The theory of the conservation of energy in the thin layer approximation has been extended to special relativity. Four models for the density of the circumstellar medium are analyzed, which are represented by constant...The theory of the conservation of energy in the thin layer approximation has been extended to special relativity. Four models for the density of the circumstellar medium are analyzed, which are represented by constant, power law, exponential and Emden (<em>n</em> = 5) profile for density. The astrophysical results are presented in a numerical way, except for a Taylor expansion of the four trajectories in the surrounding of the origin. The free parameters of the models are particularized for SN1993j, for which the radius versus time is known. Some evaluations on the time dilation are presented.展开更多
The deduction of a relativistic and mildly relativistic equation of motion in the presence of a drag force proportional to the velocity is presented. The obtained results are used to model the trajectory of the supern...The deduction of a relativistic and mildly relativistic equation of motion in the presence of a drag force proportional to the velocity is presented. The obtained results are used to model the trajectory of the supernova SN1993J and the light curves of gamma-ray bursts.展开更多
The light curves (LC) for Supernova (SN) can be modeled adopting the conversion of the flux of kinetic energy into radiation. This conversion requires an analytical or a numerical law of motion for the expanding radiu...The light curves (LC) for Supernova (SN) can be modeled adopting the conversion of the flux of kinetic energy into radiation. This conversion requires an analytical or a numerical law of motion for the expanding radius of the SN. In the framework of conservation of energy for the thin layer approximation, we present a classical trajectory based on a power law profile for the density, a relativistic trajectory based on the Navarro-Frenk-White profile for the density, and a relativistic trajectory based on a power law behaviour for the swept mass. A detailed simulation of the LC requires the evaluation of the optical depth as a function of time. We modeled the LC of SN 1993J in different astronomical bands, the LC of GRB 050814 and the LC GRB 060729 in the keV region. The time dependence of the magnetic field of equipartition is derived from the theoretical formula for the luminosity.展开更多
The equation of motion for a relativistic neutral particle that moves in a medium characterized by a friction proportional to the square of the velocity is analyzed. The relativistic trajectory is derived in a numeric...The equation of motion for a relativistic neutral particle that moves in a medium characterized by a friction proportional to the square of the velocity is analyzed. The relativistic trajectory is derived in a numerical way and in the form of a Taylor series. The astrophysical applications cover the trajectory of SN 1993J and the light curve of gamma ray bursts.展开更多
文摘The theory of the conservation of energy in the thin layer approximation has been extended to special relativity. Four models for the density of the circumstellar medium are analyzed, which are represented by constant, power law, exponential and Emden (<em>n</em> = 5) profile for density. The astrophysical results are presented in a numerical way, except for a Taylor expansion of the four trajectories in the surrounding of the origin. The free parameters of the models are particularized for SN1993j, for which the radius versus time is known. Some evaluations on the time dilation are presented.
文摘The deduction of a relativistic and mildly relativistic equation of motion in the presence of a drag force proportional to the velocity is presented. The obtained results are used to model the trajectory of the supernova SN1993J and the light curves of gamma-ray bursts.
文摘The light curves (LC) for Supernova (SN) can be modeled adopting the conversion of the flux of kinetic energy into radiation. This conversion requires an analytical or a numerical law of motion for the expanding radius of the SN. In the framework of conservation of energy for the thin layer approximation, we present a classical trajectory based on a power law profile for the density, a relativistic trajectory based on the Navarro-Frenk-White profile for the density, and a relativistic trajectory based on a power law behaviour for the swept mass. A detailed simulation of the LC requires the evaluation of the optical depth as a function of time. We modeled the LC of SN 1993J in different astronomical bands, the LC of GRB 050814 and the LC GRB 060729 in the keV region. The time dependence of the magnetic field of equipartition is derived from the theoretical formula for the luminosity.
文摘The equation of motion for a relativistic neutral particle that moves in a medium characterized by a friction proportional to the square of the velocity is analyzed. The relativistic trajectory is derived in a numerical way and in the form of a Taylor series. The astrophysical applications cover the trajectory of SN 1993J and the light curve of gamma ray bursts.
