On the validity of steady-state for nebular phase kilonovae

Abstract

The radioactively powered transient following a binary neutron star (BNS) merger, known as a kilonova (KN), is expected to enter the steady-state nebular phase a few days after merger. Steady-state holds until thermal reprocessing time-scales become long, at which point the temperature and ionisation states need to be evolved time-dependently. We study the onset and significance of time-dependent effects using the non-local thermodynamic equilibrium (NLTE) spectral synthesis code SUMO. We employ a simple single-zone model with an elemental composition of Te, Ce, Pt and Th, scaled to their respective solar abundances. The atomic data are generated using the Flexible Atomic Code (FAC), and consist of energy levels and radiative transitions, including highly forbidden lines. We explore the KN evolution from 5 to 100 days after merger, varying ejecta mass and velocity. We also consider variations in the degree of electron magnetic field trapping, as well as radioactive power generation for alpha and beta decay (but omitting fission products). We find that the transition time, and magnitude of steady-state deviations are highly sensitive to these parameters. For typical KN ejecta, the deviations are minor within the time-frame studied. However, low density ejecta with low energy deposition show significant differences from ∼10 days. Important deviation of the ionisation structure solution impacts the temperature by altering the overall line cooling. Adiabatic cooling becomes important at t ≥ 60 days which, in addition to the temperature and ionisation effects, lead to the bolometric light curve deviating from the instantaneous radioactive power deposited.

NLTE Effects on Kilonova Expansion Opacities

“…The models used in this study are taken from those of Pognan et al (2022), with the parameters and physics described therein. Our standard model has constant density ejecta with parameters 𝑀 ej = 0.05𝑀 and maximum expansion velocity 𝑣 ej = 0.1c.…”

“…This composition implies a relatively low electron fraction (𝑌 𝑒 0.2) ejecta due to the presence of 2nd and 3rd r-process peak elements (Te and Pt), as well as a lanthanide (Ce) and an actinide (Th) (Rosswog et al 2018;Nedora et al 2021;Zhu et al 2021). Since we evolve our models only up to 20 days after merger, we consider that a steady-state approach is sufficient (Pognan et al 2022).…”

“…Ionisation into excited states is currently not implemented in , and so all ionisations are allocated to the ground state. Internal collisional processes include thermal collisions, the treatment of which is described in Pognan et al (2022). Non-thermal collisional excitation and thermal collisional ionisation are not yet included for r-process elements.…”

“…Thus far, NLTE studies of KN ejecta are limited to neodymium (Nd, Z = 60) (Hotokezaka et al 2021), while Pognan et al (2022) have applied an NLTE approach to a set of models containing Te (Z = 52), Ce (Z = 58), Pt (Z = 78) and Th (Z = 90). Modelling emergent lightcurves and spectra with NLTE requires the calculation of temperature, ionisation and excitation structure, as well as the radiation field, all self-consistently, and therefore represents significant effort both in terms of physical complexity and computational power.…”

“…In Pognan et al (2022), we presented a grid of simple KN models, and focused the analysis on the significance of time-dependent terms in the energy and ionisation structure equations. We now analyse parts of this model grid with respect to the NLTE excitation and ionisation structure.…”