Statistical and theoretical atomic data calculations for moderately-charged lanthanide ions in order to compute opacities in the context of early-phase kilonovae modeling

The LIGO-VIRGO collaboration observed a neutron star merger (GW170817) thanks to the first detection of gravitational waves. An electromagnetic emission called kilonova is also observed. In the latter, nuclear reactions take place and form heavy nuclei e.g. lanthanides which contribute strongly to the luminosity and spectra of the kilonova. Such elements produce millions of lines due to their complex configurations characterized by an unfilled 4f subshell.

To interpret the spectrum of a kilonova, it is therefore crucial to precisely know the radiative parameters characterizing these elements. In recent years, several studies have been carried out, for the first degrees of ionisation (up to 3+) but almost all these investigations were limited to the analysis of kilonovae in a temperature range below 20000 K. To extend the study to early phases of kilonovae, it is essential to know the radiative parameters of lanthanide ions in higher charge stages.

The present work focusses on atomic data and opacity calculations for lanthanides (La to Lu) from the fourth to the sixth degree of ionization, for typical ejecta conditions such as the density ρ = 10^-10 g cm^-3, the time after the merger t = 0.1 day and temperatures T > 20000 K. In order to do that, we used the pseudo-relativistic Hartree-Fock (HFR) method as implemented in Cowan’s codes to calculate the radiative parameters. The expansion formalism was then used to compute the opacity, at 25000 K, 35000 K and 40000 K.

Since lanthanides (Eu to Lu) from the seventh to the ninth are characterized by complex configurations (i.e. unfilled 4f and 5p subshells), their atomic data are difficult to obtain with theoretical method. Indeed, the huge size of the energy matrices makes the diagonalization of the Hamiltonian extremely challenging. In order to simulate atomic data, we used the Resolved Transition Arrays (RTA) statistical method. Such method was tested for Sm VIII and Eu VI, two ions whose atomic data were already calculated by computational methods, in order to validate the obtained opacities by comparing them with the results deduced from full atomic calculations. Using compact formulae from RTA approach, we simulated atomic data for Dy VIII (Z = 66) and present the corresponding expansion opacity