Adiabatic and Radiative Cooling of Relativistic Electrons Applied to Synchrotron Spectra and Light-Curves of Gamma-Ray Burst Pulses

Abstract

We investigate the adiabatic and radiative (synchrotron and inverse-Compton) cooling of relativistic electrons whose injected/initial distribution with energy is a power-law above a typical energy ${\gamma }_i$. Analytical and numerical results are presented for the cooling-tail and the cooled-injected distribution that develop below and above the typical energy of injected electrons, for the evolution of the peak-energy $E_p$ of the synchrotron emission spectrum, and for the pulse shape resulting from an episode of electron injection. The synchrotron emission calculated numerically is compared with the spectrum and shape of Gamma-Ray Burst (GRB) pulses. Both adiabatic and radiative cooling processes lead to a softening of the pulse spectrum, and both types of cooling processes lead to pulses peaking earlier and lasting shorter at higher energy, quantitatively consistent with observations. For adiabatic-dominated electron cooling, a power-law injection rate $R_i$ suffices to explain the observed power-law GRB low-energy spectra. Synchrotron-dominated cooling leads to power-law cooling-tails that yield the synchrotron standard slope alpha = -3/2 provided that $R_i\sim B^2$, which is exactly the expectation if the magnetic field is a constant fraction of the post-shock energy density. Increasing (decreasing) $R_i$ and decreasing (increasing) B(t) lead to slopes alpha harder (softer, respectively) than the standard value and to non--power-law (curved) cooling-tails. Inverse-Compton cooling yields four values for the slope alpha but, as for synchrotron, other $R_i$ or B histories yield a wider range of slopes and curved low-energy spectra. Feedback between the power-law segments that develop below and above the typical injected electron leads to a synchrotron spectrum with many breaks above and below the usual 10 keV-1 MeV observing range.

19 pages, submitted to ApJ

References in corpus (4)

• Klein-Nishina Effects on Optically Thin Synchrotron and Synchrotron Self-Compton Spectrum
• Gamma-ray bursts as cool synchrotron sources
• Gamma-Ray Burst Afterglows as Probes of Environment and Blastwave Physics II: the Distribution of p and Structure of the Circumburst Medium
• Low-energy Spectra of Gamma-ray Bursts from Cooling Electrons

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• Closure Relations of Synchrotron Self-Compton in Afterglow stratified medium and Fermi-LAT Detected Gamma-Ray Bursts
• Gamma-Ray Burst prompt emission from the synchrotron radiation of relativistic electrons in a rapidly decaying magnetic field
• A numerical approach for radiative cooling in relativistic outflows
• The Synchrotron Low-Energy Spectrum Arising from the Cooling of Electrons in Gamma-Ray Bursts
• Synchrotron self-Compton Reverse Shock in Energy-Injection and Radiative Scenarios