The Magnetar Engines And The Redshift-Luminosity Distribution Of Type Ⅰ Super-luminous Super Novae

Superluminous supernova(SLSNe) are a special class of supernovae discovered in recent decades.Its peak luminosity cae be tens or hundreds of times higher than that of normal supernovae.Therefore,the traditional model that powered by the decay of 56Ni is difficult to explain such a high luminosity for SLSNe,unless some stars with more than 100 solar mass might have a detonation-like,no residual core supernova explosion due to the instability of”electron-positron pair-production".However,based on the most SLSN spectroscopic and photometric information,it is generally believed that the shock int.eraction and central activities are the two most likely energy sources leading to SLSN radiation.To some extent,these two energy mechanisms may correspond to two different types of SLSNe:type Ⅱ and type Ⅰ,although the corresponding relationship is not strict.In some cases,the existence of hybrid energy mechanisms can often be considered.In this paper,we will focus on the studies of type Ⅰ SLSNe(SLSN-I).On one hand,we investigate the case that the newly born millisecond magnetar as the central energy source and find that the model gives a reasonably well fitting of the bolometric light,curves of 5 SLSN-I observed by Pan-STARRS.The results again verify the validity of the magnetar model in explaining the observed high luminous of SLSNe.On the other hand,we investigate the relations between the SLSN-I burst rate with redshift.Assuming that the SLSN-I burst rate is proportional to the star formation rate,we study the redshift distribution of 17 SLSN-I and find that the burst rate of SLSN-I does not evolve with redshift.This result makes it distinctly different from the case of long gamma:-ray bursts(LGRBs),although the central remnants of LGRBs could be millisecond magnetars.In addition,we also obtain that the burst rate of SLSN-I is about 40 yr-1 Gpc-3(at the average redshift z＝0.89),and find that the intrinsic luminosity distribution of SLSN-I follows a power-law distribution.