A group of superluminous supernovae characterized by broad light curves have been suggested to be pair instability SNe (PISNe). Nebular spectra computed using PISN models have failed to reproduce the broad emission lines observed in these SNe, casting doubts on their true nature. Here, models of both PISNe and the explosion following the collapse of the core of a very massive star (100MΘ) are used to compute nebular spectra, which are compared to the spectrum of the prototypical PISN candidate, SN 2007bi. PISN models are confirmed to produce synthetic spectra showing narrow emission lines, resulting from the confinement of 56Ni to the lowest velocities (≤ 2000 km s-1) and in clear disagreement with the spectrum of SN 2007bi. Spectra more closely resembling SN2007bi are obtained if the PISN models are fully mixed in abundance. Massive core-collapse models produce enough 56Ni to power the light curve of PISN candidates, but their spectra are also not adequate. The nebular spectrum of SN 2007bi can be successfully reproduced if the inner region is artificially filled with oxygenrich, low-velocity ejecta. This most likely requires a grossly aspherical explosion. A major difference between PISN and massive collapse models is that the former emit much more strongly in the NIR. It is concluded that: (a) current PISN candidates, in particular SN 2007bi, are more likely the result of the collapse and explosion of massive stars below the PI limit; (b) significant asymmetry is required to reproduce the late-time spectrum of SN2007bi.
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