Gravitational wave emission in binary neutron star early post-merger within a dark environment

Using an effective Lagrangian model inspired by Takami et al. [1] we qualitatively study the early post-merger of a nearly symmetric binary Neutron Star (BNS) merger event with a non-vanishing ambient fraction of dark matter. For this we first mimic the dynamics of two oscillating Neutron Star (NS) masses in the gravitational potential well as they merge. We parametrize the dynamics and ejecta properties in the coalescence event allowing the formation of a surrounding debris disk that may be containing a non-vanishing dark matter fraction. In order to analyze the possible novel dark contribution, we start from a dark-matter free modelization as a benchmark. Using Monte Carlo Markov Chain (MCMC) techniques we approximately recover the gravitational waveforms, restricted to early post-merger time interval from existing simulations in the CoRe database. Later, we explore the impact of an additional dark viscous fluid under a prescribed velocity dependent force in the Lagrangian and obtain the resulting waveforms and some spectral features originating in the first few ms in the BNS post-merger. Finally we discuss our qualitative findings and its range of validity in light of the prospects of detectability in present or future experimental settings.