Context. The peak energy (Ep) exhibited during the prompt emission phase of gamma-ray bursts (GRBs) shows two different evolution patterns, namely hard-to-soft and intensity-tracking, of which the physical origin remains unknown. In addition to low-energy indices of GRB prompt spectra, the evolution patterns of Ep may be another crucial indicator with which to discriminate radiation mechanisms (e.g., synchrotron or photosphere) for GRBs. Aims. We explore the parameter space to find conditions that could generate different evolution patterns in the peak energy in the framework of synchrotron radiation. Methods. We have developed a code to calculate the synchrotron emission from a simplified shell numerically, considering: three cooling processes (synchrotron, synchrotron self-Compton (SSC), and adiabatic) of electrons, the effect of decaying magnetic field, the effect of the bulk acceleration of the emitting shell, and the effect of a variable source function that describes electrons accelerated in the emitting region. Results. After exploring the parameter space of the GRB synchrotron scenario, we find that the intensity-tracking pattern of Ep could be achieved in two situations. One is that the cooling process of electrons is dominated by adiabatic cooling or SSC+adiabatic cooling at the same time. The other is that the emitting region is under acceleration in addition to the cooling process being dominated by SSC cooling. Otherwise, hard-to-soft patterns of Ep are normally expected. Moreover, a chromatic intensity-tracking pattern of Ep could be induced by the effect of a variable source function.
The cosmological nature of gamma-ray bursts (GRBs) implies that a small portion of them could be gravitationally lensed by foreground objects during their propagation. The gravitational lensing effect on the GRB prompt emission and on-axis afterglows has been discussed, and some candidates have been found in the literature. In this work, considering the high detection rate of GRB orphan afterglows in future wide-field survey era, we investigate the gravitationally lensed orphan afterglows in view of three lens models, i.e. the point-mass model, the singular isothermal sphere model, and the Chang-Refsdal model. The structure of the GRB jet itself is also incorporated in calculating the lensed afterglow light curves. It is found that lensed optical/X-ray orphan afterglows in principle could be diagnosed through their temporal characteristics, and the optical band is the best band to observe the galaxy-lensed orphan afterglows. Moreover, the event rate for galaxy-lensed orphan afterglows is estimated to be ≲ 1.8 yr−1 for the whole sky. If most orphan afterglows could be identified (from other transients in the survey data), the optimistic detection rates of the 2.5m Wide Field Survey Telescope of China and 8.4m Vera Rubin Observatory Legacy Survey of Space and Time for galaxy-lensed orphan afterglows in the optical band are ≲ 0.01∼0.02 yr−1 and ≲ 0.04∼0.08 yr−1, respectively.
In the spirit of the thin-layer quantization scheme, we give the effective Hamiltonian describing the noninteracting electrons confined to an annular corrugated surface, and find that the geometrically induced potential is considerably influenced by corrugations. By using numerical calculation, we investigate the eigenenergies and the corresponding eigenstates, and find that the transition energies can be sufficiently improved by adding corrugations. Particularly, the transition energy between the adjacent eigenstates corresponds to energy levels difference based on the wavefunction of annular wire, and the number of the energy levels is equal to the number of corrugations. And the larger magnitude of corrugations is capable of increasing the number of bound states. In addition, the distribution of ground state probability density is reconstructed by the corrugations, and the energy shift is generated.
The cosmological nature of gamma-ray bursts (GRBs) implies that a small portion of them could be gravitationally lensed by foreground objects during their propagation. The gravitational lensing effect on the GRB prompt emission and on-axis afterglows has been discussed, and some candidates have been found in the literature. In this work, considering the high detection rate of GRB orphan afterglows in future wide-field survey era, we investigate the gravitationally lensed orphan afterglows in view of three lens models, i.e., the point-mass model, the singular isothermal sphere model, and the Chang-Refsdal model. The structure of the GRB jet itself is also incorporated in calculating the lensed afterglow light curves. It is found that lensed optical/X-ray orphan afterglows in principle could be diagnosed through their temporal characteristics, and the optical band is the best band to observe the galaxy-lensed orphan afterglows. Moreover, the event rate for galaxy-lensed orphan afterglows is estimated to be 0.7 yr −1 for the whole sky. The optimistic detection rates of the Wide Field Survey Telescope (WFST) and Large Synoptic Survey Telescope (LSST) for galaxy-lensed orphan afterglows in the optical band are 0.02 yr −1 and 0.08 yr −1 , respectively.
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