Spectral synthesis techniques for supernovae and kilonovae

TL;DR

Spectral synthesis of supernovae and kilonovae hinges on accurately modelling temperature, NLTE rate equations, and radioactive powering to decode ejecta composition and explosion mechanisms. The article surveys historical developments, current numerical frameworks, and key approximations (LTE vs NLTE, Sobolev line transfer, Monte Carlo methods), highlighting how temperature coupling, rate-equation solutions, and time-dependent powering shape observable spectra. A central message is that NLTE treatment of ionization and excitation, coupled to radiative transfer, is essential for reliable abundance inferences, and that continued improvements in atomic data, 3D modelling, and robust solution strategies are needed to fully exploit spectra for testing explosion models and nucleosynthesis. Ultimately, the field aims to connect event-by-event spectra to elemental origins and progenitor physics, driving progress in both theory and observations across the UV to mid-IR range.

Abstract

Supernovae (SNe) and kilonovae (KNe) are the most violent explosions in cosmos, signalling the destruction of a massive star (core-collapse SN), a white dwarf (thermonuclear SN) and a neutron star (KN), respectively. The ejected debris in these explosions is believed to be the main cosmic source of most elements in the periodic table. However, decoding the spectra of these transients is a challenging task requiring sophisticated spectral synthesis modelling. Here, the techniques for such modelling is reviewed, with particular focus on the computational aspects. We build from a historical review of how methodologies evolved from modelling of stellar winds, to supernovae, to kilonovae, studying various approximations in use for the central physical processes. Similarities and differences in the numeric schemes employed by current codes are discussed, and the path towards improved models is laid out.

Figures (12)

• Figure 1: Example of an early SN spectral model (bottom) for the photospheric spectrum of a white dwarf explosion model compared to an observed spectrum (top). From this modelling, the first identification of which lines are important for the different observed featured could be established. Image reproduced with permission from Branch1985, copyright by AAS.
• Figure 2: Characteristic evolution of SNe and KNe over the three phases of diffusion phase, early tail phase, and late tail phase.
• Figure 3: Observed spectrum of SN 2008bk (red), and a model spectrum (blue). Image reproduced with permission from Jerkstrand2018, copyright by the author(s).
• Figure 4: Left: Cooling function of Nd II in the low-density limit, from Hotokezaka2021. Right: Cooling functions of different ions of Ce, in the low density limit, from Pognan2022a.
• Figure 5: Left:Comparison between temperature time-evolution at velocity coordinate 9600 km s$^{-1}$ in Type Ia LTE SN model using different treatments. Electron temperatures $T_e$ using Eq. \ref{['eq:T_simple']} are plotted as green pluses, while those from thermal equilibrium are plotted as black points. The blue and red points are $T_R$ and $T_J$ in the thermal equilibrium model. Right: Same as the left figure, but showing profiles (temperature versus velocity) at 31 days. The black/violet/blue/green/red/orange vertical lines show the mean radii of last scattering in the $U,B,V,R,I$ bands. From Kromer2009.