Mapping for parametrized merger-ringdown parameters in beyond general relativity theories

The parametrized post-Einsteinian (ppE) formalism provides a flexible framework to carry out strong-field tests of general relativity (GR) using gravitational waves from compact binary coalescences without resorting to a particular modified theory of gravity. The ppE framework allows generic deviations from GR across inspiral-merger-ringdown phases of phenomenological gravitational waveform models--- the generalized {\tt IMRPhenom} (gIMR) models. Parameters in these gIMR models are constrained by comparing the gIMR model against the observed gravitational wave signals. By utilizing the gravitational wave events observed by the LIGO-Virgo-KAGRA (LVK) collaboration, the gIMR parameters have been translated to constraints on various modified theories of gravity as a post-processing analysis. However, such mappings were extensively worked out only for the inspiral phase due to a lack of post-inspiral or merger-ringdown simulations for modified theories of gravity. It is essential to consider the merger-ringdown phase as it probes stronger gravitational fields compared to the inspiral. In this work, for the first time, we derive a mapping between the gIMR parameters in the merger-ringdown phase with the coupling constants in Einstein dilaton Gauss-Bonnet (EDGB) and dynamical Chern-Simons (dCS) gravity. To achieve this, we use recent inspiral-merger-ringdown numerical relativity simulations of GW150914 in EDGB and dCS gravity. We subsequently employ this mapping to compute an upper limit on the coupling constants within EDGB and dCS gravity, utilizing the upper limits on the gIMR parameters provided by the LVK collaboration. The coupling constant in EDGB gravity is constrained to $\leq$ 12 km, whereas for the dCS gravity, the length scale is constrained to $\leq$ 32 km.