Both the long-duration gamma-ray bursts (LGRBs) and the Type I superluminous supernovae (SLSNe I) have been proposed to be primarily powered by central magnetars. A correlation, proposed between the initial spin period (P ₀) and the surface magnetic field (B) of the magnetars powering the X-ray plateaus in LGRB afterglows, indicates a possibility that the magnetars have reached an equilibrium spin period due to the fallback accretion. The corresponding accretion rates are inferred as M _⊙ s⁻¹, and this result holds for the cases of both isotropic and collimated magnetar wind. For the SLSNeI and a fraction of engine-powered normal Type Ic supernovae (SNe Ic) and the broad-lined subclass (SNe Ic-BL), the magnetars could also reach an accretion-induced spin equilibrium, but the corresponding distribution suggests a different accretion rate range, i.e., M _⊙ s⁻¹. Considering the effect of fallback accretion, magnetars with relatively weak fields are responsible for the SLSNeI, while those with stronger magnetic fields could power SNeIc/Ic-BL. Some SLSNeI in our sample could arise from compact progenitor stars, while others that require longer-term accretion may originate from the progenitor stars with more extended envelopes or circumstellar medium.

长期伽马射线暴 (LGRB) 和 I 型超光速超新星 (SLSN I) 都被提议主要由中央磁星提供动力。初始自旋周期 ( P ₀ ) 与为LGRB 余辉中的 X 射线平台提供动力的磁星的表面磁场 ( B )之间的相关性表明，由于回退，磁星可能已达到平衡自旋周期吸积。相应的吸积率推导出为 M _⊙ s ^-1，并且该结果适用于各向同性和准直磁星风的情况。对于 SLSNeI 和一小部分发动机驱动的正常 Ic 型超新星 (SNe Ic) 和宽线亚类 (SNe Ic-BL)，磁星也可以达到吸积诱导的自旋平衡，但相应的分布表明不同吸积率范围，即 M _⊙ s ^-1。考虑到回退吸积的影响，磁场相对较弱的磁星负责 SLSNeI，而磁场较强的磁星可以为 SNeIc/Ic-BL 提供动力。我们样本中的一些 SLSNeI 可能来自致密的前身星，而其他需要长期吸积的可能来自具有更大包层或星周介质的前身星。