Dynamical environments of relativistic binaries: The phenomenon of resonance shifting

Ivan I. Shevchenko, Guillaume Rollin, José Lages

Research output

Abstract

In this article, we explore both numerically and analytically how the dynamical environments of mildly relativistic binaries evolve with increasing the general relativity factor γ (the normalized inverse of the binary size measured in the units of the gravitational radius corresponding to the total mass of the system). Analytically, we reveal a phenomenon of the relativistic shifting of mean-motion resonances: on increasing γ, the resonances between the test particle and the central binary shift, due to the relativistic variation of the mean motions of the primary and secondary binaries and the relativistic advance of the tertiary's pericenter. To exhibit the circumbinary dynamics globally, we numerically integrate equations of the circumbinary motion of a test particle, and construct relevant scans of the maximum Lyapunov exponents and stability diagrams in the "pericentric distance -- eccentricity" plane of initial conditions. In these scans and diagrams, regular and chaotic domains are identified straightforwardly. Our analytical and numerical estimates of the shift size are in a good agreement. Prospects for identification of the revealed effect in astronomical observations are discussed.
Original languageEnglish
Article number064016
Number of pages10
JournalPhysical Review D
Volume100
Issue number6
DOIs
Publication statusPublished - 9 Sep 2019

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diagrams
shift
eccentricity
relativity
exponents
radii
estimates

Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

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abstract = "In this article, we explore both numerically and analytically how the dynamical environments of mildly relativistic binaries evolve with increasing the general relativity factor γ (the normalized inverse of the binary size measured in the units of the gravitational radius corresponding to the total mass of the system). Analytically, we reveal a phenomenon of the relativistic shifting of mean-motion resonances: on increasing γ, the resonances between the test particle and the central binary shift, due to the relativistic variation of the mean motions of the primary and secondary binaries and the relativistic advance of the tertiary's pericenter. To exhibit the circumbinary dynamics globally, we numerically integrate equations of the circumbinary motion of a test particle, and construct relevant scans of the maximum Lyapunov exponents and stability diagrams in the {"}pericentric distance -- eccentricity{"} plane of initial conditions. In these scans and diagrams, regular and chaotic domains are identified straightforwardly. Our analytical and numerical estimates of the shift size are in a good agreement. Prospects for identification of the revealed effect in astronomical observations are discussed.",
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Dynamical environments of relativistic binaries : The phenomenon of resonance shifting. / Shevchenko, Ivan I. ; Rollin, Guillaume; Lages, José.

In: Physical Review D, Vol. 100, No. 6, 064016, 09.09.2019.

Research output

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AU - Rollin, Guillaume

AU - Lages, José

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AB - In this article, we explore both numerically and analytically how the dynamical environments of mildly relativistic binaries evolve with increasing the general relativity factor γ (the normalized inverse of the binary size measured in the units of the gravitational radius corresponding to the total mass of the system). Analytically, we reveal a phenomenon of the relativistic shifting of mean-motion resonances: on increasing γ, the resonances between the test particle and the central binary shift, due to the relativistic variation of the mean motions of the primary and secondary binaries and the relativistic advance of the tertiary's pericenter. To exhibit the circumbinary dynamics globally, we numerically integrate equations of the circumbinary motion of a test particle, and construct relevant scans of the maximum Lyapunov exponents and stability diagrams in the "pericentric distance -- eccentricity" plane of initial conditions. In these scans and diagrams, regular and chaotic domains are identified straightforwardly. Our analytical and numerical estimates of the shift size are in a good agreement. Prospects for identification of the revealed effect in astronomical observations are discussed.

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