McKinney
7. C. Matzner
8. A. Tchekhovskoy

Citations in the corpus

• The expected thermal precursors of gamma-ray bursts in the internal shock model (2002, background): “Average Lorentz factors larger than 100 are required (Baring & Harding 1997; Lithwick & Sari 2001).”
• Magnetic acceleration of ultrarelativistic jets in gamma-ray burst sources (2008, background): “Although real GRB jets may be even faster (e.g. Lithwick & Sari 2001), the analytic results verified by our numerical study can be applied to such jets with a high degree of confidence.”
• Gamma-ray bursts in the comoving frame (2011, background): “From this argument lower limitsΓ0 > 100 are usually derived (Lithwick & Sari, 2001).”
• RELATIVISTIC SHOCK BREAKOUTS—A VARIETY OF GAMMA-RAY FLARES: FROM LOW-LUMINOSITY GAMMA-RAY BURSTS TO TYPE Ia SUPERNOVAE (2011, background): “The reason is that Lithwick & Sari (2001) derived their limits assuming that there is a hard spectral power-law that extends to very high energies, similarly to the one observed in long GRBs.”
• Relativistic Magnetohydrodynamics with Application to Gamma-Ray Burst Outflows. I. Theory and Semianalytic Trans-Alfvénic Solutions (2003, background): “…thing, the value ofγ∞ in this solution is about an order of magnitude higher than the minimum Lorentz factors typically inferred in real GRBs (e.g., Lithwick & Sari 2001). which is obtained after substituting all quantities in the id ntityγ2 ( 1−V2φ/c2 ) = 1+γ2V2p/c2 using equations (A1,A2) and…”
• Acceleration of GRB outflows by Poynting flux dissipation (2001, background): “To produce the high Lorentz factors of the order of 102–103 (Fenimore et al. 1993; Woods & Loeb 1995; Lithwick & Sari 2001) which are needed only a small fraction of the total energy can exist in form of rest mass energy of the matter involved.”
• Reconciling observed gamma-ray burst prompt spectra with synchrotron radiation? (2010, background): “(14) Lorentz factorsΓ∗ above 100 are necessary to avoid the presence of a high-energy cutoff in the spectrum due toγγ annihimation (see e.g. Lithwick & Sari 2001).”
• Gamma-Ray Bursts in the Swift Era (2007, methodology): “In the past, the highest energy photons have been used to constrainthe lower limit of GRB fireballs (Woods & Loeb 1995; Baring & Harding 1997; Lithwick & Sari 2001).”
• THE LARGE AREA TELESCOPE ON THE FERMI GAMMA-RAY SPACE TELESCOPE MISSION (2009, background): “Signatures of internal absorption will constrain the bulk Lorentz factorand adiabatic/radiative behavior of the GRB blast wave as a function of time for sufficiently bright bursts (Baring & Harding 1997; Lithwick & Sari 2001; Baring 2006).”
• EFFICIENCY OF MAGNETIC TO KINETIC ENERGY CONVERSION IN A MONOPOLE MAGNETOSPHERE (2009, background): “Overall, it appears that the Lorentz factor of most GRBs isγ j & 100 (Piran 2005; Meszaros 2006, up to∼ 400, Lithwick & Sari 2001) which, with the above estimates forθ j , givesγ jθ j & 3 and indicates that in principle achromatic jet breaks are possible.”
• The physics of gamma-ray bursts (2004, background): “The requirement that the source be optically thin can be used to obtain from specific bursts direct limits on the minimal Lorentz factor within those bursts sKrolik and Pier, 1991; Fenimore et al., 1993; Woods and Loeb, 1995; Baring and Harding, 1997; Piran, 1997, 1999; Lithwick and Sari, 2001d.”
• FERMI OBSERVATIONS OF GRB 090510: A SHORT–HARD GAMMA-RAY BURST WITH AN ADDITIONAL, HARD POWER-LAW COMPONENT FROM 10 keV TO GeV ENERGIES (2010, positive): “The use of γ-ray observations to constrain the bulk outflow speed of highly variable and energetic γ-ray emission from GRBs has been studied by many authors (e.g., Baring & Harding 1997; Lithwick & Sari 2001; Razzaque et al. 2004).”
• Evidence for a Canonical Gamma-Ray Burst Afterglow Light Curve in the Swift XRT Data (2005, background): “…was either (1) originally in material with an initial Lorentz factor < 102, which could therefore have not contributed to the prompt gammaray emission (due to the compactness problem; Lithwick & Sari 2001; Piran 1999), or (2) injected at late times, after the prompt gamma-ray emission was over.”
• CONSTRAINING GAMMA-RAY BURST INITIAL LORENTZ FACTOR WITH THE AFTERGLOW ONSET FEATURE AND DISCOVERY OF A TIGHT Γ0–Eγ,iso CORRELATION (2009, methodology): “Since so far no clear cutoff feature is observed, the common practice is to use the observed maximum photon energy to set a lower limit on Γ0 (Fenimore et al. 1993; Woods & Loeb 1995; Baring & Harding 1997; Lithwick & Sari 2001).”
• Simulations of ultrarelativistic magnetodynamic jets from gamma‐ray burst engines (2008, background): “The Lorentz factor required can be as high as ∼ 400 (Lithwick & Sari 2001), which necessitates a relativistic engine capable of launching plasma with an enormous amount of energy per particle.”
• Trans-Relativistic Blast Waves in Supernovae as Gamma-Ray Burst Progenitors (2000, result): “These values are lower than those commonly quoted in the literature (e.g., Lithwick & Sari 2001) because the bursts in question have relatively smooth time proÐles and because our adoption of the external shock hypothesis dictates that the age of a burst, rather than the timescale of its…”