Magnetars are one of the potential power sources for some energetic supernova explosions such as type I superluminous supernovae (SLSNe I) and broad-lined type Ic supernovae (SNe Ic-BL). In order to explore the possible link between these two subclasses of supernovae (SNe), we study the effect of fallback accretion disk on magnetar evolution and magnetar-powered SNe. In this scenario, the interaction between a magnetar and a fallback accretion disk would accelerate the spin of the magnetar in the accretion regime but could result in substantial spin-down of the magnetars in the propeller regime. Thus, the initial rotation of the magnetar plays a less significant role in the spin evolution. Such a magnetar-disk interaction scenario can explain well the light curves of both SNe Ic-BL and SLSNe I, for which the observed differences are sensitive to the initial magnetic field of the magnetar and the fallback mass and timescale for the disk. Compared to the magnetars powering the SNe Ic-BL, those accounting for more luminous SNe usually maintain faster rotation and have relatively lower effective magnetic fields around peak time. In addition, the association between SLSNe I and long gamma-ray bursts, if observed in the future, could be explained in the context of magnetar-disk system.
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