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

• Published in: The Astrophysical journal 2019-12, Vol.886 (2), p.106
• Main Author: Panaitescu, A.
• Format: Article
• Language: English
• Subjects: Adiabatic flow; ASTRONOMY AND ASTROPHYSICS; Astrophysics; Cooling; Cooling curves; Cooling rate; Electrons; Emission analysis; Energy; Energy distribution; Energy spectra; Flux density; Gamma ray bursts; Gamma rays; Injection; Light curve; Magnetic fields; methods: analytical, numerical; Non-thermal radiation sources; Power law; Pulse shape; radiation mechanisms: non-thermal; Radiative cooling; Relativism; Relativistic effects; Slopes; stars: gamma-ray burst: general; Yield
• ISSN: 0004-637X; 1538-4357; 1538-4357
• DOI: 10.3847/1538-4357/ab4e17

We investigate the adiabatic and radiative (synchrotron and inverse-Compton) cooling of relativistic electrons whose injected or initial distribution with energy is a power law. 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 Ep of the synchrotron emission spectrum. The pulse shape resulting from an episode of electron injection is also analyzed. 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 Ri 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 = −3/2 provided that Ri ∼ B2, which is exactly the expectation if the magnetic field is a constant fraction of the post-shock energy density. Increasing (decreasing) Ri and decreasing (increasing) B(t) lead to harder (softer, respectively) slopes than the standard value and to nonpower-law (curved) cooling-tails. Inverse-Compton cooling yields four values for the slope but, as for synchrotron, other Ri 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.