Paper detail

Effects of Relativistic Expansion on the Late-time Supernova Light Curves

The effects of relativistic expansion on the late-time supernova light curves are investigated analytically, and a correction term to the (quasi-)exponential decay is obtained by expanding the observed flux in terms of (β), where (β) is the maximum velocity of the ejecta divided by the speed of light (c). It is shown that the Doppler effect brightens the light curve owing to the delayed decay of radioactive nuclei as well as to the Lorentz boosting of the photon energies. The leading correction term is quadratic in (β), thus being proportional to (E_{\rm k}/(M_{\rm ej} c^2)), where (E_{\rm k}) and (M_{\rm ej}) are the kinetic energy of explosion and the ejecta mass. It is also shown that the correction term evolves as a quadratic function of time since the explosion. The relativistic effect is negligibly small at early phases, but becomes of considerable size at late phases. In particular, for supernove having a very large energy(hypernova) or exploding in a jet-like or whatever non-spherical geometry, (^{56})Ni is likely to be boosted to higher velocities and then we might see an appreciable change in flux. However, the actual size of deviation from the (quasi-)exponential decay will be uncertain, depending on other possible effects such as ionization freeze-out and contributions from other energy sources that power the light curve.