Most type-Ic core-collapse supernovae (CCSNe) produce $^{ 56}$Ni and neutron stars (NSs) or black holes (BHs). The dipole radiation of nascent NSs has usually been neglected in explaining supernovae (SNe) with peak absolute magnitude $M_{ \rm peak}$ in any band are $\gtrsim -19.5$~mag, while the $^{ 56}$Ni can be neglected in fitting most type-Ic superluminous supernovae (SLSNe Ic) whose $M_{ \rm peak}$ in any band are $\lesssim -21$~mag, since the luminosity from a magnetar (highly magnetized NS) can outshine that from a moderate amount of $^{ 56}$Ni. For luminous SNe Ic with $-21 \lesssim M_{ \rm peak}\lesssim -19.5$~mag, however, both contributions from $^{ 56}$Ni and NSs cannot be neglected without serious modeling, since they are not SLSNe and the $^{ 56}$Ni mass could be up to $\sim 0.5 M_{ \odot}$. In this paper we propose a unified model that contain contributions from both $^{ 56}$Ni and a nascent NS. We select three luminous SNe Ic-BL, SN~2010ay, SN~2006nx, and SN~14475, and show that, if these SNe are powered by $^{ 56}$Ni, the ratio of $M_{ \rm Ni}$ to $M_{ \rm ej}$ are unrealistic. Alternatively, we invoke the magnetar model and the hybrid ($^{ 56}$Ni + NS) model and find that they can fit the observations, indicating that our models are valid and necessary for luminous SNe Ic. Owing to the lack of late-time photometric data, we cannot break the parameter degeneracy and thus distinguish among the model parameters, but we can expect that future multi-epoch observations of luminous SNe can provide stringent constraints on $^{ 56}$Ni yields and the parameters of putative magnetars.
Categories: astro-ph.HE