Generalizing the relativistic precession model of quasi-periodic oscillations through anharmonic corrections
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arXiv
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| Format: | Preprint |
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2025
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| author | Giambò, Roberto Luongo, Orlando Muccino, Marco Rossi, Alessandro |
| author_facet | Giambò, Roberto Luongo, Orlando Muccino, Marco Rossi, Alessandro |
| contents | We critically reanalyze the relativistic precession model of quasi-periodic oscillations, exploring its natural extension beyond the standard harmonic approximation. To do so, we show that the perturbed geodesic equations must include anharmonic contributions arising from the higher-order expansion of the effective potential that cannot be neglected \emph{a priori}, as commonly done in all the approaches pursued so far. More specifically, independently of the underlying spacetime geometry, we find that in the radial sector the non-negligible anharmonic correction is quadratic in the radial displacement, i.e. $\propto δr^2$, and significantly affects the radial epicyclic frequency close to the innermost stable circular orbit. Conversely, polar oscillations $δθ$ remain approximately decoupled from radial ones, preserving their independent dynamical behavior. To show the need of anharmonic corrections, we thus carry out Monte Carlo-Markov chain analyses on eight neutron star sources of quasi-periodic oscillations. Afterwards, we first work out the outcomes of the harmonic approximation in Schwarzschild, Schwarzschild--de Sitter, and Kerr spacetimes. Subsequently, we apply the anharmonic corrections to them and use it to fit the aforementioned neutron star sources. Our findings indicate that the standard paradigm requires a systematic generalization to include the leading anharmonic corrections that appear physically necessary, although still insufficient to fully account for the observed phenomenology of quasi-periodic oscillations. Accordingly, we speculate on possible refinements of the relativistic precession model, showing the need to revise it at a fundamental level. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_18403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalizing the relativistic precession model of quasi-periodic oscillations through anharmonic corrections Giambò, Roberto Luongo, Orlando Muccino, Marco Rossi, Alessandro General Relativity and Quantum Cosmology Astrophysics of Galaxies We critically reanalyze the relativistic precession model of quasi-periodic oscillations, exploring its natural extension beyond the standard harmonic approximation. To do so, we show that the perturbed geodesic equations must include anharmonic contributions arising from the higher-order expansion of the effective potential that cannot be neglected \emph{a priori}, as commonly done in all the approaches pursued so far. More specifically, independently of the underlying spacetime geometry, we find that in the radial sector the non-negligible anharmonic correction is quadratic in the radial displacement, i.e. $\propto δr^2$, and significantly affects the radial epicyclic frequency close to the innermost stable circular orbit. Conversely, polar oscillations $δθ$ remain approximately decoupled from radial ones, preserving their independent dynamical behavior. To show the need of anharmonic corrections, we thus carry out Monte Carlo-Markov chain analyses on eight neutron star sources of quasi-periodic oscillations. Afterwards, we first work out the outcomes of the harmonic approximation in Schwarzschild, Schwarzschild--de Sitter, and Kerr spacetimes. Subsequently, we apply the anharmonic corrections to them and use it to fit the aforementioned neutron star sources. Our findings indicate that the standard paradigm requires a systematic generalization to include the leading anharmonic corrections that appear physically necessary, although still insufficient to fully account for the observed phenomenology of quasi-periodic oscillations. Accordingly, we speculate on possible refinements of the relativistic precession model, showing the need to revise it at a fundamental level. |
| title | Generalizing the relativistic precession model of quasi-periodic oscillations through anharmonic corrections |
| topic | General Relativity and Quantum Cosmology Astrophysics of Galaxies |
| url | https://arxiv.org/abs/2504.18403 |