Imprints of the Frequency-Domain Source Function on Black Hole Ringdown*

In recent years, substantial attention has been paid towards gathering physical information from the ringdown portion of gravitational wave (GW) signals from compact object mergers. These studies have generally been interested in inferring astrophysical parameters, such as the masses and spins of the progenitors, from quasinormal mode (QNM) amplitudes and phases. In this work, we investigate whether the structure of the source term which generates the ringdown itself can be extracted from the resulting waveform. In particular, we explore whether applying the ringdown filters of Ma et al. to a ringdown waveform leaves behind a signature characterized by the behavior of the frequency-domain source. Using black hole perturbation theory, we compute frequency‑domain Green's function for the radial Teukolsky equation on a Kerr background, employing the numerically stable Generalized Sasaki–Nakamura form. We then apply the frequency-domain filters to nontrivial radial and frequency-domain behavior and analyze whether the filters return signals which can clearly be associated with the form of the source. This framework establishes the tools needed to test whether filtered ringdown waveforms can isolate the imprint of the source, with the goal of extending the analysis to more realistic astrophysical perturbations.