Fireball Loading and the Blast‐Wave Model of Gamma‐Ray Bursts

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Abstract
A simple function for the spectral power P(,t)≡νL(ν) is proposed to model, with nine parameters, the spectral and temporal evolution of the observed nonthermal synchrotron power flux from gamma-ray bursts (GRBs) in the blast-wave model. Here =hν/mec2 is the observed dimensionless photonenergy, and t is the observing time. Assumptions and an issue of lack of self-consistency are spelled out. The spectra are found to be most sensitive to baryon loading, expressed in terms of the initial bulk Lorentz factor Γ0 and an equipartition term q, which is assumed to be constant in time and independent of Γ0. Expressions are given for the peak spectral power Pp(t)=P(p,t) at the photon energy =p(t) of the spectral power peak. A general rule is that the total fireball particle kinetic energy E0~Π0td, where td∝Γ is the deceleration timescale, and Π0≡P(p,td)∝Γ is the maximum measured bolometric power output in radiation during which it is carried primarily by photons with energy 0=p(td)∝qΓ40. This rule governs the general behavior of fireballs with different baryon loading. Clean fireballs with small baryon loading (Γ0300) are intense, subsecond, medium-to-high-energy gamma-ray events and are difficult to detect because of dead time and sensitivity limitations of previous gamma-ray detectors like EGRET on the Compton Gamma Ray Observatory. Dirty fireballs with large baryon loading (Γ0300) produce transient emissions that are longer lasting and most luminous at X-ray energies and below, but these events are lost behind the glow of the X-ray and lower energy background radiations, except for rare serendipitous detections by pointed instruments. The correlation between hardness and duration of loaded GRB fireballs (100Γ01000) follows from this rule.