Superluminous supernovae: diverse rise times explain diverse spectra

TL;DR

Hydrogen-poor SLSNe I exhibit diverse O II line profiles and velocity evolution, prompting questions about discrete sub-classes. Through a detailed look at PTF12dam, the authors show its O II spectrum evolves from a hot, W-like form to a cooler, 15bn-like form by maximum light, arguing that ejecta temperature at peak—tied to rise time—drives spectral diversity. They introduce the Brightness-Timescale-Temperature-Radius (BTTR) diagram to visualize how luminosity, rise time, and blackbody parameters co-vary, and develop an analytic photospheric-velocity model with a flat inner density structure to explain velocity trends. The combined findings support a single, engine-powered SLSN population, with a shallow density profile consistent with magnetar-inflated bubbles, and suggest rise-time–driven temperature as the key factor shaping maximum-light spectra and velocity evolution. This framework provides a practical, physically motivated basis for interpreting the growing census of SLSNe in upcoming surveys like the Rubin Observatory LSST.

Abstract

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.

Figures (5)

• Figure 1: O II lines in the early spectra of SLSNe defining the spectroscopic classes proposed in the literature (Table \ref{['tab:classes']}). Phases are given in rest-frame days from maximum light. The shaded region highlights the strongest two lines. The O II line lines in PTF12dam Nicholl2013Vreeswijk2017 transition smoothly between the 'W'-like profiles exemplified by PTF09cnd Quimby2011 and the more complex profiles exhibited by SN2015bn Nicholl2016a. SN2011ke Inserra2013, which has a much shorter rise time than the others, exhibits no O II lines by $\sim1$ week after maximum, as well as much higher velocities.
• Figure 2: Zoom-in around the two strongest O II lines in PTF12dam, compared to PTF09cnd and SN2015bn. The comparison spectra are shifted along the logarithmic wavelength axis to account for velocity differences Quimby2018. This shows clearly that while the earliest spectra of PTF12dam have a strong 'W' feature, the later spectra are much closer in character to SN2015bn.
• Figure 3: Brightness-Timescale-Temperature-Radius (BTTR) diagram for all objects in the SLSN Catalog Gomez2024. For most objects we plot a single point corresponding to the peak of its bolometric light curve. The SLSNe in Table \ref{['tab:classes']} are highlighted with a bold outline. For these four events, we plot an additional point with a narrow outline, corresponding to the time of the earliest spectrum plotted in Figure \ref{['fig:evol']}. Arrows show the effects of increasing the values of key underlying physical parameters: ejecta mass, velocity, and input heating rate. The colour of each arrow indicates the effect on the observed temperature.
• Figure 4: Analytic models for the time-dependence of $v_{\rm ph}$, compared to the observed population of SLSNe from Aamer2025. The left column shows $v_{\rm ph}$, and the right shows its time derivative, $\dot{v}$. Each row corresponds to a different slope of the ejecta density profile, as labelled. The colour scale corresponds to different ejecta masses, ranging from 2 M$_\odot$ (purple) to 40 M$_\odot$ (yellow) to cover the full range of masses reported by Gomez2024. The red dashed line uses their median inferred ejecta mass and kinetic energy.
• Figure 5: Schematic showing how the observed spectroscopic properties of a SLSN at peak depend on its rise time. The relative lengths of all arrows are indicative of the relative velocities of expansion (solid arrows) and photospheric recession (bold, dashed arrows). (a) The density profile from equation \ref{['eq:density']}. We assume the ejecta are in homologous expansion, with a dense inner region and a shallow power-law envelope ($\rho\propto v^{-\alpha}$, with $\alpha<6$; see Figure \ref{['fig:v']}). The location of the photosphere is marked for the two cases shown in panels (b) and (c). (b) For a SLSN with a short rise time, the ejecta are still compact at maximum light, and therefore hotter for a given luminosity. For temperatures $\gtrsim12,000$ K, deep 'W'-shaped O II lines are produced. The photosphere (dotted line) is at high velocity coordinate, but receding quickly through the low-density outer ejecta; an observer therefore measures both a high $v_{\rm ph}$ and a large $\dot{v}$. (c) For a SLSN with a long rise time, the ejecta have expanded to a larger radius by maximum light, and so are cooler for the same luminosity. The O II lines may have already become weak or absent by this phase. The photosphere has receded further in mass coordinate by this time, and its rate of recession has slowed as it moves through increasingly dense ejecta. An observer therefore measures a lower $v_{\rm ph}$ and $\dot{v}$ compared to the fast-rising case.