The macroscopic precession model: describing quasi-periodic oscillations including internal structures of test bodies

Abstract: The relativistic precession model (RPM) is widely-considered as a benchmark framework to interpret quasi-periodic oscillations (QPOs), albeit several observational inconsistencies suggest that the model remains incomplete. The RPM ensures \emph{structureless test particles} and attributes precession to geodesic motion alone. Here, we refine the RPM by incorporating the internal structure of rotating test bodies, while preserving the test particle approximation (TPA), and propose a \emph{macroscopic precession model} (MPM) by means of the Mathisson-Papapetrou-Dixon (MPD) equations, applied to a Schwarzschild background, which introduces 1) a shift in the Keplerian frequency and 2) an \emph{effective spin correction} to the radial epicyclic frequency that, once the spin tensor is modeled, reproduces a quasi-Schwarzschild-de Sitter (SdS) correction. We apply the MPM to eight neutron star low mass X-ray binaries (NS-LMXBs), performing Markov chain Monte Carlo (MCMC) fits to twin kHz QPOs and find observational and statistical evidence in favor of precise power law spin reconstructions. Further, our model accurately predicts the $3:2$ frequency clustering, the disk boundaries and the NS masses. From the MPM model, we thus conclude that complexity of QPOs can be fully-described including the test particle internal structure.