Superluminous supernovae: diverse rise times explain diverse spectra

Type I superluminous supernovae (SLSNe) are a diverse class of exceptionally bright massive star explosions, which typically exhibit absorption from ionised oxygen in their early spectra. While their photometric properties (luminosity and duration) both span an order of magnitude, population studies suggest that these distributions are continuous. However, spectroscopic samples have shown some indications of distinct sub-types, either through similarity to certain prototype objects, or in terms of their velocity evolution. Here we show that a well-observed SLSN, PTF12dam, completely changes its O II absorption profile as it rises to maximum light, moving from one proposed sub-type to another. This supports an interpretation where spectroscopic diversity is driven by the ejecta temperature at maximum light, rather than fundamental differences in the explosion or progenitor. Motivated by this, we develop a new diagnostic, the Brightness-Timescale-Temperature-Radius diagram, and a simple toy model for the evolution of the photospheric velocity, to show that diversity in the light curve rise time (likely due to differences in ejected mass) naturally explains why SLSNe with broader light curves generally have weaker O II lines, lower photospheric velocities after maximum, and slower changes in photospheric velocity over time. We show that the velocity distribution of the known SLSN population favours a relatively flat ejecta density profile, consistent with a hot bubble inflated by a central engine.