Mathematics – Dynamical Systems
Scientific paper
Aug 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996icar..122..347k&link_type=abstract
Icarus, Volume 122, Issue 2, pp. 347-358.
Mathematics
Dynamical Systems
8
Scientific paper
In this paper we propose a new method for detecting planets around a pulsar. Instead of direct chi^2 fitting of planetary elements to pulsar timing observations, we propose to analyze the spectrum of time of arrival (TOA) residuals. Neglecting a small noise, such residuals should be quasi-periodic if the hypothesis about the planets is true. This fact plays a fundamental role in our method. Namely, we take the idea of successive subtractions of harmonic components from a quasi-periodic signal from the frequency analysis introduced by J. Laskar for detecting chaos in dynamical systems. Using the Lomb-Scargle normalized periodogram and chi^2 fitting of a quasi-periodic function to the signal, we develop our algorithms of extracting information about Keplerian elements of planets from TOA residuals. Carrying out Fourier analysis of the Keplerian and real motion of planets, we show their qualitative and quantitative properties that are important to our method. We demonstrate that the proposed method works very well on the modeled time of arrival residuals, and that it can be used to analyze real observational TOA residuals without any problems. We show that this method gives very accurate results, allowing, for example, the detection of resonances present in the system based on observational data with time spans shorter than the period of a resonance. All these facts make our method very sensitive and useful.
Konacki Maciej
~Maciejewski Andrzej J.
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