2021ApJ...911..142L

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 multiband 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 supernova (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 usually makes the shock-breakout bumps unclear to observe. 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 relatively massive SN ejecta with M_ej ≃ 10.2-18.1M_☉ and relatively large kinetic energy of SN ejecta E_sn≃(3.8–6.5)×10⁵¹ erg are required, and the thermalization efficiency of the magnetar heating is suppressed before t_delay, which is in the range of ≃15-43 days. The model can reproduce the observed light curves well, with a reasonable and similar set of physical parameters for both the early bump and the main peak, strengthening support for the 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.