On the Energy of Gamma‐Ray Bursts

Abstract

We show that γ-ray burst (GRB) afterglow observations strongly suggest, within the fireball model framework, that radiating electrons are shock accelerated to a power-law energy distribution, dn e /dγ e ∝ γ −p e , with universal index p ≈ 2.2, and that the fraction of shock energy carried by electrons, ξ e , is universal and close to equipartition, ξ e ∼ 1/3. For universal p and ξ e , a single measurement of the X-ray afterglow flux on the time scale of a day provides a robust estimate of the fireball energy per unit solid angle, ε, averaged over a conical section of the fireball of opening angle θ ∼ 0.1.Applying our analysis to BeppoSAX afterglow data we find that: (i) Fireball energies are in the range of 4πε = 10 51.5 to 10 53.5 erg; (ii) The ratio of observed γ-ray to total fireball energy per unit solid angle, ε γ /ε, is of order unity, satisfying | log 10 (ε γ /ε)| ∼ < 0.5; (iii) If fireballs are jet like, their opening angle should satisfy θ ∼ > 0.1. Our results imply that if typical opening angles are θ ∼ 0.1, a value consistent with our analysis, the total energy associated with a GRB event is in the range of 10 50 erg to 10 51.5 erg.

Supernova 1991T and the Value of the Hubble Constant

“…1 As was done in Gibson et al (2000b) and Freedman et al (2001), the Wide Field Planetary Camera 2 (WFPC2) photometric zero-point and charge-transfer corrections adopted are essentially those of Stetson (1998), which are nearly identical to those of Whitmore, Heyer, & Casertano (1999) and Dolphin (2000). The quoted systematic uncertainty in our final result incorporates a component that allows for imprecision in our current understanding of the spatial and temporal variations of the WFPC charge-transfer inefficiency.…”

“…However, plotting H ii region metallicity versus line of 12 ϩ log (O/H) sight of reddening E(VϪI), for each of the Cepheid fields of the 30 galaxies in Table 4 The functional form for the adopted Hubble relations in our analysis is described in Freedman et al (2001) and is written (Hamuy et al 1996) and CfA 3 For SN 1991T, the adopted foreground ϩ host reddening was E(BϪ (Phillips et al 1999, Table 2). The host reddening V) p 0.16 ‫ע‬ 0.05 was derived from the favored late-time color-excess technique; as noted by Phillips et al, the color excess at maximum light should not be employed for 1991T-like events.…”

“…Using the same WFPC2 photometric zero point (Stetson 1998), LMC true modulus (Freedman et al 2001), and LMC apparent PL relations ) described above, we refitted the PL relations for each galaxy to the identical Cepheids employed by Gibson et al (2000b). 4 Table 2 shows the results of our refitting procedure, assuming no metallicity dependence in the Cepheid PL relation (m 0 ) and assuming a mild metallicity dependency of mag dex (m Z ).…”

“…Bulk flows were explored in a preliminary sense by Gibson et al (2000b) but were neglected in the quoted systematic error budget (as it was in the companion papers published in the 2000 February 1 issue of the Astrophysical Journal). More extensive modeling, including a more sophisticated multiattractor model for the local universe, allows for a ‫%5ע‬ systematic uncertainty (Freedman et al 2001).…”

On the Neutrino Flux from Gamma-Ray Bursts

“…Freedman & Waxman 2001). p 2 is required to account for observed γ-ray and afterglow spectra (Freedman & Waxman 2001). γ together with increase in the wind optical depth at the smallest internal shocks radii.…”