Physical properties of long-rising type II Supernovae -- Bayesian Analytic Modelling and Spectrophotometric Correlations

TL;DR

This work tackles the challenge of characterizing long-rising, hydrogen-rich 1987A-like SNe by inferring $E$, $M_{ m ej}$, $R_0$, and $M_{ m Ni}$ from bolometric light curves and velocities using a Ni-dependent analytic model within a Bayesian framework. It introduces SuperBAM, validates it against hydrodynamic models, and applies it to a homogeneous sample of 28 SNe to extract explosion and progenitor properties, linking them to spectrophotometric observables. The results reveal a continuous distribution of explosion energies and radii, with clear correlations between $M_{ m Ni}$, peak luminosity, and $E$, and an anti-correlation between Ba II strength and photospheric velocity, suggesting the role of progenitor compactness and ejecta density. The study also highlights that the brightest events may require additional power sources beyond $^{56}$Ni heating (e.g., magnetar spin-down or CSM interaction), underscoring the need to extend analytic models for peculiar transients to enable scalable population studies for upcoming surveys.

Abstract

Supernova (SN) 1987A, with its long-rising ($\gtrsim$40~days) light curve, defines a rare subclass of type II SNe known as 1987A-like events. Representing only $\sim$1-3\% of all core-collapse SNe and often found in low-metallicity environments, their large diversity suggests a wide range of progenitor and explosion properties. This study aims to improve the understanding of 1987A-like SNe by characterizing their explosion parameters, including kinetic energy, ejected mass, progenitor radius at explosion, and synthesized $^{56}$Ni mass. Additionally, it seeks to identify systematic trends in both the physical properties and the observed features of these peculiar events. A new Bayesian parameter estimation method, based on our $^{56}$Ni-dependent analytical model for hydrogen-rich SNe, is applied to derive explosion parameters from the light curves and expansion velocities of one of the largest and most comprehensive 1987A-like SN samples to date. These data are measured through a consistent analysis of observations available in the literature. The analysis reveals a heterogeneous population that nevertheless clusters into two main groups: (i) lower-energy explosions with modest $^{56}$Ni yields ($\sim$0.07~M$_\odot$), similar to SN~1987A, and (ii) more energetic events (up to $\sim$5~foe) with larger nickel production and, in some cases, unusually extended progenitors. We confirm a robust correlation between $^{56}$Ni mass, peak luminosity, and explosion energy, as well as between ejecta mass and recombination timescale. An anti-correlation between Ba~II line strength and photospheric velocity indicates that stronger Ba~II absorptions in 1987A-like SNe arise from more compact, slowly expanding ejecta. Our study underscores the need to extend analytical frameworks to include additional power sources, enabling scalable and accurate modelling of the growing number of peculiar transients.

Figures (6)

• Figure 1: Application of Gaussian Process Regression (GPR) to the LCs of SN 1987A, SN 2009E, and OGLE-14 to identify the main LC features. The adopted GPR employs a constant mean function combined with a Matérn 3/2 kernel. For each SN LC, the key epochs $t_m$, $\bar{t}_M$, and $t_{\rm f}^*$ are highlighted. The dashed line shows the luminosity contribution $L_{\rm Ni}$ due to $^{56}$Ni -$^{56}$Co radioactive decay with $M_{\rm Ni}$ value reported within the panel of each SN.
• Figure 2: Mosaic of $P(\theta|\bar{L})$ plots for SN 1987A. The color density maps show 2D slices of the log-posterior distribution with $\sigma$ fixed, while two modelling parameters vary at a time. The diagonal panels display the posterior PDFs along each parameter axis, keeping the other parameters fixed at their best-fit values. The lower row shows the cumulative distribution function (CDF) for each parameter axis (solid line), compared to the CDF integrated on the entire space (dotted line).
• Figure 3: Observational properties derived from the bolometric LCs and spectra of the SN sample. Top left: distribution of the peak luminosity $L_M$ as a function of the $^{56}$Ni mass estimated from the radioactive tail fit. The trend line is obtained through a linear regression $\log_{10}L_M$-$\log_{10}M_{\mathrm{Ni}}$; the correlation is highly significant ($p$-value$\ll 0.01$ and Pearson coefficient of $0.89$). Bottom left: distribution of $t_f^*$ versus the $^{56}$Ni mass for the same SN sample. Top right: pEW as a function of expansion velocity for the H$\alpha$ and Fe II lines, for the SNe with available data. The color and shape of the markers follow the top legend, while the marker border indicates the line type according to the internal legend. Bottom right: same as the top-right panel, but for the H$\beta$ and Ba II lines.
• Figure 4: Bolometric light curve data for each SN in our sample, with the name of each SN indicated within its panel. Along with the data, we present the synthetic light curves obtained from the analytical model described in PC2025. The parameters for these models were determined using the prior values given by the SR, and the best-fit model obtained from SuperBAM analysis. The shaded region marks the LCs of explored parameters in the MC method associated to SuperBAM parameters error. For comparison, the synthetic LC of the nickel-free model by popov93 is also included, calculated for the best-fit model parameters.
• Figure 5: Distribution of SNe physical properties. The diagonal panels show the histograms of the logarithm of each parameter ($M_{\rm Ni}$, $E$, $M_{\rm ej}$, $R$), with the mean value (dashed line) and quartiles (25%, 50%, and 75%; see dotted lines) indicated. The lower triangular panels show scatter plots of the parameter pairs for each SN in the sample.