How Spectral Synthesis Decodes Supernovae and Kilonovae

Supernovae and kilonovae are the most violent explosions in the cosmos, marking the destruction of a massive star, a white dwarf, or a neutron star. The debris hurled into space by these blasts is believed to be the main cosmic source of most elements in the periodic table, from the oxygen we breathe to the gold in our jewelry. Yet the light these explosions emit arrives as a tangled web of spectral lines, blended by rapid expansion and shaped by exotic physics. A comprehensive review published in Living Reviews in Computational Astrophysics by Anders Jerkstrand maps out the sophisticated spectral synthesis techniques required to untangle that light, tracing how the field evolved from modeling stellar winds in the 1970s to the cutting-edge kilonova models of today.

The historical arc of the field is one of steady, incremental extension into adjacent problems. The first synthetic supernova spectrum was presented by David Branch in 1980, who adapted the Schuster-Schwarzschild approach from stellar atmospheres and introduced the Sobolev formalism for line transfer. His tools, which eventually became the widely used SYNOW code, allowed detailed comparisons between white dwarf explosion models and observations of Type I supernovae. In the same year, Timothy Axelrod’s doctoral thesis laid the foundation for nebular-phase modeling, establishing the treatment of non-thermal and non-local thermodynamic equilibrium (NLTE) physics that still sets the standard for many codes today. The explosion of SN 1987A then drew new workers into the field, including Claes Fransson in Stockholm and Leon Lucy in London, whose Monte Carlo techniques would prove transformative.

Around 2005, a wave of development swept through the field, much of it inspired by Lucy’s work on Monte Carlo methods. Three-dimensional codes operating under the assumption of local thermodynamic equilibrium (LTE) appeared, including SEDONA and ARTIS, while one-dimensional NLTE codes such as SUMO, NERO, and CMFGEN were developed for higher-fidelity spectral calculations. The first public Schuster-Schwarzschild code, TARDIS, was released in 2014 and remains popular for rapid line identification. When the first kilonova, AT2017gfo, was discovered in 2017 following the gravitational-wave detection GW170817, the supernova toolkit was ready to be adapted. Metzger and colleagues extended SEDONA to kilonovae as early as 2010, and codes such as SuperNu, POSSIS, and a kilonova version of SUMO followed, opening the door to NLTE modeling of neutron star merger ejecta.

The review emphasizes that astrophysics grows by small extension steps into related areas, a process that takes decades. Sometimes growth in computing power drives these steps, but more often they are application-driven. This has a practical consequence: methods derived under computing constraints orders of magnitude stricter than today’s may carry simplifications that are no longer necessary. Studying the history of a code or methodology therefore reveals where modern computing power can be exploited to improve upon legacy approximations, a point the author urges researchers to keep in mind whenever they adopt an existing model.

Why invest such effort in spectral synthesis? The review identifies three main science drivers. First, identifying which elements produce which line features and determining the elemental abundances in the ejecta. For decades this seemed almost insurmountable, because supernovae blend lines through rapid Doppler expansion, cascade energy over six orders of magnitude, and involve non-thermal effects, asymmetries, molecules, and dust. Today, clear diagnostic methods exist for seventeen elements from hydrogen to nickel, and direct full-ejecta spectral tests of explosion models have been performed for all major supernova classes. Second, understanding the origin of the elements across the periodic table: with AT2017gfo, the upper two-thirds of the table opened for direct analysis, with diagnostic potential already established for elements including strontium, yttrium, tellurium, lanthanum, cerium, neodymium, and tungsten. Third, determining the progenitor systems and explosion mechanisms, since spectra diagnose both the hydrostatic life of the progenitor star and the physics of its death, from neutrino-driven core collapse to accretion disk outflows near black holes.

The physical situation these codes must capture is extreme. The ejecta expand homologously, with faster fragments outrunning slower ones, at characteristic velocities of roughly 5,000 kilometers per second for core-collapse supernovae, 8,000 for thermonuclear supernovae, and 50,000 for kilonovae. Kilonovae carry about one hundred times less mass than supernovae but comparable kinetic energy, hence their higher speeds and their rise and decline over just days. Both classes are powered by radioactivity: supernovae chiefly by the decay of nickel-56 and cobalt-56, kilonovae by a vast array of radioactive r-process nuclides whose energy is carried mainly by leptons rather than gamma rays. Because the ejecta are semi-transparent, with line opacity producing lingering radiative transfer effects for years or even decades, much of the optical and infrared spectra of both supernovae and kilonovae is formed by fluorescence.

