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

TL;DR

Quasi-periodic oscillations in NS-LMXBs have been interpreted with the relativistic precession model, but RPM struggles when treating accreting matter as structureless test particles. The authors develop a macroscopic precession model by applying the Mathisson-Papapetrou-Dixon equations on a Schwarzschild background and introducing a spin tensor $S^{tr}=C_n r^n$ to encode internal structure, leading to spin-coupled corrections to the azimuthal and radial epicyclic frequencies with a quasi Schwarzschild-de Sitter like behavior $($SdS$)$; they fit eight NS-LMXBs with MCMC and show MPD-S is competitive with SdS and strongly disfavors Schwarzschild RPM, with a robust preference for a disk-like symmetry $n=2$ and physically plausible disk radii and neutron star masses. The results imply that QPO complexity can be captured by spin-curvature coupling of extended test bodies without ad hoc changes to the spacetime, and they forecast an approximate $3:2$ frequency clustering in several sources. The work points to future extensions including Kerr geometries to assess quadrupole effects and backreaction, positioning MPD-based spin coupling as a viable mechanism for QPO production in strong gravity.

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.

Figures (4)

• Figure 1: Plots of $\Omega_\phi$ for Schwarzschild (black solid line), and numerical (dashed lines) and perturbative (dotted lines) MPD-S solutions with the percent deviations (dev) of the perturbative solutions w.r.t. the numerical ones. Left and right panels display $n=2$ and $n=3$ cases, respectively. Color codes and parameter choices are explained in the legends.
• Figure 2: Forecasts of the $3:2$ ratio approximately obtained by our MPM in four LMXBs with compact disks (see Table \ref{['tab:results2']}).
• Figure A-1: Frequency pairs $(f_{\rm L},f_{\rm U})$ for the eight NS-LMXBs and best-fitting curves for Schwarzschild (dashed red), SdS (dot-dashed green), and MPD-S (solid blue with shaded $1\sigma$ bands). Lower panels show residuals w.r.t. the MPD-S model.
• Figure A-2: Contour plots for each source, with best fit values, likelihoods and $2\sigma$ confidence levels. Masses are reported in solar masses, whereas the dimensions of $\mathcal{C}_n$ depend on the choice of $n$.