Modeling the emission lines from r-process elements in Supernova nebulae

TL;DR

This work addresses whether heavy r-process elements produced in rare, energetic supernovae (e.g., GRB-associated Type Ic events) can be identified through nebular-phase emission. It introduces a steady-state NLTE, optically thin ejecta model that couples ionization balance, level populations, and thermal balance to predict late-time spectra and assess JWST detectability in the $1-10~\mu$m range. The key finding is that heavy elements significantly affect cooling only if they constitute about $\sim1\%$ of the ejecta mass, but even a small fraction ($\sim10^{-3}-10^{-2}~M_\odot$) can produce detectable near- to mid-IR lines, notably Te I at $2.10~\mu$m, offering a practical diagnostic for r-process material with JWST. The results demonstrate that IR spectroscopy with JWST could constrain heavy-element production in GRB-SNe, providing crucial insights into the role of rare energetic explosions in enriching the universe with heavy elements, and offering a way to test r-process nucleosynthesis scenarios beyond neutron-star mergers.

Abstract

The origin of heavy r-process elements in the universe is still a matter of great debate, with a confirmed scenario being neutron star (NS) mergers. Additional relevant sites could be specific classes of events, such as gamma-ray burst (GRB) Supernovae (SNe), where a central engine could push neutron-rich material outwards, contributing to the ejecta of the massive exploding star. Here, we investigate our ability to infer the production of heavy elements in such scenarios, on the basis of the observed nebular emission. We solve the steady-state ionization, level population, and thermal balance, for optically thin ejecta in non-local thermodynamic equilibrium (NLTE), in order to explore the role of heavy elements in cooling the gas, and their imprint in the emergent spectrum a few hundreds days post-explosion. We find that heavy elements would be relevant in the cooling process of the nebula only if they account for at least $\sim1\%$ of the total ejected mass, at the typical kinetic temperatures of a few thousands K. However, even in the absence of such amount, a few $0.1\%$ of the total ejected mass could be instead sufficient to leave a detectable imprint around $\sim1-10~\mathrm{μm}$. This wavelength range, which would be relatively clean from features due to light elements, would be instead robustly populated by lines from heavy elements arising from forbidden transitions in their atomic fine structures. Hence, the new generation of telescopes, represented by the James Webb Space Telescope (JWST), will most likely allow for their detection.

Figures (11)

• Figure 1: Electron temperature as a function of the specific energy deposition rate and the number density of atoms, for a gas of ions (I-IV) of pure Fe (left panel), pure Nd (central panel), and a mixture of $50\%$ Fe and $50\%$ Nd in mass fraction (right panel). Values are computed on a 10x10 grid log-spaced, using ionization and thermal balance. For approximate visual reference, we superimpose plausible trajectories with their time evolution of a CCSN, a SN Ia, a KN with two degrees of r-process material dilution, and a CCSN polluted with r-process material.
• Figure 2: Same as Figure \ref{['fig:grid_Te']}, with the plotted quantity being the number fraction of ions as stacked histogram. For the Fe-Nd mixture case (right panel), the ion fractions of Fe and Nd are displayed on the left and the right side of each grid cell, respectively.
• Figure 3: Total radioactive heating from the decay chains of ^56Ni-Co and ^44Ti-Sc for a SE SN, compared to the decay chain of ^57Ni-Co for a variable initial amount of ^57Ni, and to the heating due to the decay of a variable amount of r-process material. The values of ^56Ni and ^44Ti are taken from the CO138H SN model by Nomoto:2000. The radioactive energy produced (dashed lines) is shown for visual reference in contrast to the deposited energy (solid lines).
• Figure 4: Contribution to the specific cooling coming from light elements ($Z<26$, $Z=29,30$), iron group elements ($Z=26,27,28$) and heavy elements ($Z>30$), for different mixtures of such groups. The specific cooling rate is shown as a function of the kinetic temperature at a fixed density of $10^6~{\rm cm^{-3}}$, and it is obtained through an iterative computation of the thermal (and ionization) balance. Two sets of variations are considered, i.e. a case with low amount of iron (left panel), and a case with high amount of iron (right panel). For each set, the amount of heavy elements is progressively increased at the expenses of light elements. Each panel also shows the set of correspondent abundance patterns, with the abundance of light elements taken from the S25 model computed by Rauscher:2001dw (right panel), and from the r0e2 model computed by Dessart:2017 (left panel), while the abundance of heavy elements being the solar r-process pattern derived by Prantzos2020.
• Figure 5: Atomic number fraction $\frac{n^p}{n}$ of the most abundant elements included in our NLTE model, targeted on SN 1998bw at 215.4 days, and informed on the r0e2 model from Dessart:2017. The composition is shown for each of the three constructed zones, and the relative amount of the different ionization stages $\frac{n^p_i}{n^p}$, as obtained from ionization and thermal balance, is displayed for each element as a stacked histogram.