Temperature emerges as the most fundamental quantity in the modeling. It governs ionization and excitation, sets the regime of spectral formation, and strongly influences opacity. The governing law is energy conservation, expressed either through the internal energy of the gas or, equivalently in NLTE treatments, through the evolution of thermal kinetic energy balanced by heating and cooling. Codes differ in whether they retain the time-derivative terms: STELLA, SuperNu, CMFGEN, and, since 2022, SUMO can solve the time-dependent energy equation with implicit or semi-implicit finite-difference schemes, typically using time steps of about ten percent, which is well matched to both the homologous expansion timescale and radioactive decay timescales. The review shows that this choice of stepping has a solid physical anchoring for both supernova and kilonova applications across all conceivable epochs.

The treatment of line cooling exposes a subtle but consequential divide between LTE and NLTE approaches. In LTE codes, a parameterized thermalization probability is often assigned to line absorptions, and surprisingly, realistic light curves and spectra require this probability to be near unity, effectively mimicking the fluorescence process that the simplified treatment omits. But when radioactivity dominates the heating, such an inflated absorption coefficient can drive temperature estimates a factor of ten too low, likely explaining why LTE codes yield significantly lower temperatures than NLTE ones from quite early phases. In NLTE, cooling is computed from net electron collision rates, which represent the small difference between two large terms and demand careful formulation. A code comparison for a simple Type Ia test model shows that even state-of-the-art tools produce temperature profiles that vary considerably, underscoring how much work remains to achieve robust temperature determinations.

Solving the NLTE rate equations presents its own numerical challenges. With potentially more than one hundred thousand levels per grid cell, the full system is split into blocks, typically one per ion, and solved iteratively. Matrix storage scales with the square of the system size and inversion time with its cube, so the standard LAPACK routine DGESV, based on LU decomposition, remains efficient only up to a few hundred levels. Superlevels, which bundle groups of levels assuming LTE distributions within them, offer dramatic savings: in one full-composition Type Ia model, 10,605 levels were grouped into 2,338 superlevels, saving a factor of sixteen in storage and up to sixty-four in matrix inversion time. Negative populations, false singularities, and oscillating Newton-Raphson steps all require layered fall-back strategies, and co-solving all ions of an element, as done in recent 3D codes, reduces such pathologies.

Radioactive powering completes the triad of central modeling blocks. High-energy decay particles transfer their energy through ionization, excitation, and heating, with the Bethe stopping-power formula, derived in the early 1930s, describing the continuous energy loss of fast particles. Gamma rays Compton-scatter to create primary electrons of 0.1 to 1 megaelectronvolt, which cascade into secondaries; the distribution of these secondaries, measured experimentally by Opal and colleagues, feeds into steady-state Boltzmann solutions of the degradation spectrum. For kilonovae, time-dependent thermalization effects become important within weeks, and modeling the powering has already allowed constraints to be placed on the composition of AT2017gfo. Looking forward, the review charts a roadmap: better physical treatments, accurate atomic data for trans-iron elements, 3D hydrodynamic explosion models, and high-quality observations from the ultraviolet to the mid-infrared. Eighteen of the thirty lightest elements now have good or moderate diagnostic potential, and with kilonova spectroscopy advancing rapidly, the goal of determining the origin of the elements directly at their production sites is coming within reach.

Subject of Research: Computational spectral synthesis modeling of supernova and kilonova spectra to infer ejecta composition and explosion physics

Article Title: Spectral synthesis techniques for supernovae and kilonovae

Article References: Jerkstrand, A. (2025). Spectral synthesis techniques for supernovae and kilonovae. Living Reviews in Computational Astrophysics, 11(1), Article 1. https://doi.org/10.1007/s41115-025-00022-2

Image Credits: AI Generated

DOI: 10.1007/s41115-025-00022-2

Keywords: supernovae, kilonovae, spectral synthesis, radiative transfer, NLTE modeling, r-process nucleosynthesis, Monte Carlo methods, neutron star mergers, radioactive powering, astrophysical transients, computational astrophysics, origin of the elements