2020ApJ...903L..24L

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 (P₀) 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 {dot}M~10^–4–10^–1M_☉ s^–1, and this result holds for the cases of both isotropic and collimated magnetar wind. For the SLSNe I 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 B–P₀ distribution suggests a different accretion rate range, i.e., {dot}M~10^–7–10^–3M_☉ s^–1. Considering the effect of fallback accretion, magnetars with relatively weak fields are responsible for the SLSNe I, while those with stronger magnetic fields could power SNe Ic/Ic-BL. Some SLSNe I 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.