  The influence of nonlinear dynamical effects is analyzed on the observed
spectra of controversial 3C and 3D astrophysically relevant x-ray lines in
neonlike Fe${}^{16+}$ and the A, B, C lines in natriumlike Fe${}^{15+}$ ions.
First, a large-scale configuration-interaction calculation of oscillator
strengths is performed with the inclusion of higher-order electron-correlation
effects. Also, quantum-electrodynamic corrections to the transition energies
are calculated. Further considered dynamical effects provide a possible
resolution of the discrepancy between theory and experiment found by recent
x-ray free-electron-laser measurements of these controversial lines. We find
that, for strong x-ray sources, the modeling of the spectral lines by a peak
with an area proportional to the oscillator strength is not sufficient and
nonlinear dynamical effects have to be taken into account. Thus, we advocate
the use of light-matter-interaction models also valid for strong light fields
in the analysis and interpretation of the associated astrophysical and
laboratory spectra. We investigate line-strength ratios distinguishing between
the coherent and incoherent parts of the emission spectrum. In addition, the
spectrum of Fe${}^{15+}$, an autoionizing ion which was also present in the
recent laboratory experiment, is also analized.
