Theoretical calculations of forbidden lines in lanthanide ions for kilonova nebular-phase analysis

On August 17, 2017, the LIGO/Virgo collaboration detected for the first time a gravitational wave signal (GW170817) associated with a neutron star merger. This event marked a milestone in multi-messenger astronomy. The merger ejected a significant amount of hot and radioactive matter into space, where nuclear reactions synthesized elements heavier than iron, including lanthanides (Z = 57–71). The radioactive decay of these elements powered a transient electromagnetic phenomenon known as a kilonova.

In the early stages, kilonova spectrum is dominated by numerous allowed transitions from heavy elements. However, in the later nebular phase, the temperature and density of the ejecta decrease significantly, limiting the ionization stage to at most doubly charged species. Under these conditions, only low-energy levels, such as metastable states, are populated, resulting in forbidden emission lines such as magnetic dipole (M1) and electric quadrupole (E2) transitions. Observations of kilonova AT2017gfo and more recently of a similar transient event recorded in March 2023 by the James Webb Space Telescope have revealed infrared spectral features in the late-time spectra potentially linked to forbidden transitions of lanthanides and other heavy elements.

To facilitate the analysis of such spectra, new calculations of transition probabilities for M1 and E2 lines between low-lying levels in singly and doubly ionized lanthanide atoms were carried out. The fully relativistic Multi-Configurational-Dirac-Hartree-Fock (MCDHF) method, implemented in the GRASP2018 code, was employed to model the atomic structure and compute radiative parameters. Results were compared to those obtained using the pseudo-relativistic Hartree-Fock (HFR) approach to ensure reliability. This work provides a consistent set of atomic data, highlighting the most intense forbidden lines of lanthanides, which are likely to be observed in the infrared spectra of kilonovae during their nebular phase.