Magnetar-driven Shock Breakout Revisited and Implications for Double-peaked Type I Superluminous Supernovae

The discovery of early bumps in some type-I superluminous supernovae (SLSNe-I) before the main peaks offers an important clue to their energy source mechanisms. In this paper, we updated an analytic magnetar-powered model for fitting the multi-band light curves of double-peaked SLSNe-I: the early bump is powered by magnetar-driven shock breakout thermal emission, and the main peak is powered by a radiative diffusion through the SN ejecta as in the standard magnetar-powered model. Generally, the diffusive luminosity is greater than the shock breakout luminosity at the early time, which makes the shock breakout bumps usually not clearly seen as observed. To obtain a clear double-peaked light curve, inefficient magnetar heating at early times is required. This model is applied to three well-observed double-peaked SLSNe-I (i.e., SN2006oz, LSQ14bdq, and DES14Xtaz). We find that a relative massive SN ejecta with $M_{\mathrm{ej}} \simeq 10.2-18.1 M_{\odot}$ and relative large kinetic energy of SN ejecta $E_{\mathrm{sn}} \simeq (3.8-6.5) \times 10^{51}$ erg are required, and the thermalization efficiency of the magnetar heating is suppressed before $t_{\mathrm{delay}}$, which are in the range of $\simeq 15- 43$ days. The model can well reproduce the observed light curves, with a reasonable and similar set of physical parameters for both the early bump and the main peak, strengthening support for magnetar-powered model. In the future, modeling of the double-peaked SLSNe-I will become more feasible as more events are discovered before the early bump.