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We study the evolution of a nonrelativistically expanding thin shell in radio-emitting tidal disruption events (TDEs) based on a one-dimensional spherically symmetric model considering the effect of both a time-dependent mass-loss rate of the disk wind and the ambient mass distribution. The analytical solutions are derived in two extreme limits; one is the approximate solution near the origin in the form of the Taylor series, and the other is the asymptotic solution in which the ambient matter is dominant far away from the origin. Our numerical solutions are confirmed to agree with the respective analytical solutions. We find that no simple power law of the time solution exists in early to middle times because the mass-loss rate varies over time, affecting the shell dynamics. We also discuss the application of our model to the observed radio-emitting TDE, AT 2019dsg.

 

ABSTRACT Recently gamma-ray bursts (GRBs) have been detected at very-high-energy (VHE) gamma-rays by imaging atmospheric Cherenkov telescopes, and a two-component jet model has often been invoked to explain multiwavelength data. In this work, multiwavelength afterglow emission from an extremely bright GRB, GRB 221009A, is examined. The isotropic-equivalent gamma-ray energy of this event is among the largest, which suggests that similarly to previous VHE GRBs, the jet opening angle is so small that the collimation-corrected gamma-ray energy is nominal. Afterglow emission from such a narrow jet decays too rapidly, especially if the jet propagates into uniform circumburst material. In the two-component jet model, another wide jet component with a smaller Lorentz factor dominates late-time afterglow emission, and we show that multiwavelength data of GRB 221009A can be explained by narrow and wide jets with opening angles similar to those employed for other VHE GRBs. We also discuss how model degeneracies can be disentangled with observations. 

Abstract GRB 221009A ( z = 0.151) is one of the closest known long γ -ray bursts (GRBs). Its extreme brightness across all electromagnetic wavelengths provides an unprecedented opportunity to study a member of this still-mysterious class of transients in exquisite detail. We present multiwavelength observations of this extraordinary event, spanning 15 orders of magnitude in photon energy from radio to γ -rays. We find that the data can be partially explained by a forward shock (FS) from a highly collimated relativistic jet interacting with a low-density, wind-like medium. Under this model, the jet’s beaming-corrected kinetic energy ( E K ∼ 4 × 10 50 erg) is typical for the GRB population. The radio and millimeter data provide strong limiting constraints on the FS model, but require the presence of an additional emission component. From equipartition arguments, we find that the radio emission is likely produced by a small amount of mass (≲6 × 10 −7 M ⊙ ) moving relativistically (Γ ≳ 9) with a large kinetic energy (≳10 49 erg). However, the temporal evolution of this component does not follow prescriptions for synchrotron radiation from a single power-law distribution of electrons (e.g., in a reverse shock or two-component jet), or a thermal-electron population, perhaps suggesting that one of the standard assumptions of afterglow theory is violated. GRB 221009A will likely remain detectable with radio telescopes for years to come, providing a valuable opportunity to track the full lifecycle of a powerful relativistic jet. 

ABSTRACT Recently, ground-based Imaging Atmospheric Cherenkov Telescopes have reported the detection of very-high-energy (VHE) gamma-rays from some gamma-ray bursts (GRBs). One of them, GRB 190829A, was triggered by the Swift satellite, and about 2 × 104 s after the burst onset the VHE gamma-ray emission was detected by H.E.S.S. with ∼5σ significance. This event had unusual features of having much smaller isotropic equivalent gamma-ray energy than typical long GRBs and achromatic peaks in X-ray and optical afterglow at about 1.4 × 103 s. Here, we propose an off-axis jet scenario that explains these observational results. In this model, the relativistic beaming effect is responsible for the apparently small isotropic gamma-ray energy and spectral peak energy. Using a jetted afterglow model, we find that the narrow jet, which has the initial Lorentz factor of 350 and the initial jet opening half-angle of 0.015 rad, viewed off-axis can describe the observed achromatic behaviour in the X-ray and optical afterglow. Another wide, baryon-loaded jet is necessary for the later-epoch X-ray and radio emissions. According to our model, the VHE gamma rays observed by H.E.S.S. at 2 × 104 s may come from the narrow jet through the synchrotron self-Compton process.