Diagnosing The Ejecta Properties of Engine-Driven Supernovae from Observables in Their Initial Phase

Engine-driven explosions with continuous energy input from the central system have been suggested for supernovae (SNe) associated with a Gamma-Ray Burst (GRB), super-luminous SNe (SLSNe), and at least a fraction of broad-lined SNe Ic (SNe Ic-BL) even without an associated GRB. In the present work, we investigate observational consequences in this scenario, focusing on the case where the energy injection is sufficiently brief, which has been suggested for GRB-SNe. We construct a simplified, spherical ejecta model sequence taking into account the major effects of the central engine; composition mixing, density structure, and the outermost ejecta velocity. Unlike most of the previous works for GRB-SNe, we solve the formation of the photosphere self-consistently, with which we can predict the photometric and spectroscopic observables. We find that these ejecta properties strongly affect their observational appearance in the initial phase (~ a week since the explosion), highlighted by blended lines suffering from higher-velocity absorptions for the flatter density distribution and/or higher outermost ejeca velocity. This behaviour also affects the multi-band light curves in a non-monotonic way. Prompt follow-up observations starting immediately after the explosion thus provides key diagnostics to unveil the nature of the central engine behind GRB-SNe and SNe Ic-BL. For SN 2017iuk associated with GRB 171205A these diagnosing observational data are available, and we show that the expected structure from the engine-driven explosion, i.e., a flat power-law density structure extending up to >~ 100,000 km/s, can explain the observed spectral evolution reasonably well.