Classical and relativistic evolution of an extra-galactic jet with back-reaction

We consider a turbulent jet which is moving in a Lane--Emden ($n=5$) medium. The conserved quantity is the energy flux, which allows finding, to first order, an analytical expression for the velocity and an approximate trajectory. The conservation of the relativistic flux for the energy allows deriving, to first order, an analytical expression for the velocity, and numerically determining the trajectory. The back-reaction due to the radiative losses for the trajectory is evaluated both in the classical and the relativistic case.Comment: 19 pages and 11 figure

The light curve in supernova modeled by a continuous radioactive decay of 56^{56}Ni

The UVOIR bolometric light curves are usually modeled by the radioactive decay. In order to model more precisely the absolute/apparent magnitude versus time relationship the continuous production of radioactive isotopes is introduced. A differential equation of the first order with separable variables is solved.Comment: 5 pages 2 figure